A manufacturer of widgets finds that the production cost, C, in dollars per unit is a function of the number of widgets produced. The selling price, S, of each widget in dollars is a function of the production cost per unit.


C(x) = –0.1x2 + 100


S(C) = 1.4C



What is the selling price per widget as a function of the number of widgets produced, and what should the selling price be if 15 widgets are produced?


A.C(S(x)) = –0.196x^2 + 100; $108.64

B.C(S(x)) = –0.196x^2 + 100; $55.90

C.S(C(x)) = –0.14x^2 + 140; $144.41

D.S(C(x)) = –0.14x^2 + 140; $108.50


This is a question on composite functions.

Answers

Answer 1

Answer:

S(C(x)) = –0.14x2 + 140; $108.50 - On edgenuity the answer is D.

Step-by-step explanation:

Answer 2

Answer:

D

Step-by-step explanation:

The value of the function at 870, the local maximum, is

= -0.02(870)2 + 34.80(870) - 4700

= -0.02(756900) + 30276 - 4700

=  -15138 + 25576

= 10438

 

So the vertex is (870, 10438)

 

The cost t the company to produce 870 widgets is  

C(870) = 4700 + 5.20(870) = 4700 + 4524 = 9224

 

So, the cost of the widgets plus the profit must be equal to the total sales, which is divided by the number of widgets reveal their individual price.

(10438 + 9224)/870 = 19662/870 = $22.60

 

P(x) = 7700

- 0.02x2 + 34.80x - 4700 = 7700

-0.02x2 + 34.80x -12400 = 0

 

x = {-34.80 ± √[(34.80)2 - 4(-0.02)(-12400)]}/2(-0.02)

x = [-34.80 ± √(1211.04 - 992)]/(-0.04)

x = (-34.80 ± √219.04)/(-0.04)

x = (-34.80 ± 14.8)/(-0.04)

x = 870 ± 370

so, $7700 in profits will be earned at either 500 widgets or 1240 widgets


Related Questions

6. Which of the following inequalities is true? (1 point)
√36 <-6
1/4> 0.5
15/2 < √81
-3>-0.7

Answers

Answer:

15/2 < √81

15/2=7.5

√81=9

7.5<9

Ahmad and Ben have a total of 78 keychains.
Ben has twice as many keychains as Charlie.
Ahmad has 6 keychains less than Charlie.
.
.
.
.
.
.
(a) How many keychains does Ahmad have?
(b) How many keychains does Charlie have?

Answers

Sorry it was tru

2C=B

C-A=6 A=C-6

A+B+C=78

78=C-6+2C+C

Evaluate (101.5)^2 – (100.5)^2 *

Answers

Answer:

[tex]\boxed{202}[/tex]

Step-by-step explanation:

[tex](101.5)^2-(100.5)^2[/tex]

[tex]= 10302.25 - 100.5^2[/tex]

[tex]= 10302.25 - 10100.25[/tex]

[tex]= 202[/tex]

Hope this helped you!

Answer:

202

Step-by-step explanation:

Hi there !

(101.5)² – (100.5)² =

use formula a² - b² = (a - b )(a + b)

= (101.5 - 100.5)(101.5 + 100.5)

= 1×202

= 202

Good luck !

Jessica has 10.75 white straw. She cut the white straw into two equal-sized pieces. What mixed number represents the length of each piece of white straw after cutting? A. 6 1/4 B. 5 13/20 C. 5 3/8 D. 5 1/8

Answers

Answer:

C: 5 3/8

Step-by-step explanation:

The length of each straw half is 5.375

A= 6.25

B = 5.65

C = 5.375

D = 5.125

8w-12=-4 anyone know the answer

Answers

Answer:

w=1

Step-by-step explanation:

8w-12=-4

8w =-4+12

8w=8

8w/8=8/8

w=1

Mark as brainliest

Answer:

Well first we have to know what -12 is -4. So I know that 8 subtracting 12 is -4 already but, i am explaining to your knowlege so  here I go.

What we can do is add 12 to -4 and it will equal what _-12=-4  

So -4+12=8

Since the variable is with 8, we have to find what the variable w is. So 8x_=8?

Thats obvious right? 8x1=8!

So 8w-12=-4 = 8x1=8-12=-4

Hope this helps and if it helps enough pls mark as brainliest!

Step-by-step explanation:

Step A: Brian went to a trading-cards event. It cost $5 to enter and $4 for each card he
purchases. Write an equation that models his total cost for the day.
Step B: How many cards did Brian purchase if he spent a total of $29?
Step C: If Brian brought a total of $65, what is the maximum amount of cards he can purchase?
Explain why in a short paragraph and in your own words.

Answers

Answer:

Step-by-step explanation:

let x be the number of cards brian gets

let y be the amount of money he spends

the y intercept will be 5, since he automatically spends $5 to enter

a. 4x+5=y

b.29=4x+5 —-> 24=4x —-> x=6. Brian got 6 card

c. Brian can’t buy more than 15 cards. When you plug in 65 for y into the equation, after solving for x you get 15 To check, 4(15)+5=65


Solve each inequality.

1. 2(k + 4) - 3k ≤ 14
2. 3(4c - 5) - 2c > 0





3. -x + 2 < 3x - 6
4. 3v - 12 > 5v + 10









Answers

3. -x + 2 < 3x - 6

=3x +x < 2 + 6

=4x < 8

=x > 8/4

=x > 2

4. 3v - 12 > 5v + 10

= 5v-3v > 10+12

=2v > 22

= v < 22/2

=v < 11

Cameron said that the Y intercept of a quadratic function always tells the maximum value of the function. explain Cameron's error

Answers

Answer:

We can have two cases.

A quadratic function where the leading coefficient is larger than zero, in this case the arms of the graph will open up, and it will continue forever, so the maximum in this case is infinite.

A quadratic function where the leading coefficient is negative. In this case the arms of the graph will open down, then the maximum of the quadratic function coincides with the vertex of the function.

Where for a generic function:

y(x) = a*x^2 + b*x + c

The vertex is at:

x = -a/2b

and the maximum value is:

y(-a/2b)

Jerry has just purchased his first home for $190,000. He put down a 20 percent down payment of $38,000 and took out a 5 percent mortgage for the rest. His mortgage payment is $700 per month. How much of his first monthly mortgage payment is amortization?

Answers

Answer:

$66.67

Step-by-step explanation:

The calculation of first monthly mortgage payment is amortization is given below:-

Amount borrowed = Purchase first home cost - Down payment

= $190,000 - $38,000

= $152,000

Annual interest = ($152,000 × 5%) ÷ 12

= $7,600 ÷ 12

= $633.33 per month

Now,

First monthly payment = Mortgage payment - Annual interest

= $700 - $633.33

= $66.67

Hence, we simply applied the above formula.

When two objects are near each other, how would increasing one object’s mass affect it?

Answers

When two objects are near each other, increasing one object's mass would cause the gravitational force of the object to increase. where m and M are the masses of the two objects, d is the distance between their centres, and G is the gravitational constant.

HELP PLZ GOD BLESS YOU HELP PLZ

Answers

                  [tex]\huge\boxed{Second\;Provided\;Answer.}[/tex]

[tex]12(8) + 13(11) = 239\\12 * 8 + 13 * 11\\12 * 8 = 96\\96 + 13 * 11\\13 * 11 = 143\\96 + 143 = 239\\[/tex]

[tex]Therefore,\;your\;final\;answer\;is\;the\;second\;provided\;answer.[/tex]

Hope this helped!

May i have brainliest?

[tex]\huge\boxed{Thanks,\;Plip.}[/tex]

what is 3(5)+(-2+4-5)? explanation needed, please. I need to turn my work for it in in about 30 minutes.

Answers

Answer:

12

Step-by-step explanation:

3(5)+(-2+4-5)

Use PEMDAS: Parentheses,  Exponents, Multiplication, Division, Addition, Subtraction

(-2+4-5)=-3

3(5)-3

3(5)=15

15-3=12

Answer:12

if ab is 2x+3 bc is 3x+5 and ac is 38 what is the value of x

Answers

Answer:

x would equal 8. because you would add AB and BC together and set it equal to AC

Hoped I helped

Can I get a brainliest

simplify: cot(θ)sin(θ)

Answers

Answer:

cos(θ)

Step-by-step explanation:

cot(θ) = cos(θ)/sin(θ)

Step 1: Write expression

cot(θ)sin(θ)

Step 2: Substitute

cos(θ)/sin(θ) · sin(θ)

Step 3: Simplify

cos(θ)

scar goes to the gym 4 times per week. Every time he walks 5 miles on the 4 points
treadmill. How many miles does he walk on the treadmill in one year?

Answers

Answer:

He walks 1,060 miles on the tremil in one year.

Step-by-step explanation:

4*5=20*53=1,060

There are 53 sometimes 52 weeks in a year,2020 wise 53 so 53*20=1,060 miles.

Solve for x
65°
40°
X+85°

Answers

Answer:40.

Step-by-step explanation:

y=-2 4x-3y=18 equations using substitution

Answers

Answer:

X = 3

Y = -2

Step-by-step explanation:

If y = -2, you can plug in -2 for y in the equation 4x - 3y. This means that this equation will become 4x -3(-2) = 4x+6=18. Solve for x from this, and you will get 3.

Answer:

x=3/y=-2

Step-by-step explanation:

ty
Which defines the piecewise function shown?
4.
O f(x) =
- x - 2, X < 0
х
2'
x > 0
2.
O f(x) =
х
- x - 2, X < 0
- x 20
xin
4.
-2
N
4.
-20
O f(x) =
-
x < 0
A
x -2, x 20
-4
O f(x) = 2
x ko
x - 2, X 2 0

Answers

The choice which defines the piecewise function shown in the graph is; Choice B.

Piecewise functions

For the line originating from the center and plotted towards the right (i.e Positive x-axis)

We can conclude that the line can be represented by the function; f(x) = -x/2 and slope = -1/2 where; x>= 0 due to the solid dot

For the line whose y-intercept is at point, (0, -2), and is plotted towards negative x; we have;

We can conclude the equation of the line can be represented by the function; f(x) = -x -2 where slope = -1, and domain; x < 0

Ultimately, the aggregate of both functions give s the required piecewise function as represented in Choice B.

Read more on piecewise functions;

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2/9 of the members are boys in a community service club. if there are 95 more girls than boys, how many girls are there in club?

Answers

Answer:

There are 171 members in the club

Number of boys = 38

Number of girls = 133

Step-by-step explanation:

Let

x = total members of the club

Boys = 2/9x

if there are 95 more girls than boys

Girls = 2/9x + 95

how many girls are there in club?

Total members in the club = boys + girls

x = 2/9x + 2/9x + 95

x = 2+2/9x + 95

x = 4/9x + 95

x - 4/9x = 95

9x-4x/9 = 95

5/9x = 95

Divide both sides by 5/9

x = 95 ÷ 5/9

= 95 × 9/5

= 855/5

= 171

boys = 2/9x

= 2/9 * 171

= 342 / 9

= 38

Girls = 2/9x + 95

= 38 + 95

= 133

Total = 38 + 133

= 171

There are 171 members in the club

Number of boys = 38

Number of girls = 133

is 15 square rooted rational​

Answers

Answer: The square root of 15 is a rational number

explanation: if 15 is a perfect square. ... Since 15 is not a perfect square, it is an irrational number. This means that the answer to the square root of 15 will have an infinite number of decimals. The decimals will not terminate and you cannot make it into an exact fraction.

help me please
(pythagorean theorem)​

Answers

Answer:

  13 cm × 12 cm

Step-by-step explanation:

The diagonal of the top or bottom faces of the box is the hypotenuse of a triangle with legs 12 cm and 5 cm. The Pythagorean theorem tells you that diagonal length is ...

  d = √(12² +5²) = √(144 +25) = √169 = 13 . . . cm

The width of the divider is 13 cm.

The height of the divider is shown as 12 cm.

The dimensions of the dividing rectangle are 13 cm by 12 cm.

Six times the sum of a number and four

Answers

Answer:

6*(x+4)

Step-by-step explanation:

The expression "Six times the sum of a number and four" can be written as 6 × (x + 4) OR 6(x+4)

The complete question is:

How do you write the expression for: Six times the sum of a number and four

To write an expression for the given statement (Six times the sum of a number and four),

Let the number be x

Therefore, the sum of the number and four would be

x + 4

Now, for the complete statement - Six times the sum of a number and four

We will get

6 × (x + 4) OR 6(x+4)

Hence, the expression "Six times the sum of a number and four" can be written as 6 × (x + 4) OR 6(x+4)

Learn more here: https://brainly.com/question/11708683

You are playing a video game. For each diamond you collect, you earn 75 points. You also earn 100 bonus points by completing the level in less than 2 minutes. You need to earn more than 1000 points to continue to the next level. Write and solve an inequality that represents the numbers d, the number of diamonds you must collect in less than 2 minutes to advance to the next level

Answers

Answer:

75x + 100 greater than 1000

Step-by-step explanation:

How many 1/4 pieces are in 5 3/4

Answers

Answer:

23

Step-by-step explanation:

3/4 has 3  of 1/4 pieces.

5 has 20 of 1/4 pieces.

The number of pieces of 1/4 in 5 3/4 is 23 pieces

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of pieces be = A

Let the number be = 1/4

Now , the number of pieces of 1/4 in 5 3/4 is calculated as

The number 5 3/4 is converted into mixed fraction is 23/4

So , the equation is

The number of pieces of 1/4 x n = 23 / 4

So , the equation will be

n x 1/4 = 23 / 4   be equation (1)

Multiply by 4 on both sides , we get

n = 23 pieces

Therefore , the number of pieces 1/4 is in 5 3/4 is 23 pieces

Hence , The number of pieces of 1/4 in 5 3/4 is 23 pieces

To learn more about equations click :

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2) A drum full of rice weighs 40 1/6 pounds . If the empty
drum weighs 3 3/4 pounds. find the
weight of rice in the
drum

Answers

Answer:

36.416 the 6 is repeating repeating

Step-by-step explanation:

I believe this is right. I hope this helps you!! I apologize if wrong.

Write the equation of the line that passes through the given points. ​(8​,0​) and ​(0​,4​)

Answers

Answer:

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

Step-by-step explanation:

The equation of a line can be written in the form of y=mx+c, where m is the gradient and c is the y-intercept.

This is also known as the slope-intercept form.

[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }, \\ where \: (x1, y1) \: is \: the \: 1st \: coordinate \: and \: (x2, y2) \: is \: the \: 2nd \: coordinate.[/tex]

Find the value of m using the gradient formula above:

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

Substitute m= -½ into the equation:

y= -½x +c

To find the value of c, substitute a pair of coordinates:

When x= 0, y=4,

[tex]4 = - \frac{1}{2} (0) + c \\ 4 = c \\ c = 4[/tex]

Thus, the equation of the line is y= -½x +4.

george floyd was what race

Answers

Answer:

African American (aka Black)

Answer:

african american blm/alm

Step-by-step explanation:

Solve -11 > -1 - 2x solve and check your answer

Answers

Answer:

x>5

Step-by-step explanation:

-11>-1-2x

2x>-1+11

2x>10

x>5

Answer:

5 > x

Step-by-step explanation:

-11 > -1 -2x ---> plus one on each side---> -10 > -2x ----> divide by -2 --> 5 > x

Jacob ordered pizza from his favorite pizzeria. The pizzeria delivers pizzas for $10 each plus a delivery charge of $2.99. Jacob paid a total of $32.99. Write an equation that models this situation. Let p = the number of pizzas delivered. Equation:

Answers

Answer:

$10p + $ 2.99 = $32.99

Step-by-step explanation:

I got this because he got multiple pizzas that are each $10, but we don't know how many there are, so I put $10p together.

He also pays $2.99 as a delivery charge.

And I ended it with the equation equaling $32.99 because that is the total he paid.

Harlon wrote the equation uppercase A = 18 (x squared + 1) to find the area of a rectangle that has a length of x squared + 1 and a width of 18. He solved for x and got x = plus-or-minus StartRoot StartFraction uppercase A Over 18 EndFraction minus 1 EndRoot Which of the following is an equivalent equation for x?

Answers

Answer: x= a-18/18

Step-by-step explanation:

The expression equivalent to this is letter A.  x= ±√(A-18/18)

What are equivalent expressions?

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

To solve for x in the equation for the area which was given to be;

A = 18(x^2 + 1),

So, we divide both sides of the equation by 18 first.

A/18 = x^2 + 1

Then, we subtract 1 from both sides of the equation;

A/18 – 1 = x^2

Then, we simplify the expression in the left side of the equation;

(A – 18)/18 = x^2

And  obtain the square root from both sides of equation,

x= ±√(A-18/18)

Therefore, The expression equivalent to this is letter A.  x= ±√(A-18/18)

Learn more about expression here;

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