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3 years ago

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Mathematics

1 answer:

Shalnov [3]3 years ago

5 0

$y = 0.25x + 40$

$60 = 0.25x + 40$

$60 - 40 = 0.25x + 40 - 40$

$20 = 0.25x$

$\frac{20}{0.25} = \frac{0.25x}{0.25}$

$80 = x$

She can buy a maximum of 80 cups.

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The largest perfect square factor of 252 is _____

slega [8]

Answer:

Step-by-step explanation:

252 is a composite number. The exponents in the prime factorization are 2, 2, and 1. Adding one to each and multiplying we get (2 + 1)(2 + 1)(1 + 1) = 3 x 3 x 2 = 18. Therefore 252 has 18 factors.

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3 years ago

A rectangular box has a base that is 4 times as long as it is wide. The sum of the height and the girth of the box is 200 feet.

enyata [817]

Answer: V(W) = (1/3)*(*W^2*800ft - 8W^3) and the domain is 0 < W < 100ft.

Step-by-step explanation:

The dimensions of the box are:

L = length

W = width

H = heigth.

We know that:

L = 4*W

And the girth of a box is equal to: G = 2*W + 2*H

then we have:

2*W + 2*H + H = 200ft

2W + 3*H = 200ft

Then we have two equations:

L = 4*W

2W + 3*H = 200ft

We want to find the volume of the box, which is V = W*L*H

and we want in on terms of W.

Then, first we can replace L by 4*W (for the first equation)

and:

2*W + 3*H = 200ft

3*H = 200ft - 2*W

H = (200ft - 2*W)/3.

then the volume is:

V(W) = W*(4*W)*(200ft - 2*W)/3

V(W) = (1/3)*(*W^2*800ft - 8W^3)

The domain of this is the set of W such that the volume is positive, then we must have that:

W^2*800ft > 8W^3

To find the maximum W we can see the equality (the minimum extreme is 0 < W, because the width can only be a positive number)

W^2*800ft = 8W^3

800ft = 8*W

100ft = W.

This means that if W is equal or larger than 100ft, the equation gives a negative volume.

Then the domain is 0 < W < 100ft.

6 0

3 years ago

Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR)

babymother [125]

Answer:

<em>The monthly payment is $450.71</em>

Step-by-step explanation:

<u>Financial Computing </u>

Given the loan amount A, the loan term t, and the APR (annual percentage rate), the montly payment is computed as

$\displaystyle P=\frac{A}{f}$

where f is

$\displaystyle f=\frac{1-(1+i)^{-n}}{i}$

The provided data is

$\displaystyle A=24,000$

$\displaystyle r=4.8\%$

$\displaystyle t=5\ years$

Since the payments will be made monthly, the values of n and i are:

$\displaystyle i=\frac{4.8}{100\times12}=0.004$

$\displaystyle n=5\times12=60\ months$

Calculating f:

$\displaystyle f=\frac{1-(1+i)^{-n}}{i}$

$\displaystyle f=\frac{1-(1+0.004)^{-60}}{0.004}$

$\displaystyle f=53.25$

Now for the payments:

$\displaystyle P=\frac{24.000}{53.25}=450.71$

$\boxed{\displaystyle P=\$450.71}$

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3 years ago

A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call

polet [3.4K]

Answer:

$p(1)=p(2)=p(3)=p(4)=0.25$

Step-by-step explanation:

-The total number of outcomes is 4.

-Given that the outcomes occur with the same frequency.

-Therefore they all occur with the same frequency, 1/4=0.25

$p(1)=p(2)=p(3)=p(4)=0.25$

-The probability distribution for the duration of a service call is attached.

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3 years ago

The area of a rectangular patio is 27 5 8 square meters. The width of the patio is 3 1 4 meters. What is the length? Enter your

DedPeter [7]

Answer:

Step-by-step explanation:

L and W are length and width, respectively.

W = 3¼ = 13/4

Area = LW = 27⅝ = 221/8 m²

L = area/W = (221/8)/(13/4) = (221/8)(4/13) + 221/26 = 17/2 = 8½ m

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3 years ago