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2 years ago

A bookstore costs $105 a day to keep open, and it spends $12 for each book

Mathematics

1 answer:

Alex2 years ago

4 0

After selling 35 books, the store will break-even.

Step-by-step explanation:

Given,

Cost required per day to keep store open = $105

Amount spent on each book = $12

Let,

n be the number of books.

Total costs = 12n + 105

Selling price of each book = $15

Total revenue = 15n

For braking even;

Costs = Revenue

$12n+105=15n\\105=15n-12n\\105=3n\\3n=105$

Dividing both sides by 3

$\frac{3n}{3}=\frac{105}{3}\\n=35$

After selling 35 books, the store will break-even.

Keywords: revenue, cost, division

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2 years ago

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Answer:

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Step-by-step explanation:

We are given that a pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome).

In the first stages of a clinical trial, it was successful for 7 out of the 14 women.

Firstly, the pivotal quantity for 95% confidence interval for the true proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of women who find success with this new treatment = $\frac{7}{14}$ = 0.50

n = sample of women = 14

Here for constructing 95% confidence interval we have used One-sample z proportion statistics.

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P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

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P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.50-1.96 \times {\sqrt{\frac{0.50(1-0.50)}{14} } }$ , $0.50+1.96 \times {\sqrt{\frac{0.50(1-0.50)}{14} } }$ ]