The width of the rectangle is the same as the length of the cylinder (h). The area of each of the two circles is \\ (\\pi r^2\\) and the area of the rectangle is \\ (2 \\pi r times h\\).

Step-by-step explanation:

6 0

2 years ago

The distance between Rosa's house and her school is 4 1/2 of a mile. She ran 3 mile. What fraction of the distance between her h

Licemer1 [7]

Answer:

Rosa ran $\frac{2}{3}$ of the total distance between her house and her school.

Step-by-step explanation:

Distance between Rosa's house and her school = $4\frac{1}{2}$ miles ≈ 4.5 miles

She ran distance = 3 miles

Therefore, fraction of the total distance between her house and school she run = $\frac{\text{Distance run by Rosa}}{\text{Total distance between her house and school}}$

= $\frac{3}{4.5}$

= $\frac{30}{45}$

= $\frac{2}{3}$

Therefore, Rosa ran $\frac{2}{3}$ of the total distance between her house and her school.

5 0

2 years ago

A test of sobriety involves measuring the subject's motor skills. Twenty randomly selected sober subjects take the test and prod

elena55 [62]

Answer:

Step-by-step explanation:

Hello!

The variable of interest is:

X: motor skills of a sober subject.

n= 20

X[bar]= 37.1

S= 3.7

The claim is that the average score for all sober subjects is equal to 35.0, symbolically: μ= 35.0

The hypotheses are:

H₀: μ = 35.0

H₁: μ ≠ 35.0

α: 0.01

The statistic to use, assuming all conditions are met, is a one sample t- test

$t= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } ~t_{n-1}$

$t_{H_0}= \frac{37.1-35.0}{\frac{3.7}{\sqrt{20} } } = 2.34$

This test is two-tailed, meaning, the rejection region is divided in two and you'll reject the null hypothesis to low values of t or to high values of t:

$t_{n-1;\alpha /2}= t_{19; 0.005}=-2.861$

$t_{n-1;1-\alpha /2}= t_{19; 0.995}= 2.861$

The decision rule using this approach is:

If $t_{H_0}$ ≤ -2.861 or if $t_{H_0}$ ≥ 2.861, you reject the null hypothesis.

If -2.861 < $t_{H_0}$ < 2.861, you do not reject the null hypothesis.

The value is within the non rejection region, the decision is to not reject the null hypothesis.

I hope this helps!

3 0

2 years ago