Answers:
1a) The next four terms are: 513, -728, 1001, -1330
1b) The direct formula is [tex]a_n = (-1)^n*n^3+1[/tex]
================================================
Explanation:
It helps to start with part B first. The direct formula will help us find the next four terms in a very efficient manner.
Start with the sequence {0, 9, -26, 65, -124, 217, -342}
Subtract 1 from each term to get this new sequence {-1, 8, -27, 64, -125, 216, -343}, which closely resembles the sequence {1, 8, 27, 64, 125, 216, 343}. This is the sequence of perfect cubes. The only difference is that each term alternates from positive to negative and vice versa.
So we will have an n^3 as part of the equation and also a (-1)^n as part of the equation. The (-1)^n portion allows us to alternate in signs. Put together we have (-1)^n*n^3 so far
The last thing we do is add 1 to this so that we undo the operation "subtract 1" we did earlier to the original list.
Therefore the formula is [tex]a_n = (-1)^n*n^3+1[/tex]
--------------------
To help verify we have the right formula, plug in n = 1 and we get
[tex]a_n = (-1)^n*n^3+1[/tex]
[tex]a_1 = (-1)^1*1^3+1[/tex]
[tex]a_1 = 0[/tex]
and plug in n = 2 to get
[tex]a_n = (-1)^n*n^3+1[/tex]
[tex]a_2 = (-1)^2*2^3+1[/tex]
[tex]a_2 = 9[/tex]
and so on. I'll let you check the other terms
--------------------
Let's find the terms a8,a9,a10,a11
This is simply a matter of plugging n = 8, n = 9, n = 10, and n = 11
Plug in n = 8
[tex]a_n = (-1)^n*n^3+1[/tex]
[tex]a_8 = (-1)^8*8^3+1[/tex]
[tex]a_8 = 513[/tex]
Repeat for n = 9
[tex]a_n = (-1)^n*n^3+1[/tex]
[tex]a_{9} = (-1)^9*9^3+1[/tex]
[tex]a_{9} = -728[/tex]
Repeat for n = 10
[tex]a_n = (-1)^n*n^3+1[/tex]
[tex]a_{10} = (-1)^{10}*10^3+1[/tex]
[tex]a_{10} = 1001[/tex]
Repeat for n = 11
[tex]a_n = (-1)^n*n^3+1[/tex]
[tex]a_{11} = (-1)^{11}*11^3+1[/tex]
[tex]a_{11} = -1330[/tex]
The exponential models describe the population of the indicated country, A, in millions, t years after 2006. Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?
A) Country 1: A= 126.4e^0.001t
B) Country 2: A= 1091.5e^0.016t
C) Country 3: A= 143.6 e^-0.005t
D) Country 4: A= 27.6 e^0.025t
Answer:
Step-by-step explanation:
Country 4 has the highest growth rate, as it has the largest exponent in its growth function.
The growth rate of each country is given by the coefficient in the exponent of the exponential equation. The greatest growth rate is for Country 4, which has a growth rate of 2.5% each year.
Explanation:The growth rate of each country is represented by the coefficient in the exponent in each exponential equation. The coefficients represent the yearly percentage increase in population. Looking at the four models given, the coefficients are 0.001 for country 1, 0.016 for country 2, -0.005 for country 3, and 0.025 for country 4. Note that the coefficient for country 3 is negative, indicating that the population is actually decreasing each year. Hence, it can be concluded that Country 4 has the greatest growth rate, which is 0.025 or 2.5% each year (when the coefficient is expressed as a percentage).
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In an electric circuit, two resistors with resistances x and y are connected in parallel. In this case, if r is the combined resistance of these two resistors, then the reciprocal of r is equal to the sum of the reciprocals of x and y. What is r in terms of x and y?(A) xy(B) x + y(C) 1/(x + y)(D) xy/(x + y)(E) (x + y)/xy
Answer:
(D) xy/(x + y)
Step-by-step explanation:
To find r in terms of x and y
Given,
two resistors with resistances x and y are connected in parallelr is the combined resistance of these two resistorsthe reciprocal of r is equal to the sum of the reciprocals of x and yThen,
1/r = 1/x + 1/y
1/r = (y + x)/xy
Find the reciprocal of both sides
r = xy/(x + y)
The right answer is option (D) xy/(x + y)
Solve the system. Show your work using Graphing OR Substitution OR Elimination.
