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DanielleElmas [232]

3 years ago

5

A. You work 30 hours a week. You need to earn $234 to cover your weekly expenses. Your dog-walking job pays $8 per hour and your

job at the car wash pays $7.5 an hour. Write a system of linear equations to represent the situation.

1 answer:

snow_tiger [21]3 years ago

8 0

Answer:

Line all of the numbers up

Step-by-step explanation:

You have $234 to cover all of your weekly expenses (bills, food, ect.) Your dog walking job pays (gives you) $8 per hour, the car wash job pays $7.50 an hour.

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Suppose that 20% of the subscribers of a cable television company watch the shopping channel at least once a week. The cable com

riadik2000 [5.3K]

Answer:

4.01% probability that the cable company will keep the shopping channel.

Step-by-step explanation:

For each subscriber, there are only two possible outcomes. Either they watch the shopping channel at least once a week, or they do not. This means that we can solve this problem using the binomial probability distribution.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 100, p = 0.20$

So

$E(X) = 100*0.20 = 20$

$\sqrt{V(X)} = \sqrt{100*0.20*0.80} = 4$

The cable company has decided to keep the shopping channel if the sample proportion is greater than 0.27. What is the approximate probability that the cable company will keep the shopping channel, even though the true proportion who watch it is only 0.20?

This probability is 1 subtracted by the pvalue of Z when $X = 0.27*100 = 27$ . So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{27 - 20}{4}$

$Z = 1.75$

$Z = 1.75$ has a pvalue of 0.9599.

So there is a 1-0.9599 = 0.0401 = 4.01% probability that the cable company will keep the shopping channel.

5 0

3 years ago

Solve this simultaneous equation by using substitution method 3x-2y=12 and x+3y=-7

ratelena [41]

Answer:

Solving this simultaneous equation by using substitution method 3x-2y=12 and x+3y=-7 we get x=2 and y=-3

Solution set = {2,-3}

Step-by-step explanation:

We need to solve this simultaneous equation by using substitution method 3x-2y=12 and x+3y=-7

let:

$3x-2y=12--eq(1)\\x+3y=-7 --eq(2)$

Finding value of x from equation 2 and putting in eq(1)

$From \ eq(2)\\x+3y=-7\\x=-7-3y$

Putting value of x in eq(1)

$3x-2y=12\\Put \ x=-7-3y\\3(-7-3y)-2y=12\\Solving\\-21-9y-2y=12\\-11y=12+21\\-11y=33\\y=\frac{33}{-11}\\y=-3$

So, we get y=-3

Now put value of y in equation 2 to find value of x

$x+3y=-7\\x+3(-3)=-7\\x-9=-7\\x=-7+9\\x=2$

So, we get value of x =2

So, solving this simultaneous equation by using substitution method 3x-2y=12 and x+3y=-7 we get x=2 and y=-3

Solution set = {2,-3}

4 0

2 years ago

X-2y=-26 x-y=-2 solution of systems equation

svp [43]

If we subtract the 2 equations we eliminate x:-

x - x - 2y - (-y) = -26--2
-y = -24
y = 24
Plug this into the first equation:-
x - 2(24) = -26
x = -26 + 48 = 22

Answer is x = 22 and y = 24

4 0

3 years ago

Can somebody please help i’ll make you brainlest answerr

RideAnS [48]

Answer:

3

Step-by-step explanation:

subtract

8 0

3 years ago

Determine the factors of 3x2 + 10x − 8. (Which is the right answer?)

VMariaS [17]

ANSWER

$(3x - 2)(x + 4)$

EXPLANATION

The given quadratic trinomial is

$3 {x}^{2} + 10x - 8$

Comparing to the general quadratic trinomial:

$a{x}^{2} + bx + c$

We have a=1, b=10 and c=-8

$ac = 3 \times - 8 = - 24$

The factors of -24 that adds up to 10 are -2 and 12.

We split the middle term to obtain;

$3 {x}^{2} + 12x - 2x- 8$

Factor;

$3x(x+ 4) - 2(x + 4)$

Factor further;

$(3x - 2)(x + 4)$

The last option is correct.

4 0

3 years ago