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3 years ago

What is the radius of a sphere with a volume of 12,348 π cubic feet?

Mathematics

1 answer:

vova2212 [387]3 years ago

5 0

Answer:

Radius = 21

Step-by-step explanation:

Volume of a sphere = 4/3 * pie * radius^3

12,348 pie = 4/3 * pie * radius ^3

12,348 = 4/3 * radius^3

(12,348 * 3)/ 4 = radius^3

9261 = radius^3

radius = $\sqrt[3]{9261}$

radius = 21

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Suppose the horses in a large stable have a mean weight of 975lbs, and a standard deviation of 52lbs. What is the probability th

Lubov Fominskaja [6]

Answer:

0.8926 = 89.26% probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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:

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

The Z-score measures how many standard deviations the measure is from the mean. 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, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 975, \sigma = 52, n = 31, s = \frac{52}{\sqrt{31}} = 9.34$

What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable?

pvalue of Z when X = 975 + 15 = 990 subtracted by the pvalue of Z when X = 975 - 15 = 960. So

X = 990

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

By the Central Limit Theorem

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

$Z = \frac{990 - 975}{9.34}$

$Z = 1.61$

$Z = 1.61$ has a pvalue of 0.9463

X = 960

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

$Z = \frac{960 - 975}{9.34}$

$Z = -1.61$

$Z = -1.61$ has a pvalue of 0.0537

0.9463 - 0.0537 = 0.8926

0.8926 = 89.26% probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable

7 0

3 years ago

Is 1/2 and 3/6 equivalent

Anvisha [2.4K]

Answer:

Yes because 1/2 is half of a circle and 3/6 is 3 of 6 of a colored circle to yes, it is equivalent.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A bag contains red balls and white balls. If five balls are to be pulled from the bag, with replacement, the probability of gett

Ipatiy [6.2K]

Answer:

Percentage of balls which are red = 80%.

Step-by-step explanation:

Let the probability of drawing a red ball be x then the probability of drawing a white ball is 1-x.

There are 5C3 = 10 ways of getting 3 reds in 5 draws so the probability of this is 10* x^3 * (1 - x)^2.

The probability of getting 1 red in 5 draws = 5C1 * x (1-x)^4.

The first probability is 32 times the last.

So we have the equation:

10x^3(1 - x)^2 / 5x(1 - x)^4 = 32

2x^2 / (1 - x)^2 = 32

2x^2 = 32(1 -x)^2

2x^2 = 32( 1 - 2x + x^2)

2x^2 = 32 - 64x + 32x^2

30x^2 - 64x + 32 = 0

15x^2 - 32x + 16 = 0

(5x - 4)(3x - 4) = 0

x = 0.8, 1.333...

The probability must be < 1 so x = 0.8 = 80%.

6 0

3 years ago

A restaurant has a main location and a traveling food truck. The first matrix A shows the number of managers and associates empl

denis-greek [22]

Answer:

A*B= $\left[\begin{array}{cc}705&80\\121&14 \end{array}\right]$

Step-by-step explanation:

Given A= $\left[\begin{array}{cc}5&25\\1&4\end{array}\right] \left[\begin{array}{cc}41&6\\20&2\end{array}\right]$ = B

Finding A*B means multiplying the first row with the first column and first row with the second column would give the first row elements. The second ro0w elements are obtained by multiplying the second row with the 1st column and second row with the second column.

so A*B= $\left[\begin{array}{cc}5*41+ 25*20&5*6 + 25*2\\ 1*41+4*20 & 1*6+ 4*2\end{array}\right]$

Now multiply and add the separate elements of the matrix A*B=

$\left[\begin{array}{cc}205+500&30+50\\41+80&6+8\end{array}\right]$

A*B= $\left[\begin{array}{cc}705&80\\121&14 \end{array}\right]$

b. The 1st element of the 1st row shows the salaries of the managers and 2nd element of the 1st row the salaries of associates at the restaurant . The second row 1 st element shows the benefits of the managers and 2nd element the benefits of the associates at the food truck.

c. The total cost of salaries for all employees (managers and associates) at the restaurant = 705 + 80 = 785

Total cost of benefits for all employees at the food truck= 121 + 14= 135

6 0

3 years ago

Amy charges $12 more for 5 hours of babysitting then she dies for 3 hours of babysitting. What does Amy charge per hour of baby

ArbitrLikvidat [17]

Answer:

Step-by-step explanation:

5-3

12/2

3 0

3 years ago