Check your answer by showing your solution works in both original equations.
y = 2x -6
y = -½ x +4
The solution is x = 4 and y = 2
Explanation:We have the following system of two linear equations in two variables:
[tex]\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}y=2x-6\\y=-\frac{1}{2}x+4\end{array}\right.[/tex]
Subtract (2) from (1):
[tex]\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}y=2x-6\\ -\left(y=-\frac{1}{2}x+4\right)\end{array}\right \\ \\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ \\ y-y=2x-6-(-\frac{1}{2}x+4) \\ \\ 0=2x-6+\frac{1}{2}x-4 \\ \\ Combine \ like \ terms: \\ \\ 2x+\frac{1}{2}x-6-4=0 \\ \\ 2.5x-10=0 \\ \\ 2.5x=10 \\ \\ x=\frac{10}{2.5} \\ \\ x=4[/tex]
Substituting the x-value into (1):
[tex]y=2(4)-6 \\ \\ y=8-6 \\ \\ y=2[/tex]
So the solution to this system is:
[tex]\boxed{x=4 \ and \ y=2}[/tex]
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Liliana used 444 dark power crystals to raise 141414 zombie soldiers. She wants to know how many zombie soldiers (z)(z)left parenthesis, z, right parenthesis she can raise with 101010 dark power crystals. How many zombie soldiers can Liliana raise with 101010 power crystals?
Question is bit incorrect, Correct question is given below.
Liliana used 4 dark power crystals to raise 14 zombie soldiers. She wants to know how many zombie soldiers (z) she can raise with 10 dark power crystals. How many zombie soldiers can Liliana raise with 10 power crystals?
Answer:
Liliana can raise 35 zombie soldiers.
Step-by-step explanation:
Let the number of zombie soldiers raised by 10 dark power crystals be 'z'.
Zombie raised by 4 power crystals = 14
Since the number of zombie and power crystals are in direct proportion.
Therefore, we get
[tex]\frac{z}{10}=\frac{14}{4}[/tex]
Multiply 10 on both the sides, we get
[tex]z=\frac{14}{4}\times 10 = 35[/tex]
Hence, Liliana can raise 35 zombie soldiers.
Answer:
35 Zombie Soldiers
Step-by-step explanation:
Suppose that you are seated next to a stranger on an airplane and you start discussing various topics such as where you were born (what state or country), what your favorite movie of all time is, your spouse's occupation, and so on. For simplicity, assume that the probability that your details match for any given topic is 1 50 and is independent from one topic to the next. If you discuss 17 topics, how surprising would it be to find that you match on at least one of them? (Round your answer to four decimal places.)
Answer:
0.2907
Step-by-step explanation:
Given that you are seated next to a stranger on an airplane and you start discussing various topics such as where you were born (what state or country), what your favorite movie of all time is, your spouse's occupation, and so on.
Since each topic is independent we find that probability for success in each topic = constant = 1/50 = 0.02
X no of topics that match is binomial with n = 17 and p = 0.02
Required probability
= Probability to find that you match on at least one of them
=[tex]P(X\geq 1)\\=1-P(X=0)\\=1-(1-0.02)^{17} \\=0.2907[/tex]
It would not be surprising as probability is reasonably large.
What is the output value for the following function if the input value is 1?
y = 3x + 1
32
0
5
4
Answer:
Output value for the following function is 4
Step-by-step explanation:
Given:
The input value are the value of x
[tex]y = 3x + 1[/tex]
Input value is 1
We substitute the value 1 for the input variable x in the given function.
[tex]y = 3x + 1[/tex]
[tex]y = 3(1) + 1[/tex]
[tex]y = 3 + 1[/tex]
[tex]y = 4[/tex]
The output value are the value of y
Therefore, for an input of 1, we have an output of 4.
