Estimate the following:

A park is mapped on a coordinate plane, where C1, C2, C3, and C4 represent chairs and SW1, SW2, and SW3 represent swings. How fa

serg [7]

Answer:

Option (B)

Step-by-step explanation:

To calculate the distance between C2 and SW1 we will use the formula of distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ .

d = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^2 }$

Coordinates representing positions of C2 and SW1 are (2, 2) and (-6, -7) respectively.

By substituting these coordinates in the formula,

Distance between these points = $\sqrt{(-6-2)^2+(-7-2)^2}$

= $\sqrt{(64)+(81)}$

= $\sqrt{145}$ units

Therefore, Option (B) will be the correct option.

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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 $n = 20$