Answer:
d. x = 7
Step-by-step explanation:
32/8 = 28/x
simplify the fraction
4/1 = 28/x
cross multiply:
4x = 28
divide both sides by 4:
x = 7
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.
If 4 − 7x is 5 less than 23, what is the value of 3x ?
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]
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:
Snow is falling steadily in Syracuse, New York. After 2 hours, 4 inches of snow has fallen. If it continues to snow at the same rate, how many inches of snow would you expect after 6.5 hours?
Answer:
13 inches of snow
Step-by-step explanation:
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
Question One
There are 7 linomen, 2 running backs, 1 fullback, and 1 quarterback on an American football team. What is the ratio, in simplest form,
of the number of linemen to the total number of players on the team?
A
1:2
B.
2:7
С
7:11
11:2
Question Two
Answer:
7:11
Step-by-step explanation:
No of linemen = 7
No of running backs = 2
No of fullback = 1
No of quarterback =1
The total no of players on the team = 7+2+1+1 = 11
We need to find the ratio of the number of linemen to the total number of players on the team.
R = 7/11
or
R = 7:11
Hence, the required ratio is 7:11.
How do you do this question?
Answer:
convergent
Step-by-step explanation:
the function increases or decreases or as the number of terms of the series increases.
Answer:
Divergent
Step-by-step explanation:
The series can be written as:
∑ 1 / (4n − 1)
We can compare this to 1 / (5n). 1 / (5n) is smaller and diverges (p-series test). Therefore, the larger function also diverges.
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.
What is the rule of the rotation. Did it rotate clockwise or counterclockwise? How many degrees did it rotate?
13 over 4 times 19 over 3
Answer:
13/4*19/3=20.5833 or 20 and 7 over 12
A dice is rolled twice.
What is the probability of getting a 2 AND a 5?
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:
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
The given table values represents a liner equation. What is the slope?
A. 2
B. 3
C. 1
D. 4
Answer:
A. 2
Step-by-step explanation:
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Use any two points given in the table of values. Let's use (1, 5), (3, 9)
Let,
[tex] (1, 5) = (x_1, y_1) [/tex]
[tex] (3, 9) = (x_2, y_2) [/tex]
Plug these values into the slope formula:
[tex] slope (m) = \frac{9 - 5}{3 - 1} [/tex]
[tex] slope (m) = \frac{4}{2} [/tex]
[tex] slope (m) = 2 [/tex]
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
multiple and divide signed numbers
Answer:
Step-by-step explanation:
Multiply answer = - 106
Divide answer = 1.25
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.
for factoring zero how do i solve? 3x^2-12x=0
Find the quotient.
−54÷−6
Answer:
9
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?
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:
giving 70 points please help I only have 20 minutes to get It.......
Answer: 8
Step-by-step explanation:
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.
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 school is purchasing new athletic uniforms for the basketball team. Each uniform costs the school $50.00. The school pays a $80.00 flat shipping fee. If the school spends $830.00 on the order, how many uniforms, did they purchase? a. Write the equation to solve the problem. b. Find the solution
Answer:
15 uniforms.
Step-by-step explanation:
830-80=750/50=15 : )
7x + 4y
if x = 5 and y = -3
Answer: 23
Step-by-step explanation: Plug in your values:
7(5) + 4(-3)
35 + (-12)
35 - 12
23
Hope this helps!
A sample of employees of Worldwide Enterprises is to be surveyed about a new health
care plan. The employees are classified as follows:
Classification Event Number of Employees
Supervisors A 120
Maintenance B 50
Production C 1,460
Management D 302
Secretarial E 68
(a) What is the probability that the first person selected is:
(i) either in maintenance or a secretary?
(ii) not in management?
(c) Are the events in part (a)(i) complementary or mutually exclusive or both
Using the probability concept, it is found that:
a) i) There is a 0.059 = 5.9% probability that the first person selected is either in maintenance or a secretary.
ii) There is a 0.849 = 84.9% probability that the first person selected is not in management.
b) The events are neither complementary nor mutually exclusive.
A probability is the number of desired outcomes divided by the number of total outcomes.
Item a:
In this problem, there is a total of 120 + 50 + 1460 + 302 + 68 = 2000 people.
Of those, 50 + 68 = 118 are either in maintenance or a secretary, hence:[tex]p = \frac{118}{2000} = 0.059[/tex]
There is a 0.059 = 5.9% probability that the first person selected is either in maintenance or a secretary.
Item ii:
2000 - 302 = 1698 people are not in management, hence:
[tex]p = \frac{1698}{2000} = 0.849[/tex]
There is a 0.849 = 84.9% probability that the first person selected is not in management.
Item b:
If a person is either in maintenance or a secretary, they are also not in management, hence the events are neither complementary nor mutually exclusive.
To learn more about the probability concept, you can take a look at https://brainly.com/question/24437717
Following are the solution to the given points:
For point a:
i)
[tex]\to P(B \cup E) = P(B) + P(E) - P( B\cap E)[/tex]
Where [tex]P(B \cap E) = 0[/tex] because they are both separate occasions It is impossible to be a member of both departments.
[tex]\to P(B\cup E) =\frac{50}{120 + 50 + 1460 + 302 + 68} +\frac{68}{120 + 50 + 1460+ 302 +68}\\\\[/tex]
[tex]=\frac{50}{2000} +\frac{68}{2000}\\\\=\frac{50+68}{2000} \\\\=\frac{118}{2000} \\\\=\frac{ 59}{1000} \\\\=0.059\\[/tex]
ii)
[tex]\to P(D^c) = 1 - P(D)[/tex]
[tex]=1- (\frac{302}{120+50+1460+302+68})\\\\=1- (\frac{302}{2000})\\\\=1- (\frac{ 151}{1000})\\\\= 1- 0.151 \\\\= 0.849\\\\[/tex]
For point b:
Please find the attached file.
For point c:
Events in a. I are mutually incompatible since [tex]P(B \cap E) = 0[/tex]. One would be a part of the both departments.
Learn more:
brainly.com/question/20661176
The body of 150lb person contains 2.3x10-4 lbs of copper. How much copper is contaned