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2 years ago

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10. Victoria has a coupon for 30% off of any item in a department store. She decides to purchase a treadmill. The original price

of the treadmill is $595. There is also 7% sales tax in her state. What is the final price of the treadmill, including tax? *

1 answer:

KonstantinChe [14]2 years ago

6 0

Answer:

Step-by-step explanation:

Original price $595.00

Discount amount 595(0.30) = $178.50

Pre tax price 595.00 - 178.50 = $416.50

tax amount 416.50(0.07) = 29.155 = $29.16

cost to Victoria 416.50 + 29.16 = $445.66

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2. In how many ways can 3 different novels, 2 different mathematics books and 5 different chemistry books be arranged on a books

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The number of ways of the books can be arranged are illustrations of permutations.

When the books are arranged in any order, the number of arrangements is 3628800
When the mathematics book must not be together, the number of arrangements is 2903040
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The given parameters are:

$\mathbf{Novels = 3}$

$\mathbf{Mathematics = 2}$

$\mathbf{Chemistry = 5}$

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<u>(a) The books in any order</u>

First, we calculate the total number of books

$\mathbf{n = Novels + Mathematics + Chemistry}$

$\mathbf{n = 3 + 2 + 5}$

$\mathbf{n = 10}$

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$\mathbf{n! = 10!}$

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If the mathematics books, must be together

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$\mathbf{Maths\ together = 2 \times 9!}$

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$\mathbf{Maths\ not\ together = 3628800 - 2 \times 9!}$

$\mathbf{Maths\ not\ together = 2903040}$

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We have:

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the novels in:

$\mathbf{Novels = 3!\ ways}$

Next, arrange the chemistry books in:

$\mathbf{Chemistry = 5!\ ways}$

Now, the 5 chemistry books will be taken as 1; the novels will also be taken as 1.

Literally, the number of books now is:

$\mathbf{n =Mathematics + 1 + 1}$

$\mathbf{n =2 + 1 + 1}$

$\mathbf{n =4}$

So, the number of arrangements is:

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$\mathbf{Arrangements = 4! \times 3! \times 5!}$

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We have:

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$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the mathematics in:

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$\mathbf{n =Chemistry + 1}$

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So, the total arrangement is:

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$\mathbf{Total = 302400}$

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