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Ira Lisetskai [31]
3 years ago
5

Julio bought soccer shoes at a $35% off sale and saved $42. What was the regular price of the shoes?

Mathematics
2 answers:
Alborosie3 years ago
8 0

Answer:

$120

Step-by-step explanation:

35% : 42

100% : X

42/35 = X/100

X = 100×42/35

X = $120

Mekhanik [1.2K]3 years ago
4 0

Original price was 120.

35/100 ÷ 5 = 7/20 (reduce)

7/20 × ? = 42/?

42 ÷ 7 = 6

7/20 × 6 = 42/120

so 120 was the regular price.

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A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained p
Studentka2010 [4]

Using the z-distribution, it is found that the needed sample sizes are:

a) 242

b) 1842

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of \alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which z is the z-score that has a p-value of \frac{1+\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

99% confidence level, hence\alpha = 0.99, z is the value of Z that has a p-value of \frac{1+0.99}{2} = 0.995, so z = 2.575.

Item a:

The estimate is:

\pi = 0.223 - 0.189 = 0.034

The sample size is <u>n for which M = 0.03</u>, then:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.03 = 2.575\sqrt{\frac{0.034(0.966)}{n}}

0.03\sqrt{n} = 2.575\sqrt{0.034(0.966)}

\sqrt{n} = \frac{2.575\sqrt{0.034(0.966)}}{0.03}

(\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.034(0.966)}}{0.03}\right)^2

n = 241.97

Rounding up, a sample of 242 is needed.

Item b:

No prior estimates, hence \pi = 0.5 is used.

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.03 = 2.575\sqrt{\frac{0.5(0.5)}{n}}

0.03\sqrt{n} = 2.575\sqrt{0.5(0.5)}

\sqrt{n} = \frac{2.575\sqrt{0.5(0.5)}}{0.03}

(\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.5(0.5)}}{0.03}\right)^2

n = 1841.8

Rounding up, a sample of 1842 is needed.

For more on the z-distribution, you can check brainly.com/question/25404151

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Answer:

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