How many solutions does the system have?

Two times a number added to another number is 25. Three times the first number minus the second number is 20. What are both numb

lawyer [7]

Answer:

the two number are 7 and 9

Step-by-step explanation:

2*x+y=25

3x-y = 20

add the two equations

2*x+y=25

3x-y = 20

---------------

5x = 45

divide by 5

5x/5 = 45/5

x = 9

lets find y

2x+y = 25

substitute x

2*9 +y =25

18+y =25

subtract 18 from both side

y = 25-18

y =7

7 0

3 years ago

D Cuales son cángulos agudo<br>?

nasty-shy [4]

Ángulo agudo es aquel que mide menos de 90º

6 0

3 years ago

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 $n = 20$