In Triangle PQR, PQ = 9, QR = 10, and RP = 12. What is the smallest angle of this triangle?

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

Given the line below.

Assoli18 [71]

Answer:

y + 1 = $\frac{1}{2}$ (x + 2)

Step-by-step explanation:

The equation of a line in point- slope form is

y - y₁ = m(x - x₁)

where m is the slope and (x₁, y₁ ) a point on the line

Calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 2, - 1 ) and (x₂, y₂ ) = (2, 1 )

m = $\frac{1-(-1)}{2-(-2)}$ = $\frac{1+1}{2+2}$ = $\frac{2}{4}$ = $\frac{1}{2}$ and (x₁, y₁ ) = (- 2, - 1 ) , then

y - (- 1) = $\frac{1}{2}$ (x - (- 2) ) , that is

y + 1 = $\frac{1}{2}$ (x + 2)

8 0

3 years ago

Brian, Chris, and Damien took a math test that had 20 questions. The number of questions Brian got right is 14 more than 1/4 the

Levart [38]

B = 1/4c + 14
d = 5/4c - 2
b = d

1/4c + 14 = 5/4c - 2 ....multiply by 4
c + 56 = 5c - 8
56 + 8 = 5c - c
64 = 4c
64/4 = c
16 = c <== Chris

b = 1/4c + 14.....b = 1/4(16) + 14.....b = 4 + 14....b = 18 <== Brian
d = 5/4c - 2....d = 5/4(16) - 2.....d = 20 - 2.....d = 18 <== Damien

solution : Brain and Damien answered 2 more questions correctly then Chris did. <===

7 0

3 years ago

The value of the 7 in the number 175,983 is Number times the value of the 7 in 58,972.

ahrayia [7]

Answer:

what are u asking here?........

4 0

3 years ago

Write 1 3/5 as an improper fraction?

CaHeK987 [17]

1 3/5 as an improper fraction is 8/5

8 0

2 years ago

Read 2 more answers