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Yakvenalex [24]
3 years ago
9

5) Mario owns a plumbing business. He charges an hourly rate plus a onetime set up fee. His first job was 4 hours and he charged

$450. His second job was 3 hours and he charged $675. If his set up fee is $150, how much does he charge per hour?
Mathematics
1 answer:
Wittaler [7]3 years ago
5 0

Answer:

Results are below.

Step-by-step explanation:

<u>First, we need to calculate the variable income per job:</u>

<u />

First job= 450 - 150= 300

Second job= 675 - 150= 525

<u>Now, the hourly rate:</u>

<u></u>

Hourly rate= total variable income / number of hours

First job= 300 / 4= $75

Second job= 525 / 3= $175

It is probably that the second job was 7 hours long. If not, he doesn't charge the same amount per hour

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(m+3n) ^2 please help me solve this question, I really need it
Charra [1.4K]

Answer:

=m2+6mn+9n2

Step-by-step explanation:

=(m+3n)(m+3n)

=(m)(m)+(m)(3n)+(3n)(m)+(3n)(3n)

=m2+3mn+3mn+9n2

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-x+4= 2x+1 equation steps
kykrilka [37]

-x + 4 = 2x + 1

add x to both sides

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subtract 1 from both sides

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4 0
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There are eight boxes. Each box holds one sweater. There are 3 blue, 2 brown, 1 green, and 2 red sweaters. What is the probabili
Reil [10]

3 + 2 + 1 + 2 = 8, which is the amount of sweaters.
The probability of a brown sweater is 2 / 8 = 0.25
And the probability of a green sweater is 1 / 8 = 0.125.

Multiply the two probabilities together to get the probability of choosing brown then green:
0.25 * 0.125 = 0.03125.

To convert a decimal to fraction, you multiply the numerator and denominator, or in this case \frac{0.03125}{1} by 1000 which gets \frac{31.25}{1000}

Which can be simplified to:
\frac{1}{32}.

Hope this helps.
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3 years ago
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7) PG &amp; E have 12 linemen working Tuesdays in Placer County. They work in groups of 8. How many
BabaBlast [244]

Part A

Since order matters, we use the nPr permutation formula

We use n = 12 and r = 8

_{n}P_{r} = \frac{n!}{(n-r)!}\\\\_{12}P_{8} = \frac{12!}{(12-8)!}\\\\_{12}P_{8} = \frac{12!}{4!}\\\\_{12}P_{8} = \frac{12*11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1}\\\\_{12}P_{8} = \frac{479,001,600}{24}\\\\_{12}P_{8} = 19,958,400\\\\

There are a little under 20 million different permutations.

<h3>Answer: 19,958,400</h3>

Side note: your teacher may not want you to type in the commas

============================================================

Part B

In this case, order doesn't matter. We could use the nCr combination formula like so.

_{n}C_{r} = \frac{n!}{r!(n-r)!}\\\\_{12}C_{8} = \frac{12!}{8!(12-8)!}\\\\_{12}C_{8} = \frac{12!}{4!}\\\\_{12}C_{8} = \frac{12*11*10*9*8!}{8!*4!}\\\\_{12}C_{8} = \frac{12*11*10*9}{4!} \ \text{ ... pair of 8! terms cancel}\\\\_{12}C_{8} = \frac{12*11*10*9}{4*3*2*1}\\\\_{12}C_{8} = \frac{11880}{24}\\\\_{12}C_{8} = 495\\\\

We have a much smaller number compared to last time because order isn't important. Consider a group of 3 people {A,B,C} and this group is identical to {C,B,A}. This idea applies to groups of any number.

-----------------

Another way we can compute the answer is to use the result from part A.

Recall that:

nCr = (nPr)/(r!)

If we know the permutation value, we simply divide by r! to get the combination value. In this case, we divide by r! = 8! = 8*7*6*5*4*3*2*1 = 40,320

So,

_{n}C_{r} = \frac{_{n}P_{r}}{r!}\\\\_{12}C_{8} = \frac{_{12}P_{8}}{8!}\\\\_{12}C_{8} = \frac{19,958,400}{40,320}\\\\_{12}C_{8} = 495\\\\

Not only is this shortcut fairly handy, but it's also interesting to see how the concepts of combinations and permutations connect to one another.

-----------------

<h3>Answer: 495</h3>
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Hey! jeny.

︎⠀⠀⠀⠀⠀⠀⠀⠀⠀How are you?

3 0
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