Suppose that in a random selection of 100 colored candies, 21% of them are blue. The candy company claims that the percentage of blue candies is equal to 28%. Use a 0.05 significance level to test that claim.
Answer:
The percentage of blue candies is equal to 28%.
Step-by-step explanation:
Sample size = n = 1000
21% of them are blue
So, No. of blue candies = [tex]21\% \times 100 =\frac{21}{100} \times 100=21[/tex]
Claim : The percentage of blue candies is equal to 28%.
[tex]H_0:\mu = 0.28\\H_a:\mu \neq 0.28[/tex]
We will use one sample proportion test
[tex]\widehat{p}=\frac{x}{n}[/tex]
[tex]\widehat{p}=\frac{21}{100}[/tex]
[tex]\widehat{p}=0.21[/tex]
Formula of test statistic =[tex]\frac{\widehat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
=[tex]\frac{0.21-0.28}{\sqrt{\frac{0.28(1-0.28)}{100}}}[/tex]
=−1.55
Now refer the p value from the z table
p value =0.0606
α =0.05
So, p value > α
So, we failed to reject null hypothesis
So, the percentage of blue candies is equal to 28%.
Given the problem, first, we denote the sample size, observed proportion of blue candies, claimed proportion of blue candies, and significance level as:
- n = 100
- p_observed = 0.21
- p_claimed = 0.28
- significance_level = 0.05
Our first step in the hypothesis testing process is to calculate the standard error. We do this using the formula:
standard_error = sqrt((p_claimed*(1 - p_claimed))/n)
which gives us a standard error of approximately 0.0449. The standard error measures the variability or dispersion of our sample proportion from the claimed proportion.
Next, we will calculate the z-score, which measures the number of standard deviations an observation (or in this case, the sample proportion) is away from the mean, or the claimed proportion. We do this using the formula:
z = (p_observed - p_claimed)/standard_error
which gives us a z-score of approximately -1.559. The negative sign indicates that the observed proportion is less than the hypothesized proportion.
Then, we need to calculate the p-value. The p-value is the probability of getting a sample as extreme, or more extreme, than the one we have, assuming the null hypothesis is true. In other words, it is the likelihood of observing our sample data if the candy company's claim of 28% blue candies is accurate.
As the observed proportion is less than the hypothesized proportion, we calculate the cumulative probability up to the z-score. Doing this gives us a p-value of approximately 0.0595.
Finally, we need to determine whether to accept or reject the null hypothesis based on the p-value and the significance level.
Here, we can see our p-value is slightly larger than the given significance level (0.0595 > 0.05), thus, we do not reject the null hypothesis. This means there is not enough evidence at the 5% significance level to reject the candy company's claim that 28% of their candies are blue.
In conclusion, given our sample and the given significance level, our analysis does not provide sufficient evidence to say with 95% confidence that the company's claim is false. Our data does not contradict the company's claimed proportion of 28%.
There are x number of students at helms. If the number of students increases by 7.8% each year, how many students will be there next year. Write an equation to express this.
There will be 1.078x students next year and equation is number of students in next year = x + 7.8% of x
Solution:Given, There are "x" number of students at helms.
The number of students increases by 7.8% each year which means if there "x" number of students in present year, then the number of students in next year will be x + 7.8% of x
Number of students in next year = number of students in present year + increased number of students.
[tex]\begin{array}{l}{\text { Number of students in next year }=x+7.8 \% \text { of } x} \\\\ {\text { Number of students in next year }=x\left(1+\frac{7.8}{100}\right)} \\\\ {\text { Number of students in next year }=x(1+0.078)=1.078 x}\end{array}[/tex]
Thus there will be 1.078x students in next year
An able order to join a health club a star a fee of $30 is required along with a monthly fee of seven dollars right in equation that Mama knows this situation
Answer:
f(t) = 30 +7t
Step-by-step explanation:
The fee f(t) in terms of months of membership t can be modeled as ...
fee = startup fee + (monthly fee)×(number of months)
f(t) = 30 + 7t
A researcher measures IQ and weight for a group of college students. What kind of correlation is likely to be obtained for these two variables?
a) a positive correlation
b) a negative correlation
c) a correlation near zero*
d) a correlation near one
Answer:
Option b
Step-by-step explanation:
Given that a researcher measures IQ and weight for a group of college students.
