1. Kim's age is three times that of her sister. When you add Kim's age to her sister's age, you get 48. How old is each sister? (a) Write an equation that represents the situation. Explain any variable used. (1 point) (b) Solve the equation from Part (a). Show your work. (4 points)

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Explanation:

If you know the cost function C(x), to find the marginal cost, we apply the derivative.

Marginal cost = derivative of cost function

Marginal cost = C ' (x)

Since we're given the marginal cost, we'll apply the antiderivative (aka integral) to figure out what C(x) is. This reverses the process described above.

[tex]\text{Cost} = \text{antiderivative of marginal cost}\\\\\displaystyle C(x) = \int \left(35x^{4/3} - 14x^{3/4} + 1\right)dx\\\\[/tex]

[tex]C(x) = \frac{1}{1+4/3}*35x^{4/3+1} - \frac{1}{1+3/4}*14x^{3/4+1} + x + D\\\\C(x) = \frac{1}{7/3}*35x^{7/3} - \frac{1}{7/4}*14x^{7/4} + x + D\\\\C(x) = \frac{3}{7}*35x^{7/3} - \frac{4}{7}*14x^{7/4} + x + D\\\\C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\[/tex]

D represents a fixed constant. I would have used C as the constant of integration, but it's already taken by the cost function C(x).

To determine the value of D, we plug in x = 0 and C(x) = 9000. This is because we're told the fixed costs are $9000. This means that when x = 0 units are made, you still have $9000 in costs to pay. This is the initial value. You'll find that all of this leads to D = 9000 because everything else zeros out.

Therefore, we go from this

[tex]C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\[/tex]

to this

[tex]C(x) = 15x^{7/3} - 8x^{7/4} + x + 9000\\\\[/tex]

which is the final answer.

Answer:

Step-by-step explanation:108 divided by 12 equals 9 so nine feet next to 108 inches.

and nine divided by 3 is 3 so nine yards in the row with 108 inches.

360 divided by 12 which is 30 so 30 feet in the row with 360 inches.

90 feet divided by three so 30 so 30 yards in the row with 360 inches.

24 inches equals 2 feet

double this length is 48 inches or 4 feet

so in all he cut 6 yards and since he only had three yards you will still have  3 yards left over.

Answer:

The value of p is -5.

Step-by-step explanation:

Given the slope and a known point, you have 3 of the 4 variables and you can use them to solve for the y-intercept of the line.

[tex]y=mx+b\\(27)=(8)(2)+b\\27=16+b\\11=b\\b=11[/tex]

Now, with the slope and the y-intercept, you can write the equation of the line:

[tex]y=8x+11[/tex]

Finally, you can use that equation to solve for y at x = -2:

[tex]y=8(-2)+11\\y=-16+11\\y=-5[/tex]

The value of p is -5.

You can also see that on a graph.

Answer:

10

Step-by-step explanation:

each tick mark is worth 5

there is the -10, then one to the right is -5, next is 0, next is 5, next one (the one where the x is) 10, next 15, next 20.

262.5 gallons of milk does the class drink in 10 weeks.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The kindergarten class at Stokes Elementary drinks about 210 pints of milk per week.

as, we know that

1 pint= 0.125 Galloon

So, 210 pints milk = 210 x 0.125 = 26.25 Galloon

Then, In 10 weeks amount of milk drink

= 26.25 x 10

= 262.5 Gallon

Learn more about Unitary Method here:

https://brainly.com/question/22056199

#SPJ2

Answer:

1000 = 450 + 50w

Step-by-step explanation:

She starts with $450 so that is why you add it. The amount she started with will not change.

She earns $50 per week so you add 50 multiplied by the number of weeks she works.

You do this until it equals 1000

Answer:

5x=-(5/2) ~~ first choice

Step-by-step explanation:

divide both sides by 5

-> x=(5/2)/5

simplify the above

-> x = - (5/2x5)

simplify

-> x = -(5/10)

simplify and solve

=> x = - 1/2

(basically trial and error)

According to the amount he drove in 5 hours, he drove an average of 62 MPH. If he continued to drive at this speed for 8 hours, he would travel 496 miles.

Answer:

it's simply what we follow and respect like we value our culture

Step-by-step explanation:

hope this will help

Answer:

A' = (-4, 7)

B' = (3, 5)

C' = (1, 2)

Step-by-step explanation:

The question is asking you to translate the function by adding 4 to the x-value of each point and 2 to the y-value of each point.

I didn't double-check my math, but since the question is asking for an ordered pair, this should be correct.

Answer:

The length of XY is 22.5

Step-by-step explanation:

Since you need to hurry I will not write an explanation

Hope this helps! :)

૮ ・ﻌ・ა

Answer:

check online for more information

Answer:

338.63 ounces

Step-by-step explanation:

1=35.274

35.274 times 9.6 is 338.6304

Answer:13 percent would have cats and the other 13 percent wouldn’t

Step-by-step explanation:plz mark for brainlist

Thank you

Answer:

133 sodas and 87 hotdogs were sold.

