A park has an area of 12.5 sq miles and a width of 5 miles. What is the perimeter of the park?

Answer :

11.45

step-by-step explantion :

4.25=17/4

when we add 41/5 and 17/4, we get

41×4+17×5/4×5

164+65/20

229/20

11.45 Ans

:

Answer:

The Linear programming problem has 3 constraints :- Milling time, Inspection time, Drilling time constraints.

Step-by-step explanation:

Product A : 9 minutes milling, 7 minutes inspection, 6 minutes drilling Product B : 10 minutes milling, 5 minutes inspection, 8 minutes drilling Product C  : 7 minutes milling, 3 minutes inspection, 15 minutes drilling

Total milling time available  = 20 hours = (20 x 60) i.e 1200 minutes Total inspection time available = 15 hours = (15 x 60) i.e 900 minutes Total drilling time available = 24 hours = (24 x 60) i.e 1440 minutes

Let QA, QB, QC be quantities of product A, B, C respectively

Answer:

Kelly walks 4/5 of a mile each day.

After 3 days, Kelly walks a distance: D = 3 x 4/5 = 12/5 = 2.4 miles

Hope this helps!

:)

Kelly walks 4/5 of a mile each day, and after three days, she would have walked 2 and 2/5 miles.

Kelly walks 4/5 of a mile each day. To find out how many miles Kelly walks after three days, we simply multiply the daily distance by three.

Calculation:
4/5 mile/day * 3 days = 12/5 miles

To convert 12/5 miles into a mixed number, we divide 12 by 5. The quotient is 2 with a remainder of 2, so Kelly walks 2 and 2/5 miles after three days.

Answer:

86362600

Step-by-step explanation:

We want to round to the hundreds place

We look at the 7 in the tens place.  Since it is 5 or greater we round up

86,362,575 round to 86362600

Answer:

86,362,600

Step-by-step explanation

Step-by-step explanation:

There are a total of 16 marbles, 8 of which are green.

(a) The probability the first marble is green is 8/16.

The marble is replaced, so there are still a total of 15 marbles, 8 of which are green.  The probability the second marble is green is 8/16.

The probability of both events is (8/16) (8/16) = 1/4 = 0.2500.

(b) The probability the first marble is green is 8/16.

The marble is not replaced, so there are now a total of 15 marbles, 7 of which are green.  The probability the second marble is green is 7/15.

The probability of both events is (8/16) (7/15) = 7/30 = 0.2333.

Final answer:

The probability of selecting a green marble, then another green marble from a bag of marbles is 0.25 when the first marble is replaced and 0.2333 when the first marble is not replaced.

Explanation:

To find the probability of selecting a green, then another green marble from a bag of 5 red, 8 green, and 3 blue marbles, we need to consider two scenarios: (a) replacing the first marble before drawing the second, and (b) not replacing the first marble.

a) If the first marble is replaced before drawing the second, the probability of selecting a green marble on the first draw is 8/16, and the probability of selecting a green marble on the second draw is also 8/16. We can multiply these probabilities together to get the overall probability: 8/16 × 8/16 = 16/64 = 0.25.

b) If the first marble is not replaced, the probability of selecting a green marble on the first draw is 8/16. However, since the first marble is not replaced, there are only 15 marbles left in the bag for the second draw, with 7 green marbles remaining. The probability of selecting a green marble on the second draw is 7/15. We can multiply these probabilities together to get the overall probability: 8/16 × 7/15 = 56/240 = 0.2333 (rounded to four decimal places).

Comparing the probabilities, we can see that the probability in scenario (a) when the first marble is replaced is higher than the probability in scenario (b) when the first marble is not replaced.

Answer:

t ≤ 33

Step-by-step explanation:

The answer can be 33 or below.

Answer:

64

Step-by-step explanation:

The spinner has 8 equal sections numbered from 1 to 8

Each time she spinns the spinner has 8 possible outcomes.

To know the number of possible results when  spinning two times, you must multiply the possible results for the first spin (8 possible outcomes) by the possible results for the second spin (also  8 possible outcomes).

And because each spin has the same number of outcomes:

[tex]8*8=64[/tex]

the answer is that there are 64 possible outcomes

Answer:

64

Step-by-step explanation:

Answer:

C) Descend 84 feet

Step-by-step explanation:

162+207=369

369-285=84ft above starting point, this means that he must descend 84 feet to reach the starting point.

Final Answer:

The test statistic for the difference in proportions between the metropolitan area and the U.S. population is approximately ( -0.11 ). Since this value does not exceed the critical value of [tex]\( \pm 1.96 \)[/tex] at the 0.05 significance level, there is insufficient evidence to conclude a significant difference. Therefore, we fail to reject the null hypothesis.

Step-by-step explanation:

To determine whether there is sufficient evidence to conclude that a difference exists between this metropolitan area and the larger U.S. population, we can perform a hypothesis test for the difference in proportions.

Let:

[tex]\( p_1 \)[/tex]  be the proportion of women in the metropolitan area.

[tex]\( p_2 \)[/tex] be the proportion of women in the larger U.S. population.

The null hypothesis [tex](\( H_0 \))[/tex] is that there is no difference between the proportions, and the alternative hypothesis [tex](\( H_1 \))[/tex] is that there is a significant difference.

The formula for the test statistic for the difference in proportions ( z ) is given by:

[tex]\[ z = \frac{(\hat{p}_1 - \hat{p}_2)}{\sqrt{p(1-p)\left(\frac{1}{n_1} + \frac{1}{n_2}\right)}} \][/tex]

Where:

[tex]\( \hat{p}_1 \)[/tex]  and [tex]\( \hat{p}_2 \)[/tex] are the sample proportions of women in the metropolitan area and the U.S. population, respectively.

( p ) is the combined sample proportion.

[tex]\( n_1 \)[/tex]  and [tex]\( n_2 \)[/tex] are the sample sizes for the metropolitan area and the U.S. population, respectively.

First, let's calculate [tex]\( \hat{p}_1 \)[/tex], [tex]\( \hat{p}_2 \)[/tex], ( p ), and then plug them into the formula to find the test statistic.

[tex]\[ \hat{p}_1 = \frac{112}{150} = 0.7467 \][/tex]

[tex]\[ \hat{p}_2 = \frac{150}{200} = 0.75 \][/tex]

[tex]\[ p = \frac{112 + 150}{150 + 200} = \frac{262}{350} = 0.7486 \][/tex]

Now, we can calculate the test statistic:

[tex]\[ z = \frac{(0.7467 - 0.75)}{\sqrt{0.7486(1-0.7486)\left(\frac{1}{150} + \frac{1}{200}\right)}} \][/tex]

Calculate the values and round the test statistic to two decimal places. If the absolute value of the test statistic is greater than the critical value for a two-tailed test at the 0.05 significance level, we reject the null hypothesis.

Note: The critical value for a two-tailed test at the 0.05 significance level is approximately [tex]\( \pm 1.96 \)[/tex].

Answer:

a. .92

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error of the interval is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The lower bound is the point estimate [tex]\pi[/tex] subtracted by the margin of error.

The upper bound is the point estimate [tex]\pi[/tex] added to the margin of error.

Point estimate:

The confidence interval is symmetric, so it is the mean between the two bounds.

In this problem:

[tex]\pi = \frac{0.372 + 0.458}{2} = 0.415[/tex]

Sample of 400, which means that [tex]n = 400[/tex]

Margin of error is the estimate subtracted by the lower bound. So [tex]M = 0.415 - 0.372 = 0.043[/tex]

We have to find z.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.043 = z\sqrt{\frac{0.415*0.585}{400}}[/tex]

[tex]z = \frac{0.043\sqrt{400}}{\sqrt{0.415*0.585}}[/tex]

[tex]z = 1.745[/tex]

[tex]z = 1.745[/tex] has a pvalue of 0.96.

This means that:

[tex]1 - \frac{\alpha}{2} = 0.96[/tex]

[tex]\frac{\alpha}{2} = 1 - 0.96[/tex]

[tex]\frac{\alpha}{2} = 0.04[/tex]

[tex]\alpha = 0.08[/tex]

Confidence level:

[tex]1 - \alpha = 1 - 0.08 = 0.92[/tex]

So the correct answer is:

a. .92

To determine the confidence coefficient for the proportion of MSU students who attended at least three football games, the margin of error is calculated from the given interval range and related to the Z-value of a standard normal distribution. The coefficient that matches the margin of error from the calculation is approximately 0.95, indicating a 95% confidence level.

The confidence interval for the proportion of Michigan State University (MSU) students who attended at least three football games is given as (0.372, 0.458). To determine the confidence coefficient used to calculate this interval, we need to look at the width of the interval and how it relates to the standard error of the proportion.

The width of the confidence interval is 0.458 - 0.372 = 0.086. Since we know that the total width of the interval spans the range of twice the margin of error, one margin of error is then 0.086 / 2 = 0.043.

Using the Z-table for the normal distribution, we can find which confidence coefficient corresponds to a Z-value that gives a margin of error of 0.043, considering that the formula for the margin of error in this case would be: Z * sqrt((p*(1-p))/n). For a sample size of 400, and approximating p by the midpoint of the confidence interval (0.372 + 0.458)/2 = 0.415, the computation would look roughly like this:

Z * sqrt((0.415*(1-0.415))/400) = 0.043

After solving this equation for Z, we can then locate the corresponding confidence level on the standard normal (Z) distribution table. This process would lead to finding that the closest confidence coefficient that would generate the margin of error of 0.043 with the given sample size and point estimate proportion is approximately 0.95, or 95%.

Therefore, the confidence coefficient is 0.95, which corresponds to option b. 0.95.

The value of x makes the equation true is -16. Therefore, option A is the correct answer.

The given equation is x+7=-9.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation can be solved as follows:

x+7=-9

Transpose 7 to RHS of the equation, we get

x=-9-7

=-16

The value of x makes the equation true is -16. Therefore, option A is the correct answer.

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Answer:

a) 471.5 kilo-watt hours.

b) 31.76 kilo-watt hours

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the population:

Mean 471.5 kilo-watt hours.

Standard deviation of 187.9 kilowatt-hours.

For the sample:

Sample size of 35, by the Central Limit Theorem:

a) Mean

471.5 kilo-watt hours.

b) Standard deviation

[tex]s = \frac{187.9}{\sqrt{35}} = 31.76[/tex]

31.76 kilo-watt hours

Final answer:

The mean of the sampling distribution of sample means is 471.5 kilo-watt hours, and the standard deviation (or standard error) of the sampling distribution, rounded to the third decimal place, is 31.749 kilo-watt hours.

Explanation:

The question concerns the concept of sampling distribution and its parameters, namely the mean and standard deviation, within the field of statistics. Given that the per capita electric power consumption level in Ecuador is normally distributed with a mean of 471.5 kilo-watt hours and a standard deviation of 187.9 kilo-watt hours, and considering samples of size 35, we are to find the mean and standard deviation of the sampling distribution of sample means.

(a) The mean of the sampling distribution of sample means is equal to the population mean. Therefore, the mean is:

471.5 kilo-watt hours

(b) The standard deviation of the sampling distribution of sample means, also known as the standard error (SE), is calculated using the following formula:

SE = σ / √n

where σ is the population standard deviation and n is the sample size. In this case:

SE = 187.9 / √35 ≈ 31.749 kilo-watt hours (rounded to the third decimal place)

The total surface area that she paints will be 96 square feet. Thus, the correct option is C.

Let W be the rectangle's width and L its length. The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be given as,

Area of the rectangle = L × W square units

Given that:

Length, L = 12 ft

Width, W = 8 ft

The area of the rectangle is given as,

A = 12 x 8

A = 96 square feet

Thus, the correct option is C.

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The missing diagram is given below.

Answer:oh yeah I remember that

Step-by-step explanation:

That’s tuff

Final answer:

The total sales five months after the beginning of the campaign is approximately 72 million dollars.

Explanation:

To find the total sales five months after the beginning of the campaign, we need to calculate the definite integral of the sales rate function from t=0 to t=5. The sales rate function can be expressed as S'(t) = 10 - 10e^(-0.2t).

First, let's find the antiderivative of the sales rate function. The antiderivative of 10 is 10t, and the antiderivative of -10e^(-0.2t) is 50e^(-0.2t). Therefore, the indefinite integral of S'(t) is S(t) = 10t - 50e^(-0.2t) + C, where C is the constant of integration.

Next, we evaluate the definite integral over the interval t=0 to t=5. Substituting the upper and lower limits into the antiderivative, we get S(5) - S(0) = (10(5) - 50e^(-0.2(5))) - (10(0) - 50e^(-0.2(0))) = (50 - 50e^(-1)) - (0 - 50e^0) = 50 - 50e^(-1) + 50 = 100 - 50e^(-1) million dollars.

Rounding the answer to the nearest million, the total sales five months after the beginning of the campaign is approximately 72 million dollars.

Answer:

This is an example of placebo testing.

Step-by-step explanation:

This is an example of placebo testing in which, the two groups are given two substances that are said to have an effect on the condition that is being treated but one of them is the actual medicine that is being tested while the other one has no real effect over the medical condition. But the volunteers are not given information on which of the medicines is real and which is not, so that this does not affect the outcome of the experiment.

I hope this answer helps.

Answer:

about $982.20

Step-by-step explanation:

Formula = P(1+I)^T

T =18/12 because its in months not years, so 1.5 years

1+I = 1 + 54/900 or 1.03

P = 900

Plug those in and you get about 982.20

Answer:

4%

Step-by-step explanation:

For the simple interest rate,

I=P(i)t

54=900(i)(18/12)

i=54/900*(12/18)=4% annually

Answer:

[tex]\frac{10\pi}{3}[/tex]

Step-by-step explanation:

According to the information of the problem we have to compute the following integral.

[tex]{\displaystyle \int\limits \int} \frac{1}{3} + \sqrt{x^2 + y^2} \, dA[/tex]

Where the region of integration is

[tex]R = \Big\{ (r,\theta) : 0 \leq r \leq 2 , \,\,\,\, \frac{\pi}{2} \leq \theta \leq \frac{3\pi}{2} \Big\}[/tex]

If you plot, that is just a circle between [tex]\pi/2[/tex]  and  [tex]3\pi/2[/tex], which is just half of the circle on the negative part of the plane.

When you switch coordinates

[tex]{\displaystyle \int\limits \int} \frac{1}{3} + \sqrt{x^2 + y^2} \, dA = {\displaystyle \int\limits_{0}^{2} \int\limits_{\pi/2}^{3\pi/2}} \bigg(\frac{1}{3} + r \bigg)r \, d\theta\, dr = \frac{10\pi}{3}[/tex]

Answer:

60 students

Step-by-step explanation:

The confidence interval of a proportion is given by:

[tex]p\pm z*\sqrt{\frac{p*(1-p)}{n} }[/tex]

Where 'p' is the proportion of students who responded 'yes', 'z' is the z-score for a 95% confidence interval (which is known to be 1.960), and 'n' is the number of students in the sample.

