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2 years ago

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The volume of air inside a rubber ball with radius r can be found using the function V(r) = four-thirds pi r cubed. What does V

and five-sevenths represent?
the radius of the rubber ball when the volume equals five-sevenths cubic feet
the volume of the rubber ball when the radius equals five-sevenths feet
that the volume of the rubber ball is 5 cubic feet when the radius is 7 feet
that the volume of the rubber ball is 7 cubic feet when the radius is 5 feet

2 answers:

enot [183]2 years ago

5 0

Answer:

5/7

Step-by-step explanation:

the volume of the rubber ball when the radius equals five-sevenths feet

Nat2105 [25]2 years ago

4 0

Corrected Question

The volume of air inside a rubber ball with radius r can be found using the function V(r) = four-thirds pi r cubed. What does V(5/7) represent?

Answer:

(B)the volume of the rubber ball when the radius equals five-sevenths feet

Step-by-step explanation:

The Volume of a sphere of radius r can be found using the formula:

$V(r)=\dfrac43 \pi r^3$

Therefore comparing the expression: $V(\dfrac57)$ with V(r):

$Radius, r=\dfrac57$

Thus, $V(\dfrac57)$ is the volume of a ball of radius $\dfrac57$ feet.

The correct option is B.

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A company purchased a delivery van for $28,000 with a salvage value of $3,000 on September 1, Year 1. It has an estimated useful

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Answer:

Depreciation till December 31, Year 1 will be equal to 1,250$

Step-by-step explanation:

Purchasing Cost = 28,000$

Salvage Value = 3,000$

Total Depreciation:

Total Depreciation over 5 years (60 Months) = Purchasing Cost - Salvage Value

Total Depreciation over 5 years (60 Months) = 28,000 - 3,000

Total Depreciation over 5 years (60 Months) = 25,000$

Monthly Depreciation:

Using the unity method we have monthly depreciation by dividing the total depreciation by the total no. of months as below:

Total Depreciation over a single month =25,000/60

Total Depreciation over a single month = 416.67$ (Monthly Depreciation)

Depreciation till December 31, Year 1

As from September 1, Year 1 to December 31, Year 1, its been 3 months therefore total depreciation will be = 3 * Monthly Depreciation

Depreciation till December 31, Year 1 = 3 * 416.67

Depreciation till December 31, Year 1 = 1,250$

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2 years ago

Minato drove 390 miles. Part of the drive was along local roads, where his average speed was 20 mph, and the rest was along a hi

pashok25 [27]

Answer:

45 miles.

Step-by-step explanation:

Given that the:

Total distance covered = 390 miles

Total time = 8 hours

Let the distance covered along the local way = L

And the distance covered along the highway = H

Along with local way,

Speed = distance/ time

20 = L / T

T = L /20 .... (1)

Along the highway,

Distance covered H = 390 - L

Let the time = t

Speed = distance/time

60 = (390 - L)/t

t = ( 390 - L)/60

But total time = T + t

That is

8 = L/20 + (390 - L)/60

The LCM at right hand side will be 60

8 = ( 3L + 390 - L )/60

Cross multiply

480 = 2L + 390

Collect the like terms

2L = 480 - 390

2L = 90

L = 90/2

L = 45 miles.

Therefore, the distance Minato drive along local roads is 45 miles

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2 years ago

The Census Bureau reports that 82% of Americans over the age of 25 are high school graduates. A survey of randomly selected resi

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Answer:

a) Mean = 1030; Standard deviation = 12.38.

b) The county result is unusually high.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

(a) Find the mean and standard deviation for the number of high school graduates in groups of 1210 Americans over the age of 25.

This first question is a binomial propability distribution.

We have a sample of 1210 Amricans, so $n = 1210$ .

The mean of the sample is 1030.

The probability of a success is $\pi = \frac{1030}{1210} = 0.8512$ .

The standard deviation of the sample is $s = \sqrt{n\pi(1-\pi)} = \sqrt{1210*0.8512*0.1488} = 12.38$

(b) Is that county result of 1030 unusually high, or low, or neither?

The first step is find the zscore when $X = 1030$ .

Then we find the pvalue of this zscore.

If this pvalue is bigger than 0.95, the county result is unusually high.

If this pvalue is smaller than 0.05, the county result is unusually low.

Otherwise, it is neither.

The national mean is 82%. So,

$\mu = 0.82(1210) = 992.2$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1030 - 992.2}{12.38}$

$Z = 3.05$

$Z = 3.05$ has a pvalue of 0.9989.This means that the county result is unusually high.

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We can model this situation as a system of linear equation, where n is the number of nickels and q is the number of quarters.

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2 years ago

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If line b is perpendicular to line a, and line c is perpendicular to line a, what is the slope of line c?

slega [8]

we know that

If line b is perpendicular to line a, and line c is perpendicular to line a,

then

line b and line c are parallel

and two lines parallel have the same slope

so

<u>Find the slope of the line b</u>

Let

$A(-3,-2)\\B(2,3)$

The formula to calculate the slope between two points is equal to

$m=\frac{(y2-y1)}{(x2-x1)}$

$(x1,y1)=(-3,-2)\\(x2,y2)=(2,3)$

substitute

$m=\frac{(3+2)}{(2+3)}$

$m=\frac{(5)}{(5)}$

$m=1$

therefore

<u>the answer is</u>

<u>the slope of the line c is</u>

$mc=1$

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2 years ago

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