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NikAS [45]
3 years ago
14

A cone has volume of 12\pi cubic inches. Its height is 4 inches. What is its radius?

Mathematics
1 answer:
asambeis [7]3 years ago
6 0

The radius of cone is 3 inches.

Step-by-step explanation:

Given,

Volume of cone = 12π cubic inches

Height of cone = 4 inches

Let,

r be the radius of cone.

Volume of cone = \pi r^2\frac{h}{3}

\pi r^2\frac{4}{3}=12\pi

Multiplying both sides by 3

3*\pi r^2\frac{4}{3}=12\pi * 3\\4\pi r^2 =36\pi

Dividing both sides by 4π

\frac{4\pi r^2}{4\ pi}=\frac{36\pi }{4\pi }\\\\r^2=9

Taking square root on both sides

\sqrt{r^2}=\sqrt{9}\\r=3

The radius of cone is 3 inches.

Keywords: volume, radius

Learn more about volume at:

  • brainly.com/question/10364988
  • brainly.com/question/10435816

#LearnwithBrainly

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A random sample of 400 Michigan State University (MSU) students were surveyed recently to determine an estimate for the proporti
Gre4nikov [31]

Answer:

a. .92

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error of the interval is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

The lower bound is the point estimate \pi subtracted by the margin of error.

The upper bound is the point estimate \pi added to the margin of error.

Point estimate:

The confidence interval is symmetric, so it is the mean between the two bounds.

In this problem:

\pi = \frac{0.372 + 0.458}{2} = 0.415

Sample of 400, which means that n = 400

Margin of error is the estimate subtracted by the lower bound. So M = 0.415 - 0.372 = 0.043

We have to find z.

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.043 = z\sqrt{\frac{0.415*0.585}{400}}

z = \frac{0.043\sqrt{400}}{\sqrt{0.415*0.585}}

z = 1.745

z = 1.745 has a pvalue of 0.96.

This means that:

1 - \frac{\alpha}{2} = 0.96

\frac{\alpha}{2} = 1 - 0.96

\frac{\alpha}{2} = 0.04

\alpha = 0.08

Confidence level:

1 - \alpha = 1 - 0.08 = 0.92

So the correct answer is:

a. .92

7 0
3 years ago
Help me please and thank you
NeTakaya

Answer:

use formula

area =1/4*π*d^2

81π=1/4*π*d^2(here two pie gets cancel)

81=1/4*d^2

81*4=d^2

\sqrt{324}=d

18=d

Step-by-step explanation:

5 0
3 years ago
if a father has 70% more money in his daughter account than his daughter has in her savings account, and the daughter has $4.500
mr_godi [17]
The answer is $ 3150
7 0
4 years ago
Alicia cashed her paycheck and used half her earnings to take three friends out to dinner. She spent $42.15 and she brought home
Phoenix [80]
If you would like to write an inequality to represent the situation, using X to represent the amount of Alicia's paycheck, you can calculate this using the following steps:

X ... the amount of Alicia's paycheck

X/2 - $42.15 >= $20
X/2 >= $20 + $42.15
X/2 >= $62.15     /*2
X >= $62.15 * 2
X >= $124.3

The correct result would be <span>X >= $124.3</span>.
5 0
3 years ago
Christian randomly selects students from his grade to rate a math test as easy, moderate, or difficult. Of the students he surve
IRINA_888 [86]

Answer:

84

Step-by-step explanation:

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Amount that found it something OTHER than easy: 14 (11 moderate + 3 difficult)

This means that \frac{14}{27} found it something other than easy

Multiply that by 162 to find the proportion for the larger population:

162 * (14/27), and we get 84.

4 0
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