Cone is sliced so the cross section is perpendicular to the base and passes through the vertex. What shape would it make?

2. Find the fraction which is exactly halfway between 1/7 and 4/7

Ksivusya [100]

Answer:

That would be the fraction exactly between 2/7 and 3/7

which would be 2.5 / 7 or 5 / 14

Step-by-step explanation:

4 0

3 years ago

Find the least common denominator for these two rational expressions. 3/2n -2/5n

Zielflug [23.3K]

Every rational expression can be written in infinitely many equvialent forms which is 3/3n-15/2.

8 0

3 years ago

Read 2 more answers

The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are indepen

vfiekz [6]

Answer:

a) 0.2581

b) 0.4148

c) 17

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

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

And p is the probability of X happening.

In this problem we have that:

$p = 0.75$

a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{12,9}.(0.75)^{9}.(0.25)^{3} = 0.2581$

b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 16) = C_{20,16}.(0.75)^{16}.(0.25)^{4} = 0.1897$

$P(X = 17) = C_{20,17}.(0.75)^{17}.(0.25)^{3} = 0.1339$

$P(X = 18) = C_{20,18}.(0.75)^{18}.(0.25)^{2} = 0.0669$

$P(X = 19) = C_{20,19}.(0.75)^{19}.(0.25)^{1} = 0.0211$

$P(X = 20) = C_{20,20}.(0.75)^{20}.(0.25)^{0} = 0.0032$

So

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1897 + 0.1339 + 0.0669 + 0.0211 + 0.0032 = 0.4148$

c. If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

So

$E(X) = 22*0.75 = 16.5$

The closest integer to 16.5 is 17.

7 0

3 years ago

A tour company charges a given price per ticket based on the number, n, of people who take the tour. the maximum number of peopl

UkoKoshka [18]

Harper goes on a tour where the ticket price is $10.50 along with 29 people according to the given expression. Solving the given expression for 'n' results in the required number.

<h3>How to solve an algebraic expression?</h3>

Solving an expression algebraically involves basic operations like addition, subtraction, multiplication, and division.

In the expression, add/subtract the constant terms on both sides
Multiply/divide the coefficient of the variable on both sides
Solve for the variable.

<h3>Calculation:</h3>

Given that,

A tour company charges a given price per ticket based on the number 'n' of people who take the tour.

The maximum number of people who are allowed to take the tour is 35. I.e., n ≤ 35.

The price per ticket is $20 for n < 10 people and the price per ticket is given by the expression 20-(n-10)/2 for n > 10 people.

Harper goes on a tour where the ticket price is $10.50.

Since the price is less than $20, so the number of people who went on this tour is known by the expression 20-(n-10)/2 for n > 10 people.

So, solving the given expression:

20-(n-10)/2 = $10.50

-(n-10)/2 = 10.50 - 20

-(n-10)/2 = -9.5

(n-10) = 9.5 × 2

n -10 = 19

∴ n = 19 + 10 = 29

Therefore, 29 people went on this tour for a ticket price of $10.50.

Learn more about solving an expression here:

brainly.com/question/723406

#SPJ4

3 0

2 years ago

How do you determine the slope interscept equation of two given pointa

DiKsa [7]

Step-by-step explanation:

To find the slope intercept form of any equation using two points, you first need to find the slope. You can do this using the slope formula below.

m(slope) = (y2 - y1)/(x2 - x1)

In this equation, we find the slope by putting in the values we have given the points. The first point you have would be (x1, y1). So if your first point is (3, 1), you would put 3 in for x1 and 1 in for y1. Then you do the same for the second point using (x2, y2).

After you've solved that equation and got m, you can use point-slope form. Take your first point and your newly found slope and plug the values into the following equation.

y - y1 = m(x - x1)

After this, you can solve for y and that will be your slope intercept form.

7 0

3 years ago