Choose the scenario that describes a proportional relationship.




Miguel earns $7.50 per hour while babysitting.


A hotel charges a flat rate of $12.00 to park in their parking lot.


A cellphone plan is $25 plus $0.05 per megabyte, MB, of data usage.


Raphael sells paintings for $200 each at a market but has to pay $100 to reserve a table.

Answer:

D: 14.5

Step-by-step explanation:

4.1 = d - 10.4    add 10.4 to each side

14.5 = d

Answer:

14.5

Step-by-step explanation:

10.4 - 4.1 = 14.5

Answer:

112

Step-by-step explanation:

16 ounce multiply that by 7. 112. This correct i googed it

Answer:

x=-13

Step-by-step explanation:

Hope this helped :)

Answer:

x = -13

Step-by-step explanation:

-2x + 10 + 3x = 2x + 6 + 17

x + 10 = 2x + 6 + 17

x + 10 = 2x + 23

10 = 2x + 23 - x

10 = x + 23

10 - 23 = x

-13 = x

x = -13

Answer:

6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Multiply the 2 denominators which gives you 6. P.S make sure to do cross multiplication for the numerator cause if the rest of the question asks for the full answer then you would get it wrong if you don't.

Answer:

D

Step-by-step explanation:

the equation for Josh is 500 + 40x while the equation for Vanessa is only 60x

if josh's account balance is greater than it would be josh > vanessa or vanessa < josh

Answer:

56p + 48q + 88

Step-by-step explanation:

When you see parentheses in math, it usually means that you are distributing (multiplying).

So here you would multiply everything inside the parentheses by 8.

7q x 8 = 56q

6p x 8 = 48p

8 x 11 = 88

56q + 48p + 88

There are no like terms here so the answer cannot be simplified any further.

Answer: -18

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total number of workers is our unknown. If 40% of this unknown number are women and the number of women is 1380, then the equation looks like this:

(remember that the word "of" generally means to multiply)

(also remember that we have to use the decimal form of a percent in an equation)

.40(x) = 1380 then divide to get the number of total workers:

x = 3450

Answer:

The gas pump filling the gallons in 1 minute will be: 15

Step-by-step explanation:

As there are 60 seconds in 1 minute.

Thus,

Gas pump filling the gallons in 1 minute will be:

[tex]60\:\times 2^{-2}[/tex]

[tex]=60\times \frac{1}{2^2}[/tex]             ∵ [tex]a^{-b}=\frac{1}{a^b}[/tex]

[tex]\mathrm{Multiply\:fractions}:\quad \:a\times \frac{b}{c}=\frac{a\:\times \:b}{c}[/tex]

[tex]=\frac{1\times \:60}{2^2}[/tex]

[tex]=\frac{60}{2^2}[/tex]

[tex]=\frac{2^2\times \:3\times \:5}{2^2}[/tex]

[tex]=3\times \:5[/tex]

[tex]=15[/tex] gallons in one minute

Therefore, the gas pump filling the gallons in 1 minute will be: 15

(-2,-2) is the answer .............

Answer:

9/3 is greater

Step-by-step explanation:

Convert it to decimals.

9/3=3

2 and 3/4= 2.75

Answer:

x should be 101

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

the rest of the numbers are closer to each other but if you plot these you see that 29 doesnt belong

I assume you're referring to the product,

[tex]\log_{5t}(5t+1)\cdot\log_{5t+1}(5t+2)\cdot\cdots\cdot\log_{5t+n}(5t+n+1)[/tex]

Recall the change-of-base identity:

[tex]\log_ab=\dfrac{\log_cb}{\log_ca}[/tex]

where c > 0 and c ≠ 1. This means the product is equivalent to

[tex]\dfrac{\log(5t+1)}{\log(5t)}\cdot\dfrac{\log(5t+2)}{\log(5t+1)}\cdot\cdots\cdot\dfrac{\log(5t+n+1)}{\log(5t+n)}[/tex]

and it telescopes in the sense that the numerator and denominator of any two consecutive terms cancel with one another. The above then simplifies to

[tex]\dfrac{\log(5t+n+1)}{\log(5t)}=\boxed{\log_{5t}(5t+n+1)}[/tex]

Answer:

The Answer should be....

