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Mariulka [41]
3 years ago
15

The equation a company uses to

Mathematics
1 answer:
crimeas [40]3 years ago
5 0

The equation solved for s is s = 4p - 48h

<em><u>Solution:</u></em>

Given that equation a company uses to  calculate pay checks is p = 12h +0.25s

Therefore the given equation is:

p = 12h + 0.25s

Where "h" is the number of hours worked

"s" is the total sales

To find: equation for "s"

Let us solve the given equation for "s"

p = 12h + 0.25s

Now move 12h from R.H.S to L.H.S

p - 12h = 0.25s

Now move from 0.25 from R.H.S to L.H.S

s = \frac{p-12h}{0.25}\\\\s = \frac{p}{0.25} -\frac{12h}{0.25}

We know that, 0.25 = \frac{1}{4}

s = \frac{p}{\frac{1}{4}} -\frac{12h}{\frac{1}{4}}\\\\s = p \times \frac{4}{1} - 12h \times \frac{4}{1}\\\\s = 4p - 48h

Thus the equation for s is s = 4p - 48h

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A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an
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<h3>27 different dessert platters can be offered by restaurant</h3>

<em><u>Solution:</u></em>

Given that,

A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter

Each dessert platter contains an equal number of kinds of cheese and kinds of fruit

<em><u>For this problem there are two scenarios: </u></em>

1 ) one cheese and one fruit

2 ) two cheese and two fruit

<em><u>For one cheese and one fruit</u></em>

<em><u></u></em>6C_1 \times 2C_1

Use the combination formula

C(n, r) = \frac{n !}{r ! (n-r) ! }

Where, n is total items and r is the items being chosen at a time

6C_1 \times 2C_1 = \frac{ 6 ! }{ 1 ! (6 - 1) ! } \times \frac{ 2 ! }{ 1 ! ( 2 -1 ) ! }\\\\6C_1 \times 2C_1 = \frac{ 6 ! }{ 1 ! 5 ! } \times \frac{ 2 ! }{ 1 ! 1 ! }\\\\6C_1 \times 2C_1 = \frac{ 6 \times 5 \times 4 \times 3 \times 2 \times 1}{ 5 \times 4 \times 3 \times 2 \times 1} \times 2 \times 1\\\\6C_1 \times 2C_1 = 6 \times 2 = 12

<em><u>For 2 cheese and 2 fruits</u></em>

6C_2 \times 2C_2

6C_2 \times 2C_2 = \frac{ 6 ! }{ 2 ! ( 6 - 2) ! } \times 2C_2\\\\We\ know\ that\ 2C_2 = 1\\\\6C_2 \times 2C_2 = \frac{ 6 ! }{ 2 ! ( 6 - 2) ! } \times  1\\\\6C_2 \times 2C_2 = \frac{ 6 \times 5 \times 4 \times 3 \times 2 \times 1 }{2 \times 1 \times 4 \times 3 \times 2 \times 1 }\\\\6C_2 \times 2C_2 = 15

So, total ways = 12 + 15 = 27

Thus, 27 different dessert platters can be offered by restaurant

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