The diameter, D, of a sphere is 15.2m. Calculate the sphere's volume, V.

Certify Completion Icon Tries remaining:2 A town recently dismissed 10 employees in order to meet their new budget reductions. T

anyanavicka [17]

Answer:

0.055 = 5.5% probability that exactly 5 employees were over 50.

Step-by-step explanation:

The employees are removed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

7 + 18 = 25 employees, which means that $N = 25$

7 over 50, which means that $k = 7$

10 dismissed, which means that $n = 10$

What is the probability that exactly 5 employees were over 50?

This is P(X = 5). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055$

0.055 = 5.5% probability that exactly 5 employees were over 50.

5 0

3 years ago

The quotient of any two numbers, with the condition that the denominator is different from zero

elena-s [515]

Answer:

The quotient of any two numbers can be written as:

A/B

such that:

A, B ∈ {R}

Where {R} is the set of all real numbers.

But we also have the restriction that the denominator, B in this case, must be different than zero.

So we can define the set:

{R \ {0}}

As the set of all the real numbers minus the element 0.

So in this set we do not have the number zero, so now we can write our expression as:

A/B

A ∈ {R}, B ∈ {R \ {0}}

3 0

3 years ago

What is the volume of a cube whose edges each have a measure of 1.6cm?

Finger [1]

B is the answer
${1.6}^{3} = 4.096$
hope this helps

8 0

3 years ago

A journalist is interested in whether there is a significant difference in the salary offered to electrical engineering and chem

serious [3.7K]

Answer:

the appropriate conclusion is that

The samples provide evidence that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014.

Step-by-step explanation:

Since the p-value is small, it indicates statistically significant results. This means that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014.

4 0

3 years ago

Suppose that F(x) = x^3 and G(X) = -3x^3. Which statement best compares the

Alik [6]

Answer:

D. The graph of G(x) is the graph of F(x) flipped over the y-axis and

stretched vertically.

Step-by-step explanation:

since there is a negative, there must be a reflection. the reflection is over the y-axis because it is outside the x-value (-F(x) not F(-x))

the same goes for the vertical stretch. we know it is a vertical stretch because the 3 is outside the x-value (3F(x) not F(3x))

6 0

3 years ago