3q + 21

Answer:

27*1000=27000ml

600ml

Now, 27000ml+600ml=27600ml

Step-by-step explanation:

Answer:

Parallel

Step-by-step explanation:

Slopes of the line

Answer:

1.25,but your teacher is prolly looking for a fraction so 1 1/4

Step-by-step explanation:

DO NOT PUT 20 THAT PERSON S WRONG

Answer:

X²(4+x)

Step-by-step explanation:

You pick out the common term

Greetings.

The answer is x²(4+x)

Explanation:

[tex]4x^2+x^3\\[/tex]

By using a common factor, we factor x-term out. We factor the x-term with least degree and that is 2-degree. So we factor x² out.

When factored out, It's similar to dividing. When x² is divided by itself, the result is 1. When x³ is divided by x², the result is x (From the property of exponent.)

Similar to dividing, but we pull x² out.

[tex]4x^2+x^3\\x^2(4+x)[/tex]

Therefore, the answer/factored form is x²(4+x)

Answer:

L = 3x cm

Step-by-step explanation:

For this problem, let's consider the relation that is stated:

Length is 3 times as much as the width.  The width is x cm.

Mathematically we can say the following:

L = 3W

W = x cm

So we can say the following about the length:

L = 3W

L = 3(x cm)

L = 3x cm

Cheers.

Answer:

17*200/17+83

Step-by-step explanation:

Points A and B are 200 mi apart. A cyclist started from point A and a motorcyclist started from point B, moving towards each other. The speed of the cyclist was 17 mph, the speed of motorcyclist was 83 mph. At what distance from point A will they meet?

The distance under the question is 17*200/17+83= 17*2 = 34 miles.

17+83 = 100 mph in the denominator is the relative speed of the participants,  the rate of decreasing the distance between them.

200/17+83=200/100= 2 hours is the time before they meet.

therefore  17*200/17+83 is the time before they meet

Answer:

60ft

Step-by-step explanation:

        multiple the length by 2

15 times two equals 30

       multiple the width by two

15 times two equals 30

       add the total lengths and widths

30 plus 30 equals 60

ans=60

Answer:

a. The number of units which will minimize average cost is approximately 5,130 units.

b. The firm should produce 12,500 items, x, for maximum profit.

c. The number of items, x, that will produce a maximum profit is 60 items.

Step-by-step explanation:

Note: This question is not complete as there are some signs are omitted there. The complete question is therefore provided before answering the question as follows:

1. If the total cost function for a product is C(x) = 200(0.02x + 6)^3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?

2. A firm can produce only 3900 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total venue is given by R(x) = 450x-1/100x^2 dollars, how many items, x, should the firm produce for maximum profit?

3. If the profit function for a product is P(x) = 3600x + 60x2 - x3 - 72,000 dollars, selling how many items, x, will produce a maximum profit?

The explanation to the answer is now given as follows:

1. If the total cost function for a product is C(x) = 200(0.02x + 6)3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?

Given;

C(x) = 200(0.02x + 6)^3 ……………………………………….. (1)

We first simplify (0.02x + 6)^3 as follows:

(0.02x + 6)^3 = (0.02x + 6)(0.02x + 6)(0.02x + 6)

First, we have:

(0.02x + 6)(0.02x + 6) = 0.004x^2 + 0.12x + 0.12x + 36 = 0.004x^2 + 0.24x + 36

Second, we have:

(0.02x + 6)^3 = 0.004x^2 + 0.24x + 36(0.02x + 6)

(0.02x + 6)^3 = 0.00008x^3 + 0.048x^2 + 7.20x + 0.0024x^2 + 1.44x + 216

(0.02x + 6)^3 = 0.00008x^3 + 0.048x^2 + 0.0024x^2 + 7.20x + 1.44x + 216

(0.02x + 6)^3 = 0.00008x^3 + 0.0504x^2 + 8.64x + 216

Therefore, we have:

C(x) = 200(0.02x + 6)^3 = 200(0.00008x^3 + 0.0504x^2 + 8.64x + 216)

C(x) = 0.016x^3 + 10.08x^2 + 1,728x + 43,200

Therefore, the average cost (AC) can be calculated as follows:

AC(x) = C(x) / x = (0.016x^3 + 10.08x^2 + 1,728x + 43,200) / x

AC(x) = (0.016x^3 + 10.08x^2 + 1,728x + 43,200)x^(-1)

AC(x) = 0.016x^2 + 10.08x + 1,728 + 43,200x^(-1) …………………………. (2)

Taking the derivative of equation (2) with respect to x, equating to 0 and solve for x, we have:

0.032x + 10.08 - (43,300 / x^2) = 0

0.032x + 10.08 = 43,300 / x^2

X^2 * 0.32x = 43,300 – 10.08

0.32x^3 = 43,189.92

x^3 = 43,189.92 / 0.32

x^3 = 134,968.50

x = 134,968.50^(1/3)

x = 51.30

Since it is stated in the question that x represents the number of hundreds of units produced, we simply multiply by 100 as follows:

x = 51.30 * 100 = 5,130

Therefore, the number of units which will minimize average cost is approximately 5,130 units.

2. A firm can produce only 3900 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total revenue is given by R(x) = 450x-1/100x^2 dollars, how many items, x, should the firm produce for maximum profit?

P(x) = R(x) - C(x) ……………. (3)

Where;

P(x) = Profit = ?

R(x) = 450x-1/100x^2

C(x) = 500 + 200x

Substituting the equations into equation (3), we have:

P(x) = 450x - 1/100x^2 - (500 + 200x)

P(x) = 450x - 0.01x^2 - 500 - 200x

P(x) = 450x - 200x - 0.01x^2 - 500

P(x) = 250x - 0.01x^2 – 500 …………………………………. (4)

Taking the derivative of equation (4) with respect to x, equating to 0 and solve for x, we have:

250 - 0.02x = 0

250 = 0.02x

x = 250 / 0.02

x = 12,500 items

Therefore, the firm should produce 12,500 items, x, for maximum profit.

3. If the profit function for a product is P(x) = 3600x + 60x2 – x^3 - 72,000 dollars, selling how many items, x, will produce a maximum profit?

Given;

P(x) = 3600x + 60x2 – x^3 - 72,000 …………………………. (5)

Taking the derivative of equation (5) with respect to x, equating to 0 and solve for x, we have:

3600 + 120x - 3x^2 = 0

Divide through by 3, we have:

1200 + 40x – x^2 = 0

1200 + 60x – 20x – x^2 = 0

60(20 + x) – x(20 + x) = 0

(60 – x)(20 + x) = 0

Therefore,

x = 60, or x = - 20

The negative value of x (i.e. x = - 20) will be will be ignored because it has no economic significance. Therefore, the number of items, x, that will produce a maximum profit is 60 items.

Answer:

8 months for cost to be same, cost will be $408

Step-by-step explanation:

x = months

176 + 29x = 0 + 51x

176 = 22x

8 = x

176 + (29*8) = 408

0 + (51*8) = 408

Answer:

its to small

Step-by-step explanation:

We want the maximun or minimum of [tex]g(x)=-4x^2+4x-2[/tex]

Firstly, notice that we have a leading coefficient of -4, wich means our parabola is concave down. Thus, our function will have a maximum.

To find what is the maximum, let's firstly find on wich value of x it happens. We'll start by taking the first derivative of the function:

[tex]g'(x)=-8x+4[/tex]

To find the extremes of the function, we just need to find where the derivative equals zero. Setting g'(x)=0 we have

[tex]0 = -8x+4\\8x=4\\x=\frac{1}{2}[/tex]

So we found that the x coordinate of the maximum is x=1/2. To find the y coordinate we just need to substitute the value of x into the original function.

[tex]g(1/2)=-4(1/2)^2+4(1/2)-2\\g(1/2)=-1+2-2\\g(1/2) = -1[/tex]

Therefore, the maximum point [tex]M[/tex] of the function is

[tex]\boxed{M=(0.5,-1)}[/tex]

 Glad to help! Wish you great studies.

If you found this helpful consider giving this answer brainliest ;)

Answer:

D

Step-by-step explanation:

We know that MRT = 133 which means that is the total. Angle MRN and NRT are what makes the total angle which is 133. To find what each angle is individually, we can add them both together.

(2g - 2) + (4q - 9) = 133

6q - 11 = 133

6q = 144

q = 24

Best of Luck!

D. (2g - 2)+(4g -9) = 133

Because,

Given, angle MRT = 133°

and MRN = 2g - 2 °

and NRT = 4g - 9°

and MRT = MRN + NRT .........(equation (i))

Placing values in equation (i) we get,

133° = (2g - 2)° + (4g - 9)°

=> 133 = (2g - 2) + (4g - 9)

=> (2g - 2) + (4g - 9) = 133

It is E

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