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3 years ago

Carole has $53.95 and washes cars for $8 each. Carole wants to attend a musical that costs $145.75.

Mathematics

2 answers:

V125BC [204]3 years ago

8 0

Answer:

Step-by-step explanation:

Let x represent the minimum number of cars Carole must wash to be able to buy the ticket to the musical.

Carole has $53.95 and washes cars for $8 each. This means that the total amount that she would earn after washing x cars is

8x + 53.95

Carole wants to attend a musical that costs $145.75. Therefore, the inequality to determine the minimum number of cars that Carole must wash to be able to buy the ticket to the musical is

8x + 53.95 ≥ 145.75

8x ≥ 145.75 - 53.95

8x ≥ 91.8

x ≥ 91.8/8

x ≥ 11.475

b) it is not the same. The minimum number of cars that Carole must wash is 12 because the number of cars cannot be a fraction and if she washes 11 cars, she cannot raise the needed amount.

yawa3891 [41]3 years ago

6 0

Answer:

53.95+8x ≥145.75

Carole needs to wash at leas 12 cars

Step-by-step explanation:

A. 53.95+8x ≥145.75

subtract 53.95

8x ≥91.8

divide by 8

x ≥11.475

round

Carole needs to wash at leas 12 cars

b. what is the solution?

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Case n =5

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Case n =15

$z=\frac{4.8-5}{\frac{0.5}{\sqrt{15}}}=-1.549$

Case n = 40

$z=\frac{4.8-5}{\frac{0.5}{\sqrt{40}}}=-2.530$

P value

Case n =5

$p_v =P(z$

Case n =15

$p_v =P(z$

Case n =40

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Step-by-step explanation:

Data given and notation

$\bar X=4.8$ represent the sample mean

$\sigma=0.5$ represent the population standard deviation

$n$ sample size

$\mu_o =5$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

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We need to conduct a hypothesis in order to check if the mean is lower than 5, the system of hypothesis would be:

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Alternative hypothesis: $\mu < 5$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

Case n =5

$z=\frac{4.8-5}{\frac{0.5}{\sqrt{5}}}=-0.894$

Case n =15

$z=\frac{4.8-5}{\frac{0.5}{\sqrt{15}}}=-1.549$

Case n = 40

$z=\frac{4.8-5}{\frac{0.5}{\sqrt{40}}}=-2.530$

P-value

Since is a left tailed test the p value would be:

Case n =5

$p_v =P(z$

Case n =15

$p_v =P(z$

Case n =40

$p_v =P(z$

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