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3 years ago

5

the original price of a coat was $290.00, the store put the coat on sale for $175.70 how much did the store reduce the price of

the coat

2 answers:

Ghella [55]3 years ago

7 0

2.90 - 175.70 = 114.3

UkoKoshka [18]3 years ago

3 0

Inital-sale
$290.00
-$175.70
--------------
=$114.3

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A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence

Varvara68 [4.7K]

Answer:

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

$n = 30$ -- sample size

$\bar x = 50$ -- sample mean

$\sigma = 10$ --- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {30}}$

$\sigma_x = \frac{10}{5.478}$

$\sigma_x = 1.825$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.825$

$E = 3.577$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 3.577$

$Lower = 46.423$

$Lower = 46.4$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 3.577$

$Upper = 53.577$

$Upper = 53.6$ --- approximated

<em>So, the 95% confidence interval is (46.4, 53.6)</em>

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{10}{\sqrt {90}}$

$\sigma_x = \frac{10}{9.49}$

$\sigma_x = 1.054$

The 95% confidence interval for the z value is:

$z = 1.960$

Calculate margin of error (E)

$E = z * \sigma_x$

$E = 1.960 * 1.054$

$E = 2.06584$

The confidence bound is:

$Lower = \bar x - E$

$Lower = 50 - 2.06584$

$Lower = 47.93416$

$Lower = 47.9$ --- approximated

$Upper = \bar x + E$

$Upper = 50 + 2.06584$

$Upper = 52.06584$

$Upper = 52.1$ --- approximated

<em>So, the 95% confidence interval is (47.9, 52.1)</em>

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

$n = 30$ $E = 3.577$

In (b), we have:

$n = 90$ $E = 2.06584$

<em>Notice that the margin of error decreases when the sample size increases.</em>

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3 years ago

A pair of basketball shoes was originally priced at $80, but was marked up 47.5%. What was the retail

Lelu [443]

47.5% in decimal form is 0.475.

Since the price was increased, we add 1 to 0.475 to get 1.475.

80 * 1.475 = 118

Another way to solve this is to multiply 80 by 0.475, which is 38, then add it to 80.

The retail price of the shoes is $118.

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MrRa [10]

Parallel = same slope
y = -2/3x + b
Plug in point
15 = -2/3(-3) + b
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3 years ago

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GrogVix [38]

Answer: 12 days

Step-by-step explanation:

For us to know the number of days whereby Julie will have both basketball and track practice, we've to find the lowest common multiple of both 6 and 4. This will be:

Multiples of 4 = 4, 8, 12, 16, 24.

Multiples of 6 = 6, 12, 18, 24, 30.

The lowest common multiple is 12. Therefore, she'll have basketball and track practice in 12 days

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3 years ago

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iris [78.8K]

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4 years ago