Charlotte is running a rate of 9 km per hour. What is her rate at meters per second?

A classic counting problem is to determine the number of different ways that the letters of millennium can be arranged. Find tha

Eddi Din [679]

Answer:

The correct answer is that the number of different ways that the letters of the word "millennium" can be arranged is 226,800

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Number of letters of the word "millennium" = 10

Letters repeated:

m = 2 times

i = 2 times

l = 2 times

n = 2 times

2. The number of different ways that the letters of millennium can be arranged is:

We will use the n! or factorial formula, this way:

10!/2! * 2! * 2! * 2!

(10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/(2 * 1) * (2 * 1) * (2 * 1) * (2 *1)

3'628,800/2*2*2*2 = 3'628,800/16 = 226,800

The correct answer is that the number of different ways that the letters of the word "millennium" can be arranged is 226,800

7 0

3 years ago

There are 81 members in the marching band. The director wants to arrange the band members in rows and columns so that there are

OLga [1]

9 rows and 9 columns

3 0

2 years ago

Read 2 more answers

A survey of 340 randomly chosen US adults found that 60% of the 150 men and 50% of the 190 women ran a five-kilometer race durin

Andrej [43]

Answer:

The p-value is less than the significance level, so we will reject the null hypothesis, and conclude that at 5% significance level, the proportion for women that ran 5 km is more than the proportion of male that ran the 5 km. Thus, women are more likely to run the 5 km race.

Step-by-step explanation:

We are given;

Number of males selected; n₁ = 150

Number of females selected; n₂ = 190

Proportion of the males; p₁ = 0.6

Proportion of females; p₂ = 0.5

Let's define the hypotheses;

Null hypothesis; H0: p₁ ≥ p₂

Alternative hypothesis; Ha: p₁ < p₂

Now, the z score formula for this is;

z = (p₁ - p₂)/√(p^(1 - p^))(1/n₁ + 1/n₂))

Where;

p^ = (p₁ + p₂)/2

p^ = (0.6 + 0.5)/2

p^ = 0.55

Thus;

z = (0.6 - 0.5)/√(0.55(1 - 0.55))((1/150) + (1/190))

z = 0.1/0.0543

z = 1.84

From online p-value from z-score calculator attached, using z = 1.84, significance level = 0.05, one tailed hypothesis, we have;

P-value = 0.033

The p-value is less than the significance level, so we will reject the null hypothesis, and conclude that at 5% significance level, the proportion for women that ran 5 km is more than the proportion of male that ran the 5 km. Thus, women are more likely to run the 5 km race.

Although if we check at 0.01 significance level, we will not have the same answer as the p-value will be greater.

3 0

3 years ago

After how many audio books will both book clubs cost the same amount.

bulgar [2K]

Answer:

2 books

Step-by-step explanation:

10 + 5x = 16 + 2x

- 2x - 2x

10 + 3x = 16

-10 -10

3x = 6

/3 /3

x = 2

4 0

3 years ago

Which function has the greatest rate of change on the interval from x = 3 pi over 2 to x = 2π?

vodka [1.7K]

The average rate of change for the function f(x) can be calculated from the following equation
$\frac{f( x_{2})-f( x_{1} )}{ x_{2} - x_{1} }$

By applying the last formula on the given equations
(1) the first function f
from the table f(3π/2) = -2 and f(2π) = 0
∴ The average rate of f = $\frac{f(2 \pi)-f( \frac{3 \pi}{2} )}{2 \pi - \frac{3 \pi}{2} } = \frac{0-(-2)}{ \frac{\pi}{2} }= \frac{2}{ \frac{\pi}{2} } = \frac{4}{\pi}$

(2) the second function g(x)
from the graph g(3π/2) = -2 and g(2π) = 0
∴ The average rate of g = $\frac{g(2 \pi)-g( \frac{3 \pi}{2} )}{2 
\pi - \frac{3 \pi}{2} } = \frac{0-(-2)}{ \frac{\pi}{2} }= \frac{2}{ 
\frac{\pi}{2} } = \frac{4}{\pi}$

(3) the third function h(x) = 6 sin x +1
∴ h(3π/2) = 6 sin (3π/2) + 1 = 6 *(-1) + 1 = -5
 h(2π) = 6 sin (2π) + 1 = 6 * 0 + 1 = 1
∴ The average rate of h = $\frac{f(2 \pi)-f( \frac{3 \pi}{2} )}{2 
\pi - \frac{3 \pi}{2} } = \frac{1-(-5)}{ \frac{\pi}{2} }= \frac{6}{ 
\frac{\pi}{2} } = \frac{12}{\pi}$

By comparing the results, The function which has the greatest rate of change is h(x)


So, the correct answer is option C) h(x)

4 0

3 years ago