A company has determined that its profit for a product can be described by a linear function.
The profit from the production and sale of 150 units is $455, and the profit from
250 units is $895.
(i) What is the average rate of change of the profit for this product when
between 150 and 250 units are sold?
(ii) Write the equation of the profit function for this product.
(iii) How many units give break-even for this product?
(b) You are the CEO for a lightweight compasses manufacturer. The demand
function for the lightweight compasses is given by p = 40 − 4q
2where q
is the number of lightweight compasses produced in millions.It costs the company $15
to make a lightweight compass.
(i) Write an equation giving profit as a function of the number of lightweight compasses
produced.
(ii) At the moment the company produces 2 million lightweight compasses and makes a profit
of $18,000,000, but you would like to reduce production. What smaller number of
lightweight compasses could the company produce to yield the same profit?
Step-by-step explanation:
(a)(i) The average rate of change is:
(895 − 455) / (250 − 150)
4.4
(a)(ii) Since the profit is linear, the slope of the line is equal to the average rate of change. Using point-slope form:
y − 455 = 4.4 (x − 150)
Simplifying to slope-intercept form:
y − 455 = 4.4x − 660
y = 4.4x − 205
(a)(iii) The break-even point is when the profit is 0.
0 = 4.4x − 205
4.4x = 205
x = 46.6
(b)(i) The "demand function" is the selling pice of the compasses:
p = 40 − 4q²
where p is the price in dollars and q is the quantity in millions of units.
Profit is revenue minus cost.
P = R − C
P = pq − 15q
P = (p − 15) q
P = (25 − 4q²) q
P = 25q − 4q³
where P is the profit in millions of dollars and q is the quantity in millions of units.
(b)(ii) Find values of q when P = 18.
18 = 25q − 4q³
4q³ − 25q + 18 = 0
We know that q=2 is a root of this equation. Using grouping:
4q³ − 8q² + 8q² − 25q + 18 = 0
4q² (q − 2) + (q − 2) (8q − 9) = 0
(q − 2) (4q² + 8q − 9) = 0
4q² + 8q − 9 = 0
Solve with quadratic formula.
x = [ -b ± √(b² − 4ac) ] / 2a
q = [ -8 ± √(8² − 4(4)(-9)) ] / 2(4)
q = (-8 ± √208) / 8
q = (-8 ± 4√13) / 8
q = (-2 ± √13) / 2
Since q is positive, q = (-2 + √13) / 2, or approximately 0.803.
The price of a holiday was increased by 11% to £870. What was the price before the increase?
Give your answer to the nearest penny.
Answer:
784
Step-by-step explanation:
My bad don't know how to explain..
(Score for Question 1: ___ of 6 points)
Refer to the equation 4x+3y=24
A Complete the table of values for at least 2 points. Show your work.
B How did you find these two values? Answer in complete sentences.
C Use the table of values to graph the line.
You must complete all parts to receive full credit.
Answer:
x y
(Score for Question 2: ___ of 5 points)
Jack's grades on his last 4 tests were 85%, 76%, 95%, and 81%. What does he need to get on his fifth test to have an average of at least 85%?
Answer:
he has to get at least a score of 88
Step-by-step explanation:
Answer:
84.25%
Step-by-step explanation:
85+76+95+81 = 337
337/4= 84.25
so Jack needs to get at least 84.25% on his fifth test to have an average of at least 85%:)
A washer and a dryer cost $796 combined. The washer cost $54 less than the dryer. What is the cost of the dryer?
Answer:
The cost of the dryer would be 425$
Step-by-step explanation:
796 - 54 = 742
742 ÷ 2 = 371
371 = washer cost
371 + 54 = 425
425 = dryer price
======================================================
Explanation:
w = cost of washer
d = cost of dryer
costs are in dollars
w+d = 796 since the two costs combine to get a total cost of $796
w = d-54 because the washer is $54 cheaper
-------------------------
Let's start with the first equation and plug in the second equation
w+d = 796
(w) + d = 796
(d-54)+d = 796 ... replace w with d-54
d-54+d = 796
2d-54 = 796
2d = 796+54 ... adding 54 to both sides
2d = 850
d = 850/2 ... dividing both sides by 2
d = 425
The dryer costs $425
We can stop here.
-------------
If you want to find the cost of the washer, then,
w = d-54
w = 425-54 .... plug in d = 425
w = 371
The washer costs $371
Note that
w+d = 371+425 = 796
which matches with the total cost we were given. This confirms our answer.
4) Cindy works part-time and earns $5.75 an hour. One week she worked
38 hours, How much money did she earn in that one week
Answer:
$218.50
Step-by-step explanation:
5.75×38=218.5
turn into dollars $218.50
please help this is timed
Philip is 4 years older than his brother. The sum of their ages is 26. How old is Philip's brother?
Answer:
Phillips brother is 11.
Step-by-step explanation:
11 + 15 = 26
Let x be age of Philip's brother.