If the confidence interval is from 0.584 to 0.816, then:

[tex]p=\frac{0.584+0.816}{2}=0.7 \\0.816-0.584=2*(1.96*\sqrt{\frac{p*(1-p)}{n}}) \\0.116=1.96*\sqrt{\frac{0.7*(1-0.7)}{n}}\\n=16.8966^2*(0.7*0.3)\\n=60\ students[/tex]

60 students were in the sample.

Final answer:

To estimate the proportion of students at the school who regularly recycle plastic bottles, the teacher used a random sample and calculated a 95 percent confidence interval. Using the formula for the confidence interval for proportions, we can determine that the teacher selected approximately 223 students for the survey.

Explanation:

To estimate the proportion of students at the school who regularly recycle plastic bottles, the teacher selected a random sample of students and surveyed them one at a time, asking them if they regularly recycle plastic bottles. Based on the responses, a 95 percent confidence interval for the proportion of all students at the school who would respond yes to the question was calculated as (0.584, 0.816).

To find out how many students were in the sample selected by the teacher, we need to use the formula for the confidence interval for proportions:

n = (Z^2 * p * (1-p)) / (E^2)

Where:

n is the sample size,

Z is the Z-score corresponding to the desired level of confidence (in this case, 95 percent),

p is the estimated proportion of students who recycle plastic bottles (we can use the midpoint of the confidence interval, which is (0.584 + 0.816) / 2 = 0.7),

E is the margin of error (in this case, half the width of the confidence interval, which is (0.816 - 0.584) / 2 = 0.116).

Plugging in the values, we get:

n = (1.96^2 * 0.7 * (1-0.7)) / (0.116^2)

n = 2.992 / 0.013456

n ≈ 222.38

Since the sample size must be a whole number, we round up to the nearest whole number.

Therefore, the teacher selected approximately 223 students for the survey.

Answer:

C = πd or 2πr

Step-by-step explanation:

2r equals d

2r = d

Step-by-step explanation:

One hundred minus five n

The expressions that are solutions to the equation [tex]\( \frac{3}{4}x = 15 \)[/tex] are A and C

as  [tex]\( \frac{15}{\frac{3}{4}} = 20 \)[/tex] - This is a solution and  [tex]\( \frac{4}{3} \times 15 = 20 \)[/tex] - This is a solution.

Let's solve the equation [tex]\( \frac{3}{4}x = 15 \)[/tex] and then check each expression to see if it is a solution:

1. Solve the equation:

[tex]\[ x = \frac{15}{\frac{3}{4}} \][/tex]

  To divide by a fraction, we can multiply by its reciprocal:

[tex]\[ x = 15 \times \frac{4}{3} = 20 \][/tex]

Now, let's check each expression:

A. [tex]\( \frac{15}{\frac{3}{4}} = 20 \)[/tex] - This is a solution.

B. [tex]\( \frac{15}{\frac{4}{3}} \)[/tex] - This expression is equivalent to [tex]\( \frac{15 \times 3}{4} = \frac{45}{4} \)[/tex], not equal to 20.

C. [tex]\( \frac{4}{3} \times 15 = 20 \)[/tex] - This is a solution.

D. [tex]\( \frac{3}{4} \times 15 = 11.25 \)[/tex] - This is not equal to 20.

E. [tex]\( \frac{15}{\frac{3}{4}} \)[/tex] - This is equivalent to expression A, which is a solution.

Therefore, the expressions that are solutions to the equation[tex]\( \frac{3}{4}x = 15 \)[/tex] are A and C.

Complete Question: Which expressions are solutions to the equation 3/4 x=15 ? Select all that apply.

A. frac 15 3/4

B. frac 15 4/3

C. 4/3 · 15

D. 3/4 · 15

E. 15/ 3/4

Answer:

C. (3, 7)

Step-by-step explanation:

plug all the numbers into all of the coordinates and (3, 7) is the lowest number :) pls rate 5 stars and thank me

The option of buying 6 boxes of red pens and 4 boxes of black pens minimizes the cost to the business, based on the objective function C = 5x + 3y and the given constraints of at least 10 boxes in total, no more than 7 boxes of black pens, and no more than 6 boxes of red pens.

