The football stadium was approximately 5,000 thousand square feet.
Explanation:The given cost function is [tex]\( C(x) = \frac{7,250,000}{x} + 60 \)[/tex], where C(x) represents the cost to build a football stadium of x thousand square feet. To find the size of the stadium when the cost is $8,000, we set C(x) equal to $8,000 and solve for x :
[tex]\[ 8,000 = \frac{7,250,000}{x} + 60 \][/tex]
Subtracting 60 from both sides:
[tex]\[ 7,940 = \frac{7,250,000}{x} \][/tex]
Now, solving for x , we multiply both sides by x :
[tex]\[ x = \frac{7,250,000}{7,940} \][/tex]
Performing the division:
x approx 912.66
Since x represents the size of the stadium in thousand square feet, the final answer is approximately 912.66 thousand square feet. Therefore, the stadium was approximately 5,000 thousand square feet.
In summary, to determine the size of the football stadium, we set the cost function equal to the given cost, solved for x , and found that the stadium was approximately 912.66 thousand square feet.
The football stadium was approximately x = 916.67 thousand square feet.
Explanation:The given cost function for building a football stadium is [tex]\(C(x) = \frac{7,250,000}{x} + 60\)[/tex], where \(x\) represents the size of the stadium in thousand square feet. We are asked to find the size of the stadiumx when the cost[tex](\(C(x)\))[/tex] is $8,000.
To solve for x, we set [tex]\(C(x)\)[/tex] equal to $8,000 and solve for x:
[tex]\[ 8,000 = \frac{7,250,000}{x} + 60 \][/tex]
First, subtract 60 from both sides:
[tex]\[ 7,940 = \frac{7,250,000}{x} \][/tex]
Next, multiply both sides by x to isolate x in the denominator:
[tex]\[ 7,940x = 7,250,000 \][/tex]
Finally, solve for [tex]\(x\)[/tex] by dividing both sides by 7,940:
[tex]\[ x = \frac{7,250,000}{7,940} \approx 916.67 \text{ thousand square feet} \][/tex]
Therefore, the football stadium was approximately 916.67 thousand square feet in size.
In summary, by substituting the given cost into the cost function and solving the resulting equation, we find that the stadium size is approximately 916.67 thousand square feet. This process involves algebraic manipulation to isolate [tex]\(x\)[/tex] and perform the necessary arithmetic calculations.e
a motorboat takes 3 hours to travel 108 mi going upstream. the return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
1.Rate of the boat in still water is_________.
2.Rte of the current is__________.
Answer: The speed of the motorboat in still water is 45mph
The current rate is 9mph.
Step-by-step explanation:
Let u be the motorboat speed in still water and v be the current rate.
The effective speed going upstream is
Distance÷Time = 108÷3 = 36mph
It is the DIFFERENCE of the motorboat speed in still water and the rate of the current. It gives you your first equation
u - v = 36. (1)
The effective speed going downstream is
Distance÷Time = 108÷2 = 54mph
It is the SUM of the motorboat speed in still water and the rate of the current. It gives you your second equation
u + v = 54. (2)
Thus you have this system of two equations in 2 unknowns
u - v = 36, (1) and
u + v = 54. (2)
Add the two equations. You will get
2u = 36 + 54 = 90 ====> u = 90÷2 = 45mph
So, you just found the speed of the motorboat in still water. It is 45mph
Then from the equation (2) you get v = 54 = 45 = 9mph is the current rate.
Answer. The speed of the motorboat in still water is 45mph
The current rate is 9mph
The mean height of women in a country (ages 20minus29) is 64.2 inches. A random sample of 50 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume sigmaequals2.58. Round to four decimal places.
Answer: 0.0142
Step-by-step explanation:
Given : The mean height of women in a country (ages 20 - 29) is 64.2 inches.
i.e. [tex]\mu=64.2[/tex]
Also, [tex]\sigma=2.58[/tex]
Sample size : n= 50
Let x denotes the height of women.
Then, the probability that the mean height for the sample is greater than 65 inches :-
[tex]P(x>65)=1-P(x\leq 65)\\\\=1-P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\leq\dfrac{65-64.2}{\dfrac{2.58}{\sqrt{50}}})\\\\=1-P(z\leq2.193)\ \ [\because z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9858463\ \ [\text{By using z-value table or calculator}]\\\\=0.0141537\approx0.0142[/tex]
Hence, the the probability that the mean height for the sample is greater than 65 inches = 0.0142
Bruce went to the hardware store and bought 66 yellow ropes. The total length of the ropes was 5,586.5 meters. To the nearest hundredth of a meter, how long was each rope? meters
Each rope was 84.64 meters long.
Step-by-step explanation:
Given,
No. of ropes bought = 66
Total length = 5586.5 meters
Length of one rope = [tex]\frac{Total\ length}{No.\ of\ ropes\ bought}\\[/tex]
[tex]Length\ of\ one\ rope=\frac{5586.5}{66}\\Length\ of\ one\ rope=84.64\ meters[/tex]
Hence,
Each rope was 84.64 meters long.
Keywords: Division.
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Please help with this question I really need it right now please show work and please if you don't understand this question please don't answer . Question number 12
Answer:a is the correct option
Step-by-step explanation:
The table is divided into columns for month, sales and expense
Total number of sales for four months is determined by adding up the sales for each month. It becomes
35.75+65.34+12.15+49.68= $162.92
Total number of sales for four months is determined by adding up the expenses for each month. It becomes
43.18+52.24+41.09+59.50=196.01
Profit or loss = total sales - total expenses
Therefore 162.92-196.01 = - $33.09
It's a loss because it is negative
A college bookstore ordered six boxes of red pens. The store sold 28 red pens last week and 38 red pens this week. 6 pens were left on the shelf. How many pens were in each box?
Answer:
Step-by-step explanation:
28 + 38 = 66
66 divided by 6 = 11
This means that there would be 11 pens in each box.
Answer: there were 12 red pens in each box
Step-by-step explanation:
Let x = the number of red pens that were initially in each box.
The college bookstore ordered six boxes of red pens.
This means that the total number of red pens ordered is 6×x = 6x
The store sold 28 red pens last week and 38 red pens this week. This means that the total number of red pens sold = 28 + 38 = 66
The number of red pens left will be the total number of red pens minus the number of red pens that were sold. It becomes 6x - 66
6 pens were left on the shelf. This means that
6x - 66 = 6
6x = 6 + 66 = 72
x = 72/6 = 12
Find the distance between points P (-1,5) and Q (3,4)
Answer:
Step-by-step explanation:
the formular for distance between two points is: [tex]\sqrt{(x2-x1)^2+(y2-y1)^2} \\\\\sqrt{4^{2}+1^{2} } \\\sqrt{17}\\ = 4.12[/tex]
Answer: Distance = 4.123
Step-by-step explanation:
The given coordinates are P(-1,5) and Q (3,4)
- 1 = x1 = the horizontal coordinate(along the x axis) at P
3 = x2 = the horizontal coordinate (along the x axis) at Q
5 = y1 = vertical coordinate( along the y axis) at P
4 = y2 = vertical coordinate(along the y axis) at Q
The distance between points P and Q is expressed as square root of the sum of the square of the horizontal distance and the square of the vertical distance. It becomes
Distance = √(x2 - x1)^2 + (y2 - y1)^2
Distance = √(3 - - 1)^2 + (4 - 5)^2
Distance = √ 4^2 + (-1)^2
Distance = √16+1 = √17
Distance = 4.123
Why do internal users need financial data? A. to make business decisions and compare business performance with previous years B. to invest in the business’s stocks C. to invest in stocks and make business decisions D. to analyze the risk involved in lending money to the business E. to understand the risk involved in lending resources to the business
Answer:
Internal users refer to management members of a company and other people who use financial information to run and manage the business
Explanation:
They work within the business and make business decisions. Accounting information is important for all management levels. In order to make decisions about the company's future, the top managers need information about the past performance of the company.
To determine the results of their past decisions, they need data. The financial statements will determine the company's performance and its financial position and guide them in making future decisions.
Answer: A. To make business decisions and compare business performance with previous years
Explanation:
Management uses accounting information for evaluating and analyzing an organization's financial performance and position, to take important decisions and appropriate actions to improve the business performance in terms of profitability, financial position, and cash flows.
Internal users refer to the members of a company's management and other individuals who use financial information in running and managing the business. They work within the company and make decisions for the business.
Write the equation of the ellipse 36x^2 + 25y^2 + 360x + 100y + 100 = 0 in standard form
Answer:
Step-by-step explanation:
An ellipse is of the form:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex] if it is horizontally stretched, or
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex] if it is vertically stretched.
To begin writing the equation of the ellipse, we will group together all the x-terms and then all the y-terms, moving the constant to the other side of the equals sign in order to make completing the square on these 2 terms a bit easier.