4 + x +x = 26
2x = 26 -2
2x = 22
x = 22/2
x = 11
Philip's brother is 11 years old
What is the rule of the rotation. Did it rotate clockwise or counterclockwise? How many degrees did it rotate?
You have 12 balloons to blow up for a party. You blow up 13 of them, and your friend blows up 5 of them. What fraction of the balloons still need blowing up?
Answer:
None
Step-by-step explanation:
First of all you have 12 balloonas, and you blow up 13 of them and your friend blows up 5 of them but you only have 12. So you can’t find the right amoun.
Answer:
The Awnser is 1/4
Step-by-step explanation:
How many solutions exist for the given equation? 3x+13 3(x + 6)+1
zero
one
two
infintely many
Answer:
Two solutions.
hope that will help you
Answer:
A. zero
Step-by-step explanation:
3x + 13 = 3(x + 6) + 1
step 1. distribute 3 through the parantheses:
3x + 13 = 3(x + 6) + 1
step 2. cancel equal terms on both sides of the equation:
3x + 13 = 3x + 18 + 1
13 = 18 + 1
step 3. add the numbers:
13 = 18 + 1
13 = 19
13 ≠ 19, so there is no solution.
may i please have brainliest?
how many letters is supercalifragilisticexpialidocious i will give brainlist also give goog explination why i sholud give it to you
Answer:
Supercalifragilisticexpialidocious is 34 letters long.
Step-by-step explanation:
I see you like Fortnite by your profile picture, I play as well. I'm an OG, I have Black Knight. That's why I think you should give it to me.
еthaȵ is my Epic if you ever want to play.
which one is the coldest AMD why
Answer:
Raleigh.
Step-by-step explanation:
Just look for the Fahrenheit with the smallest number.
Answer:Raleigh
Step-by-step explanation:Your going to go for the smallest and I just took the quiz
I WILL MARK BRIANLIEST PLEASE HELP!!!
Answer:
50 degrees
Step-by-step explanation:
Angle ABE is the opposite of the angle given on two converging lines, making it the same degree :)
the top angle is angle X, but the question is "which of the following congruence statements is true?
A. none of the above
B. XYZ = XZY
C. XYZ = YXZ
D. XYZ =ZYX
You are correct. The answer is choice B.
The base angles of an isosceles triangle are congruent. The base angles are opposite the congruent sides as shown by the tickmarks.
Prove the polynomial identity. (2x−1)2+2(2x−1)=(2x+1)(2x−1) Drag and drop the expressions to correctly complete the proof of the polynomial identity. (2x−1)2+2(2x−1)=(2x+1)(2x−1) Response area+4x−2=(2x+1)(2x−1) Response area=(2x+1)(2x−1) Response area=(2x+1)(2x−1)
Answer:
Step-by-step explanation:
Given expression is,
(2x - 1)² + 2(2x - 1) = (2x - 1)(2x + 1)
To prove this identity we will take the left hand side of the equation and will prove equal to the right side.
(2x - 1)² + 2(2x - 1) = (2x - 1)(2x + 1)
4x² - 4x + 1 + 4x - 2 = (2x - 1)(2x + 1)
4x² - 1 = (2x - 1)(2x + 1)
(2x - 1)(2x + 1) = (2x - 1)(2x + 1) [Since a² - b² = (a - b)(a + b)]
2.
The heights of horses who compete in the Melbourne Derby are
normally distributed with a mean of 66 inches and a standard
deviation of 3 inches.
(a) If a horse is randomly selected from this race, what height
would you expect it to be?
(b) What percentage of horses who compete in the Melbourne
Derby have heights between 60 and 72 inches?
(c) In a particular year there are 25 horses running in the
Melbourne Derby. How many of these would you expect
to have a height of less than 63 inches?
Answer:
66 inches ;
95.44 ;
4
Step-by-step explanation:
Given that:
Normal distribution with;
Mean(m) = 66 inches
Standard deviation (s) = 3 inches
A.) If a horse is chosen at random, Expected height will be equal to the mean of the distribution = 66 inches
B.) percentage horses who are between 60 and 72 inches
Zscore = ( x - m) / s
x = 60
Zscore = (60 - 66) / 3
Zscore = - 6/3
= - 2
P(Z < - 2) = 0.0228
Zscore = ( x - m) / s
x = 72
Zscore = (72 - 66) / 3
Zscore = 6/3
= 2
P(Z < 2). = 0.9772
Between 60 and 72
0.9772 - 0.0228 = 95.44
c) In a particular year there are 25 horses running in the Melbourne Derby. How many of these would you expect to have a height of less than 63 inches?
Zscore = ( x - m) / s
x = 63
Zscore = (63 - 66) / 3
Zscore = - 3/3
= - 1
P(Z < - 1) = 0.1587
0.1587 * 25 = 3. 967 = 4
What is the solution (x,y) to the system of equations given? 2 x + 4 y = − 16 2x+4y=−16 2 y − x = = 16 2y−x==16
Answer:
(-12,2)
Step-by-step explanation:
2x + 4y = -16
2y - x = 16
Multiply the bottom part by 2.
2x + 4y = -16
4y - 2x = 32
Add the equations and the answers to the equations up, and they will equal each other.
(2x + 4y) + (4y - 2x) = -16 + 32
8y = 16
y = 2
Plug y = 2 to the 2nd equation.
2*2 - x = 16
4 - x = 16
Subtract 4 from both sides.
-x = 12
Multiply both sides by -1.
x = -12
How are 18:3 and 6:1 equivalent ratios
Answer:
You know 18:3 and 6:1 are equivalent ratios because if you take 18:3 and divide both sides by 3, 18/3:3/3, then you will get 6:1, which is clearly equal to 6:1.
18:3 and 6:1 are equivalent ratio because two ratios are in proportion
Given :
We are given with two ratios 18:3 and 6:1
We need to show that two ratios are equal
Lets take ration 18:3
Both 18 and 3 are divisible by 3
We can write the ratio in fraction form
[tex]\frac{18}{3} \\[/tex]
When we divide both top and bottom by 3 , we get
[tex]\frac{6}{1}[/tex]
we can say that [tex]\frac{18}{3} =\frac{6}{1}[/tex]
Hence, the ratios are equivalent ratios
18:3 and 6:1 are equivalent ratios
Learn more : brainly.com/question/18431407
If 4 − 7x is 5 less than 23, what is the value of 3x ?
Each student was asked to create an expression whose quotient is 1/3. each student and the response can be seen on table below.
Answer:hi I believe is is Ben and Elizabeth
Step-by-step explanation:
why? just why. why are we here? should i off myself? should i stay?
Answer:
It can be a passing thought or a question that launches a full-on existential exploration. Having a sense of meaning and purpose in life is usually a positive motivator, at home and at work. But maybe the questioning itself is where life's true mission is found...
Step-by-step explanation:
You have solved a radical equation. What should you do to check whether your proposed solution is correct?
You should check your proposed solution in any of the equations you found while looking for the solution.
You don't need to check whether your proposed solution is correct. You know you followed the proper method, so it should be fine.
You should check the proposed solution in the original equation.
You should check the proposed solution in the back of the book because it is always right.
Answer:You should check the proposed solution in the original equation.
Step-by-step explanation:
The radical is the symbol that is used to represent the root in the expression n√x. The correct option is C.
What is a radical?The radical is the symbol that is used to represent the root in the expression n√x.
You have solved a radical equation. Now, to check whether your proposed solution is correct You should check the proposed solution in the original equation.
Hence, the correct option is C.
Learn more about the Radical:
https://brainly.com/question/1369233
#SPJ2
If you lower your monthly payment, do you think the total interest you pay will increase or decrease? Why?
Answer:
increase
Step-by-step explanation:
Once Your Monthly Payment Has Been Lowered, More People Will Be Interested Do To Its Lower Payment.
The back of Dante's property is a creek. Dante would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is 960 feet of fencing available, what is the maximum possible area of the pasture?
Answer:
Step-by-step explanation:
960/3. that's 320 a side. They said maximum, I'm guessing they just wanted you to use base times height as if it was a square, since I'm not seeing any other information. the maximum possible area would be, if the sides were 320 each would be 102,400 square feet. Maximum
Use the Distributive property to find the product. 3x891=3(?-?)
Answer:
900,9
Step-by-step explanation:
distribute the 891 into something more simpler. 900 and 9. you can do 3 times 900 which is 2700 and subtract 3 times 9 from 2700 which is just saying 2700 minus 27, which in turn gives you 2673
A store sells 6 bottles of water for $2.88. Find the unit price
Answer:27 ://///
Step-by-step explanation:
Answer:
$.48 per bottle
Step-by-step explanation:
The unit price is the total price divided by the number of items
2.88/6
$.48 per bottle
Jacqueline needs 8 gallons of gas. She only has $25. The constant of proportionality of the gas is $3.75. Does she have enough money to get 8 gallons of gas?
Answer:
D. No
Step-by-step explanation:
Answer:
its D
Step-by-step explanation:
0.11+12.74(x+3)=0.08+13.49
Answer:
x = 2.210526316
Step-by-step explanation:
Answer:
[tex]x = −1.9434851[/tex]
Step-by-step explanation:
[tex]0.11 +1 2.74(x + 3) = 0.08 + 13.49 \\ 0.11 + 12.74x + 38.22 = 0.08 + 13.49 \\ 12.74x + 38.33 = 13.57 \\ 12.74x = 13.57 - 38.33 \\ 12.74x = −24.76 \\ \frac{12.74x}{12.74} = \frac{ - 24.76}{12.74} \\ x = −1.9434851[/tex]
13 over 4 times 19 over 3
Answer:
13/4*19/3=20.5833 or 20 and 7 over 12
which complex number has a distance of v17 from the origin on the complex plain
Answer:c
Step-by-step explanation: