In the figure, angle G measures 117°, angle C measures 22°, and angle E measures 40°.

If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar

Oksana_A [137]

Answer:

$n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}$

Step-by-step explanation:

Lets divide it in cases, then sum everything

Case (1): All 5 numbers are different

In this case, the problem is reduced to count the number of subsets of cardinality 5 from a set of cardinality n. The order doesnt matter because once we have two different sets, we can order them descendently, and we obtain two different 5-tuples in decreasing order.

The total cardinality of this case therefore is the Combinatorial number of n with 5, in other words, the total amount of possibilities to pick 5 elements from a set of n.

${n \choose 5 } = \frac{n!}{5!(n-5)!}$

Case (2): 4 numbers are different

We start this case similarly to the previous one, we count how many subsets of 4 elements we can form from a set of n elements. The answer is the combinatorial number of n with 4 ${n \choose 4} .$

We still have to localize the other element, that forcibly, is one of the four chosen. Therefore, the total amount of possibilities for this case is multiplied by those 4 options.

The total cardinality of this case is $4 * {n \choose 4} .$

Case (3): 3 numbers are different

As we did before, we pick 3 elements from a set of n. The amount of possibilities is ${n \choose 3} .$

Then, we need to define the other 2 numbers. They can be the same number, in which case we have 3 possibilities, or they can be 2 different ones, in which case we have ${3 \choose 2 } = 3$ possibilities. Therefore, we have a total of 6 possibilities to define the other 2 numbers. That multiplies by 6 the total of cases for this part, giving a total of $6 * {n \choose 3}$

Case (4): 2 numbers are different

We pick 2 numbers from a set of n, with a total of ${n \choose 2}$ possibilities. We have 4 options to define the other 3 numbers, they can all three of them be equal to the biggest number, there can be 2 equal to the biggest number and 1 to the smallest one, there can be 1 equal to the biggest number and 2 to the smallest one, and they can all three of them be equal to the smallest number.

The total amount of possibilities for this case is

$4 * {n \choose 2}$

Case (5): All numbers are the same

This is easy, he have as many possibilities as numbers the set has. In other words, n

Conclussion

By summing over all 5 cases, the total amount of possibilities to form 5-tuples of integers from 1 through n is

$n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}$

I hope that works for you!

4 0

3 years ago

The mean hours of sleep that students get per night is 7 hours, the standard deviation of hours of sleep is 1.7 hours, and the d

densk [106]

Answer:

c. 3.6 and 10.4 hrs

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean 7, standard deviation 1.7.

For about 95% of students, nightly amount of sleep is between

7 - 2*1.7 = 7 - 3.4 = 3.6 hours

7 + 2*1.7 = 7 + 3.4 = 10.4 hours

So the correct answer is:

c. 3.6 and 10.4 hrs

5 0

3 years ago

Chose all the values of x that are not in the domain of this rational function. Picture attached, 15 points and I'll give Brainl

pogonyaev

Answer:

All of them.

Step-by-step explanation:

For rational functions, the domain is all real numbers <em>except</em> for the zeros of the denominator.

Therefore, to find the x-values that are not in the domain, we need to solve for the zeros of the denominator. Therefore, set the denominator to zero:

$x(x-1)(x^2-4)=0$

Zero Product Property:

$x\neq 0\text{ or }x-1\neq 0\text{ or }x^2-4\neq 0$

Solve for the x in each of the three equations. The first one is already solved. Thus:

$x-1\neq 0 \text{ or }x^2-4\neq 0\\x\neq 1\text{ or }x^2\neq 4\\x\neq 1 \text{ or }x\neq\pm 2$

Thus, the values that <em>cannot</em> be in the domain of the rational function is:

$x=-2,0,1,2$

Click all the options.

6 0

3 years ago

Read 2 more answers

Miss Lewis has $523.50 in her savings account. Her bank pays 5 3/4% if interest. If the interest is computed once per year, how

cluponka [151]

Answer:

Interest She'll make in a year is $30.10125

Step-by-step explanation:

Interest = PRT ÷ 100

Principal = $523.50

Rate = 5³/₄% = 5.75%

Time= 1year

Interest I = (523.50 × 5.75 × 1) ÷ 100 = $30.10125

Interest She'll make in a year is $30.10125

5 0

3 years ago

Question 5

Vikentia [17]

The amount of sales (S) of statin in billions of dollars by 2017 is 34.5 billions

<h3>Linear equations</h3>

Linear equation are equation that has a leading degree of 1. Given the equation that represents Statins used to keep cholesterol in check and are a top-selling drug in the U.S.

S-1.5x = 6

where

S is the amount of sales

x is the number of years after 1998

By 2017, the total number of years is 19 years

Substitute

S = 1.5x + 6

S = 1.5(19) + 6

S = 28.5 + 6

S = 34.5

The amount of sales (S) of statin in billions of dollars by 2017 is 34.5 billions

Learn more on linear equation here: brainly.com/question/14323743

#SPJ1

6 0

1 year ago