[tex](36x^2+360x)+(25y^2+100y)=-100[/tex]
The first rule for completing the square is that the leading coefficients on the squared terms HAVE to be a 1. Neither of ours is, so we factor those out, getting:
[tex]36(x^2+10x)+25(y^2+4y)=-100[/tex]
Now we can complete the squares. We will start with the x-term. The rule is to take half the linear term, square it, then add it to both sides. Our linear x-term is a 10. Half of 10 is 5, and 5 squared is 25. So we add 25 inside the parenthesis with the x stuff, BUT we cannot forget about that 36 hanging around out front refusing to be ignored. It is a multiplier. That means that we didn't just add in 25, we added in 25 * 36 which is 900. So what we have right now is
[tex]36(x^2+10x+25)+25(y^2+4y)=-100+900[/tex]
Now we will do the same with the y-term. Take half the linear term, square it, and add it (along with its multiplier) to both sides. Our linear y-term is 4. Half of 4 is 2, and 2 squared is 4, so now we have:
[tex]36(x^2+10x+25)+25(y^2+4y+4)=-100+900+100[/tex]
Now we will do 2 things simultaneously. We will simplify the right side which is easy, and then create the perfect square binomials on the left that was the whole point of doing all that. It now looks like this:
[tex]36(x+5)^2+25(y+2)^2=900[/tex]
Almost there. Last thing we do is divide everything by 900 so we get a 1 on the right:
[tex]\frac{36(x+5)^2}{900}+\frac{25(y+2)^2}{900}=1[/tex]
Simplifying by division in both the rational terms:
[tex]\frac{(x+5)^2}{25}+\frac{(y+2)^2}{36}=1[/tex]
That means that this is a vertically stretched ellipse with a = 6 and b = 5. In an ellipse, the a value is always the bigger one. So if the bigger value in the denominator is under the x fraction, then it is a horizontal ellipse. If the bigger value in the denominator is under the y fraction, like ours, then it is a vertical ellipse.
Need help with easy logarithm. Show work step by step
Answer:
[tex] log_{4}(2) = log_{ {2}^{2} }(2) = \frac{ log_{2}(2) }{2} = \frac{1}{2} [/tex]
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A manufacturer of precision measuring instruments claims that the standarddeviation in the use of the instruments is less than 0.00002 millimeter. An analyst,who is unaware of claim, uses the instrument eight times and obtains a samplestandard deviation of 0.00001 millimeter. Assume normal population(i) Confirm using a test procedure and α level of 0.01 that there is insufficient evidence to support the claim that the standard deviation of the instruments is less than 0.00002 millimeters.(ii) Find the P-value for this test? How does it compare with α(greater than or less than)? Does it make sense with respect to your conclusionin part (i)?
Answer:
i) There is insufficient evidence to support the claim that the standard deviation of the instruments is less than 0.00002 millimeters.
ii) [tex] p_v= P(\chi^2_{7} <1.75)=0.0276[/tex]
Step-by-step explanation:
[tex]s=0.00001[/tex] represent the sample standard deviation
[tex]\alpha =0.01[/tex] represent the significance level for the test
[tex]\sigma_o =0.00002[/tex] represent the value that we want to test
n=8 represent the sample size
A chi-square test can be used to test "if the standard deviation of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test".
Null and alternatve hypothesis
The system of hypothesis on this case would be given by:
Null Hypothesis: [tex]\sigma \geq 0.00002[/tex]
Alternative Hypothesis: [tex]\sigma <0.00002[/tex]
The statistic to test this is given by:
[tex]T=(n-1)(\frac{s}{\sigma_0})^2 [/tex] (1)
Part i) Calculate the statistic
If we replace into formula (1) we got this:
[tex]T=(8-1)(\frac{0.00001}{0.00002})^2 =1.75 [/tex] (1)
The critical region for a for a lower one-tailed alternative is given by
[tex]T< \chi^2_{1-\alpha/2,N-1}[/tex]
The degrees of freedom are given by
[tex] df=n-1=8-1=7[/tex]
And if we use the Chi Square distribution with 7 degrees of freedom we see that [tex] \chi^2_{1-0.01/2,7}=1.239[/tex]
And our critical region would be [tex]T< 1.239[/tex] so on this case we can conclude that we fail to reject the null hypothesis. So it's not enough evidence to conclude that the population standard deviation is less than 0.00002 mm.
Part ii) Calculate the p value
In order to calculate the p value we can do this:
[tex] p_v= P(\chi^2_{7} <1.75)=0.0276[/tex]
If we compare this value with the significance level (0.01) we see that [tex]p_v>\alpha[/tex]
This agrees with the conclusion since when the p values is greater than the significance level we FAIL to reject the null hypothesis, same conclusion as part i).
Erica is a sheep farmer. She is having a problem with wolves attacking the flock. She starts with an initial 200 sheep and notices that the population is two-thirds of the previous year. Write an equation for the situation? How long will it take for her to have around 5 sheep?