In general, we think that the weight has nothing to do with IQ of a person and hence not correlated.
But if we go deep, we find that after a certain weight, the person becomes lazy and inactive with a chance to have reduced IQ
Weight gain causes also health problems including less activity of both brain and body and hence there is a chance for less IQ
So we find that as weight increases iq decreases and when weight decreases, IQ increases.
Thus we can say that there is a negative correlation but not necessarily near to one.
Hence option b is right
The most likely correlation between IQ and weight among college students is near zero, indicating no meaningful relationship between these variables.
Explanation:When it comes to the likelihood of obtaining a correlation between IQ and weight among college students, the correlation is expected to be c) a correlation near zero. This is because there is no theoretical basis or empirical evidence to suggest that these two variables are related in any systematic way. A correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables. A coefficient close to 0 indicates a very weak or no correlation, whereas one closer to +1 or -1 indicates a strong positive or negative correlation, respectively. In our scenario, since weight and IQ are not assumed to be related, the correlation would likely be close to 0, suggesting no meaningful relationship.
Joelle earns her regular pay of $7.50 per hour for up to 40 hours of work in a week. For each hour over 40 hours of work in a week, Joelle is paid 1 1/2 times her regular pay. How much does Joelle earn for a week in which she works 42 hours? *How much does Joelle earn for a week in which she works 42 hour?
A. $126.00
B. $315.00
C. $322.50
D. $378.00
E. $472.
Final answer:
Joelle would earn $322.50 for a week in which she works 42 hours.
Explanation:
To calculate Joelle's earnings for a week in which she works 42 hours, we need to determine the regular pay for the first 40 hours and the overtime pay for the additional 2 hours.
Regular pay for 40 hours = $7.50/hour x 40 hours = $300
Overtime pay for 2 hours = 1.5 x $7.50/hour x 2 hours = $22.50
Therefore, Joelle's total earnings for a week of 42 hours would be $300 (regular pay) + $22.50 (overtime pay) = $322.50.
The correct answer is C. $322.50. Joelle earns $322.50 for a week in which she works 42 hours.
To calculate Joelle's earnings for the week, we need to consider both her regular pay for the first 40 hours and her overtime pay for the additional hours worked beyond 40 hours.
First, let's calculate her regular pay for 40 hours:
Joelle's regular pay rate is $7.50 per hour. Therefore, for 40 hours, her regular pay is calculated as:
Regular pay = Hourly pay rate × Number of regular hours
Regular pay = $7.50/hour ×40 hours
Regular pay = $300.00
Next, we calculate her overtime pay for the 2 hours of overtime work. Joelle earns 1 1/2 times her regular pay rate for overtime hours. So her overtime pay rate is:
Overtime pay rate = 1 1/2 × Regular pay rate
Overtime pay rate = 1.5 × $7.50/hour
Overtime pay rate = $11.25/hour
Now, we calculate her overtime pay for the 2 hours of overtime work:
Overtime pay = Overtime pay rate × Number of overtime hours
Overtime pay = $11.25/hour × 2 hours
Overtime pay = $22.50
Finally, we add her regular pay and overtime pay to find her total earnings for the week:
Total earnings = Regular pay + Overtime pay
Total earnings = $300.00 + $22.50
Total earnings = $322.50
Therefore, Joelle earns $322.50 for a week in which she works 42 hours.
Yolanda is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of 'English is Fun' she sells. Suppose that x and y are related by the equation y=1900+80x.
a. What is the change in Yolanda's total pay for each copy of 'English is Fun' she sells?
b. What is Yolanda's total pay if she doesn't sell any copies of 'English is Fun'?
Answer: a) $80 b)$1900
Step-by-step explanation:
a) change in Yolanda total pay y, for each 'English is fun' sold x, i.e ∆y/∆x = dy/dx
y = 1900+80x
differentiating the equation above
dy/dx = 80
Therefore, dy/dx = $80
change in Yolanda total pay y, for each 'English is fun' sold x, is $80
b) if she doesn't sell any copy of ' English is fun ',x=0
Therefore,
y = 1900 + 80x
Substituting x = 0, into the equation above
y = 1900 = $1900
Therefore her total pay is $1900 if she did not sell any ' English is fun'
Fill in the missing amounts in the balance sheet after the following transactions. You start with $2,500 in cash and in owner's equity.
a. You purchase testing equipment for $815.
b. You purchace product for $500 and then sell it for $1750.00.
c. You receive next month's utility bill for $185.00.
d. You pay the rent by check for $300.
Total assets: $3,450
Total liabilities and equity: $3,450
Explanation:
Cash: $2635
Equipment: $815
Total assets: $3,450
Accounts Payable: $185
Owner's Equity: $3,450 - $185 = $3,265
Total liabilities and equity: $3,450
the guy up there didn't understand.
Brainliest?
Meg is walking around her neighborhood. She stands 150 meters from the grocery store, and she wants to know the distance between the store and the bank.
Which answer is closest to the distance between the store and the bank?
Answer:
162.5 meters
Step-by-step explanation:
With respect to the angle given, the side from Meg to Store (150m) is the side that is "opposite" to the angle.
The side from Store to Bank is the side that is "adjacent" to the angle.
So, we have Opposite side and want to know the Adjacent side.
Which trigonometric ratio relates "opposite" to "adjacent"??
Yes, it is Tan!
We write the trig equation and solve for the distance (letting it be x):
[tex]Tan(42.71)=\frac{Opposite}{Adjacent}=\frac{150}{x}\\x=\frac{150}{Tan(42.71)}\\x=162.49[/tex]
Rounding the answer to 1 decimal place, it is:
162.5 meters
A newborn baby has extremely low birth weight if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean weight at birth was 810 grams. This sample mean is an unbiased estimator of the mean weight m in the population of extremely low birth weight babies. This means that:
a. when the sample is a simple random sample from the population, the mean of the sampling distribution of the sample mean is the same as the population mean.
b. as we take larger and larger samples from this population the sample mean, x-bar, will get closer and closer to the population mean.
c. in many samples from this population, the many values of x-bar will have a distribution that is close to Noral.
d. in many births from this population the many values of x-bar will be equal to m.
The statements mostly describe properties of an unbiased estimator in statistics, which typically involves large sample sizes, the mean of the sampling distribution being equivalent to the population mean, and the distribution of sample means approaching a normal distribution. One incorrect statement suggests that each individual sample mean will be equivalent to the population mean.
Explanation:This question pertains to the concept of statistical estimation. The statements reflect the properties of an unbiased estimator in a simple random sample from the population. Let's analyze each choice:
When the sample is a simple random sample from the population, the mean of the sampling distribution of the sample mean is the same as the population mean. This statement is true. The mean of the sampling distribution (expected value of sample means) should be equal to the population mean if the estimator is unbiased. As we take larger and larger samples from this population the sample mean, x-bar, will get closer and closer to the population mean. This statement is true. It is based on the law of large numbers which implies that as the sample size increases, the sample mean converges to the population mean. In many samples from this population, the many values of x-bar will have a distribution that is close to normal. This statement is usually true due to the central limit theorem which states that when samples of sufficiently large size are taken, the distribution of sample means tends to approach normal distribution. In many births from this population, the many values of x-bar will be equal to m. This statement is false. Each individual sample mean (x-bar) will not be equal to the population mean (m), but the average of many x-bars from many samples will be close to m if the estimator is unbiased.Learn more about Unbiased Estimator here:https://brainly.com/question/32063886
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The sample mean is an unbiased estimator of the population mean when the sample is a simple random sample; the mean of the sampling distribution of the sample mean will equal the population mean.
The student's question relates to the concept of an unbiased estimator in statistics, particularly the sample mean as an unbiased estimator of the population mean. The correct statement that defines an unbiased estimator is:
a. when the sample is a simple random sample from the population, the mean of the sampling distribution of the sample mean is the same as the population mean.This means that if you were to take many samples from the population and calculate the mean of each sample, the average of all these sample means would be equal to the population mean. This property is fundamental in inferential statistics for making generalizations about a population from a sample.
In the past month, Abdul rented 4 video games and 3 DVDs. The rental price for each video game was $3.20. The rental price for each DVD was $3.80. What is the total amount that Abdul spent on video game and DVD rentals in the past month?
Answer:
$24.20
Step-by-step explanation:
Multiply and add.
5.6% CompleteToolbox 55.6% complete This is a Single Choice Question; skip ahead to question content A B C D E Confirm Drainage tubing comes in large rolls. At your hardware store, you cut tubing to the lengths the customers want. You also provide customers with the volume of their tubing because they need to fill tubing with gravel as they install it. The tubing’s inside radius is 2 inches. Which of the following is an expression for the volume of L feet of drainage tubing, in cubic feet? 0.09L 3.14L 6.28L 12.56L 150.72L
Answer: V = 0.09L feet^3
Step-by-step explanation:
The tubing has the shape of a cylinder. Formula for determining the volume of a cylinder is
Volume of cylinder = πr^2h
Where π = 22/7 or 3.14
r = the inner radius of the drainage tubing. It is given as 2 inches. We would convert the 2 inches to feets
If 12 inches = 1 foot,
2 inches will be 2/12 inches
h = height of the cylinder and it is replaced by L in feets. L is the length of the cut drainage tubing.
An expression for the volume of L feets of drainage tubing will be
V = πr^2L
= 3.14 × (2/12)^2 × L
= 3.14 × 4/144 × L
V = 0.087L feet^3
V = 0.09L feet^3
The temperature T of an object in degrees Fahrenheit after t minutes is represented by the equation T(t) = 69e−0.0174t + 79. To the nearest degree, what is the temperature of the object after one and a half hours?
To determine the temperature of an object after a specific time using the given equation T(t) = 69e−0.0174t + 79, you replace t with the desired time in minutes and calculate the result. In case of one and a half hours (90 minutes), the temperature can be found using T(90) = 69e−0.0174*90 + 79.
Explanation:The subject of this question is mathematics, more specifically an application of exponential decay in the context of temperature change. The equation T(t) = 69e−0.0174t + 79 represents the temperature T of an object after time t in minutes. To find the temperature after one and a half hours, we need to convert this to minutes because the given equation uses time in minutes. One and a half hours is equivalent to 90 minutes. So we will plug t=90 into the equation:
T(90) = 69e−0.0174*90 + 79.
Around this value to the nearest degree will give us the desired temperature in degrees Fahrenheit after one and a half hours.
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The temperature of the object after one and a half hours is approximately [tex]\( {93^\circ} \)[/tex] Fahrenheit.
To find the temperature of the object after one and a half hours, we need to substitute t = 90 minutes into the equation [tex]\( T(t) = 69e^{-0.0174t} + 79 \)[/tex], since there are 60 minutes in an hour and a half.
Let's calculate:
[tex]\[ T(90) = 69e^{-0.0174 \times 90} + 79 \]\[ T(90) = 69e^{-1.566} + 79 \][/tex]
Using a calculator:
[tex]\[ T(90) \approx 69 \times 0.208 + 79 \]\[ T(90) \approx 14.352 + 79 \]\[ T(90) \approx 93.352 \][/tex]
Identify the fraction that is equivalent to 5 __ 9 1. 20\ 45 2. 25\36 3.25\ 45 4. 30\45
Answer:
3. 25/45
Step-by-step explanation:
[tex]\dfrac{5}{9}=\dfrac{5\cdot 5}{5\cdot 9}=\bf{\dfrac{25}{45}}[/tex]
It takes the high-speed train x hours to travel the z miles from Town A to Town B at a constant rate, while it takes the regular train y hours to travel the same distance at a constant rate. If the high-speed train leaves Town A for Town B at the same time that the regular train leaves Town B for Town A, how many more miles will the high-speed train have traveled than the regular train when the two trains pass each other?
(A) z(y – x)/x + y
(B) z(x – y)/x + y
(C) z(x + y)/y – x
(D) xy(x – y)/x + y
(E) xy(y – x)/x + y
Answer:
B
Step-by-step explanation:
To solve this, we use ratio.
Firstly, we need to know the number of hours traveled. The total number of hours traveled = x+y
Ratio of this used by high speed train = x/(x +y).
Total distance traveled before they meet = [x/(x + y)] × z
For low speed train = [y/(x + y)] × z.
The difference would be distance by high speed train - distance by low speed train.
= z [ (x - y)/x + y)]
one number is 5 more than twice the other number. if the sum of the two numbers is 32 find the two numbers
Answer:
9 and 23
Step-by-step explanation:
You can adjust the problem a little bit and make it easier to solve.
Subtracting 5 from the larger number makes it twice the smaller, and their sum be 32-5 = 27. So 27 is 3 times the smaller number, 9, and the larger is 32-9 = 23, which is 5 more than two times 9.
The two numbers are 9 and 23.
_____
You can let x represent "the other number". Then "one number" is 2x+5, and their sum is ...
(x) +(2x+5) = 32
3x +5 = 32
3x = 27 . . . . . subtract 5
x = 9 . . . . . . . divide by 3
(This working out should look familiar if you followed the above verbal solution.)
"One number" is 27 and "the other number" is 9.
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f the chance of rain for tomorrow is 40%, what is the chance that it will NOT rain?
Note: You can choose more than one answer.
40%
10%
60%
100%
Answer:
OPTION C: 60%
Step-by-step explanation:
Chances of raining the next day + Chances that it will not rain = 100%
One of them should definitely be true.
So, if the chance of it raining tomorrow is 40% then there is 60% chance that it will not rain tomorrow.
This can also seen as follows:
Probability of rain tomorrow + Probability of no rain = 1
Given Probability of rain tomorrow = 40% = [tex]$ \frac{40}{100} = \frac{2}{5} $[/tex]
Probability of no rain tomorrow = 1 - Probability of rain tomorrow
⇒ Probability of no rain = 1 - [tex]$ \frac{2}{5} $[/tex]
⇒ Probability of no rain = [tex]$ \frac{3}{5} $[/tex]
Expressing it as percentage: [tex]$ \frac{3}{5} \times 100 $[/tex] = 60%.
Determine whether Rolle's Theorem can be applied to the function on the given interval; if so, find the value(s) of c guaranteed by the theorem. (Enter your answers as a comma-separated list. If Rolle's Theorem does not apply, enter DNE.) f(x) = x (5 − x) on [0, 5]
Step-by-step explanation:
1) Check if the function is differentiable on that interval. In this case, yes, because all polynomials are differentiable.
2) plug in the bounds of the interval to see if the y-values equal 0.
f(0)=0
f(5)=0
since the last 2 conditions are satisfied, DNE will not be an answer choice.
3)take derivative and make it equal to 0
f' (×) = 5- 2x
0 = 5- 2x
x = 5/2
4) at c = 5/2, f(x) satisfies rolle's theorem.
Rolle's Theorem can be applied to the function f(x) = x(5 - x) on the interval [0, 5], and the value of c guaranteed by the theorem is c = 2.5.
Explanation:The function f(x) = x(5 - x) on the interval [0, 5] is continuous on the closed interval and differentiable on the open interval (0, 5). To check if Rolle's Theorem can be applied, we first need to verify that the function is continuous on [0, 5] and differentiable on (0, 5). Both of these conditions are satisfied by the given function.
To find the value(s) of c guaranteed by Rolle's Theorem, we need to find the values of x where the derivative of the function is zero. Let's find the derivative of f(x):
f'(x) = 5 - 2x
Setting f'(x) = 0 and solving for x:
5 - 2x = 0
2x = 5
x = 2.5
Therefore, Rolle's Theorem can be applied to the function f(x) = x(5 - x) on the interval [0, 5], and the value of c guaranteed by the theorem is c = 2.5.
