First you need to find the area of the circle, which is πr^2
With a radius of 8 inches, the area of the circle will be π*8^2 or 64π.
Next you want to find the area of the 120 degree section of that circle.
120 degrees is 1/3 of a circle, so all you have to do next is multiply the are of the circle by 1/3 (because 360/120= 1/3).
(1/3)(64π) --> All you really have to do here is multiply 64 by 1/3 or divide it by 3 (because to divide by a number is the same a multiplying by it's reciprocal) so you get (64/3)(π).
64/3 is 21 and 1/3 or 21.333..., so however you choose to write it, I will leave the answer as (64/3)π squared inches.

5 0

3 years ago

Given f(x) = 2x + 9, if f(x) = 15, find x.

AleksandrR [38]

Answer:

Step-by-step explanation:

$f(x)=2x+9\\\\\text{Substitute}\ f(x)=15:\\\\15=2x+9\qquad\text{subtract 9 from both isdes}\\\\15-9=2x+9-9\\\\6=2x\qquad\text{divide both sides by 2}\\\\\dfrac{6}{2}=\dfrac{2x}{2}\\\\3=x\to x=3$

4 0

3 years ago

The median of the following data will ________________________ when you in add a data value of 1? (DO MATH on paper!) 8, 9, 9, 4

svlad2 [7]

Answer:

B decrease

Step-by-step explanation:

First, lets put the numbers in order from greatest to least.

10 9 9 8 6 4 4

Second, let's find the median without number 1. (The median is in bold.)

10 9 9 8 6 4 4

Third, let's add the number 1.

10 9 9 8 6 4 4 1

Fourth, let's find the median with the number 1.

10 9 9 8 6 4 4 1

Since there are two numbers in the middle let's find the average between them.

8+6=14

14/2= 7

Last, let's compare the two medians.

8>7

So when you add the number 1 the median decreases. So your answer is B decrease

7 0

3 years ago

A counselor at a community college claims that the mean GPA for students who have transferred to State University is more than 3

Lena [83]

Answer:

$t=\frac{3.25-3.1}{\frac{0.3}{\sqrt{36}}}=3$

If we compare the p value and the significance level for example $\alpha=1-0.99=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

And the best conclusion would be:

a) Yes. The counselor's claim is valid

Because we reject the null hypothesis in favor to the alternative hypothesis.

Step-by-step explanation:

Data given and notation

$\bar X=3.25$ represent the sample mean

$s=0.3$ represent the sample standard deviation

$n=36$ sample size

$\mu_o =3.1$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is more than 3.1, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.1$

Alternative hypothesis: $\mu > 3.1$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{3.25-3.1}{\frac{0.3}{\sqrt{36}}}=3$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=36-1=35$

Since is a one right tailed test the p value would be:

$p_v =P(t_{(35)}>3)=0.00247$

Conclusion

If we compare the p value and the significance level for example $\alpha=1-0.99=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

And the best conclusion would be:

a) Yes. The counselor's claim is valid

Because we reject the null hypothesis in favor to the alternative hypothesis.

5 0

3 years ago