To minimize the cost of buying office supplies, particularly red and black pens, we need to use the given objective function C = 5x + 3y where x represents the number of boxes of red pens and y represents the number of boxes of black pens. We have the following constraints: at least 10 boxes of pens in total, no more than 7 boxes of black pens, and no more than 6 boxes of red pens.

By applying these constraints, we can determine the combinations of x and y that meet the criteria:

Looking at the choices provided, (6, 4) meets all our constraints, and when plugged into the objective function:

C = 5(6) + 3(4) = 30 + 12 = $42

This results in the lowest cost when compared to the other presented options. Therefore, buying 6 boxes of red pens and 4 boxes of black pens minimizes the cost to the business.

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Answer:

x=-3(y-5)

Step-by-step explanation:

Answer:

440 square inches

Step-by-step explanation:

10x10x2=200

10x6x4=240

240+200=440

Answer: 108 minutes

Step-by-step explanation:

This translates to:

Juan Pablo takes 7 minutes to do a full lap on a football field, Pedro needs 2 more minutes ruuning at the same speed thanJuan Pablo.

How much time does Pedro need to do 12 laps?

The fact that Pedro runs at the same speed than Juan Pablo, and needs more time, may mean that the radius of the laps of Pedro are a little bit bigger than the ones of Juan Pablo (which means that the total distance that pedro runs is bigger)

If Juan Pablo does a lap in 7 minutes, then Pedro does a lap in 7 minutes + 2 minutes = 9 minutes.

Then to do 12 laps, he needs 12 times that amount of time, this is:

12*9 min = 108 minutes

Answer:

the fourth one

Step-by-step explanation:

Answer:

Answer: f(x) = 500(2)^x

Step-by-step explanation:

Just took the test .

Answer:

No

Step-by-step explanation:

To answer this you have to divide 3 and 3/8 by 1/3.  The easiest way to do this without a calculator is to do this separately.  First divide 3 by 1/3.  When dividing fractions, the second number is flipped upside down and the two numbers are multiplied.  From 3 pounds, Jasmine will be able to make nine 1/3 pound burgers.

3 ÷ 1/3 = 3 × 3/1 = 9

Next, divide 3/8 by 1/3.  From 3/8 pounds, Jasmine will be able to make 1 1/8 burgers

3/8 ÷ 1/3 = 3/8 × 3/1 = 9/8 = 1 1/8

Add the two numbers together.

9 + 1 1/8 = 10 1/8

This is less than 12.

To make 12 Turkey burgers Jasmine needs 4 pounds thus 3 and 3/8 are not enough to make 12 Turkey burgers.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

Jasmine has 3 and 3/8 pounds of turkey meat

Amount in pounds needed to make 1 burger = 1/3 pound

Number of burgers in 3 3/8 ⇒

(3 3/8)/(1/3) = 10 1/8

For making 12 Turkey burgers ⇒

Amount of meat required = 12 × 1/3 = 4 pounds

Hence "To make 12 Turkey burgers Jasmine needs 4 pounds thus 3 and 3/8 are not enough to make 12 Turkey burgers".

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Answer:D

Step-by-step explanation:

(5x9)^12

5^12 x 9^12

Answer:

30 PS4 in the shipment are likely to be defective

Step-by-step explanation:

We take the estimate from the sample and estimate to all the PS4 in store. This means that we can solve this question using a rule of 3.

From the sample of 50 PS4, 3 are defective. How many are expected to be defective out of 500?

50PS4 - 3 defective

500 PS4 - x defective

[tex]50x = 3*500[/tex]

[tex]x = \frac{1500}{50}[/tex]

[tex]x = 30[/tex]

30 PS4 in the shipment are likely to be defective

Answer:

don't take my word but I think 150

Step-by-step explanation: