A company that manufactures hair ribbons knows that the number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation below.
x = 1,000 − 100p
At what price should the company sell the ribbons if it wants the weekly revenue to be $1,600? (Remember: The equation for revenue is R = xp.)
p = $ (smaller value)
p = $ (larger value)

Answers

Answer 1

Given:

The number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation:

[tex]x=1000-100p[/tex]

To find:

The selling price if the company wants the weekly revenue to be $1,600.

Solution:

We know that the revenue is the product of quantity and price.

[tex]R=xp[/tex]

[tex]R=(1000-100p)p[/tex]

[tex]R=1000p-100p^2[/tex]

We need to find the value of p when the value of R is $1600.

[tex]1600=1000p-100p^2[/tex]

[tex]1600-1000p+100p^2=0[/tex]

[tex]100(16-10p+p^2)=0[/tex]

Divide both sides by 100.

[tex]p^2-10p+16=0[/tex]

Splitting the middle term, we get

[tex]p^2-8p-2p+16=0[/tex]

[tex]p(p-8)-2(p-8)=0[/tex]

[tex](p-8)(p-2)=0[/tex]

Using zero product property, we get

[tex]p-8=0[/tex] or [tex]p-2=0[/tex]

[tex]p=8[/tex] or [tex]p=2[/tex]

Therefore, the smaller value of p is $2 and the larger value of p is $8.


Related Questions

3T-2 + T -5T= -1
Solve it out please

Answers

Answer: T = -1

Step-by-step explanation:

**Disclaimer** I assume that the [T] is a variable. If it was, then you may refer to my answer. If it was not, then you may point it out and I'll redo it.

Given

3T - 2 + T - 5T = -1

Combine like terms

-T - 2 = -1

Add 2 on both sides

-T - 2 + 2 = -1 + 2

-T = 1

Divide -1 on both sides

-T / (-1) = 1 / (-1)

T = -1

Hope this helps!! :)

Please let me know if you have any questions

The graph of f(x) = |x| is translated 6 units to the right and 2 units up to form a new function. Which statement about the range of both functions is true?

The range is the same for both functions: {y | y is a real number}.
The range is the same for both functions: {y | y > 0}.
The range changes from {y | y > 0} to {y | y > 2}.
The range changes from {y | y > 0} to {y | y > 6}.

Answers

The range is the same for both functions: {y | y is a real number}.

Translation and range of a function

Given the parent function expressed as  f(x) = |x|. If the function is translated 6 units to the right and 2 units up to form a new function, the resulting function will be;

g(x) = |x + 6| + 2

The range is the value of the dependent variable for which it exist. For the given function, the range will exist on all real numbers.

Learn more on range of a function here: https://brainly.com/question/1466393

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Find the value of a,b,c and x from the following figure

Answers

Answer:

L=110

d=110

b=70

a=70

c=110

Would the function ƒ(x) = 4 be considered a step function? Explain your reasoning.

Answers

Hey there! I'm happy to help!

A step function is a function that looks like stairs when you graph it. Normally the end of one line will be graphed as an open circle (less or greater than, not equal to) while the other end would be a closed circle. This allows for a new line of the function to start directly above it without it not being a function (an input cannot have two outputs)

The function f(x)=4 is just a horizontal line as it has a slope of 0 (there is no x on the right side of the equation), so this doesn't resemble a step function.

Have a wonderful day and keep learning! :D

The average weight of 10 boys is 77.0 pounds. If the
youngest boy is excluded, the average weight of the
9 remaining boys is 78.0 pounds. What is the weight,
in pounds, of the youngest boy?

Answers

Answer:

68 pounds.

Step-by-step explanation:

Find the total weight when there are 10 boys and when there are 9 boys then calculate the difference.

I'll let x = total weight.

[tex]\frac{x}{10}=77\\(10)\frac{x}{10}=77(10)\\x=770\\\\ \frac{x}{9}=78\\(9)\frac{x}{9}=78(9)\\x=702\\\\ 770-702=68[/tex]

Therefore, the youngest boy weighs 68 pounds.


Find the measure of

Answers

Answer:

74 degrees

.................

Answer:

74

Step-by-step explanation:

BEC and CED form a straight line so they add to 180

BEC+CED = 180

106+ CED = 180

CED = 180-106

CED = 74

Use the special angles to evaluate: a) cosec 60° cot 30° + cos 45º cosec 45° 2​

Answers

Answer:

the required answer is 4√2+1/2√2

Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ?

f(x)= x3 - 2x2 - 3x + 6
f(x)= x3 - 2x2 + 3x + 6
f(x)= x3 + 2x2 - 3x + 6
f(x)= x3 + 2x2 - 3x - 6

Answers

Using the factor theorem, it is found that the polynomial is:

[tex]f(x) = x^3 - 2x^2 - 3x + 6[/tex]

Given by the first option

---------------------------

Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] using the factor theorem it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.

---------------------------

In this question:

[tex]x_1 = 2[/tex][tex]x_2 = \sqrt{3}[/tex][tex]x_3 = -\sqrt{3}[/tex]By the options, leading coefficient [tex]a = 1[/tex]

Thus:

[tex]f(x) = (x - 2)(x - \sqrt{3})(x + \sqrt{3})[/tex]

[tex]f(x) = (x - 2)(x^2 - 3)[/tex]

[tex]f(x) = x^3 -2x^2 - 3x + 6[/tex]

Which is the polynomial.

A similar problem is given that: https://brainly.com/question/4786502

I really need an answer as soon as possible. 10 pts worth it

Answers

Answer:

A. Correct: When we plug in g(x) for the x in f(x), we get H(x).

B. Correct: When we plug in g(x) for the x in f(x), we get H(x).

C. Correct: When we plug in g(x) for the x in f(x), we get H(x).

D. Correct: When we plug in g(x) for the x in f(x), we get H(x).

Step-by-step explanation:

Brainliest, please!

Select the correct answer.
Simplify the following expression.
(3x^2 - 11x - 4) – (x – 2) (2x + 3)

Answer choices

5x^2 - 12x - 10
x^2 - 10x + 2
x^2 + 10x - 2
x^2 – 12x – 10

Answers

Answer:

x^2 -10x+2

Step-by-step explanation:

(3x^2 - 11x - 4) – (x – 2) (2x + 3)

FOIL

(3x^2 - 11x - 4) – (2x^2-4x+3x-6)

Combine like terms

(3x^2 - 11x - 4) – (2x^2 -x-6)

Distribute the minus sign

3x^2 - 11x - 4 – 2x^2 +x+6

Combine like terms

x^2 -10x+2

Find the measure of PR.
PLEASE HELP ASAP!!
A. 18
B. 19
C. 25
D. 22

Answers

Answer:

A. 18

Step-by-step explanation:

the equation :

RF×RS = PR×RQ

16×9 = PR × 8

144 = PR×8

PR = 144/8

PR = 18

If the length of FR is 16 units then the length of PR is 18 units which is option A.

What is circle?

Circle is a figure whcih is having an arc showing points which are at equidistant from the centre point. The distance of arc from the centre point is known as radius.

How to find length?

From the rule of tangents and point outside the circle we can say that,

RF×RS = PR×RQ

16×9 = PR × 8

144 = PR×8

PR = 144/8

PR = 18 units

Hence if the length of FR is 16 units then the length of PR is 10 units.

Learn more about circle at https://brainly.com/question/24375372

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Please help please with geometry

Answers

Answer:

33

Step-by-step explanation:

HJ = HI + IJ

HJ = 3x - 9, HI = x and IJ = x + 5

So 3x - 9 = x + x + 5

Solve for x

Combine like terms

3x - 9 = 2x + 5

Add 9 to both sides

3x = 2x + 14

Subtract 2x from both sides

x = 14

Find HJ

HJ = 3x - 9

We have found that x = 14

HJ = 3(14) - 9

Multiply 3 and 14

HJ = 42 - 9

Subtract

HJ = 33

In a sports club of 150 members, 88 play golf, 63 play bowls, and 45 play golf and bowls. Find the probability that:
a) a member plays golf only.
b) a member doesn't play golf or bowls.
pls explain too if u could. thanks!​

Answers

Answer:

a) .287

b) .293

Step-by-step explanation:

The answers are boxed in red in the picture.

First I found how many people only golfed. Then I did the same for the people that only bowled. Next I found how many members didn't golf or bowl.

From there I found the probabilities by dividing

a.) # of members that only golf / total # of members

b.) # of members that don't bowl or golf / total # of members

Find the slope of the line graphed below.​

Answers

Answer:

Y =1.2X +-1.6

Step-by-step explanation:

x1 y1  x2 y2

3 2  -2 -4

   

(Y2-Y1) (-4)-(2)=   -6  ΔY -6

(X2-X1) (-2)-(3)=    -5  ΔX -5

   

slope= 1  1/5    

B= -1  3/5    

   

Y =1.2X +-1.6    

a student takes a rectangular piece of paper 30 cm long and 21 cm wide find the area of the biggest circle that can be cut out from the paper also find the area of the paper left after cutting out the circle​

Answers

Answer:

Step-by-step explanation:

diameter of the circle=smallest of the length and width=21 cm

r=21/2

area of the circle=πr²=22/7 ×(21/2)²=(21×441)/(7×4)=1323/4=330.75 cm²

PLEASE HELP!! Find the slant height of the come

Answers

The slant height of an object (such as a cone, or pyramid) is the distance along the curved surface, drawn from the edge at the top to a point on the circumference of the circle at the base.
...
s=√h2+b22
s = slant height.
h = vertical height.
b = base.

х
у
1
-4 -7
7
13
- 10
19
-13
3
Is the relationship shown by the data linear? If so, model the data with an equation.

Answers

Answer:

Yes and the equation is 2y=-x-7

Step-by-step explanation:

Yes the relation is linear, the slope of the equation will be - 3/6=-1/2, the equation of line will be y=(-1/2)x-3.5. 2y=-x-7

Given m||n, find the value of x.
t
(9x+23)
m
(10x+6)
an
Answer:
Submit Answer
attempt 1 out of 2
Pls help I’ve already got it wrong once

Answers

Answer:

x=17

Step-by-step explanation:

These are alternate interior angles and alternate interior angles are equal when the lines are parallel

9x+23= 10x+6

Subtract 9x from each side

9x+23 -9x= 10x-9x+6

23 = x+6

Subtract 6 from each side

23-6 = x+6-6

17 =x

Select the correct answer (for Edmentum/PLATO).

Which expression represents the series 1 + 5 + 25 + 125 + 625?

Answers attached in photo.​

Answers

Answer:

Correct answer is A. Trust me

Step-by-step explanation:

2 similar cardboards have areas of 24cm square and 150cm square. if the length of the bigger one is 10cm, what is the length of the smaller one​

Answers

Answer:

4 cm

Step-by-step explanation:

Given 2 similar figures with sides in ratio a : b , then

ratio of areas = a² : b²

let n be the length of the smaller one , then

ratio of sides = n : 10

ratio of areas = n² : 10² = n² : 100

Using proportion

( [tex]\frac{ratio}{area}[/tex] )

[tex]\frac{n^2}{24}[/tex] = [tex]\frac{100}{150}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

3n² = 48 ( divide both sides by 3 )

n² = 16 ( take the square root of both sides )

n = [tex]\sqrt{16}[/tex] = 4

length of the smaller one is 4 cm

What is the vertex of g(x) = 3x2 − 12x + 7?

(−6, −5)
(−2, −5)
(2, −5)
(6, −5)

Answers

(h ,k) —> (2 , –5)

g(x)=3x²-12x+7 —> y= 3(x-2)²-5

y=a(x–h)²+k —> a= 3 , h=2 , k= –5

(h ,k ) —> (2, –5)

I hope I helped you^_^

Answer:

C, Option 2, or (2,-5)

Step-by-step explanation:

edge 2021

Find the measure of <3. 90 50 40 130

Answers

Answer:  90 degrees

=============================================================

Explanation:

This figure is a kite since we have two pairs of adjacent sides that are congruent, but not all sides are the same length.

One property of kites is that the diagonals are always perpendicular (this applies to rhombuses as well). This means angle 3 is 90 degrees.

The measure of ∠3 is 90°

Because in a kite the diagonals bisects at 90°

Therefore ∠3 is 90°

Answered by Gauthmath must click thanks and mark brainliest

Does this graph show a function? Explain how you know.
A. No; the graph fails the vertical line test.
• B. No; there are y-values that have more than one x-value.
• C. Yes; the graph passes the vertical line test.
D. Yes; there are no y-values that have more than one x-value.

Answers

Answer:

C. Yes; the graph passes the vertical line test.

Step-by-step explanation:

Reasons the others are wrong:

A. It does pass the vertical line test.

B. Y-values can have any x values. It is x-values that can't have multiple y-values.

D. There are y-values with more than one x-value on this graph so that's just false. Even if it were true, that still doesn't invalidate it due to the reasons given in Answer B.

can anyone help with this? im confused

Answers

Circumference/ Pigreco = 22 / 3,14 = 7
So it’s letter A

CP = Rs 720 and SP = Rs 810​

Answers

Answer:

Bro what to do in this question. Hope you understand me

Sammy and Hannah are finalists in a cooking competition. For the final round, each of them will randomly select a card without replacement that will reveal what their star ingredient must be. Here are the available cards:
Cabbage
Spinach
Kale
Leeks
Carrots
Turnips

Cabbage


Leeks




Spinach


Carrots




Kale


Turnips




Sammy and Hannah both want to get leeks as their star ingredient. Sammy will draw first, followed by Hannah.
What is the probability that NEITHER contestant draws leeks?
Round your answer to two decimal places.

Answers

The probability that neither of them draws the Leeks card is P = 4/6 = 0.667

Here we can assume that all the cards have the same probability of being randomly drawn.

The cards are:

Cabbage Spinach Kale Leeks Carrots Turnips

So we have 6 cards. We want to find the probability that neither contestant draws the "Leeks" card.

Sammy draws first, the probability of drawing the Leeks card will be equal to the quotient between the number of Leeks cards (one) and the total number of cards (6).

Then the probability of drawing the leeks card is p = 1/6

This means that the probability of NOT drawing the leeks card is:

q = 1 - 1/6 = 5/6.

Now draws Hanna, now there are 5 cards in the deck (because one was already drawn). With the same approach as before, the probability of drawing the Leeks card is p = 1/5, then the probability of NOT drawing the card is:

q = 1 - 1/5 = 4/5.

The joint probability (this is, the probability of both of these events to happen together) is just the product of the individual probabilities.

Then the probability that neither of them draws the Leeks card is:

P = (4/5)*(5/6) = 4/6 = 0.667

If you want to learn more about probability, you can read:

https://brainly.com/question/24349426

Arrange in descending order.
10,-5,-1, 12, 0, -13​

Answers

Answer:

12, 10, 0, -1, -5, -13

Step-by-step explanation:

{24a - 18b} =24a−18b I neeed help

Answers

0

(24a - 18b) = 24a - 18b

24a - 18b = 24a - 18b

collect like terms

24a - 24a = -18b + 18b

0 = 0

Categorize the graph as linear increasing, linear decreasing, exponential growth, or exponential decay

Answers

Answer:

D. Exponential growth

Step-by-step explanation:

Hope this helps

Function that is similar to exponential.

Option (A) is correct.

What is exponential decay?

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula  [tex]y=a(1-b)^{x}[/tex] wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed.

We can observe that

First, y increases as x increases

Last it is a function that is similar to exponential.

Function is an exponential decay.

Option (A) is correct.

Find out more information about exponential decay here

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the diagonal of a square is 50cm long. how long are the sides of the square?

Answers

#1
avatar
+5
The diagonal is the hypotenuese of a Right Triangle, so use the Pythagorean Theorom
a^2 + b^2 = c^2

Since it is a square a = b
so a^2 + a^2 = 50^2
2a^2 = 2500
a^2 =1250
a = 35.355 cm = lenght of a side
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