Step-by-step explanation:

math

Answer:

number of sodas: x+46 (46 more than hotdogs)

number of hotdogs: x

x+x+46=220

2x+46=220

2x=174

x=87

87+46=133

number of sodas: 133

number of hotdogs: 87

Answer:

7.2

Step-by-step explanation:

20/12 = 12/x

20x = 144

x = 144/20

x = 7.2

Check to make sure your answer is right:

20/12 = 1.66666666667

12/7.2 = 1.66666666667

First, let's find the area! The formula to find the area of a circle is πr²

πr²

3.14 · 4²

50.24 yds²

Now let's find the circumference. The formula for this is 2πr

2πr

2 · 3.14 · 4

25.12 yds

Hope this helps!

PEMDAS, notice Parentheses is first, then Exponents 2nd

[tex]16\div\left(2 + \left( \frac{1}{2} \right)^2 \right)\implies 16\div\left(2 + \left( \frac{1^2}{2^2} \right) \right)\implies 16\div\left(2+\frac{1}{4} \right)[/tex]

now that the exponent got done, let's keep in the parentheses

[tex]16\div\left(\frac{2}{1}+\frac{1}{4} \right)\implies 16\div\left(\cfrac{8+1}{\underset{\textit{using this LCD}}{4}} \right)\implies 16\div \left( \cfrac{9}{4} \right)[/tex]

PEMDAS, after all that we'll do D, Division next

[tex]16\div \left( \cfrac{9}{4} \right)\implies \cfrac{16}{1}\div \cfrac{9}{4}\implies \cfrac{16}{1}\cdot \cfrac{4}{9}\implies \cfrac{64}{9}\implies 7\frac{1}{9}[/tex]

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this just some addition to your previous posting, since you kinda got spammed some

[tex]\stackrel{\stackrel{\textit{E first}}{\downarrow }}{2^3}+4\cdot 2-7\implies 8+4\cdot 2-7\implies 8+\stackrel{\stackrel{\textit{M second}}{\downarrow }}{8}-7\implies \stackrel{\textit{AS last from left to right}}{16-7\implies 9}[/tex]

notice, PEMDAS, P first and so on, AS are last, from left to right.

answer

a.) y=2.5x

area=2.5x^2

b.)2560

Step-by-step explanation:

a.  The construct the expression for the area of the rectangle in terms of x is y=2.5x

b. The area should be 2,560.

Given that,

Based on the above information, the calculation is as follows:

a) The expression should be y = 2.5x

b) The area should be

[tex]=2.5x^2\\\\= 2.5(32)^2[/tex]  

= 2560

Learn more: https://brainly.com/question/1301963?referrer=searchResults

Answer:

5/8 of a tank

Step-by-step explanation:

Divide 1/2 by 4 to get how much of a tank you would be able to fill in 1/5 of an hour.  1/2 ⁒ 4 is 1/8 so she can fill 1/2+1/8 of a tank or 5/8 of a tank.

Answer:

During the 16th and early 17th Century, the equals, multiplication, division, radical (root), decimal and inequality symbols were gradually introduced and standardized. ... In the Renaissance Italy of the early 16th Century, Bologna University in particular was famed for its intense public mathematics

Prior to the invention of the Mathematical Symbols, mathematical equations were written in words.

For example, Y + 10 = 4.5 would be written as

The thing plus ten equal to eight.

It is true that MOST, that is, the majority of the mathematical symbols we have today were invented in the 16th century. Examples of such symbols are:

Prior to the 16th century, some mathematical signs were already in use. They are:

See the link below for more about Mathematical Signs:

https://brainly.com/question/11855662

Answer:

5.243 is less than 5.4....

Answer:

A) Yes...ABC and GFC are similar using AA.

Step-by-step explanation:

Answer: X = 4/61

Step-by-step explanation

105/2^9

Step-by-step explanation:

The probability of getting a head in a single toss

p=12

The probability of not getting a head in a single toss

q=1−12=12

Now, using Binomial theorem of probability,

The probability of getting exactly r=4 heads in total n=10 tosses

=10C4(1/2)4(1/2)10−4

=10×9×8×7/4! 1/2^4 1/2^6

=2^44⋅9⋅35/24(2^10)

=105/2^9

Answer:

P = 0.205  (20.5%)

Step-by-step explanation:

[tex]f(x)=(10nCr4)(.5)^{4} (.5)^{6} =(210)(0.0625)(0.015625)=0.205[/tex]

Hope this helps

[tex]Hiya![/tex]

Sokka is here to help!!

Here's a explanation!

[tex]\frac{38}{100} (12)[/tex]

[tex]=(\frac{38}{100} )(\frac{12}{1} )[/tex]

[tex]=(\frac{19}{50} )(\frac{12}{1} )[/tex]

[tex]=\frac{(19)(12)}{(50)(1)}[/tex]

[tex]=\frac{228}{50}[/tex]

[tex]4.56[/tex]

ANSWER:

[tex]\frac{114}{25}, OR: 4.56[/tex]

Hopefully, this helps you!!

[tex]Sokka[/tex]

Answer:

I think 38.7 if you do<j it would be 38.7

Answer:

59 centimeters

Step-by-step explanation: