If f(x)=3x^3 then what is the area enclosed by the graph of the function, the horizontal axis, and vertical lines at x=2 and x=4

Answers

Answer 1

Answer:

Area: 180 units2 (units 2 is because since the are no specific unit given but every area should have a unit  of measurement)

Step-by-step explanation:

The area enclosed by the graph of the function, the horizontal axis, and vertical lines is the integral of the function between thos two points (x=2 and x=4)

So , let's solve the integral of f(x)

Area =[tex]\int\limits^2_4 3{x}^3 \, dx = 3*x^4/4[/tex]+C

C=0

So if we evaluate this function in the given segment:

Area= 3* (4^4)/4-3*(2^4)/4= 3*(4^4-2^4)/4=180 units 2

Goos luck!


Related Questions

fraction subtract 4/5-1/6​

Answers

Answer:

19/30

Explanation:

1. Exchange them to a common factor which happens to be 30 for both of them

2. Multiply by that factor on both the top and bottom to get the number equivalent to a fraction of that category

3. Subtract

4. Simplify, however in this case simplification isn't doable.

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees 0° and standard deviation of 1.00 degrees °C. Assume 3 3​% of the thermometers are rejected because they have readings that are too high and another 3 3​% are rejected because they have readings that are too low. Draw a sketch and find the two readings that are cutoff values separating the rejected thermometers from the others.

Answers

Answer:

The two readings that are cutoff values are T=1.84 deg C and T=-1.84 deg C.

Step-by-step explanation:

Thermometers rejected by measurements above normal represent 3.3% of the total, which indicates, by normal probability distribution data, that accepted thermometers are 96.7% likely to measure less than the maximum allowable temperature.  

This value (P(X>x)=0.967) corresponds to z = 1.8388. Since the mean and standard deviation values are the same as the standard normal probability distribution (mean = 0, sd = 0), the z value is equivalent to the measured value (temperature).

Given the symmetry of the probability distribution, we can affirm that the thermometers rejected by measurements below the permissible measured a temperature lower than -1.8388.

Final answer:

The cutoff values separating the rejected thermometers are -1.88°C for the low end and 1.88°C for the high end, based on a normal distribution with a mean of 0°C and a standard deviation of 1.00°C.

Explanation:

To find the two readings that are cutoff values separating the rejected thermometers, we look at the normal distribution curve with a mean of 0°C and a standard deviation of 1.00°C. Since 3% of thermometers are rejected for high readings and another 3% for being too low, these correspond to the tail ends of the distribution.

Using the Z-score table, find the Z-score that has 3% in the tail. For the lower end, we seek the Z-score where the left tail (the area to the left of the Z-score) is 0.03, and for the higher end, we look for a Z-score where the right tail is 0.03. These Z-scores are approximately -1.88 for the low end and +1.88 for the high end (using the 97th percentile since we want the upper 3%).

To find the actual thermometer readings:

For the low cutoff: cutoff low = mean + (Z-score * standard deviation) = 0 + (-1.88 * 1) = -1.88°C.

For the high cutoff: cutoff high = mean + (Z-score * standard deviation) = 0 + (1.88 * 1) = 1.88°C.

Therefore, thermometers reading lower than -1.88°C or higher than 1.88°C will be rejected.

Find the general solution to each of the following ODEs. Then, decide whether or not the set of solutions form a vector space. Explain your reasoning. Compare your answers to the previous problem. Recall that the general solution has the form y(t) = yh(t) + yp(t).

(A) y' - 2y = 0
(B) y' - 2y = 1
(C) y" - 4y = 0
(D) y" - 4y = e^(3t)

Answers

Answer:

(A) [tex]y=ke^{2t}[/tex] with [tex]k\in\mathbb{R}[/tex].

(B) [tex]y=ke^{2t}/2-1/2[/tex] with [tex]k\in\mathbb{R}[/tex]

(C) [tex]y=k_1e^{2t}+k_2e^{-2t}[/tex] with [tex]k_1,k_2\in\mathbb{R}[/tex]

(D) [tex]y=k_1e^{2t}+k_2e^{-2t}+e^{3t}/5[/tex] with [tex]k_1,k_2\in\mathbb{R}[/tex],

Step-by-step explanation

(A) We can see this as separation of variables or just a linear ODE of first grade, then [tex]0=y'-2y=\frac{dy}{dt}-2y\Rightarrow \frac{dy}{dt}=2y \Rightarrow  \frac{1}{2y}dy=dt \ \Rightarrow \int \frac{1}{2y}dy=\int dt \Rightarrow \ln |y|^{1/2}=t+C \Rightarrow |y|^{1/2}=e^{\ln |y|^{1/2}}=e^{t+C}=e^{C}e^t} \Rightarrow y=ke^{2t}[/tex]. With this answer we see that the set of solutions of the ODE form a vector space over, where vectors are of the form [tex]e^{2t}[/tex] with [tex]t[/tex] real.

(B) Proceeding and the previous item, we obtain [tex]1=y'-2y=\frac{dy}{dt}-2y\Rightarrow \frac{dy}{dt}=2y+1 \Rightarrow  \frac{1}{2y+1}dy=dt \ \Rightarrow \int \frac{1}{2y+1}dy=\int dt \Rightarrow 1/2\ln |2y+1|=t+C \Rightarrow |2y+1|^{1/2}=e^{\ln |2y+1|^{1/2}}=e^{t+C}=e^{C}e^t \Rightarrow y=ke^{2t}/2-1/2[/tex]. Which is not a vector space with the usual operations (this is because [tex]-1/2[/tex]), in other words, if you sum two solutions you don't obtain a solution.

(C) This is a linear ODE of second grade, then if we set [tex]y=e^{mt} \Rightarrow y''=m^2e^{mt}[/tex] and we obtain the characteristic equation [tex]0=y''-4y=m^2e^{mt}-4e^{mt}=(m^2-4)e^{mt}\Rightarrow m^{2}-4=0\Rightarrow m=\pm 2[/tex] and then the general solution is [tex]y=k_1e^{2t}+k_2e^{-2t}[/tex] with [tex]k_1,k_2\in\mathbb{R}[/tex], and as in the first items the set of solutions form a vector space.

(D) Using C, let be [tex]y=me^{3t} [/tex] we obtain that it must satisfies [tex]3^2m-4m=1\Rightarrow m=1/5[/tex] and then the general solution is [tex]y=k_1e^{2t}+k_2e^{-2t}+e^{3t}/5[/tex] with [tex]k_1,k_2\in\mathbb{R}[/tex], and as in (B) the set of solutions does not form a vector space (same reason! as in (B)).  

A store has clearance items that have been marked down by 25%. They are having a sale, advertising an additional 40% off clearance items. What percent of the original price do you end up paying? Give your answer accurate to at least one decimal place.

Answers

Final answer:

To find the percent of the original price you end up paying after a 25% discount and an additional 40% discount, first calculate the discounted prices and then determine the final price. In this case, you end up paying 45% of the original price.

Explanation:

To find the percent of the original price you end up paying, you need to calculate the final price after both discounts. Let's say the original price of the item is $100. First, apply the 25% discount by multiplying the original price by 0.75 (1 - 0.25 = 0.75). This gives you a price of $75. Next, apply the additional 40% discount by multiplying the discounted price by 0.60 (1 - 0.40 = 0.60). This gives you a final price of $45. Therefore, you end up paying 45% of the original price.

On rainy days, Izzy goes from his house to the school by running 1.2 miles on West St, then makes a 90º turn and runs 0.5 miles on North Ave.

a. If Izzy runs 7.5 miles per hour, approximately how much time will it take her to run to school on rainy days?

b. On dry days, Izzy runs on the dashed path through the woods. How far is she traveling?

c. If Izzy runs 7.5 miles per hour, how much time will she save by cutting through the woods?

Answers

Final answer:

To calculate the time Izzy takes to run to school on rainy days, we use the distance and speed to find that she runs 1.7 miles in approximately 13.6 minutes. We are unable to calculate the distance through the woods or the time saved without further information.

Explanation:

Calculation of Time and Distance

To calculate the time Izzy takes to run to school on rainy days, we use the following formula:

Time (in hours) = Distance (in miles) / Speed (in miles per hour)

Izzy runs a total distance of 1.2 miles on West St and then 0.5 miles on North Ave, summing up to 1.7 miles. Given Izzy's speed is 7.5 miles per hour, the time taken to run to school on rainy days can be calculated as:

Time = (1.2 + 0.5) miles / 7.5 mph = 1.7 / 7.5

To find the time in minutes, multiply the time in hours by 60:

Time in minutes = (1.7 / 7.5)  imes 60
= 13.6 minutes (approximately)

As the dashed path through the woods on dry days is not described in the question, we cannot calculate the exact distance Izzy is traveling through the woods. Without this information, we also cannot calculate the time saved by cutting through the woods.

A problem states: "There are 2 more horses than cows in a field. There are 16 animals in the field in all. How many horses are there in the field?"

Let h represent the number of horses.

Which equation represents the situation?




2h + 2 = 16

2(h+2)=16

h + 2 = 16

2h−2=16

Answers

Answer:

2h-2=16

Step-by-step explanation:

Let

h -----> the number of horses

c ----> the number of a cows

we know that

h+c=16 -----> equation A

h=c+2

c=(h-2) ----> equation B

Substitute equation B in equation A and solve for h

h+(h-2)=16

2h-2=16

2h=16+2

2h=18

h=9

therefore

The equation that represent the situation is

2h-2=16

Among users of automated teller machines​ (ATMs), 94​% use ATMs to withdraw cash and 28​% use them to check their account balance. Suppose that 95​% use ATMs to either withdraw cash or check their account balance​ (or both). Given a woman who uses an ATM to check her account​ balance, what the probability that she also uses an ATM to get​ cash?

Answers

Answer:

96%

Step-by-step explanation:

Conditional probability is defined as:  

P(A|B) = P(A∩B) / P(B)  

Or, in English:  

Probability that A occurs, given that B has occurred = Probability that both A and B occur / Probability that B occurs

We want to find the probability that a woman uses an ATM to get cash, given that she uses an ATM to check her balance.

P(withdraws cash | checks account)

Using the definition of condition probability, this equals:

P = P(withdraws cash AND checks account) / P(checks account)

We know that P(checks account) = 0.28.

But we don't know what P(withdraws cash AND checks account) is.  To find that, we need to use the definition of P(A∪B):

P(A∪B) = P(A) + P(B) − P(A∩B)

This says that the probability of A or B occurring (or both) is the probability of A occurring plus the probability of B occurring minus the probability of both A and B occurring.

P(withdraws cash OR checks account) = P(withdraws cash) + P(checks account) − P(withdraws cash AND checks account)

0.95 = 0.94 + 0.28 − P(withdraws cash AND checks account)

P(withdraws cash AND checks account) = 0.27

Therefore:

P = 0.27 / 0.28

P ≈ 0.96

Final answer:

The probability that a woman who checks her account balance at an ATM also withdraws cash is approximately 96.43%.

Explanation:

To solve the problem, we can apply the probability rule for conditional probability. We are provided with the following probabilities:

The probability that ATM users withdraw cash (P(Cash)) is 94%, or 0.94.The probability that ATM users check their account balance (P(Balance)) is 28%, or 0.28.The probability that ATM users either withdraw cash or check their account balance (or both) (P(Cash ∪ Balance)) is 95%, or 0.95.

Using this information, we're interested in finding the probability that a user who checks their account balance also withdraws cash, represented as P(Cash|Balance).

The formula for conditional probability is:

P(A|B) = P(A ∩ B) / P(B)

Where A and B are two events, and P(A|B) is the conditional probability of A given B.

Using the inclusion-exclusion principle, we can express P(Cash ∩ Balance) as:

P(Cash ∩ Balance) = P(Cash) + P(Balance) - P(Cash ∪ Balance)

Substitute the given probabilities:

P(Cash ∩ Balance) = 0.94 + 0.28 - 0.95 = 0.27

The probability that a woman who checks her balance also gets cash (P(Cash|Balance)) is:

P(Cash|Balance) = P(Cash ∩ Balance) / P(Balance)

P(Cash|Balance) = 0.27 / 0.28 ≈ 0.9643

Therefore, the probability is approximately 96.43%.

Prove that (from i=1 to n) sum([1/((2i-1)(2i+1))] = n/(2n+1). If true use induction, else give smallest value of n that it is false for.

Answers

Answer:

The statement is true

Step-by-step explanation:

We will prove by mathematical induction that, for every natural n,

[tex]\sum^{n}_{i=1}\frac{1}{(2i-1)(2i+1)} =\frac{n}{2n+1}[/tex]

We will prove our base case, when n=1, to be true.

base case:

[tex]\sum^{1}_{i=1}\frac{1}{(2-1)(2+1)} =\frac{1}{3}=\frac{n}{2n+1}[/tex]

Inductive hypothesis:

[tex]\sum^{n}_{i=1}\frac{1}{(2i-1)(2i+1)} =\frac{n}{2n+1}[/tex]

Now, we will assume the induction hypothesis and then uses this assumption, involving n, to prove the statement for n + 1.

Inductive step:

[tex]\sum^{n+1}_{i=1}\frac{1}{(2i-1)(2i+1)} =\sum^{n}_{i=1}\frac{1}{(2i-1)(2i+1)}+\frac{1}{(2(n+1)-1)(2(n+1)+1)}=\frac{n}{2n+1}+\frac{1}{(2n+1)(2n+3)}=\frac{n(2n+3)+1}{(2n+1)(2n+3)}=\frac{2n^2+3n+1}{(2n+1)(2n+3)}=\frac{(2n+1)(n+1)}{(2n+1)(2n+3)}=\frac{n+1}{2n+3}=\frac{n+1}{2(n+1)+1}[/tex]

With this we have proved our statement to be true for n+1.

In conlusion, for every natural [tex]n[/tex].

[tex]\sum^{n}_{i=1}\frac{1}{(2i-1)(2i+1)} =\frac{n}{2n+1}[/tex]

In an arithmetic​ sequence, the nth term an is given by the formula An=a1+(n−1)d​, where a1is the first term and d is the common difference.​ Similarly, in a geometric​ sequence, the nth term is given by an=a1•rn−1.

Use these formulas to determine the indicated term in the given sequence.

The 19th term of 19​,42​,65​,88​,...

Answers

Answer: 433

Step-by-step explanation:

The given sequence : 19​,42​,65​,88​,...

Here we can see that the difference in each of the two consecutive terms is 23.  [88-65=23, 65-42=23, 42-19=23]

i.e. it has a common difference of 23.

Therefore, it is an arithmetic sequence .

In an arithmetic​ sequence, the nth term an is given by the formula[tex]A_n=a_1+(n-1)d[/tex] , where [tex]a_1[/tex] is the first term and d is the common difference.​

For the given sequence , [tex]a_1=19[/tex]  and [tex]d=23[/tex]

Then,  to find the 19th term of  the sequence, we put n= 19 in the above formula:-

[tex]A_{19}=19+(19-1)(23)=19+(18)(23)=19+414+433[/tex]

Hence, the 19th term of  the sequence = 433

Final answer:

To find the 19th term of the arithmetic sequence 19, 42, 65, 88, ..., the common difference (23) is determined from the sequence and applied in the arithmetic sequence formula. Substituting the values into the formula, the 19th term is calculated to be 433.

Explanation:

To find the 19th term, we must first determine the common difference, d, of the sequence. Observing the given sequence, we see that the difference between consecutive terms is 42 - 19 = 23. Therefore, the common difference is 23.

Next, we apply the formula for the nth term of an arithmetic sequence which is An = a1 + (n-1)d. Here, a1 is the first term, n is the term number, and d is the common difference.

Substituting the values for the 19th term, we have: A19 = 19 + (19-1) × 23 = 19 + 18 × 23 = 19 + 414 = 433. Therefore, the 19th term of the sequence is 433.

A concrete mix is designed to withstand 3000 pounds per square inch​ (psi) of pressure. The following data represent the strength of nine randomly selected casts​ (in psi). 3970​, 4100​, 3100​, 3200​, 2950​, 3830​, 4100​, 4050​, 3460 Compute the​ mean, median and mode strength of the concrete​ (in psi). Compute the mean strength of the concrete. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The mean strength of the concrete is nothing psi of pressure. ​(Round to the nearest tenth as​ needed.) B. The mean does not exist.

Answers

Answer:

Mean = 3640

Mode = 4100

Median = 3830.

Step-by-step explanation:

We are given the following data in the question:

Strength of casts (in psi):

3970,4100,3100,3200,2950,3830,4100,4050,3460

Formula:

[tex]Mean = \displaystyle\frac{\text{Sum of all observation}}{\text{Total number of observations}}[/tex]

[tex]\displaystyle\frac{3970+4100+3100+ 3200+ 2950+ 3830+4100+ 4050+ 3460}{9} = \displaystyle\frac{32760} {9} = 3640[/tex]

Mode is the entry with most frequency. Thus, for the given sample mode = 4100.

Median

Since n = 9 is odd,

Formula:

[tex]Median = \displaystyle\frac{n+1}{2}th~term[/tex]

Data in ascending order:

2950,3100,3200,3460,3830,3970,4050,4100,4100

Median = 5th term = 3830.

The mean strength of the concrete is 3640.

The mode strength of the concrete is 4100.

The median strength of the concrete is 3830.

Given

A concrete mix is designed to withstand 3000 pounds per square inch​ (psi) of pressure.

The following data represent the strength of nine randomly selected casts​ (in psi).

3970​, 4100​, 3100​, 3200​, 2950​, 3830​, 4100​, 4050​, 3460

What formula is used to calculate the mean value?

The mean value of the data is given by;

[tex]\rm Mean = \dfrac{Sum \ of \ all \ observation}{Total \ number \ of \ observation}[/tex]

The mean of the strength of the concrete is;

[tex]\rm Mean = \dfrac{Sum \ of \ all \ observation}{Total \ number \ of \ observation}\\\\Mean =\dfrac{3970+4100+3100+3200+2950+3830+ 4100+4050+3460 }{9}\\\\Mean =\dfrac{32760}{9}\\\\Mean=3640[/tex]

The mean strength of the concrete is 3640.

Mode is the entry with the most frequency.

Thus, for the given sample mode = 4100.

The mode strength of the concrete is 4100.

The mid-value of the data is called the median.

The median strength of the concrete is 3830.

To know more about Mean click the link given below.

https://brainly.com/question/12513463

Find the optimal solution for the following problem. (Round your answers to 3 decimal places.)

Maximize C = 9x + 7y
subject to 8x + 10y ≤ 17
11x + 12y ≤ 25
and x ≥ 0, y ≥ 0.
1. what is the optimal value of x?

2. What is the optimal value of y?

3. What is the maximum value of the objective function?

Answers

Answer:

Maximize C =[tex]9x + 7y[/tex]

[tex]8x + 10y \leq 17[/tex]

[tex]11x + 12y\leq 25[/tex]

and x ≥ 0, y ≥ 0

Plot the lines on graph

[tex]8x + 10y \leq 17[/tex]

[tex]11x + 12y\leq 25[/tex]

[tex]x\geq 0[/tex]

[tex]y\geq 0[/tex]

So, boundary points of feasible region are (0,1.7) , (2.125,0) and (0,0)

Substitute the points in  Maximize C

At  (0,1.7)

Maximize C =[tex]9(0) + 7(1.7)[/tex]

Maximize C =[tex]11.9[/tex]

At  (2.125,0)

Maximize C =[tex]9(2.125) + 7(0)[/tex]

Maximize C =[tex]19.125[/tex]

At   (0,0)

Maximize C =[tex]9(0) + 7(0)[/tex]

Maximize C =[tex]0[/tex]

So, Maximum value is attained at   (2.125,0)

So, the optimal value of x is 2.125

The optimal value of y is 0

The maximum value of the objective function is 19.125

There are several ways to calculate optimal solution; one of them, is by using graphs.

The optimal value of x is 2.125The optimal value of y is: 0The maximum value of the objective function is: 19.125

The given parameters are:

[tex]\mathbf{Max\ C = 9x + 7y}[/tex]

[tex]\mathbf{8x + 10y \le 17}[/tex]

[tex]\mathbf{11x + 12y \le 25}[/tex]

[tex]\mathbf{x,y\ge 0}[/tex]

See attachment for the graphs of [tex]\mathbf{8x + 10y \le 17}[/tex] and [tex]\mathbf{11x + 12y \le 25}[/tex]

From the graph, the feasible regions are:

[tex]\mathbf{(x,y) = (0,1.7), (2.125,0)}[/tex]

Test these values in the objective function

[tex]\mathbf{Max\ C = 9x + 7y}[/tex]

[tex]\mathbf{C = 9 \times 0 + 7 \times 1.7 = 11.9}[/tex]

[tex]\mathbf{C = 9 \times 2.125 + 7 \times 0 = 19.125}[/tex]

So, the value of C is maximum at: [tex]\mathbf{(x,y) = (2.125,0)}[/tex]

So, we have:

The optimal value of x is 2.125The optimal value of y is: 0The maximum value of the objective function is: 19.125

Read more about maximizing functions at:

https://brainly.com/question/11212148

The gross domestic product (GDP) of a certain country, which measures the overall size of the economy in billions of dollars, can be approximated by the function g(y) = 557y +8883, where y = 10 corresponds to the year 2010. Estimate the GDP (to the nearest billion dollars) in the given years. (a) 2007 (b) 2011 (c) 2012 (a) What value of y corresponds to the year 2007? y=O (Type a whole number.)

Answers

Answer:

The estimated GDP in 2007 is 12782 billion dollars.

The estimated GDP in 2011 is 15010 billion dollars.

The estimated GDP in 2012 is 15567 billion dollars.

Step-by-step explanation:

Consider the provided function.

[tex]g(y) = 557y +8883[/tex]

Where y = 10 corresponds to the year 2010.

Part (b) Estimate the GDP (to the nearest billion dollars) in 2007.

If y = 10 corresponds to the year 2010 then y = 7 corresponds to the year 2007.

Substitute the value of y = 7 in the provided function.

[tex]g(y) = 557(7) +8883[/tex]

[tex]g(y) = 3899+8883[/tex]

[tex]g(y) = 12782[/tex]

Hence, the estimated GDP in 2007 is 12782 billion dollars.

Part (b) Estimate the GDP (to the nearest billion dollars) in 2011.

If y = 10 corresponds to the year 2010 then y = 11 corresponds to the year 2011.

Substitute the value of y = 11 in the provided function.

[tex]g(y) = 557(11) +8883[/tex]

[tex]g(y) = 6127+8883[/tex]

[tex]g(y) = 15010[/tex]

Hence, the estimated GDP in 2011 is 15010 billion dollars.

Part (C) Estimate the GDP (to the nearest billion dollars) in 2012.

If y = 10 corresponds to the year 2010 then y = 12 corresponds to the year 2012.

Substitute the value of y = 12 in the provided function.

[tex]g(y) = 557(12) +8883[/tex]

[tex]g(y) = 6684+8883[/tex]

[tex]g(y) = 15567[/tex]

Hence, the estimated GDP in 2012 is 15567 billion dollars.

Final answer:

To estimate the GDP of a certain country for different years using the function g(y) = 557y + 8883, the value of y is adjusted according to the respective year, and the GDP is calculated by substituting this value into the formula. For 2007, 2011, and 2012, respective GDPs estimated are 12019, 14311, and 14868 billion dollars.

Explanation:

The question asks us to estimate the GDP of a certain country for different years using the function g(y) = 557y + 8883, where y=10 corresponds to the year 2010. To find the GDP for the given years, we first need to calculate the correct value of y for each year and then substitute these values into the function.

For the year 2007, y would be 7 (as y=0 corresponds to 2000, so 2007-2000=7). Substituting y=7 into the function gives us a GDP of g(7) = 557*7 + 8883 = 12019 (to the nearest billion dollars).For 2011, y would be 11 (2011-2000), and substituting it yields g(11) = 557*11 + 8883 = 14311.For 2012, with y=12, the GDP would be g(12) = 557*12 + 8883 = 14868.

This approach allows us to quantify economic growth over different years, comparing these figures to gain insight into the economic health and trends of the country.

The accompanying observations are on stabilized viscosity (cP) for specimens of a certain grade of asphalt with 18% rubber added: 2767 2924 3042 2844 2895 (a) What are the values of the sample mean x and sample median x tilde?

Answers

Answer:

Step-by-step explanation:

Given are the observations are on stabilized viscosity (cP) for specimens of a certain grade of asphalt with 18% rubber added:

2767 2924 3042 2844 2895

No of items = 5

If written in ascending order the order would be

2767   2844   2895   2924   3042

Hence median is the middle value in the ordered row = 2895

Mean = sum/5

=[tex]\frac{14472}{5} =2894.4[/tex]

In an arithmetic​ sequence, the nth term an is given by the formula an=a1+(n−1)d​, where a1 is the first term and d is the common difference.​ Similarly, in a geometric​ sequence, the nth term is given by 1an=a1•rn−1​,

where r is the common ratio. Use these formulas to determine

the indicated term in the given sequence.

The 105th term of 1/2, 1, 3/2, 2,..

Answers

Answer:

The 105th term of given sequence is [tex]\frac{105}{2}[/tex].

Step-by-step explanation:

The given sequence is

[tex]\frac{1}{2},1,\frac{3}{2},2[/tex]

It can be rewritten as

[tex]0.5,1,1.5,2[/tex]

Here the first term is 0.5.

It is an arithmetic​ sequence because it has common difference.

[tex]d=a_2-a_1=1-0.5=0.5[/tex]

[tex]d=a_3-a_2=1.5-1=0.5[/tex]

[tex]d=a_4-a_3=2-1.5=0.5[/tex]

The nth term of an AP is

[tex]a_n=a_1+(n-1)d[/tex]

where, [tex]a_1[/tex] is first term and d is common difference.

Substitute [tex]a_1=0.5[/tex] and [tex]d=0.5[/tex] in the above formula.

[tex]a_n=0.5+(n-1)0.5[/tex]

[tex]a_n=0.5+0.5n-0.5[/tex]

[tex]a_n=0.5n[/tex]

We need to find the 105th term of given sequence.

Substitute n=105 in the above equation.

[tex]a_n=0.5(105)[/tex]

[tex]a_n=52.5[/tex]

[tex]a_n=\frac{105}{2}[/tex]

Therefore the 105th term of given sequence is [tex]\frac{105}{2}[/tex].

How many kW-hr are used when one 100W light bulbs is used for 2 hours?

Answers

Answer:

0.2 kW-hr

Step-by-step explanation:

First, we are going to transform 100W in kW. We can use a rule of three in which we know that 1000W is equivalent to 1 kW, then how many kW are equivalent to 100W. This is:

1000W ------------- 1 kW

100W -------------- X

Where X is the the number of kW that are equivalent to 100W. Solving for X, we get:

[tex]X=\frac{100W * 1kW}{1000W} =0.1kW[/tex]

Then, for calculate the number of kW-hr we need to multiplicate the number of kW with the number of hours, This is:

0.1 kW * 2 hours = 0.2 kW-hr

Finally, when one 100W light bulbs is used for 2 hours, it used 0.2 kW-hr

PLEASE HELP

Both Alex and Chris left their homes at 7:00 a.m. and walked to school. The graph shows the distances that each boy was from school as they walked. Which statement is best supported by the graph?


Alex lives farther from the school than Chris lives, and Alex walked to school at a faster rate than Chris walked.
Alex lives closer to the school than Chris lives, and Alex walked to school at a faster rate than Chris walked.
Chris lives farther from the school than Alex lives, and Chris walked to school at a faster rate than Alex walked.
Chris lives closer to the school than Alex lives, and Chris walked to school at a faster rate than Alex walked

Answers

Answer:

Chris lives farther from school than Alex lives, and Chris walks to school at a faster rate than Alex

Step-by-step explanation:

Chris walked 4 miles.

Alex walked 2.

Alex takes 25 minutes to walk one mile. (50÷2) and Chris takes 15 minutes to walk one mile (60÷4), meaning Chris walks at a faster rate although he lives farther away.

Answer:

Chris lives farther from the school than Alex lives, and Chris walked to school at a faster rate than Alex walked.

The price of a calculator is currently $23, which is a 532% decrease from the price thirty years ago. What was the price of the calculator thirty years ago?

Answers

Answer:

The price of calculator before 30 years = $30+$122.36 = $145.36

Step-by-step explanation:

We have given price current price of calculator = $23

It is given that current price of calculator is after decrease of 532 %

We have to find the price of calculator before 30 years

The price of calculator will be more than 532 % from the current price

So 532% of 23 [tex]=\frac{23\times 532}{100}=$122.36[/tex]

So the price of calculator before 30 years = $30+$122.36 = $145.36

While completing a race, Edward spent 54 minutes walking. If his ratio of time walking to jogging was 6:5, how many minutes did he spend completing the race?

Answers

Answer:   99 minutes

Step-by-step explanation:

Given: While completing a race, Edward spent 54 minutes walking.

The ratio of time walking to jogging was 6:5 i.e. [tex]\dfrac{6}{5}[/tex]     (1)

Let x be the time taken ( in minutes ) by him for jogging.

then, the ratio of time walking to jogging will be [tex]\dfrac{54}{x}[/tex]  (2)

From (1) and (2), we have

[tex]\dfrac{6}{5}=\dfrac{54}{x}\\\\\Rightarrow\ 6x=54\times5\\\\\Rightarrow\ x=\dfrac{54\times5}{6}=45[/tex]  

So, the number of minutes he took for jogging = 45 minutes

Now, the total time he spent on completing the race= 54+45=99 minutes


convert 1 cal/(m^2 * sec * °C) into BTU/(ft^2 * hr * °F)

Its easy enough to convert the energy, time, and area units, but how am I suppose to convert the temp units?

Answers

Answer:

[tex]1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=0.03926\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}[/tex]

Step-by-step explanation:

To find : Convert [tex]1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}[/tex] into [tex]\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}[/tex]

Solution :

We convert units one by one,

[tex]1\text{ m}^2=10.7639\text{ ft}^2[/tex]

[tex]1\text{ sec}=\frac{1}{3600}\text{ hour}[/tex]

[tex]1\text{ cal}=0.003968\text{ BTU}[/tex]

Converting temperature unit,

[tex]^\circ C\times \frac{9}{5}+32=^\circ F[/tex]

[tex]1^\circ C\times \frac{9}{5}+32=33.8^\circ F[/tex]

So, [tex]1^\circ C=33.8^\circ F[/tex]

Substitute all the values in the unit conversion,

[tex]1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=\frac{0.003968}{10.7639\times \frac{1}{3600}\times 33.8}\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}[/tex]

[tex]1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=\frac{0.003968}{0.101061}\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}[/tex]

[tex]1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=0.03926\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}[/tex]

Therefore, The conversion of unit is [tex]1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=0.03926\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}[/tex]

Solve the system of linear equations using the Gauss-Jordan elimination method.

(x,y,z)=__________________

2x + 2y − 3z = 16
2x − 3y + 2z = −4
4x − y + 3z =
−4

Answers

Answer:

(x,y,z)=(2,0,-4)

Step-by-step explanation:

First we create the extended matrix from the equations

[tex]\left[\begin{array}{ccc|c}2&2&-3&16\\2&-3&2&-4\\4&-1&3&-4\end{array}\right][/tex]

Using the elementary operations

Substract to the 2nd line the first one, and the 3rd one twice the first:

[tex]\left[\begin{array}{ccc|c}2&2&-3&16\\0&-5&5&-20\\0&-5&9&-36\end{array}\right][/tex]

Divide the first line by 2, the 2nd one by -5 and substract to the 3rd the 2nd:

[tex]\left[\begin{array}{ccc|c}1&1&-3/2&8\\0&1&-1&4\\0&0&4&-16\\\end{array}\right][/tex]

Divide the 3rd by 4:

[tex]\left[\begin{array}{ccc|c}1&1&-3/2&8\\0&1&-1&4\\0&0&1&-4\\\end{array}\right][/tex]

Add the 3rd to the 2nd:

[tex]\left[\begin{array}{ccc|c}1&1&-3/2&8\\0&1&0&0\\0&0&1&-4\\\end{array}\right][/tex]

Substract the 2nd to the 1st

[tex]\left[\begin{array}{ccc|c}1&0&-3/2&8\\0&1&0&0\\0&0&1&-4\\\end{array}\right][/tex]

Add the 3rd multiplied by 3/2:

[tex]\left[\begin{array}{ccc|c}1&0&0&2\\0&1&0&0\\0&0&1&-4\\\end{array}\right][/tex]

The answer is determined:

x=2

y=0

z=-4

You can check they are correct, by entering in the original formulas.

Consider all the whole numbers from 0 to 1500. What is the sum of all digits needed to write down these numbers? No calculators

Answers

Answer:757

Step-by-step explanation:

the earth rotates about its axis once every 23 hours, 56 minutes and 4 seconds. Approximate the number of radians the earth rotates in one second.

Answers

Answer:

[tex]\frac{\pi}{43082}\text{ radians per second}[/tex]

Step-by-step explanation:

Given,

Time taken in one rotation of earth = 23 hours, 56 minutes and 4 seconds.

Since, 1 minute = 60 seconds and 1 hour = 3600 seconds,

⇒ Time taken in one rotation of earth = (23 × 3600 + 56 × 60 + 4) seconds

= 86164  seconds,

Now,  the number of radians in one rotation = 2π,

That is, 86164 seconds = 2π radians

[tex]\implies 1\text{ second }=\frac{2\pi}{86164}=\frac{\pi}{43082}\text{ radians}[/tex]

Hence, the number of radians in one second is [tex]\frac{\pi}{43082}[/tex]

Final answer:

The Earth completes a 2π radian rotation about its axis in 23 hours, 56 minutes, and 4 seconds. After converting this time to 86,164 seconds, the number of radians the Earth rotates in one second can be calculated by dividing 2π by 86,164, giving a result of approximately 0.00007292115 radians.

Explanation:

The Earth completes one full rotation about its axis in 23 hours, 56 minutes and 4 seconds. This rotation can be converted into radians, using the principle that one complete rotation is equivalent to 2π radians. So first, convert the rotation time into seconds: (23 x 60 x 60) + (56 x 60) + 4 = 86,164 seconds. Therefore, the Earth rotates through 2π radians in this time.

Now, we want to find out how many radians the Earth rotates in one second. To calculate this, divide 2π (which represent a full rotation in radians), by the total number of seconds in one rotation: 2π/86,164. This will give you approximately 0.00007292115 radians, which is the angular velocity or the number of radians the Earth rotates in one second.

Learn more about Angular Velocity of Earth here:

https://brainly.com/question/32821466

#SPJ3

Prove using the principle of mathematical induction: (i) The number of diagonals of a convex polygon with n vertices is n(n − 3)/2, for n ≥ 4, (ii) 2n < n! for for all n > k > 0, discover the value of k before doing induction.

Answers

Step-by-step explanation:

Proof for i)

We will prove by mathematical induction that, for every natural [tex]n\geq 4[/tex], the number of diagonals of a convex polygon with n vertices is [tex]\frac{n(n-3)}{2}[/tex].

In this proof we will use the expression d(n) to denote the number of diagonals of a convex polygon with n vertices

Base case:

First, observe that:, for n=4, the number of diagonals is

[tex]2=\frac{n(n-3)}{2}[/tex]

Inductive hypothesis:  

Given a natural [tex]n \geq 4[/tex],

[tex]d(n)=\frac{n(n-3)}{2}[/tex]

Now, we will assume the induction hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

Observe that, given a convex polygon with n vertices, wich we will denote by P(n), if we add a new vertix (transforming P(n) into a convex polygon with n+1 vertices, wich we will denote by P(n+1)) we have that:

Every diagonal in P(n) will still be a diagonal in P(n+1). One (and only one) side of P(n) will be a diagonal in P(n+1).There would be an extra n-2 diagonals (those that connect with the new added vertix).

Because of these observation we know that, for every [tex]n\geq 4[/tex],

[tex]d(n+1)=d(n)+1+(n-2)=d(n)+n-1[/tex]

Therefore:

[tex]d(n+1)=d(n)+n-1=\frac{n(n-3)}{2}+n-1=\frac{n^2-3n+2n-2}{2}=\frac{n^2-n-2}{2}=\frac{(n+1)(n-2)}{2}[/tex]

With this we have proved our statement to be true for n+1.    

In conlusion, for every natural [tex]n \geq 4[/tex],

[tex]d(n)=\frac{n(n-3)}{2}[/tex]

Proof for ii)

Observe that:

For n=1 [tex]2n=2>1=n![/tex]For n=2 [tex]2n=4>2=n![/tex]For n=3 [tex]2n=6=n![/tex]

Then, the statement is not true for n=1,2,3.

We will prove by mathematical induction that, for every natural [tex]n \geq 4[/tex],

[tex]2n<n![/tex].

Base case:

For n=4, [tex]2n=8<24=n![/tex]

Inductive hypothesis:  

Given a natural [tex]n \geq 4[/tex], [tex]2n<n![/tex]

Now, we will assume the induction hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

Observe that,

[tex]n!+2\leq (n+1)! \iff n!+2\leq n!(n+1) \iff 1+\frac{2}{n!}\leq n+1 \iff 2\leq n*n![/tex]

wich is true as we are assuming [tex]n\geq 4[/tex]. Therefore:

[tex]2(n+1)=2n+2<n!+2\leq (n+1)![/tex]

With this we have proved our statement to be true for n+1.    

In conlusion, for every natural [tex]n \geq 4[/tex],

[tex]2n<n![/tex]

Way back in the olden days, Blockbuster tallied all their US movie rental data and found that on average, individuals rent 10 movies a year with a standard deviation of 3. Treat these as population statistics. They wanted to see if movie rental rates in Yuma, Arizona, were different from those of the country as a whole (why Yuma? Who knows ). A random sample of 25 blockbuster members in Yuma yielded a mean rental rate of 11.3 movies per year. Use alpha = .05

Answers

Answer with explanation:

By considering the given information we have ,

[tex]H_0: \mu = 10\\\\ H_a: \mu\neq10[/tex]

Since, the alternative hypothesis is two tailed so the test is a two-tailed test.

Given : Population mean : [tex]\mu=10[/tex]

Standard deviation: [tex]\sigma= 3[/tex]

Sample size : n=25 , whihc is less than 30 so the sample is small and we use t-test.

Sample mean : [tex]\overline{x}=11.3[/tex]

Significance level : [tex]\alpha= 0.5[/tex]

Formula to find t-test statistic is given by :-

[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

i.e. [tex]t=\dfrac{11.3-10}{\dfrac{3}{\sqrt{25}}}\approx2.17[/tex]

By using the standard normal distribution table,

The p-value corresponds 2.17 (two-tailed)=0.0300068

Since , the p-value is less than the significance level, so we reject the null hypothesis.

Hence, we conclude that there are enough evidence to to support the claim that movie rental rates in Yuma, Arizona, were different from those of the country as a whole .

Final answer:

A hypothesis test is conducted to see if the average movie rental rate in Yuma, Arizona, is statistically different from the national average. This problem is resolved in several steps including stating hypotheses, formulating an analysis plan, analyzing sample data, and interpreting the results. The rental rate is then compared to a critical value determined by the significance level (α = .05).

Explanation:

The subject here is a hypothesis testing problem related to the mean rental rate of DVDs in Yuma, Arizona. Blockbuster found that the average nation-wide movie rental rate was 10 movies per year with a standard deviation of 3. In Yuma, a sample of 25 people resulted in a mean rental rate of 11.3 movies per year. The company wanted to check whether this difference was significant or not. So, they used an alpha level of .05 to conduct this hypothesis test.

Here are the steps of the hypothesis test:

State the hypotheses. The null hypothesis H0 would be that the mean rental rate in Yuma is the same as the average across the US (μ = 10). The alternative hypothesis Ha would be that the mean rental rate in Yuma is not equal to the average across the US (μ ≠ 10).Formulate an analysis plan. For this analysis, the significance level is defined as alpha (α) = .05. As per the conditions, the population standard deviation (σ) is known and equals 3.Analyze sample data. Using the sample data and the information provided, we can calculate the test statistic (z).Interpret the results. If the test statistic is beyond the critical value, we reject the null hypothesis. Otherwise, we do not have enough evidence to reject it.

Learn more about Hypothesis Testing here:

https://brainly.com/question/34171008

#SPJ11


You wish to ship six crude oil samples from your drill site to your laboratory. Each sample has a density of 0.8240 kg/L and fills a 1.090e-4 m3container. How much mass, X g , of crude oil will you be shipping?

(HINT: |X| is near an order of magnitude of 102 g ).

Answers

Answer:

total mass of 6 samples = 538.896 g

in terms of X = 5.283 g

Step-by-step explanation:

Given:

Number of crude oil samples = 6

Density of each sample = 0.8240 kg/L

Volume filled by each sample = 1.09 × 10⁻⁴ m³

now,

1 m³ = 1000 L

thus,

1.09 × 10⁻⁴ m³ = 1.09 × 10⁻⁴ m³ × 1000 = 0.109 L

also,

Mass = Density × Volume

or

Mass of each sample = 0.8240 × 0.109 = 0.089816 kg

Thus,

total mass of 6 samples = Mass of each sample × 6

or

total mass of 6 samples = 0.089816 kg × 6 = 0.538896 kg

or

total mass of 6 samples = 538.896 g

or

in X = [tex]\frac{\textup{total mass of 6 samples}}{\textup{102}}[/tex]

= 5.283 g


Compare the values of the underline digits (2 is underline in both numbers in problem 1)

1.) 2,783 and 7,283 The value of 2 in_____ is ___times the value of 2 in____

(7 is underline in both numbers for problem 2)

2.) 503,497 and 26, 475 The value of 7 in____is___times the value of 7 in____

(4 is underline in both numbers for problem 3)

3.) 34,258 and 47,163 The value of 4 in____is___times the value of 4 in____

Answers

Answer with Step-by-step explanation:

1.We are given

2783 and 7283

We have to compare the values of the underline digits

Place value of 2 in 2783 =2000 because 2 is at thousand place

2 in 7283 is at hundred place

Therefore, the place value of 2 in 7283=200

Therefore, the value of 2 in 2783 is 10 times the value of 2 in 7283.

2.We have to compare the values of 7  in both numbers

Place of 7 in 503497=one's

Therefore, place value of 7 =7

7 in 26475 is at tens place

Therefore, the place value of 7 in 26475=70

Hence, the value of 7 in 26475 is 10 times the value of 7 in 503497.

3.We have to compare the values of 4 in both given numbers

Place of 4 in 34258=Thousand

Place value of 4 in 34258=4000

Place of 4 in 47163=Ten thousand

Place value of 4 in 47163=40000

Hence, the value of 4 in 47163 is 10 times the value of 4 in 34258.

In a sample of 408 new websites registered on the Internet, 37 were anonymous (i.e., they shielded their name and contact information). (a) Construct a 95 percent confidence interval for the proportion of all new websites that were anonymous. (Round your answers to 4 decimal places.)

Answers

Answer: [tex](0.0628,\ 0.1186)[/tex]

Step-by-step explanation:

Given : Significance level : [tex]\alpha:1-0.95=0.05[/tex]

Critical value : [tex]z_{\alpha/2}=\pm1.96[/tex]

Sample size : n= 408

Proportion of new websites registered on the Internet were anonymous :

[tex]\hat{p}=\dfrac{37}{408}\approx0.0907[/tex]

The formula to find the confidence interval for population proportion is given by :-

[tex]\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

i.e. [tex]0.0907\pm (1.96)\sqrt{\dfrac{0.0907(1-0.0907)}{408}}[/tex]

[tex]=0.0907\pm0.0278665515649\\\\\approx 0.0907\pm0.0279\\\\=(0.0907-0.0279,\ 0.0907+0.0279)\\\\=(0.0628,\ 0.1186)[/tex]

Hence,  the 95 percent confidence interval for the proportion of all new websites that were anonymous = [tex](0.0628,\ 0.1186)[/tex]

Yesterday's World Cup final had viewing figures of 138,695,157.

What is the value of the 3?

Answers

Answer:

The value of the 3 is 30,000,000.

Step-by-step explanation:

From the digit at the right, you go multiplying each element by 10 powered to a counter that starts at zero and increases at every digit. So:

Our counter is i

i = 0;

v(7) is the value of the 7

[tex]v(7) = 7*10^{0} = 7[/tex]

i = 1;

v(5) is the value of the 5

[tex]v(5) = 5*10^{1} = 50[/tex]

i = 2;

v(1) is the value of the 1

[tex]v(1) = 1*10^{2} = 100[/tex]

i = 3;

v(5) is the value of the 5

[tex]v(5) = 5*10^{3} = 5,000[/tex]

i = 4;

v(9) is the value of the 9

[tex]v(9) = 9*10^{4} = 90,000[/tex]

i = 5;

v(6) is the value of the 6

[tex]v(6) = 6*10^{5} = 600,000[/tex]

i = 6;

v(8) is the value of the 8

[tex]v(8) = 8*10^{6} = 8,000,000[/tex]

i = 7;

v(3) is the value of the 3

[tex]v(3) = 3*10^{7} = 30,000,000[/tex]

The value of the 3 is 30,000,000.

The digit 3 in the number 138,695,157 represents a value of 300 million, indicating its substantial contribution to the overall magnitude of the figure in the context of place value and powers of 10.

The value of the digit 3 in the number 138,695,157 is 3 hundred million. In this number, each place value represents a power of 10, with the rightmost digit being ones, the next one being tens, the next hundreds, and so on. The digit 3 in the hundred million's place means that it represents 3 multiplied by 100,000,000.

In other words, the digit 3 in this context signifies 300 million. This is because when you see a digit in a number, its place value determines its weight in terms of powers of 10. So, the digit 3 in the hundred million's place is equivalent to 3 x 100,000,000, which is indeed 300 million.

So, in the number 138,695,157, the digit 3 holds the value of 300 million, contributing significantly to the overall magnitude of the figure.

