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3 years ago

The volume of a sphere is 972π ft3. What is the radius of the sphere? Use the formula V = 4 3 πr3 to find your answer.

Mathematics

2 answers:

djyliett [7]3 years ago

6 0

$972 \pi = \frac{4}{3} \pi r^{3}$
$729 = r^{3}$
$r = 9$

Ede4ka [16]3 years ago

5 0

Answer:

The radius of the sphere is 9 ft.

Step-by-step explanation:

Given : The volume of a sphere is 972π ft³.

To find : What is the radius of the sphere?

Solution :

The formula of volume of sphere is $V=\frac{4}{3}\pi r^3$

Where, Volume of the sphere is 972π ft³.

r is the radius of the sphere.

Substitute the value in the formula,

$972\pi=\frac{4}{3}\pi r^3$

$r^3=\frac{972\pi\times 3}{4\pi}$

$r^3=729$

$r=\sqrt[3]{729}$

$r=9$

Therefore, The radius of the sphere is 9 ft.

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Angles 1 and 2 are supplementary. 2 lines intersect to form angles 1 and 2. Which equation represents the relationship between t

mamaluj [8]

Answer:

$\angle 1 + \angle 2 = 180^o$

Step-by-step explanation:

Given

$\angle 1$ and $\angle 2$

Required

The relationship between them $\angle 1$ and $\angle 2$

From the question, we understand that $\angle 1$ and $\angle 2$ are supplementary

Supplementary angles add up to 180.

So, the relationship between $\angle 1$ and $\angle 2$ is:

$\angle 1 + \angle 2 = 180^o$

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2 years ago

You invest $2,500 in an account that grows 5% each year. what will be your investment amount after 6 years?

lesantik [10]

Answer: b. $3,374.65

Step-by-step explanation:

The exponential equation of growth (continuously) is given by :-

$y=Ae^{rx}$ , where A is the initial amount, r is the rate of growth ( in decimal) and x is the time period.

Given : You invest $2,500 in an account that grows 5% each year.

i.e. A= $2,500 and r= 5%=0.05

Then, the equation model this situation will be :-

$y=2500e^{0.05x}=2500(1.05)^x$

Now, At x= 6

$y=2500e^{0.05\times6}\\\\\Rightarrow\ y=2500e^{0.3}=3374.64701894\approx3374.65$

Hence, the investment amount after 6 years will be $3,374.65.

4 0

3 years ago

Solve the inequality. 2(4 + 2x) ≥ 5x + 5? x ≤ ?

NikAS [45]

2(4+2x)≥5x+5
4+2x≥5/2x+5/2 (divide both sides by 2)
3/2+2x≥5/2x (subtract 5/2 from both sides)
3/2≥1/2x (subtract 2x from both sides)
3≥x (multiply both sides by 2)
or x≤3

Hope this helps

5 0

3 years ago

Read 2 more answers

A Gallup Poll in July 2015 found that 26% of the 675 coffee drinkers in the sample said they were addicted to coffee. Gallup ann

emmasim [6.3K]

Answer:

The 95% confidence interval for the percent of all coffee drinkers who would say they are addicted to coffee is between 21% and 31%.

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 is:

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

A confidence interval has two bounds, the lower and the upper

Lower bound:

$\pi - M$

Upper bound:

$\pi + M$

In this problem, we have that:

$\pi = 0.26, M = 0.05$

Lower bound:

$\pi - M = 0.26 - 0.05 = 0.21$

Upper bound:

$\pi + M = 0.26 + 0.05 = 0.31$

The 95% confidence interval for the percent of all coffee drinkers who would say they are addicted to coffee is between 21% and 31%.

4 0

3 years ago

A survey of 2500 subscribers to a certain news paper revealed that 2250 people subscribe to the daily morning edition and 1250 s

Aleks04 [339]

1500 people subscribed Sunday edition and 250 people subscribed only sunday edition.

Solution:

Given, A survey of 2500 subscribers to a certain news paper revealed that 2250 people subscribe to the daily morning edition

And 1250 subscribe to both the daily and the sunday editions.

We have to find how many subscribe to the Sunday edition? how many subscribe to the Sunday edition only?

Let x denote the number who subscribe to the Sunday edition.

Then the addition rule with overlap tells us that

Those who subscribe daily edition + those who subscribe sunday edition - those who subscribe both daily and sunday edition = total subscribers in survey

2250 + x – 1250 = 2500

1000 + x = 2500

x = 1500

so, 1500 subscribe to the Sunday edition and 1500 – 1250 = 250 subscribe to the Sunday edition only.

Hence, 1500 people subscribed Sunday edition and 250 people subscribed only sunday edition.

6 0

3 years ago