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1 year ago

Solve the system by any method. (3x – 4y = -5 (5x + 8y = -1

Mathematics

2 answers:

Pachacha [2.7K]1 year ago

5 0

The answer is (-1,1/2)

Taya2010 [7]1 year ago

4 0

Answer:

( x , y ) = ( -1,1/2)

Step-by-step explanation:

Solve the equation for X

$\left \{ {{x=-5/3+4/3y} \atop {5x+8y=-1}} \right.$

Substitute the given value of x into the equation 5x + 8y = -1

5(-5/3+4/3y)+8y=-1

Solve the equation for Y

y=-1/2

Substitute the given value of y into the equation x = -5 / 3 + 4 / 3y

x=-5/3+4/3×1/2

Solve the equation for X

x=-1

The system solution is the computer pair

(x,y)=(-1,1/2)

Check if the ordered pair given to the solution of the system of equations

$\left \{ {{3*(-1)-4*1/2=-5} \atop {5*(-1)+8*1/2=-1}} \right.$

Simplify the equations

$\left \{ {{-5=-5} \atop {-1=-1}} \right.$

The ordered pair is the solution of the system of equations, since both equations are true

(x,y)=(-1,1/2)

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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

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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 $n = 20$