The equation for the situation is [tex]y=200(\frac{2}{3})^{x}[/tex]
It will take around 9 years for her to have around 5 sheep
Step-by-step explanation:
The exponential decay growth/decay equation is [tex]y=a(b)^{x}[/tex] , where
a is the initial valueb is the growth/decay factorIf b > 1, then it is a growth factorIf 0 < b < 1, then it is a decay factorErica is a sheep farmer. She is having a problem with wolves attacking the flock. She starts with an initial 200 sheep and notices that the population is two-thirds of the previous year
∵ The population is decreased
∴ The equation is decay
∵ The population is two-thirds of the previous year
∴ The decay factor is [tex]\frac{2}{3}[/tex]
∵ She starts with an initial 200 sheep
∴ the initial value is 200
∵ The decay equation is [tex]y=a(b)^{x}[/tex] , where y represent the
population in x years
∵ a = 200
∵ b = [tex]\frac{2}{3}[/tex]
∴ [tex]y=200(\frac{2}{3})^{x}[/tex]
The equation for the situation is [tex]y=200(\frac{2}{3})^{x}[/tex]
∵ The population after x years is around 5 sheep
- Substitute y by 5 to find x
∵ [tex]5=200(\frac{2}{3})^{x}[/tex]
- Divide both sides by 200
∴ [tex]0.025=(\frac{2}{3})^{x}[/tex]
- Insert ㏒ for both sides
∴ [tex]log(0.025)=log(\frac{2}{3})^{x}[/tex]
∴ [tex]log(0.025)=xlog(\frac{2}{3})[/tex]
- Divide both sides by [tex]log(\frac{2}{3})[/tex]
∴ 9.098 = x
∴ x is around 9 years
It will take around 9 years for her to have around 5 sheep
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A producer of personal computer mouse pads determines that the number, N, of pads sold is related to the price, X, of a pad by N=35x-x^2. at what roice is th ecost so high, that no one wants to buy the any mouse pads?
Answer:
If the cost X is higher or equal than 35, then no one wants to buy the any mouse pads.
Step-by-step explanation:
When N is 0 or lower then it means that no one buys it.
N=35x-[tex]x^{2}[/tex], if N=0 then
0=35x-[tex]x^{2}[/tex] or
35x=[tex]x^{2}[/tex] dividing each side by x we get:
35=x
This is the cost which nobody will buy the mouse pad anymore.
Answer:
oooooooooo yea
Step-by-step explanation:
Hello Kitty has created a new system of conversion for the residents of Kitty Nation. The standard for measurement of length in Kitty Nation is that 3 lenthii = 35 inches and 3 gianthii = 380.5 lenthii. If a design to be sent to Kitty Nation is 287.4 feet long, how many gianthii long will it be? (Include units)
Answer:
A local café serves tea, coffee, cookies, scones, and muffins. They recently gathered data about their customers who purchase both a drink and a snack. The given frequency table shows the results of the survey.
If approximately 24% of the customers surveyed have a scone with their tea and approximately 36% of the customers surveyed buy a muffin, complete the column and row headings for the given table.
Step-by-step explanation:
you have a list of conversion factors.Just use them to cancel the unwanted units:246.6ft * 12in/1ft * 6lenthi/39in * 7ganthi/345.6lenthii= (246.6*12*6*7)/(1*39*345.6) ganthii
With both the cold water and hot water faucets open it takes five minutes to fill a bathtub. The cold water facet alone takes 15 minutes to fill the tub. How long will it take to fill the tub with just the hot water faucet?
Answer:
7 1/2 minutes
Step-by-step explanation:
When the time with both faucets is a submultiple of the time with one faucet, you can use this sort of reasoning to figure the missing time.
Filling the tub in 5 minutes is equivalent to having 3 faucets open, each of which can fill the tub in 15 minutes. Since we know the cold water faucet can fill the tub in 15 minutes, the hot water faucet is equivalent to two open 15-minute faucets. That is, it can fill the tub in 15/2 = 7 1/2 minutes.
_____
Perhaps a more conventional way to approach the problem is to consider "tubs per minute." The cold faucet runs at 1/15 tubs per minute, and the two faucets together run at 1/5 tub per minute. Then the hot runs at ...
(1/5) - (1/15) = (3 -1)/15 = 2/15 . . . tubs per minute
So it will fill 2 tubs in 15 minutes, or 1 tub in 7 1/2 minutes.
A watch manufacturer believes that 60% of men over age 50 wear watches. So, the manufacturer took a simple random sample of 275 men over age 50 and 170 of those men wore watches. Test the watch manufacturer's claim at a=.05.
Answer:
The total number of men is 32. Of these men, 25 wore a watch. So, the number of men who didn’t wear a watch is 7, because 32 − 25 = 7.
Step-by-step explanation:
If five times the measure of an angle is decreased by 30, the result is the same as when two times the measure of the angle is increased by 18. What is the measure of the angel
Answer:
16
Step-by-step explanation:
Let "a" represent the measure of the angle. Then ...
5a -30 = 2a +18
3a = 48 . . . . . . . add 30-2a
a = 16 . . . . . . . . . divide by 3
An angel is beyond measure, but this angle has measure 16.
Determine the seating capacity of an auditorium with 35 rows of seats if there are 20 seats in the first row, 23 seats in the second row, 26 seats in the third row, 29 seats in the forth row, and so on.
Answer:
2485
Step-by-step explanation:
The number of seats in row n is given by the explicit formula for an arithmetic sequence:
an = a1 +d(n -1)
an = 20 +3(n -1)
The middle row is row 18, so has ...
a18 = 20 + 3(18 -1) = 71 . . . . seats
The total number of seats is the product of the number of rows and the number of seats in the middle row:
capacity = (71)(35) = 2485
The seating capacity is 2485.
The average cost of tuition and room and board at a small private liberal arts college is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α = 0.05. What is the critical z value for this test?
Answer:
H₀: µ ≤ $8,500; H₁: µ > $8,500
z= +1.645
Step-by-step explanation:
From the given problem As average cost of tuition and room and board at a small private liberal is less than the financial administrator As hypothesis is true.
As standard deviation is $ 1,200
α = 0.05
H₀: µ ≤ $8,500
if the null hypothesis is true then value for critical z is +1.645.
The critical z-value for a one-tailed test at a significance level (α) of 0.05 is approximately 1.645. This statistic is used in hypothesis testing to make informed financial decisions about tuition costs.
Explanation:We are asked to find the critical z-value for a one-tailed test at a significance level (α) of 0.05. In this case, the financial administrator believes the average cost is higher, thus the test is one-tailed to the right. Looking up the z-table, we know that for a one-tailed test with a significance level of 0.05, the critical z-value is 1.645 (approximate).
The information about rising tuition costs and student loan debt demonstrates the real-world importance of using statistical analysis to understand trends and make informed financial decisions.
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Suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. How many times would we have to flip the coin in order to obtain a 95.8% confidence interval of width of at most .14 for the probability of flipping a head? (note that the z-score was rounded to three decimal places in the calculation)
a) 217
b) 153
c) 212
d) 209
e) 150
f) None of the above
Answer:
153 times
Step-by-step explanation:
We have to flip the coin in order to obtain a 95.8% confidence interval of width of at most .14
Width = 0.14
ME = [tex]\frac{width}{2}[/tex]
ME = [tex]\frac{0.14}{2}[/tex]
ME = [tex]0.07[/tex]
[tex]ME\geq z \times \sqrt{\frac{\widecap{p}(1-\widecap{p})}{n}}[/tex]
use p = 0.5
z at 95.8% is 1.727(using calculator)
[tex]0.07 \geq 1.727 \times \sqrt{\frac{0.5(1-0.5)}{n}}[/tex]
[tex]\frac{0.07}{1.727}\geq sqrt{\frac{0.5(1-0.5)}{n}}[/tex]
[tex](\frac{0.07}{1.727})^2 \geq \frac{0.5(1-0.5)}{n}[/tex]
[tex]n \geq \frac{0.5(1-0.5)}{(\frac{0.07}{1.727})^2}[/tex]
[tex]n \geq 152.169[/tex]
So, Option B is true
Hence we have to flip 153 times the coin in order to obtain a 95.8% confidence interval of width of at most .14 for the probability of flipping a head
To get a 95.8% confidence interval of width 0.14 for the probability of flipping a head with a fair coin, we need to flip the coin approximately 213 times. This is achieved by setting the standard error of the confidence interval to half the desired width, and solving for n, the number of flips.
Explanation:To answer the question, we need to use the formula for the confidence interval for a proportion, which uses the Z-score, the standard deviation of the distribution of sample proportions, and the desired width of the confidence interval.
In this case, we want a 95.8% confidence interval. The Z-score for a 95.8% confidence interval is approximately 2.054 (since the z-score was mentioned to be rounded to 3 decimal places in the question).
The standard deviation of the distribution of sample proportions (standard error, SE) is sqrt([P*(1-P)]/n), where P is the assumed probability of heads (0.5 for a fair coin), and n is the number of flips.
The desired width of the confidence interval is 0.14, so the maximum standard error we want is 0.14/2, or 0.07. Setting the standard error formula equal to 0.07 and solving for n, we get n = 0.5*(1-0.5)/(0.07/2.054)^2, which comes out to approximately 212.6.
However, since we can't have a partial flip of a coin, we round this up to the next whole number, 213, which is close to the choice (c) 212. Hence, the answer should be (f), None of the above.
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Bill Casler bought a $8000, 9-month certificate of deposit (CD) that would earn 8% annual simple interest. Three months before the CD was due to mature, Bill needed his CD money, so a friend agreed to lend him money and receive the value of the CD when it matured.
(a) What is the value of the CD when it matures?
(b) If their agreement allowed the friend to earn a 10% annual simple interest return on his loan to Bill, how much did Bill receive from his friend? (Round your answer to the nearest cent.)
Final answer:
The value of the CD when it matures is $8480, calculated using simple interest. Bill received $8366.02 from his friend, who extended a loan expecting a 10% annual simple interest return.
Explanation:
To calculate the value of the CD when it matures, we use the formula for simple interest: Interest = Principal × Rate × Time. In this case, the Principal is $8000, the Rate is 8% per annum, and since the CD is for 9 months, the Time is ⅓ year. The simple interest earned on the CD is calculated as:
Interest = $8000 × 0.08 × ⅓ = $8000 × 0.08 × ⅔ = $480.
So, the mature value of the CD is the principal plus the interest, which is $8000 + $480 = $8480.
To determine how much Bill received from his friend with a 10% annual simple interest rate, the friend would expect to get the mature value of the CD in 3 months, which is one-quarter of a year. The agreement suggests that the friend treats the loan to Bill as an investment, thus expecting the same return as the interest he could have earned elsewhere at his desired 10% rate for the time frame. So, the calculation would be:
8480 = Principal × (1 + (10% × ⅔)), solving for Principal gives Bill:
Principal = 8480 ÷ (1 + (0.10 × ⅔)) = $8366.02 (rounded to the nearest cent).
Consider the sequence: 1536, 768, 384, 192, 96, ... Determine the 11th term of the sequence. Group of answer choices
1.5
3
6
12
Answer:
The answer is 1.5
Step-by-step explanation:
You have to find the pattern and work your way down to the 11th term.
Answer:
1.5
Step-by-step explanation:
The sequence given is a geometric progression (G.P). For a G.P where the first term is a, the common ratio (which is the ratio between successive terms), the nth term of the GP is given as
Tn = ar^n-1
From the sequence given
a = 1536
r = 768/1536
= 1/2
= 0.5
Hence the 11th term of the sequence
T11 = 1536 (1/2)^11-1
= 1536 (1/2)^10
= 1536/1024
= 1.5
what symbol compare fractions 5/7 1/13
Answer:
5/7 > 1/13. Hence Greater than Symbol will be used to compare the fractions.
Step-by-step explanation:
Given:
Two fractions given are 5/7 and 1/13
We will first calculate each of the fraction and then we will decide which one is greater and which one is smaller accordingly we will assign the symbol for the same.
First we will find the answer for 5/7.
Now dividing the number 5 from 7 we get;
[tex]5/7= 0.714[/tex]
Now we will find the answer for 1/13
Now dividing the number 1 from 13 we get;
[tex]\frac{1}{13}= 0.076[/tex]
From above we can see that 0.714 is greater than 0.076.
Hence we can say that 5/7 is greater than 1/13.
So the symbol used will be greater than > where number 5/7 is greater than 1/13
5/7 > 1/13
5/7>1/13 is the answer because 5/7 is closer to its whole when a number is closer to its whole its bigger for example 4/5>7/10 hope it helps
In 2016 the Bureau of Labor Statistics reported that there were 71.9 million people over age 25 who had at least a bachelor’s degree. Of these 52.1 million were employed and 1.3 million were unemployed. What were the labor-force participation rate and the unemployment rate for this group?
Answer: a) Labor force participation rate = 72.46%, b) Unemployment rate = 1.8%.
Step-by-step explanation:
Since we have given that
Number of people who have at least a bachelor's degree = 71.9 millions
Number of people who were employed = 52.1 millions
Number of people who were unemployed = 1.3 millions
So, Labor- force participation rate would be
[tex]\dfrac{Employed}{Total}\times 100\\\\=\dfrac{52.1}{71.9}\times 100\\\\=72.46\%[/tex]
Unemployment rate for this group would be
[tex]\dfrac{Unemployed}{total}\times 100\\\\=\dfrac{1.3}{71.9}\times 100\\\\=1.8\%[/tex]
Hence, a) 72.46%, b) 1.8%.
determine the domain of the function f(x) = x^2 + 6x +5/x^2 - 25
a. (-1, 5)
b. (5, 5)
c. (-infinity, -1) U (-1,5) U (5, infinity)
d. (-infinity, -5) U (-5, 5) U (5, infinity)
Answer:
The answer to your question is the last option
Step-by-step explanation:
Here there is a rational function so, we need to find the values where the denominator equals zero.
[tex]f(x) = \frac{x^{2} + 6x + 5}{x^{2}- 25 }[/tex]
[tex]x^{2} - 25 = 0[/tex]
Factor (x - 5)(x + 5) = 0
x₁ - 5 = 0 x₂ + 5 = 0
The function does not exist in -5 and 5
x₁ = 5 x₂ = -5
Domain
( -∞ , -5) U (-5, 5) U (5, ∞)
Answer:
the answer is d in edge
Step-by-step explanation:
(–∞, –5) U (–5, 5) U (5, ∞)
Ashley recently opened a store that uses only natural ingredients she wants to advertise your product by distributing bags of samples in your neighborhood it takes actually 2/3 of a minute to prepare one day it takes each of her friends 75% long to repair a bag. How many hours will it take Ashley in forever friendship repair 1575 bags of samples
Answer:
Ashley and her 4 friends would required 5.33 hours to repair 1575 bags of sample.
Step-by-step explanation:
75% is written as 0.75 as a decimal or 3/4 as a fraction.
Her friends take 75% longer, so multiply the time it takes Ashley by 1 + the percentage: 1.75 as a decimal or [tex]1 \frac{3}{4} \ \ or \ \ \frac{7}{4}[/tex] as a fraction.
[tex]\frac{2}{3} \times \frac{7}{4} =\frac{14}{12} = 1 \frac{2}{12} = 1 \frac{1}{6} minutes[/tex].
1 hour = 60 minutes.
Divide minutes in an hour by minutes per pack:
Ashley can pack: [tex]\frac{60}{\frac{2}{3}} = 90 \ bags\ per \ hour[/tex]
1 friend can pack: [tex]\frac{60}{1\frac{1}{6}}=\frac{360}{7} = 51 \frac{3}{7} \ bags \ per \ hour.[/tex]
multiply the amount 1 friend can pack by 4 friends: [tex]51 \frac{3}{7} \times 4 = \frac {1440}{7} = 205 \frac{5}{7} \ bags \ per \ hour[/tex]
Ashley and her friends can pack [tex]90 + 205 \frac{5}{7} = 295 \times \frac{5}{7} \ bags \ per \ hour.[/tex]
Now divide the total bags by bags per hour:
[tex]\frac{1575}{295 \frac{5}{7}} = 5.33 \ hours[/tex] ( Round answer as needed.)
Hence, Ashley and her 4 friends would required 5.33 hours to repair 1575 bags of sample.
The major difference between a calculator and a computer, when performing calculations, is that a
A. calculator is slower and needs more human assistance.
B. calculator is faster but needs more human assistance.
C. computer is slower but needs less human assistance.
D. computer is faster but needs more human assistance.
Final answer:
The major difference between a calculator and a computer in performing calculations is that a calculator requires more human interaction for input and verification, whereas a computer can process complex tasks with less human assistance and is generally faster. Therefore, option A is the correct answer.
Explanation:
The primary difference between a calculator and a computer when performing calculations is that calculators typically require more human interaction to input and verify data, while computers can process complex tasks with less human assistance. A calculator is designed for straightforward numerical computations and requires accurate input from the user. Meanwhile, a computer can carry out a wide range of tasks, including calculations, with greater speed and autonomy, thanks to its ability to run complex software programs. However, even though computers are powerful, solving certain mathematical problems, such as differential equations, can be challenging since they cannot make infinitely fine time steps and must approximate using small ones. Moreover, calculators, being simpler devices, require very little energy to operate and often rely on solar cells or small batteries, unlike computers, which have a greater energy demand. Therefore, option A is the correct answer.
Which of the graphs below represents the equation 8x − y = -4?
Answer:
8x-y+4=0
Step-by-step explanation:
because 8x-y+4=-4+4
For a finite sequence of nonzero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, –3, 2, 5, –4, –6 ?
A. 1
B. 2
C. 3
D. 4
E. 5
Answer:
Option C.
Step-by-step explanation:
The given given sequence is
1, –3, 2, 5, –4, –6
We need to find the pairs of consecutive terms of the sequence and their product.
Pairs of consecutive terms | Product
1, -3 -3
-3, 2 -6
2, 5 10
5, -4 -20
-4, -6 24
Here the product of three pairs of consecutive terms is negative.
The number of variations in sign for the sequence is 3. Therefore, the correct option is C.
To find the number of sign variations in the sequence 1, -3, 2, 5, -4, -6, you count the changes from positive to negative or negative to positive between consecutive terms. The sequence has three such changes, so the answer is C. 3.
Explanation:The question asks for the number of variations in sign within a given finite sequence of nonzero numbers. To find this, we need to count how many times the sign changes between consecutive numbers in the sequence 1, -3, 2, 5, -4, -6.
Between 1 and -3 the sign changes from positive to negative.Between -3 and 2 the sign changes from negative to positive.Between 2 and 5, both numbers are positive so there's no sign change.Between 5 and -4 the sign changes from positive to negative.Finally, between -4 and -6, both numbers are negative, and thus, no sign change here either.Counting these, we have a total of three variations in sign. Hence, the correct answer is C. 3.
The general form of a regression equation is Y = a + bX. In this equation, Y is the score we wish to predict and X is the known score. What is "a"? It is a constant. It is a weighting adjustment factor that is multiplied by X. It is the slope of the line created with this equation. It is the difference between X and Y.
Answer:
Option A) It is a constant.
Step-by-step explanation:
We are given the following information in the question:
The general form of regression equation is:
[tex]Y = a + bX[/tex]
[tex]Y-bX = a[/tex]
where Y is the dependent variable and we want to predict the value of Y and X is the independent variable and the predictor.
If we compare the above equation with the point slope form:
[tex]y = mx + c[/tex]
where m is the slope of the line and c is the y-intercept.
We get,
Slope, m = b
Y-intercept = a
Thus, a is the y-intercept that is the value of Y when X is 0.
It is a constant.
It can also be interpreted as the difference of Y and X when slope is 1.
The constant 'a' in the regression equation represents the y-intercept, which is the value of Y when X is equal to 0.
Explanation:The constant a in the regression equation Y = a + bX is called the y-intercept. It represents the value of Y when X is equal to 0. In other words, it is the point where the regression line crosses the y-axis.
Learn more about Linear Regression here:https://brainly.com/question/36829492
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A fountain has two drainage valves. With only the first valve open, the fountain completely drains in 4 hours. With only the second valve open, the fountain completely drains in 5.25 hours. About how many hours will the fountain take to completely drain with both valves open?
You can use variables to model the situation and convert the description to mathematical expression.
The time that the fountain will take to get drained completely with both valves open is approximately 2.27 hours.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
Using above methodology to get to the solutionLet the fountain contains V amount of water
Let the first valve emits x liter of water per hour
Let the second valve emits y liter of water per hour
Then, from the given description, we have:
With only the first valve open, the fountain completely drains in 4 hours
or
[tex]x \times 4 = V\\\\x = \dfrac{V}{4}[/tex] (it is since V volume of water is drained when we let x liter of water drained for 4 hours, thus adding x 4 times which is equivalent of x times 4)
Similarly,
With only the second valve open, the fountain completely drains in 5.25 hours
or
[tex]y \times 5.25 = V\\y = \dfrac{V}{5.25}[/tex]
Let after h hours, the fountain gets drained, then,
[tex]x \times h + y \times h = V\\\\\dfrac{V}{4}h + \dfrac{V}{5.25}\times h = V\\\\\text{Multiplying both the sides with} \: \dfrac{4 \times 5.25}{V}\\\\5.25 \timses h + 4 h = 4 \times 5.25\\9.25h = 21\\\\h = \dfrac{21}{9.25} \approx 2.27[/tex]
Thus,
The time that the fountain will take to get drained completely with both valves open is approximately 2.27 hours.
Learn more about linear equations representing situations here:
https://brainly.com/question/498084
Final answer:
By adding the work rates of the two valves and then calculating the reciprocal of the combined rate, it is estimated that it will take approximately 2.27 hours for the fountain to drain with both valves open.
Explanation:
To find out how long it will take for the fountain to drain with both valves open, you can use the rate of work formula, which states that work is the product of rate and time. When dealing with two independent work rates that contribute to completing a single job, we can add their work rates together to find the combined work rate.
Valve 1's rate of work is draining the fountain in 4 hours, which means its rate is 1/4 fountain per hour. Valve 2's rate of work is draining the fountain in 5.25 hours, which means its rate is 1/5.25 fountain per hour.
To find the combined rate, we add these two rates together:
1/4 + 1/5.25 = 0.25 + 0.19 = 0.44 (approximately)
This combined rate is 0.44 fountain per hour. Now, to find the total time to drain the fountain with both valves open, we take the reciprocal of the combined rate:
1 / 0.44 = 2.27 hours (approximately)
Therefore, it will take approximately 2.27 hours for the fountain to drain with both valves open.