Learn more about Rolle's Theorem here:https://brainly.com/question/30809316
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Jayden gets a piece of candy for every 15 minutes he spends reading each day. The number of pieces of candy he receives each day is shown in the chart Monday = * * * Tuesday = * * Wednesday = * * * * * Thursday = Friday = * * * * If he spends 300 minutes reading during the week, how many pieces of candy did Jayden get on Thursday?
Answer:
20 peices
Step-by-step explanation:
Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?A. 1.5B. 1.7C. 2.3D. 2.5E. 3.0
Answer:
Q = 1.84
Step-by-step explanation:
If we poured 0,5 gallon of mixture A with 0.5 gallon of mixture B we will get a gallon of:
( 15 + 50 )/ 2 = 32.5 %
Now by ule of three
If with 0, 5 gl of A we get 32.5 %
?? x 30
x = (0.5)*(0.3)/ 0.325
x = 0,462 gl t get a mixture of 30%
Then for 4 gl
Q = 4 * 0.462
Q = 1.84
With no air resistance, the time, t, it takes an object to fall h feet, can be determined by the equation t = square root of h/4. What is the height when the time to reach the ground is 25 seconds?
Answer:
10,000 ft
Step-by-step explanation:
We can solve the given relation for h:
[tex]t=\dfrac{\sqrt{h}}{4}\\\\4t=\sqrt{h}\\\\h=16t^2[/tex]
Putting t=25 into this formula, we get ...
h = 16(25²) = 10,000
With no air resistance the object will take 25 seconds to fall from 10,000 feet.
Find an equation of the line through the given point and perpendicular to the given line
Y=2x-2 and (-3, 5)
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
For two lines to be perpendicular, the slope of one line is the negative reciprocal of the other line. The equation of the given line is
y = 2x - 2
Comparing with the slope intercept form,
Slope, m = 2
This means that the slope of the line that is perpendicular to it is -1/2
The given points are (-3, 5)
To determine c,
We will substitute m = -1/2, y = 5 and x = - 3 into the equation, y = mx + c
It becomes
5 = -1/2 × - 3 + c
5 = - 3/2 + c
c = 5 + 3/2
c = 13/2
The equation becomes
y = -x/2 + 13/2
Victor Malaba has a net income of $1,240 per month. If he spends $150 on food, $244 on a car payment , $300 on rent, and $50 on savings, what percent of his net income can he spend on other things?
Answer:
40%
Step-by-step explanation:
The amount of income allocated to the items listed totals $744, so there is $496 he can spend on other things. As a percentage of income, that is ...
496/1240 × 100% = 40%
Malaba can spend 40% of his net income on other things.
Write the solution to the given inequality in interval notation.
A) [2,∞)
B) (-∞,2]
C) (-∞,2)
D) (2,∞)
Answer:
The answer should be C.
Answer:
c
Step-by-step explanation:
5.
The present value of a sum of money is the
amount that must be invested now, at a given
rate of interest, to produce the desired sum at a
later date. Find the present value of 10,000 if
interest is paid at a rate of 6.2% compounded
weekly for 8 years.
Answer:
The present value of 10,000 if interest is paid at a rate of 6.2% compounded weekly for 8 years is 6097.56
Explanation:
We know that compound interest is given by
[tex]A=P\left(1+\frac{r}{n}\right)^{n t}[/tex]
Where ,
Where A = final amount (which is given to be = 10000)
P = Principal amount (which is the present amount which we have to find)
r = interest rate = 6.2 = 0.062
n = no. of times interest applied per time period = it is given that the interest is applied weekly, so in one year there are 52 weeks so n = 52
t = time period = 8 years
Substituting the given values, we get
[tex]10000=\mathrm{P}\left(1+\frac{6.2}{52}\right)^{52\times 8}[/tex]
P = 6097.5
We get, P = 6097.56 which is the present value of a sum of money