Learn more about place value here:

https://brainly.com/question/25137147

#SPJ3

Orders for a computer are summarized by the optional features that are requested. The proportion of orders with no optional features is 0.40. The proportion of orders with one optional feature is 0.34. The proportion of orders with more than one optional feature is 0.26. (a) What is the probability that an order requests at least one optional feature? Round your answer to two decimal places (e.g. 98.76). (b) What is the probability that an order does not request more than one optional feature? Round your answers to two decimal places (e.g. 98.76).

Answers

Answer:

a) The probability that an order requests at least one optional feature is 34%+26% = 60%.

b) The probability that an  order does not request more than one optional feature is 40% + 34% = 74%.

Step-by-step explanation:

Probability:

What you want to happen is the desired outcome.

Everything that can happen iis the total outcomes.

The probability is the division of the number of possible outcomes by the number of total outcomes.

In our problem, the probabilities are:

-40% that no optional features are requested.

-34% that one optional feature is requested

-26% that more than one optional feature is requested.

(a) What is the probability that an order requests at least one optional feature?

There is a 34% probability that one optional feature is requested and a 26% probability that more than one optional feature is requested.

So the probability that an order requests at least one optional feature is 34%+26% = 60%.

(b) What is the probability that an order does not request more than one optional feature?

There is a 40% probability that no optional features are requested and a 34% probability that one optional feature is requested.

So the probability that an  order does not request more than one optional feature is 40% + 34% = 74%.

Final answer:

The probability an order requests at least one optional feature is 0.60, and the probability an order does not request more than one optional feature is 0.74.

Explanation:

The question involves calculating probabilities based on provided proportions of orders with optional features.

Part (a): Probability of at least one optional feature

The proportion of orders with no optional features is 0.40. Therefore, the probability that an order requests at least one optional feature is 1 - 0.40 = 0.60. So, the probability is 0.60 when rounded to two decimal places.

Part (b): Probability of not more than one optional feature

We are given that orders with one optional feature make up 0.34 and those with no optional features constitute 0.40. Adding these together gives us a probability of 0.34 + 0.40 = 0.74 for orders not requesting more than one optional feature. Thus, this probability is 0.74, rounded to two decimal places.

How many sets of two or more consecutive positive integers can be added to obtain a sum of 1800?

Answers

Answer:

n = 60

Step-by-step explanation:

GIVEN DATA:

Total sum of consecutive number is 1800

sum of n number is given as

[tex] sum = \frac{ n(n+1)}{2}[/tex]

where n is positive number and belong to natural number i.e 1,2,3,4,...

from the data given we have[tex]1800 = \frac{n(n+1)}{2}[/tex]

solving for n we get

[/tex]n^2 + n -3600 = 0[/tex]

n = 59.5, -60.5

therefore n = 60

Other Questions
Please answer this correctly Salt Corporation's contribution margin ratio is 75% and its fixed monthly expenses are $55,000. Assume that the company's sales for May are expected to be $114,000. Required: Estimate the company's net operating income for May, assuming that the fixed monthly expenses do not change. Need help with this ready to eat foods includes In recent years, there has been controversy among biologists about whether Neanderthals should be placed within the same species as modern humans or into a separate species of their own. Most DNA sequence data analyzed at this point indicated that there was probably little or no gene flow between Neanderthals and Homo sapiens. Which species concept is most applicable in this example? Jennifer decided that Governor Bentley would not get her vote for his re-election until he provided some clarification on whathis plans were for the state highway system.Which sentence, if placed after this sentence, would provide the most coherence?08Governor Bentley spoke on a wide variety of pressing and crucial issuesfacing the state.One of Governor Bentley's most passionate projects is wildlife and pineforest preservationUnfortunately, Governor Bentley never provided any clarification aboutthat vital state issue.Governor Bentley won his first election in a landslide, barely spending anymoney on publicityPs able Page ScrollingThe Invisible ManRead the passage on the left to answer the following questions: gizmos student exploration density laboratory How can you tell if a crown is made of solid gold? What is the theme of a play?A. the sequence of events as they occur in a playB. the comment the play makes on a topicC. the conflict between the play's charactersD. the chronological sequence of events in a play Which of the following is Not a symptom of a strong emotions A) impulsiveness B) Hostility C)BlinderssD) Distraction The US Constitution has 7 articles and 27 amendments, Frances constitution has 92 articles, and Chinas has 243 sections. What are the benefits of having a shorter written constitution? Why didnt the leaders of the United States opt to simply revise or improve the Articles of Confederation in 1787?Great Britain had recognized the weakness of the United States under the Articles of Confederation and was planning to attack and conquer the country.The citizens of every state signed petitions demanding that their leaders scrap the Articles of Confederation and create a new plan of government.They accepted that the country needed a stronger central government than the one created by the Articles of Confederation could provide.The Articles of Confederation had always been envisioned as a temporary document, not a long-term plan for the countrys government. Cells of plants and animals have _____________.a. central vacuole and mitochondriab. cell membrane and cell wallc. chromosomes and chloroplastsd. nucleus and DNA In the game of billiards called 14.1, players lose points if they receive penalties. Find the difference in the scores of the winner with 50 points and the opponent with 17 points. Which pairs of triangles can be shown to be congruent using rigid motions?Select Congruent or Not Congruent for each pair of triangles.CongruentNot CongruentABC and DEFABC and JKLABC and QRSJKL and DEFJKL and QRSQRS and DEF A bicyclist starts from rest and accelerates at a rate of 2.3 m/s^2 until it reaches a speed of 23 m/s. It then slows down at a constant rate of 1.0 m/s^2 until it stops. How much time elapses from start to stop? We assume an answer in seconds Which of the following statements is correct? rev: 05_15_2018 Multiple Choice Both perfectly competitive and monopolistic firms are price takers. A perfectly competitive firm is a price taker, while a pure monopoly is a price maker. Both perfectly competitive and monopolistic firms are price makers. A perfectly competitive firm is a price maker, while a pure monopoly is a price taker. (15+70-5 2) divided by (36-6) A hospital claims that the proportion, p, of full-term babies born in their hospital that weigh more than 7 pounds is 36%. In a random sample of 170 babies born in this hospital, 56 weighed over 7 pounds. Is there enough evidence to reject the hospital's claim at the level of significance? Which short-term outcome would underage drinkers most likely to experience?kidney failurecirrhosis of the riverheadachesheart disase High transaction costs will tend to a. reduce the number of mutually beneficial exchanges. b. lead to more specialization in accordance with the law of comparative advantage. c. increase the total gains from trade. d. increase the number of mutually beneficial exchanges. Rewrite the following statements in if then form a) Catching the 8:05 bus is a sufficient condition for my being on time for work b) Being divisible by 3 is a necessary condition for this number to be divisible by 9 o) The Cubs will win the pennant only if they win tomorrow's game.