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3 years ago

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What is the volume of a cone (in cubic inches) of radius 5 inches and height 3 inches? Use 3.14 for π. Round your answer to the

nearest hundredth.
A. 47.10 B. 78.50 C.157.00 D.235.50

1 answer:

Kay [80]3 years ago

5 0

I hope this helps you

Volume=4/3.pi.r^2.h

Volume =4/3.3,14.5^2.3

Volume =314

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Use differentials to approximate the change in the volume of a cube when the side is decreased from 8 to 7.99 cm. (in cm3)

Firlakuza [10]

Answer:

-1.92 cm³

Step-by-step explanation:

The formula for the volume of a cube in terms of side length is ...

V = s³

Then the first-order approximation of volume for a small change ∆s in side length is ...

V(s +∆s) ≈ V(s) + V'(s)·∆s

and the change in volume is ...

∆V ≈ V(s +∆s) -V(s) = V'(s)·∆s

The derivative V'(s) is ...

V'(s) = 3s²

so the change in volume for s = 8 cm and ∆s = -0.01 cm is ...

∆V ≈ 3s²·∆s = 3(8 cm)²(-0.01 cm) = -1.92 cm³

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3 years ago

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2 years ago

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Jose earned 5h + 5 dollars for h hours and Alex earned 8h – 10 for h hours mowing lawns. If they earned the same amount

AlekseyPX

Answer:

5 hours

Step-by-step explanation:

This is a classic pre-algebra question.

$5h+5=8h-10\\5=3h-10\\15=3h\\h=5$

3 0

3 years ago

For students who first enrolled in two year public institutions in a recent semester, the proportion who earned a bachelor's d

kondaur [170]

Answer:

Null hypothesis = $H_0:p=0.395$

Alternate hypothesis = $H_a:p>0.395$

Step-by-step explanation:

Given : In a recent semester, the proportion who earned a bachelor's degree within six years was 0.395.

The president of a certain college believes that the proportion of students who enroll in her institution have a higher completion rate.

To Find : Determine the null and alternative hypotheses.

Solution:

In a recent semester, the proportion who earned a bachelor's degree within six years was<u> 0.395. </u>

Claim : the proportion of students who enroll in her institution <u>have a higher completion rate.</u>

So,null hypothesis = $H_0:p=0.395$

Alternate hypothesis = $H_a:p>0.395$

6 0

2 years ago

construct a 90% confidence interval of the population proportion using the giver information x=74 n=150

FrozenT [24]

Answer:

The 90% confidence interval of the population proportion is (0.43, 0.56).

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for population proportion <em>p</em> is:

$CI=\hat p\pm z_{\alpha/2}\ \sqrt{\frac{\hat p(1-\hat p)}{n}}$

The information provided is:

<em>X</em> = 74

<em>n</em> = 150

Confidence level = 90%

Compute the value of sample proportion as follows:

$\hat p=\frac{X}{n}=\frac{74}{150}=0.493$

Compute the critical value of <em>z</em> for 90% confidence level as follows:

$z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645$

*Use a <em>z</em>-table.

Compute the 90% confidence interval of the population proportion as follows:

$CI=\hat p\pm z_{\alpha/2}\ \sqrt{\frac{\hat p(1-\hat p)}{n}}$

$=0.493\pm 1.645\times \sqrt{\frac{0.493(1-0.493)}{150}}\\\\=0.493\pm 0.0672\\\\=(0.4258,\ 0.5602)\\\\\approx (0.43,\ 0.56)$

Thus, the 90% confidence interval of the population proportion is (0.43, 0.56).

3 0

3 years ago