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ikadub [295]
2 years ago
15

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

t number. The number of different ways that the letters of millennium can be arranged is
Mathematics
1 answer:
Eddi Din [679]2 years ago
7 0

Answer:

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

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

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

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Line l has a slope of 2. The line through which of the following pair of points is perpendicular to l?
djverab [1.8K]

Answer:

D

Step-by-step explanation:

If two lines are perpendicular, the products of their slopes will be -1. Therefore, we're looking for a line with slope of -1/2. Let's check each answer:

A: 5 - 3 / (-2 - 3) = 2 / -5    

B: 6 - 5 / 6 - 5 = 1

C: 5 - 3 / 4 - 3 = 2

D: 4 - 3 / 3 - 5 = -1/2

The answer is D.

8 0
2 years ago
Read 2 more answers
The box office took in a total of $2905 in paid admissions for the high-school musical. Adult tickets cost $8 each, and student
Svet_ta [14]
There are no equations to choose from but it should look like the following.

a= # of adult tickets
s= # of student tickets

QUANTITY EQUATION
a + s= 560

COST EQUATION
$8a + $3s= $2905

***If you have to also solve for the number of adults and students, here are the steps.

STEP 1:
multiply quantity equation by -8

-8(a + s)= -8(560)
-8a - 8s= -4480

STEP 2:
add cost equation and step 1 equation

$8a + $3s= $2905
-8a - 8s= -4480
a term cancels out to zero
-5s= -1575
divide both sides by -5
s= 315 students

STEP 3:
substitute s=315 in quantity equation
a + s= 560
a + 315= 560
subtract 315 from both sides
a= 245 adults

ANSWER:
Quantity Equation
a + s= 560

Cost Equation
$8a + $3s= $2905

Hope this helps! :)
7 0
2 years ago
25 9 ​ start fraction, 9, divided by, 25, end fraction of Polly's co-workers prefer tea over coffee. What percent of Polly's co-
MrRa [10]

Answer: 36\%

Step-by-step explanation:

<h3> The complete exercise is: "\frac{9}{25} of Polly's co-workers prefer tea over coffee. 25 What percent of Polly's co-workers prefer tea over coffee".</h3>

In order to solve this exercise, you need to follow the steps shown below:

<em>Step 1:</em> Divide the numerator 9  of the fraction by the denominator 25. Then:

9\div25=0.36

<em>Step 2: </em>To calculate the percent of Polly's co-workers that prefer tea over coffee, you must multiply the quotient obtained before (this is 0.36) by 100.

Therefore, you get the following result:

Percent=(0.36)(100)\\\\Percent=36\%

Then, you can conclude that 36% of Polly's co-workers prefer tea over coffee.

8 0
2 years ago
A summer camp cookout is planned for the campers and their families. There is room for 450 people. Each adult costs $7, and each
Tanya [424]

Answer:

\left\{\begin{array}{l}x+y\le 450\\7x+4y\le 1,150\end{array}\right.

Step-by-step explanation:

Let  x be the number of adults and y be the number of campers.

There are rooms for 450 people, so

x+y≤450.

Each adult costs $7, then x adults cost $7x.

Each camper costs $4, then y campers cost $4y.

There is a maximum budget of $1,150, so

7x+4y≤1,150

Hence, you get the system of two inequalities:

\left\{\begin{array}{l}x+y\le 450\\7x+4y\le 1,150\end{array}\right.

3 0
2 years ago
Throughout the 2016 Presidential election primaries, Millennials (those aged 20 t 36 years) consistently supported Senator Berni
Dmitrij [34]

Answer:

The 90% confidence interval for the support of Sanders by millenials is between 53% and 57%.

0.53 \leq p \leq 0.57

Step-by-step explanation:

In this question we have to calculate a confidence interval (90% CI) on the proportion of millenials that had a favorable opinion on Sanders.

The sample size is n=1,754.

The p-hat, taken from the poll, is

\hat{p}=0.55

The estimated standard deviation is equal to:

\sigma_p=\sqrt{\frac{p(1-p)}{N}}=\sqrt{\frac{0.55*0.45}{1754}}=0.012

For a 90% CI, the z-value is z=1.645.

Then, the confidence interval is

\hat{p}-z*\sigma_p\leq p\leq\hat{p}-z*\sigma_p\\\\0.55-1.645*0.012\leq p\leq 0.55-1.645*0.012\\\\0.55-0.02 \leq p \leq 0.55+0.02\\\\0.53 \leq p \leq 0.57

6 0
2 years ago
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