MATHEMATICS COLLEGE

A zoo has a circular pool for its seals. The diameter of the pool is 32 feet. How much fence is needed to enclose the pool?

Answers

Answer 1
Answer:

Answer:

The answer is 32 \pi\ feet or 100.53\ feet

Step-by-step explanation:

we know that

To calculate how much fence is needed to enclose the circular pool, find the circumference of the circular pool

The circumference of a circle is equal to

C=\pi D

where

D is the diameter of the circle

In this problem we have

D=32\ feet

Substitute

C=\pi (32)=32 \pi\ feet

C=32 \pi\ feet=100.53\ feet

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Find the highest common factor (HCF) of 90 and 126

Answers

Answer:

18

Step-by-step explanation:

18*5=90

18*7=126
The greatest common factor(GCF) for 90 and 126 is 18

Calculate the weighted mean from the following sales: $400, $700, $300, $600, $300, $400, $700

Answers

I got $485 ,I added all the numbers together and divided by how many numbers there are in the equation.

Complete the standard form of the equation of a hyperbola that has vertices at (-10, -15) and (70, -15) and one of its foci at (-11, -15).

Answers

Answer:

((x-30)^(2))/(40^(2)) - ((y+15)^(2))/(3^(2)) = 1

Step-by-step explanation:

The equation of the horizontal hyperbola in standard form is:

((x-k)^(2))/(a^(2)) - ((y-k)^(2))/(b^(2)) = 1

The position of its center is:

C(x,y) = \left((-10 + 70)/(2), -15 \right)

C(x, y) = (30,-15)

The values for c and a are respectively:

a = 70 - 30

a = 40

c = 30 - (-11)

c = 41

The remaining variable is computed from the following Pythagorean identity:

c ^(2) = a^(2) + b^(2)

b = \sqrt{c^(2)-a^(2)}

b = \sqrt{41^(2)-40^(2)}

b = 3

Now, the equation of the hyperbola is:

((x-30)^(2))/(40^(2)) - ((y+15)^(2))/(3^(2)) = 1

Answer:

The above answer is correct but the 3 should be a 9

Step-by-step explanation:

Plato

I need help please!!

Answers

Answer:

2 remainder 5 ily

Step-by-step explanation:

A direct mailing company sells computers and computer parts by mail. The company claims that at least 90% of all orders are mailed within 72 hours after they are received. The quality control department at the company often takes samples to check if this claim is valid. A recently taken random sample of 150 orders showed that 129 of them were mailed within 72 hours. Set up the null and alternative hypotheses to test whether the company’s claim is true?

Answers

Answer:

The null and alternative hypothesis are:

H_0: \pi=0.9\n\nH_a:\pi<0.9

There is not enough evidence to support the claim that the company is worng and less than 90% of all orders are mailed within 72 hours after they are received.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The company claims that at least 90% of all orders are mailed within 72 hours after they are received. The company's claim is the null hypothesis, the claim that is going to be tested is if this proportion is significantly less than 90%.

Then, the null and alternative hypothesis are:

H_0: \pi=0.9\n\nH_a:\pi<0.9

The significance level is 0.05.

The sample has a size n=150.

The sample proportion is p=0.86.

p=X/n=129/150=0.86

The standard error of the proportion is:

\sigma_p=\sqrt{(\pi(1-\pi))/(n)}=\sqrt{(0.9*0.1)/(150)}\n\n\n \sigma_p=√(0.0006)=0.024

Then, we can calculate the z-statistic as:

z=(p-\pi+0.5/n)/(\sigma_p)=(0.86-0.9+0.5/150)/(0.024)=(-0.037)/(0.024)=-1.497

This test is a left-tailed test, so the P-value for this test is calculated as:

\text{P-value}=P(z<-1.497)=0.0672

As the P-value (0.0672) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that less than 90% of all orders are mailed within 72 hours after they are received.

Final answer:

The null hypothesis is that 90% of all orders are shipped within 72 hours, denoted as H0: p = 0.90. The alternative hypothesis is that less than 90% of all orders are shipped within 72 hours, expressed as HA: p < 0.90.

Explanation:

In hypothesis testing, the null hypothesis represents the theory that has been put forward, either because it is believed to be true or because it is used as a basis for argument. In this case, the null hypothesis would be that 90% of all orders are shipped within 72 hours. This can be formulated as H0: p = 0.90 where p represents the proportion of all orders shipped within 72 hours.

The alternative hypothesis on the other hand is the hypothesis used in hypothesis testing that is contrary to the null hypothesis. Here, the alternative hypothesis would be that less than 90% of all orders are shipped within 72 hours. It can be expressed as HA: p < 0.90 where p remains the proportion of orders shipped within 72 hours.

Learn more about Hypothesis Testing here:

brainly.com/question/31665727

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You are renting a limousine that charges certain rates to visit each of the following cities. You needto visit each city once and you need to start in Athens and end in Athens. Use the "Brute Force"
Algorithm to find the cheapest route to visit each city and return home again to Athens.

Answers

Answer:

the answer is Athens-Buford-Cu-Dacul-Athens

Step-by-step explanation:
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