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2 years ago

9

Figure PQR is an equilateral triangle with a semicircle attached to it. What is the perimeter of figure PQR? Use 3.14 to approxi

mate pi.

1 answer:

____ [38]2 years ago

8 0

If it's an equilateral triangle than all the sides are the same. So 20 would be the base. Multiply 20 by 3, which is 60.

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A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is current

lapo4ka [179]

Using the z-distribution, we have that:

a)

The hypothesis test is:

$H_0: \mu = 7.4$

$H_1: \mu < 7.4$

The p-value is of 0.0668.

The critical value is $z^{\ast} = -1.28$

b) Since the <u>test statistic is less than the critical value</u> for the left-tailed test, there is enough evidence to conclude that the null hypothesis will be rejected.

Item a:

At the null hypothesis, it is <u>tested if the mean is of 7.4 minutes</u>, that is:

$H_0: \mu = 7.4$

At the alternative hypothesis, it is <u>tested if the mean is lower than 7.4 minutes</u>, that is:

$H_1: \mu < 7.4$

We have the <u>standard deviation for the population</u>, hence, the z-distribution is used.

The test statistic is given by:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

The parameters are:

$\overline{x}$ is the sample mean.

$\mu$ is the value tested at the null hypothesis.

$\sigma$ is the standard deviation of the sample.

n is the sample size.

For this problem, the values of the <em>parameters </em>are: $\overline{x} = 7.1, \mu = 7.4, \sigma = 1.2, n = 36$ .

Hence, the value of the <em>test statistic</em> is:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{7.1 - 7.4}{\frac{1.2}{\sqrt{36}}}$

$z = -1.5$

Using a z-distribution calculator, the p-value is of 0.0668.

Also using a calculator, considering a <u>left-tailed test</u>, as we are testing if the mean is less than a value, the critical value with a <u>significance level of 0.1</u> is of $z^{\ast} = -1.28$ .

Item b:

Since the <u>test statistic is less than the critical value</u> for the left-tailed test, there is enough evidence to conclude that the null hypothesis will be rejected.

You can learn more about the use of the z-distribution to test an hypothesis at brainly.com/question/16313918

5 0

1 year ago

The fish population in a local stream is decreasing at a rate of 2.5% per year. The original population was 45,000. Write an exp

Julli [10]

Answer:

y=45000(1-0.03)^x

Step-by-step explanation:

1) the exponential decay formula is

y=c(1-r)^x

where c= starting amount

r=rate of change

x=time

so

y=45000(1-0.03)^x

y=45000-1350x

4 0

3 years ago

Please help I need it ASAP

Anastasy [175]

Answer:

-83/51

Step-by-step explanation:

i used an app called Symbolab that solves any math problem for u

3 0

2 years ago

The Layer of the upper mantle that can flow is called the what?

inna [77]

Your answer is the athenosphere.

5 0

3 years ago

1st. (2 root 2 + root 3 ) ( 2 root 3 - root 2)

satela [25.4K]

Answer:

1st: 3*root6 + 5

2nd: 35*root2 + 115

3rd: 24*root2 - 20*root6 + 15*root3 - 18

4th: 17*root6 - 38

5th: 13*root10 - 42

Step-by-step explanation:

To simplify these expressions we need to use the distributive property:

(a + b) * (c + d) = ac + ad + bc + bd

So simplifying each expression, we have:

1st.

(2 root 2 + root 3 ) ( 2 root 3 - root 2)

= 4*root6 - 2*2 + 2*3 - root6

= 3*root6 - 4 + 9

= 3*root6 + 5

2nd.

(root 5 + 2 root 10) (3 root 5 + root 10)

= 3 * 5 + root50 + 6*root50 + 2*10

= 15 + 5*root2 + 30*root2 + 100

= 35*root2 + 115

3rd.

(4 root 6 - 3 root 3) (2 root 3 - 5)

= 8*root18 - 20*root6 - 6*3 + 15root3

= 24*root2 - 20*root6 + 15*root3 - 18

4rd.

(6 root 3 - 5 root 2 ) (2 root 2 - root 3)

= 12*root6 - 6*3 - 10*2 + 5*root6

= 17*root6 - 18 - 20

= 17*root6 - 38

5th.

(root 10 - 3 ) ( 4 - 3 root 10)

= 4*root10 - 3*10 - 12 + 9*root10

= 13*root10 - 30 - 12

= 13*root10 - 42

8 0

2 years ago