Find two numbers whose sum 7500 and whose product is the maximum value.
(Round your answer to the nearest whole number.)
Blank = 1
Blank = 2

Answers

Answer 1

The two numbers whose sum is 7500 and whose product  is a maximum value are 3750 and 3750.

Let the two numbers be x and y.

Since their sum equals 7500,

x + y = 7500  (1)

Their product f(x,y) = xy  (2)

We desire to maximize the product.

From (1), x = 7500 - y

Substituting x into (2), we have

f(x,y) = xy

f(x,y) = (7500 - y)y

f(y) = 7500y - y²

To maximize the product, we find the value of y that maximizes f(y), we differentiate f(y) and equate it to zero.

So, df(y)/dy = d(7500y - y²)/dy

f'(y)/dy = d(7500y)/dy - dy²/dy

f'(y)/dy = 7500 - 2y

Equating it to zero, we have

7500 - 2y = 0

7500 = 2y

y = 7500/2

y = 3750

To determine if this gives a maximum for f(y), we differentiate f'(y) with respect to y.

So, f"(y) = d(7500 - 2y)dy

f"(y) = 0 - 2

f"(y) = -2 < 0.

So, y = 3750 gives a maximum for f(y) = f(x, y)

Since x = 7500 - y

Substituing y = 3750 into the equation, we have

x = 7500 - 3750

x = 3750

So, the two numbers whose sum is 7500 and whose product is a maximum product are 3750 and 3750.

Learn more about product of two numbers here:

https://brainly.com/question/15607519


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L=30 W=15

Step-by-step explanation:

90 divided by 6 is 15. 15 is the Width. Multiply 15 by 2 and you get 30 which is the Length.

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

Answer:

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Answers

Answer:

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Step-by-step explanation:

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23 seconds later Erin will catch up

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Answer:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Answer:

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Step-by-step explanation:

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Answer:

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[tex]\rule{2000pt}{1000000pt}[/tex]

3
Johnny has been hired to draw a mural on the window of the pet store. The scale drawing he is using is shown below.
4.5 cm
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OA.
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ОВ.
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Answer:

OD 60 in by 45 in

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

i really don’t know 555

[tex]x = 23[/tex]

Step-by-step explanation:

First, we need to write the equations in their standard form, i.e., all the variables and their coefficients are to be placed on the left hand side and the plain numbers on the right hand side. The first equation is already in its standard form:

[tex]2x + 5y = 35\;\;\;\;\;(1)[/tex]

but we need to rewrite the 2nd one. So the standard form of the 2nd equation can be written as

[tex]x + 15y = -10\;\;\;\;\;(2)[/tex]

Now that the equations are in their standard forms, the next step that we need to do is to eliminate one of the variables, namely the y. To do that, we need to multiply either one of the equations so that when we add them together, the y-variable gets eliminated. Note if we multiply Eqn(1) by -3, we'll get -15y on one equation and a +15y on the other equation so that when they are added together, they cancel out. So if we do that, we get

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or

[tex]x = \dfrac{-115}{-5} = 23[/tex]

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Answers

Answer:

[tex]-2^{-2} = \frac{1}{-2^{2} } = \frac{1}{4} = 0.25[/tex]

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[tex]-2^{1} = -2[/tex]

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Step-by-step explanation:

Write -37.75 as a mixed number.​

Answers

Answer:

[tex]-37\frac{3}{4}[/tex]

Step-by-step explanation:

0.75 is equivalent to three quarters, or (3/4).

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[tex]-37.75 = \boxed{-37\frac{3}{4}}[/tex]

Hope this helps.

Answer:

- 37 3/4

Step-by-step explanation:

Dog slept 3 hours . If the dog snored 1/3 of an hour . How many times did he snore

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Answer:

it depends how much the god snores within a certain time period

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Answers

Answer:

huh

Step-by-step explanation:

2 + 2 = 3
prove me wrong

Answers

Answer:

2+2=4................

Answer:

you are wrong because 2+2=4

Answer them all please ​

Answers

Answer:

see the attachment

i hope it helps u ✌️✌️✌️☠️

a) The highest common factor and the least common multiple are 12 and 48, respectively.

b) The highest common factor and the least common multiple are 12 and 72, respectively.

c) The highest common factor and the least common multiple are 8 and 160, respectively.

d) The highest common factor and the least common multiple are 12 and 48, respectively.

e) The highest common factor and the least common multiple are 14 and 840, respectively.

Procedure - Determination of the Highest Common Factor and the Least Common Multiple of two integers

In this question we must determine the highest common factor and the least common multiple of two integers.

The highest common factor consists in the maximum product of common prime numbers, of the two numbers that divides it, and the least common multiple consists in the product of prime numbers, common and not, of the two numbers, that creates a product that it is greater or equal to the greater integer.

Now, we proceed to determine the numbers for each case:

a) 12 and 48

First, we factorize each integer:

[tex]12 = 2^{2}\times 3[/tex], [tex]48 = 2^{4}\times 3[/tex]

Then the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{4}\times 3 = 48[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]

The highest common factor and the least common multiple are 12 and 48, respectively. [tex]\blacksquare[/tex]

b) 24 and 36

First, we factorize each integer:

[tex]24 = 2^{3}\times 3[/tex], [tex]36 = 2^{2}\times 3^{2}[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{3}\times 3^{2} = 72[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]

The highest common factor and the least common multiple are 12 and 72, respectively. [tex]\blacksquare[/tex]

c) 32 and 40

First, we factorize each integer:

[tex]32 = 2^{5}[/tex], [tex]40 = 2^{3}\times 5[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{5}\times 5 = 160[/tex], [tex]HCF = 2^{3} = 8[/tex]

The highest common factor and the least common multiple are 8 and 160, respectively. [tex]\blacksquare[/tex]

d) 24, 48 and 60

First, we factorize each integer:

[tex]24 = 2^{3}\times 3[/tex], [tex]48 = 2^{4}\times 3[/tex], [tex]60 = 2^{2}\times 3 \times 5[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{4}\times 3 \times 5 = 48[/tex], [tex]HCF = 2^{2}\times 3 = 12[/tex]

The highest common factor and the least common multiple are 12 and 48, respectively. [tex]\blacksquare[/tex]

e) 42, 56 and 70

First, we factorize each integer:

[tex]42 = 2\times 3 \times 7[/tex], [tex]56 = 2^{3}\times 7[/tex], [tex]70 = 2\times 5\times 7[/tex]

Then, the highest common factor and the least common multiple are, respectively:

[tex]LCM = 2^{3} \times 3 \times 5 \times 7 = 840[/tex], [tex]HCF = 2\times 7 = 14[/tex]

The highest common factor and the least common multiple are 14 and 840, respectively. [tex]\blacksquare[/tex]

To learn more on prime numbers, we kindly invite to check this verified question: https://brainly.com/question/4184435

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show all work

Answers

Answer:

(4 − 3)(−3 + 6) − (2 )

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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