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Temka [501]
3 years ago
15

The amount of money it takes to fill up a gas tank varies directly with the number of gallons bought. It cost $21.87 to fill up

a car with gasoline with 9 gallons of gasoline. What is the constant of variation?
Mathematics
2 answers:
Snowcat [4.5K]3 years ago
8 0
I think the answer is 

2.43
Arisa [49]3 years ago
6 0

Answer:

$2.43 per gallon of gas.

Step-by-step explanation:

We have been given that the amount of money it takes to fill up a gas tank varies directly with the number of gallons bought.

We know that the equation for two directly proportional quantities is in form: y=kx, where,

k = The constant of variation and y is directly proportional to x.

To find the constant of variation for our given equation, we will substitute the given values in above equation as:

\$21.87=k*9\text{ gallons}

Let us divide both sides of our equation by 9 gallons.

\frac{\$21.87}{9\text{ gallons}}=\frac{k*9\text{ gallons}}{9\text{ gallons}}

\frac{\$2.43}{\text{ gallon}}=k

Therefore, the constant of variation is $2.43 per gallon of gas.

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2. In a given population of two-earner male-female couples, male earnings have a mean of $40,000 per year and a standard deviati
Kobotan [32]

Answer: $85,000

Step-by-step explanation:

Given : In a given population of two-earner male-female couples, male earnings have a mean of $40,000 per year and a standard deviation of $12,000.

\mu_M=40,000\ \ ;\sigma_M=12,000

Female earnings have a mean of $45,000 per year and a standard deviation of $18,000.

\mu_F=45,000\ \ ;\sigma_F=18,000

If  C denote the combined earnings for a randomly selected couple.

Then, the mean of C will be :-

\mu_c=\mu_M+\mu_F\\\\=40,000+45,000=85,000

Hence, the mean of C = $85,000

8 0
3 years ago
The Mad Hat Company must ship two different-sized boxes: The small ones cost them 45 cents each and weigh 6 ounces, and the larg
Viefleur [7K]

Given :

The Mad Hat Company must ship two different-sized boxes: The small ones cost them 45 cents each and weigh 6 ounces, and the large ones weigh 25 ounces and cost $1.20 each.

The total shipment this morning weighed 20 pounds 7 ounces and cost $18.45.

To Find :

How many packages of each size were shipped.

Solution :

We know, 1 pound = 16 ounces.

So, 20 pound = 20×16 = 320 ounces.

Let, number of large and small box are l and s.

So,

25l + 6s = 327 ...1)

0.45s + 1.20l = 18.45 ...2)

Solving both the equations, we get :

x = 9 and y = 17

Therefore, package smaller and big size are 17 and 9 respectively .

Hence, this is the required solution.

6 0
3 years ago
The length of the hypotenuse of the right triangle is 25 cm, the length of one of the legs is 10 cm. What is the length of the s
Anna007 [38]

Answer:

  21 cm

Step-by-step explanation:

Call the triangle ABC, with the right angle at B, the hypotenuse AC=25, and the given leg AB=10. The altitude to the hypotenuse can be BD. Since the "other leg" is BC, we believe the question is asking for the length of DC.

The right triangles formed by the altitude are all similar to the original. That means ...

  AD/AB = AB/AC . . . . . . ratio of short side to hypotenuse is a constant

Multiplying by AB and substituting the given numbers, we get ...

  AD = AB²/AC = 10²/25

  AD = 4

Then the segment DC is ...

  DC = AC -AD = 25 -4

  DC = 21 . . . . . centimeters

6 0
3 years ago
If f(x) = 2x² - 6x + 8, find f(a - 2).
yan [13]

Answer: f(a-2) = 2a² - 14a + 28

Step-by-step explanation:

f(x) = 2x² - 6x + 8

you can take a-2 and substitute it for each x, which would look like this:

f(a-2) = 2(a-2)² - 6(a-2) + 8

then distribute those in ( )

f(a-2) = 2a² - 8a + 8 - 6a + 12 + 8

combine like terms

f(a-2) = 2a² - 14a + 28

7 0
2 years ago
10) Find the area of a circle that has the<br> circumference of 117 cm. Leave it as it.
garik1379 [7]

Step-by-step explanation:

Using the formulas

A

=

π

r

2

C

=

2

π

r

Solving for

A

A

=

C

2

4

π

=

117

2

4

·

π

≈

1089.33601

cm²

A

≈

1089.34

cm²

8 0
3 years ago
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