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3 years ago

Find an equation of the circle that has center (−1,2) and passes through ( 2,−2) .

1 answer:

8 0

Equation of a circle that has a center at (h,k) and radius of r is
(x-h)²+(y-k)²=r²

so

given center (-1,2)
(x-(-1))²+(y-2)²=r²
(x+1)²+(y-2)²=r²

sub the other point to find r or r²

it passes through (2,-2)
sub 2 for x and -2 for y

(2+1)²+(-2-2)²=r²
(3)²+(-4)²=r²
9+16=r²
25=r²
5=r

the equation is
(x+1)²+(y-2)²=5²

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I'm doing simplifying expressions with exponents

VladimirAG [237]

Answer:

Expressing a number in a power of 2 means that you have to figure out how many times you should multiply 2 by itself so the product will be that number.

The number is expressed as 2^n

For example:

Express 16 as a power of 2:

To get 16, you have to multiply 2 by 4 times.

2 × 2 × 2 × 2 = 16

16 = 2^4

Then the answer is 2^4

7 0

2 years ago

A manager is comparing wait times for customers in a coffee shop based on which employee is

anyanavicka [17]

Using the t-distribution, as we have the standard deviation for the sample, it is found that there is a significant difference between the wait times for the two populations.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, we test if there is no difference, that is:

$H_0: \mu_A - \mu_B = 0$

At the alternative hypothesis, it is tested if there is difference, that is:

$H_1: \mu_A - \mu_B = 0$

<h3>What are the mean and the standard error of the distribution of differences?</h3>

For each sample, we have that:

$\mu_A = 73, s_A = \frac{2}{\sqrt{100}} = 0.2$

$\mu_B = 74, s_B = \frac{4}{\sqrt{100}} = 0.4$

For the distribution of differences, we have that:

$\overline{x} = \mu_A - \mu_B = 73 - 74 = -1$

$s = \sqrt{s_A^2 + s_B^2} = \sqrt{0.2^2 + 0.4^2} = 0.447$

<h3>What is the test statistic?</h3>

It is given by:

$t = \frac{\overline{x} - \mu}{s}$

In which $\mu = 0$ is the value tested at the null hypothesis.

Hence:

$t = \frac{\overline{x} - \mu}{s}$

$t = \frac{-1 - 0}{0.447}$

$t = -2.24$

<h3>What is the p-value and the decision?</h3>

Considering a one-tailed test, as stated in the exercise, with 100 - 1 = 99 df, using a t-distribution calculator, the p-value is of 0.014.

Since the p-value is less than the significance level of 0.05, it is found that there is a significant difference between the wait times for the two populations.

More can be learned about the t-distribution at brainly.com/question/16313918

8 0

2 years ago

A town’s January high temperatures average 36 degrees (F) with a standard deviation of 10 degrees while in July the mean high

n200080 [17]

Answer:

55 degrees is more unusual in July as it is away from mean temperature as compared to January.

Step-by-step explanation:

We are given the following information in the question:

January:

Mean, μ = 36 degrees

Standard Deviation, σ = 10 degrees