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3 years ago

Her senior year of college, Giselle decides to live off campus. In order to cover rent, she wants to get a job as a waitress.

1 answer:

5 0

She would have to work at least 12 hours.

At Chili’s, she would be paid 11.75x + 33 per week, with x being the number of hours she worked.

At the Cheesecake Factory, Giselle would be paid 14.50x per week, with x being how many hours she worked.

We want to know how many hours Gisele would have to work for her pay at the Cheesecake Factory to be more than her pay at Chili’s

The inequality 11.75x + 33 < 14.50x is what has to be set up to solve the problem. At how many hours will the pay on the left be less than the pay on the right?

11.75x + 33 < 14.50x
33 < 2.75x
12 < x

So Giselle has to work greater 12 hours a week for her to make more money at the Cheesecake Factory.

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It is Irrational because is can not be written as a fraction

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Step-by-step explanation:

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3 years ago

A student solves the following equation and

Phoenix [80]

Answer:

Since the equation is undefined for -2

Therefore, NO SOLUTION for the given equation.

Step-by-step explanation:

Considering the expression

$\frac{3}{a+2}-6\cdot \frac{a}{-4+a^2}=\frac{1}{a-2}$

$\frac{3}{a+2}-\frac{6a}{-4+a^2}=\frac{1}{a-2}$

$\mathrm{Find\:Least\:Common\:Multiplier\:of\:}a+2,\:-4+a^2,\:a-2:\quad \left(a+2\right)\left(a-2\right)$

$\mathrm{Multiply\:by\:LCM=}\left(a+2\right)\left(a-2\right)$

$\frac{3}{a+2}\left(a+2\right)\left(a-2\right)-\frac{6a}{-4+a^2}\left(a+2\right)\left(a-2\right)=\frac{1}{a-2}\left(a+2\right)\left(a-2\right)$

$\frac{3}{a+2}\left(a+2\right)\left(a-2\right):\quad 3\left(a-2\right)$

$-\frac{6a}{-4+a^2}\left(a+2\right)\left(a-2\right):\quad -6a$

$\frac{1}{a-2}\left(a+2\right)\left(a-2\right):\quad a+2$

so equation becomes

$3\left(a-2\right)-6a=a+2$

$-3a-6=a+2$

$-3a-6+6=a+2+6$

$-4a=8$

$\mathrm{Divide\:both\:sides\:by\:}-4$

$\frac{-4a}{-4}=\frac{8}{-4}$

$a=-2$

$\mathrm{Verify\:Solutions}$

$\mathrm{Take\:the\:denominator\left(s\right)\:of\:}\frac{3}{a+2}-6\frac{a}{-4+a^2}-\frac{1}{a-2}\mathrm{\:and\:compare\:to\:zero}$

$\mathrm{Solve\:}\:a+2=0:\quad a=-2$

$\mathrm{Solve\:}\:-4+a^2=0:\quad a=2,\:a=-2$

$\mathrm{Solve\:}\:a-2=0:\quad a=2$

So the following points are undefined

$a=-2,\:a=2$

Since the equation is undefined for -2

Therefore, NO SOLUTION for the given equation.

4 0

3 years ago

A new roller coaster at an amusement park requires individuals to be at least 4' 8" (56 inches) tall to ride. It is estimated

Maksim231197 [3]

Answer:

a) 34.46% of 10-year-old boys is tall enough to ride this coaster.

b) 78.81% of 10-year-old boys is tall enough to ride this coaster

c) 44.35% of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a

Step-by-step explanation:

When the distribution is normal, we use 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.

In this question, we have that:

$\mu = 54, \sigma = 5$

a. What proportion of 10-year-old boys is tall enough to ride the coaster?

This is 1 subtracted by the pvalue of Z when X = 56.

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

$Z = \frac{56 - 54}{5}$

$Z = 0.4$

$Z = 0.4$ has a pvalue of 0.6554

1 - 0.6554 = 0.3446

34.46% of 10-year-old boys is tall enough to ride this coaster.

b. A smaller coaster has a height requirement of 50 inches to ride. What proportion of 10-year-old boys is tall enough to ride this coaster?

This is 1 subtracted by the pvalue of Z when X = 50.

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

$Z = \frac{50 - 54}{5}$

$Z = -0.8$

$Z = -0.8$ has a pvalue of 0.2119

1 - 0.2119 = 0.7881

78.81% of 10-year-old boys is tall enough to ride this coaster.

c. What proportion of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a?

Between 50 and 56 inches, which is the pvalue of Z when X = 56 subtracted by the pvalue of Z when X = 50.

From a), when X = 56, Z has a pvalue of 0.6554

From b), when X = 50, Z has a pvalue of 0.2119

0.6554 - 0.2119 = 0.4435

44.35% of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a

5 0

3 years ago