Answers
Answer:
[tex]12 {y}^{9} - 6 {y}^{5} + 4 {y}^{2} + 21[/tex]
Step-by-step explanation:
divide each term by 2y^3
Multiply through by the least common denominator.
Related Questions
Why should you find the least common denominator when adding or subtracting rational expressions?
Answers
Answer:
It is necessary to look for the least common denominator when one is trying to add or subtract rational expressions that do not have the same denominator.
Step-by-step explanation:
for example the denominator of the two addends are not the same. One has (x+2), the other (x-2).
which of the following graph represents the solution set for the inequality 3 - 1/2 x > 10
Answers
Answer:
56
Step-by-step explanation:
Evaluate 7(-4) - |-6| + |4| a 13 b -18 c -30
Answers
Answer:
C. -30
Step-by-step explanation:
We would have to do order of operations or P.E.M.D.A.S. So fist we would do 7 times -4 which is -28 than we would do the absolute value of -6 which is 6 so we would do -28-6 which is -34 and we would do the absolute value of 4 which is 4 and we would add it to -34 which is -30 so our final answer would be C. -30
Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter λ = 0.0143. (a) What is the probability that the distance is at most 100 m? What is the probability that the distance is at most 200 m? What is the probability that the distance is between 100 m and 200 m? (b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations? (c) What is the value of the median distance?
Answers
Answer and Step-by-step explanation: For an exponential distribution, the probability distribution function is:
f(x) = λ.[tex]e^{-\lambda.x}[/tex]
and the cumulative distribution function, which describes the probability distribution of a random variable X, is:
F(x) = 1 - [tex]e^{-\lambda.x}[/tex]
(a) Probability of distance at most 100m, with λ = 0.0143:
F(100) = 1 - [tex]e^{-0.0143.100}[/tex]
F(100) = 0.76
Probability of distance at most 200:
F(200) = 1 - [tex]e^{-0.0143.200}[/tex]
F(200) = 0.94
Probability of distance between 100 and 200:
F(100≤X≤200) = F(200) - F(100)
F(100≤X≤200) = 0.94 - 0.76
F(100≤X≤200) = 0.18
(b) The mean, E(X), of a probability distribution is calculated by:
E(X) = [tex]\frac{1}{\lambda}[/tex]
E(X) = [tex]\frac{1}{0.0143}[/tex]
E(X) = 69.93
The standard deviation is the square root of variance,V(X), which is calculated by:
σ = [tex]\sqrt{\frac{1}{\lambda^{2}} }[/tex]
σ = [tex]\sqrt{\frac{1}{0.0143^{2}} }[/tex]
σ = 69.93
Distance exceeds the mean distance by more than 2σ:
P(X > 69.93+2.69.93) = P(X > 209.79)
P(X > 209.79) = 1 - P(X≤209.79)
P(X > 209.79) = 1 - F(209.79)
P(X > 209.79) = 1 - (1 - [tex]e^{-0.0143*209.79}[/tex])
P(X > 209.79) = 0.0503
(c) Median is a point that divides the value in half. For a probability distribution:
P(X≤m) = 0.5
[tex]\int\limits^m_0 f({x}) \, dx[/tex] = 0.5
[tex]\int\limits^m_0 {\lambda.e^{-\lambda.x}} \, dx[/tex] = 0.5
[tex]\lambda.\frac{e^{-\lambda.x}}{-\lambda}[/tex] = [tex]-e^{-\lambda.x} + e^{0}[/tex]
[tex]1 - e^{-\lambda.m}[/tex] = 0.5
[tex]-e^{-\lambda.m}[/tex] = - 0.5
ln([tex]e^{-0.0143.m}[/tex]) = ln(0.5)
-0.0143.m = - 0.0693
m = 48.46
Find the area of the trapezoid in the figure below round your final answer to the nearest tenth
Answers
Answer: 60.9 u^2
Step-by-step explanation:
The area of a trapezoid can be calculated as seen in the attachment.
Thus:
[tex]A = \frac{3.7+14.2}{2} * 6.8\\A = \frac{17.9}{2} *6.8\\A = 8.95*6.8\\A = 60.86\\Round\\\left[\begin{array}{c}A=60.9\end{array}\right][/tex]
Hope it helps <3
Answer:
60.9 units^2
Step-by-step explanation:
Well the formula for the area of a trapezoid is,
[tex]\frac{b1+b2}{2} h[/tex]
So b1 and b2 are 142 and 3.7,
14.2 + 3.7 = 17.9
17.9 ÷ 2 = 8.95
8.95 × 6.8 = 60.86
60.9 units^2 rounded to the nearest tenth.
Thus,
the area of the trapezoid is 60.9 units^2.
Hope this helps :)
Enter the correct answer in the box by replacing the values of a and b. f(x) = a(b)^x
Answers
Answer:
f(x)= 8(0.5)^x
Step-by-step explanation:
As you can see on the graph there are two specific points labeled:
(0,8) and (1,4)
The 8 would be the initial value and starting point of the "design"
A is always the initial value so replace that.
Then proceed to divide 4 by 8 to figure out the percentage change its 0.5
leave x as it is
Tubby Toys estimates that its new line of rubber ducks will generate sales of $7 million, operating costs of $4 million, and a depreciation expense of $1 million. If the tax rate is 25%, what is the firm’s operating cash flow?
Answers
Answer:
2.5m
Step-by-step explanation:
Using the adjusted accounting profits method.
Operating cash flow = After - tax profit + Depreciation. .......... ( 1 )
Given that :
* depreciation expense = $1 million
* Sales generated $7 million
* Tax rate = 25%
Tax rate = 25/100
= 0.25
From equation 1
= ( 7m - 4m - 1m ) ×( 1 - 0.25 ). + 1m
= ( 7m - 5m ) × ( 0.75 ) + 1m
= 2m × 0.75 + 1m
= 1.5m + 1m
= 2.5m
The firm operating cash flow = 2.5m
Suppose you deposit $600 into an account that pays 5% annual interest, compounded continuously. How much will you have in the account in 4 years? ƒ(t) = aert A) $4,433.43 B)635.62 C)$729.30 D)$732.84
Answers
Answer:
D)$732.84
Step-by-step explanation:
A=p(1+r/n)^nt
P=principal=$600
r=5%=0.05
t=4 years
n=12 months
A=p(1+r/n)^nt
=600(1+0.05/12)^12*4
=600(1+0.0041666666666 )^48
=600(1.0041666666666 )^48
=600( 1.2208953550215 )
=732.53
A=$732.53
Option D)$732.84 is the answer
assume that when adults with smartphones are randomly selected 42 use them in meetings or classes if 15 adult smartphones are randomly selected, find the probability that "fewer" than 4 of them use their smartphones
Answers
Complete Question
Assume that when adults with smartphones are randomly selected 42% use them in meetings or classes if 15 adult smartphones are randomly selected, find the probability that "fewer" than 4 of them use their smartphones
Answer:
The probability is [tex]P[X < 4]= 0.00314[/tex]
Step-by-step explanation:
From the question we are told that
The proportion of those that use smartphone in meeting and classes is p = 0.42
The sample size is [tex]n = 15[/tex]
The proportion of those that don't use smartphone in meeting and classes is
[tex]q = 1- p[/tex]
=> [tex]q = 1- 0.42[/tex]
=> [tex]q = 0.58[/tex]
Now from the question we can deduce that the usage of the smartphone is having a binomial distribution since there is only two outcome
So the probability that "fewer" than 4 of them use their smartphones is mathematically evaluated as
[tex]P[X < 4 ] = P[X = 0] + P[X = 1] +P[X = 2] +P[X = 3][/tex]=
=> [tex]P[X < 4] = [ \left 15} \atop {0}} \right. ] p^{15-0} * q^0 + [ \left 15} \atop {1}} \right. ] p^{15-1 }* q^1 + [ \left 15} \atop {2}} \right. ] p^{15-2 }* q^2 + [ \left 15} \atop {3}} \right. ] p^{15-3 }* q^3[/tex]
Where [tex][\left 15} \atop {0}} \right. ][/tex] implies 15 combination 0 which has a value of 1 this is obtained using a scientific calculator
So for the rest of the equation we will be making use of a scientific calculator to obtain the combinations
[tex]P[X < 4] = 1 * ^{15} * q^0 + 15 * p^{14 }* q^1 + 105 * p^{13 }* q^2 + 455 * p^{12 }* q^3[/tex]
substituting values
[tex]= 1 * (0.42)^{15} * (0.58)^0 + 15 * (0.42)^{14 }* (0.58)^1[/tex]
[tex]+ 105 * (0.42)^{13 }* (0.58)^2 + 455 * (0.42)^{12 }* (0.58)^3[/tex]
=> [tex]P[X < 4]= 0.00314[/tex]
Belen wants to create a nut-mix. She can buy peanuts for $1.80 per pound and cashews for $4.50 per pound. If she wants to make a 10 pounds of nut-mix at a cost of $2.61 per pound, how many pounds of peanuts and how many pounds of cashews should she buy?
Answers
Answer:
7 and 3 respectively
Step-by-step explanation:
Peanuts (p/lb) = $1.80
Cashews (p/lb) = $4.50
Total pound = 10 pounds
Aggregate amount (at $2.61 per lb) = $26.1
Pound of peanut to buy = x
Pound of cashew to buy = y
x + y = 10..........(i)
1.8x + 4.5y = 26.1.....(ii)
Multiply equ (i) by 1.8 and equ (ii) by 1
1.8x + 1.8y = 18
1.8x + 4.5y = 26.1
Subtract (i) from (ii)
4.5y - 1.8y = 26.1 - 18
2.7y = 8.1
y = 3
Sub y = 3 into (i)
x + y = 10
x + 3 = 10
x = 10 - 3
= 7
Pounds of peanut to buy = 7 pounds
Pounds of cashew to buy = 3 pounds
Please help with this
Answers
Answer: B
Step-by-step explanation:
Because of Supplementary Angles, we know that the two angles in the right side of the equation add up to 90.
Hope it helps <3
A scale diagram of a garden shows the length as 14.5cm. If the scale is 1:150, what is the actual length? The garden is _______m in length.
Answers
Answer:
21.75m
Step-by-step explanation:
14.5×150 =2175cm
1m =100cm
to convert into m divide 2175 by 100
=21.75m
Geographers use negative numbers to represent points below sea level and positive numbers to represent points above sea level. For example, the lowest point in Minnesota is at -17.3−17.3minus, 17, point, 3 meters, and the highest point is at 14.114.114, point, 1 meters.
What does 000 meters represent?
plzz hurry
Choose 1 answer:
Choose 1 answer:
(Choice A, Checked)
A
The lowest point in Apple Valley
(Choice B)
B
The lowest point in Minnesota
(Choice C)
C
Sea level
Answers
Answer:
C . Sea level
Step-by-step explanation:
If points below the sea level are represented using negative numbers; and
Points above the sea level are represented using positive numbers.
The point labeled 0 meters represents the sea level since it is the indicator of whether a point is positive or negative.
The correct option is C.
Answer:
A) Sea level
Step-by-step explanation:
Determine which type of correlation is shown in the graphed relationship
Answers
Answer:
No correlation
Step-by-step explanation:
Hey there! :)
This has no correlation because all the points are spread out throughout the graph making no correlation.
Answer:
D no correlation
Step-by-step explanation:
too many scattered dot all over the place if its some going up down its NO CORRELATION!!!
Identify the parameter n in the following binomial distribution scenario. A basketball player has a 0.479 probability of
making a free throw and a 0.521 probability of missing. If the player shoots 17 free throws, we want to know the probability
that he makes more than 9 of them. (Consider made free throws as successes in the binomial distribution.)
Answers
Answer:
n = 17
Step-by-step explanation:
Assuming
- probability of success (making free throw) does not vary
We have
n = 17 (trials)
p = 0.479
x > 9
The answer is "[tex]\bold{p(x>9)=0.2550319}[/tex]"
[tex]\to X:[/tex] Number of creating free throws in a set [tex]\bold{17\ \ x \sim bin(17,0.479)}[/tex]
Know we calculating the P(makes more than 9 of them)
[tex]=\bold{9(X>9)=1-P(Z<=9)}[/tex]
Using the R-code:
[tex]\to \bold{1-p\ binom(9,17,0.479)}\\\\\to \bold{[1]0.2550319}\\\\\bold{\therefore}\\\\ \to \bold{p(x>9)=0.2550319}[/tex]
Learn more:
binomial distribution: brainly.com/question/9065292
x/3 ≥−33 solve for x answer must be simplified
Answers
Answer:
[tex]\boxed{x\geq -99}[/tex]
Step-by-step explanation:
[tex]\frac{x}{3} \geq -33[/tex]
[tex]\sf Multiply \ both \ sides \ by \ 3.[/tex]
[tex]\frac{x}{3} (3) \geq -33(3)[/tex]
[tex]x\geq -99[/tex]
Answer:
[tex]\boxed{\red{x \geqslant - 99}}[/tex]
Step-by-step explanation:
[tex] \frac{x}{3} \geqslant - 33 \\ x \geqslant - 33 \times 3 \\ x \geqslant - 99[/tex]
hope this helps you!
A jet flies 425 km from Ottawa to Québec at rate v + 60. On the return flight, the
plane encountered wind resistance and travelled at rate v - 40. What is the
difference in flight times of the initial and return flights?
Answers
Answer:
a. [tex] \frac{- 42,500}{(v + 60)(v - 40)} [/tex]
Step-by-step Explanation:
Given:
Distance Ottawa to Québec = 425 km
Initial flight rate = v + 60
Return flight rate = v - 40
[tex] t = \frac{d}{r} [/tex]
Required:
Flight times difference of the initial and return flights
Solution:
=>Flight time of the initial flight:
[tex] t = \frac{d}{r} [/tex]
[tex] t = \frac{425}{v + 60} [/tex]
=>Flight time of the return flight:
[tex] t = \frac{425}{v - 40} [/tex]
=>Difference in flight times:
[tex] \frac{425}{v + 60} - \frac{425}{v - 40} [/tex]
[tex] \frac{425(v - 40) -425(v + 60)}{(v + 60)(v - 40)} [/tex]
[tex] \frac{425(v) - 425(40) -425(v) -425(+60)}{(v + 60)(v - 40)} [/tex]
[tex] \frac{425v - 17000 -425v - 25500}{(v + 60)(v - 40)} [/tex]
[tex] \frac{425v - 425v - 17000 - 25500}{(v + 60)(v - 40)} [/tex]
[tex] \frac{- 42,500}{(v + 60)(v - 40)} [/tex]
6th grade math help me, please :)))
Answers
Answer:
700✖️0.08=56 people is late
700✖️0.12=84 people bought the shirt.
Step-by-step explanation:
8%=0.08
12%=0.12
700✖️0.08=56 people is late
700✖️0.12=84 people bought the shirt.
HOPE THIS HELPS!
Find the balance in Asturos savings account if he deposits $2100 at 3.5% simple interest for 2 years
Answers
Answer:
2250
Step-by-step explanation:
Balance : 2100
2 Years
2100 ÷ 100 x 103.5 ÷ 100 x 103.5 = 2249.5725
How much would a computer system cost if you pay $200 down and made 12 monthly payments of only $98.95?
Answers
Answer:
$1387.4
Step-by-step explanation:
Total cost for the computer will be sum of down payments and monthly installments.
____________________________________
Given
down payment = $200
monthly installment value = $98.85
no. of installments = 12
total value of monthly installments = 12*98.95 = $1187.4
Total cost of computer system = $200+ $1187.4 = $1387.4
PLEASE HELP QUICK!!! A bowl has 85 pieces of candy. Nineteen children empty the bowl of candy. Some children take 3 pieces, some children take 5 pieces, and 1 child takes 7 pieces of candy. How many children take 3 pieces of candy?
Answers
Answer: 3 kids take 3 pieces of candy each
Step-by-step explanation:
Let the number of children that took 3 pieces is x ( total take 3*x pieces of candy)
Number of children that took 5 pieces is y ( total take 5*y pieces of candy)
1 child took 1 piece that actually means that x+y=18 and 3*x+5*y=84.
( Because total number of all kids is 19. We just deduct one kid (Let his name is John) who took only 1 candy. So we have 19-1 =18 kids without John. The similar is with the candies. Total number is 85. We deduct 1 piece which John has taken. )
So we have 2 equations or the system of 2 equations:
1). x+y=18
2). 3*x +5*y=84
Multuply both sides of equation 1) by 3
We have 3*x+3*y=18*3
Deduct 3*y from both sides of this equation
3*x+3*y-3*y=54-3*y
3*x=54-3*y
Substitute 3*x in equation 2). by 54-3*y
2) 54-3*y+5*y=84
2*y=30
y=15 ( kids take 5 pieces of candy each)
Using equation 1) find x
x+15=18
x=3 (kids take 3 pieces of candy each)
I really need help on this question
Answers
Answer:
d. 38
Step-by-step explanation:
AB = AD - BD = 54 - 36 = 18
AC = AB + BC = 18 + 20 = 38
An anchor lowered at a constant rate into the ocean takes 5 seconds to move -17.5 meters. What is the rate of the anchor in meters per second?
Answers
Answer:
-3.5 meters per second
Step-by-step explanation:
Take the distance and divide by the time
-17.5 meters/ 5 seconds
-3.5 meters per second
Answer:
-3.5 m/s
Step-by-step explanation:
Rate of the anchor = [tex]\frac{distance}{time}[/tex]
[tex]\frac{-17.5}{5}[/tex]
-3.5 meters per second.
A car with a standard engine costs $14 000 to purchase and 25€/km to drive. An electric car costs S15 000
to purchase and 20¢/km to operate. How many kilometres would you have to drive for the costs of the
cars to be the same?
Answers
Answer:
200km
Step-by-step explanation:
Car A purchase worth = $14000
Car B purchase worth = $15000
Car A drive worth= 25€ per km
Car B drive worth= 20€ per km
For the worth of the two cars to be equal let's first assume all of the currency to be in dollars$
For A
Worth= 14000+25(x)
For B
Worth= 15000+20(x)
Where x is the distance covered
For the both worth to be equal we equate.
14000+25(x)= 15000+20(x)
25x-20x= 15000-14000
5x= 1000
X= 200
The distance covered by the two cars for the worth to be equal is 200km
the endpoints of GH are g(-7,3) and h(1,-2) what’s the midpoint of GH
Answers
Answer: [tex]\bigg(-3,\dfrac{1}{2}\bigg)[/tex]
Step-by-step explanation:
G = (-7, 3) H = (1, -2)
[tex]M_{GH}=\bigg(\dfrac{X_G+X_H}{2},\dfrac{Y_G+Y_H}{2}\bigg)\\\\\\.\qquad = \bigg(\dfrac{-7+1}{2},\dfrac{3+(-2)}{2}\bigg)\\\\\\.\qquad = \bigg(\dfrac{-6}{2},\dfrac{1}{2}\bigg)\\\\\\.\qquad = \large\boxed{\bigg(-3,\dfrac{1}{2}\bigg)}[/tex]
The mid point of the line GH whose end points are (-7,3) and (1,-2) is (-3,1/2).
What is the mid point of a line?The mid point is a line which divides the line into two equal parts. The formula to calculate the mid point of line whose end points are (x1,y1) and (x2,y2) is {(x1+x2)/2,(y1+y2)/2}.
How to calculate mid point of a line?To calculate the mid point of the line GH we have to put x1=-7, x2=1,y1=3 and y2=-2 so,
the mid point is {(-7+1)/2,(3-2)/2}
=(-3,1/2)
Hence the mid points of a line GH whose end points are g(-7,3) and h(1,-2) is (-3/1/2).
Learn more about mid point of a line at https://brainly.com/question/18315903
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Determine all numbers at which are function Continuous..
f(x)={
x^2 + 5x - 36/
x^2 + 8x - 9
if x≠-9
if x= -9}
a.
continuous at every real number except x = 1 and x = -9
b. continuous at every real number except x = -9
c.continuous at every real number except x = 1
d. continuous at every real number except x = -9 and x = 4
Answers
Answer:
For this case we have this function:
[tex] f(x) =\frac{x^2 +5x-36}{x^2 +8x-9}, x=9[/tex]
We can factor the denominator and we got:
[tex] f(x) =\frac{x^2 +5x-36}{(x+9)(x-1)}, x=9[/tex]
And since we can't divide by 0 then the value of x can't be 1 or -9 so then the best answer for this case would be:
Continuous at every real number except x=1 and x=-9
Step-by-step explanation:
For this case we have this function:
[tex] f(x) =\frac{x^2 +5x-36}{x^2 +8x-9}, x=9[/tex]
We can factor the denominator and we got:
[tex] f(x) =\frac{x^2 +5x-36}{(x+9)(x-1)}, x=9[/tex]
And since we can't divide by 0 then the value of x can't be 1 or -9 so then the best answer for this case would be:
Continuous at every real number except x=1 and x=-9
Answer:
A or continuous at every real number except x=1 and x=-9
Step-by-step explanation:
Just took the test :)
What would be the Excel Formula to solve this question?
Deb and Rusty know that buying a house will save them money on taxes because they get to deduct the interest they pay to the bank each year and the property taxes they pay each year. First create a separate worksheet from the amortization schedule. Title this worksheet Analysis. In this worksheet, create a column titled Income starting at $90,000 and increasing at 3% for 20 years. What is their income after 20 years?
Answers
Answer:
Income after 20 years = 162550.01
Step-by-step explanation:
In cell B2, enter 90000
In cell B3, enter +B2*1.03
Copy cell B3 to cells B4:B22
Set number format for column B to 2 decimal places.
Read cell B22 = 162550.01
Income after 20 years = 162550.01
Their income after 20 years would be; 72,550 dollars.
What is income tax?Income tax is a tax applied on individuals or entities concerning income or profit earned by them.
The income after 20 years can easily be determine by using compounding
Thus the formula;
Future Value = Present Value (1 + I)^ 20
= 90,000 (1 + 0.03)^ 20
= 162,550 dollars
Income can be determing by subtracting Pv from Fv i.e
Income = 162,550 - 90,000 = 72,550
Calculation on excel sheet;
A B C D
1 90,000 1.03 = A1 x1.03 = C1-A1
2 = D1 1.03 = A2 x 1.03 = C2-A2
20 = D19 1.03 = A20 x 1.03 = A20 - C20
Thus, In work sheet colunm D will show the income on investment.
Learn more about income;
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A movie earned $438 million at the box office in
2013. That is 24% more than book of the same
name earned. Estimate how much the book
earned?
Round your answer to the nearest hundredth of
a million dollars.
Answers
Answer:
332.88 million
Step-by-step explanation:
you do the thing
You can take 76% of 438 to find the answer
x(x+3)(x+3)=0 Please I NEED HELP FAST! PLLLLLLLLLLLLLLLLLLLLLLLLLLEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEAAAAAAAAAAAAAAAAAAAAAAAAAAAAASSSSSSSSSSSSSSSSSSSSSSSSSSEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!
Answers
Answer:
[tex]\boxed{x^3+6x^2+9x}[/tex]
Step-by-step explanation:
[tex]x(x+3)(x+3)[/tex]
Resolving the first parenthesis
[tex](x^2+3x) (x+3)[/tex]
Using FOIL
[tex]x^3+3x^2+3x^2+9x[/tex]
Adding like terms
[tex]x^3+6x^2+9x[/tex]
[tex]\text{If } \: a\cdot b \cdot c = 0 \text{ then } a=0 \text{ or } b =0 \text{ or } c=0 \text{ or all of them are equal to zero.}[/tex]
[tex]x(x+3)(x+3) =0[/tex]
[tex]\boxed{x_1 =0}[/tex]
[tex]x_2+3 =0[/tex]
[tex]\boxed{x_2 = -3}[/tex]
[tex]x_3+3 =0[/tex]
[tex]\boxed{x_3 = -3}[/tex]
During the summer months Terry makes and sells necklaces on the beach. Last summer he sold the necklaces for $10 each and his sales averaged 20 per day. When he increased the price by $1, he found that the average decreased by two sales per day. If the material for each necklace costs Terry $6, what should the selling price be to maximize his profit?
Answers
Answer:
The selling price in other to maximize his profit is $13
Step-by-step explanation:
In the above question we are given the following information:
Cost of material per necklace = $6
Firstly, terry sold 20 necklaces per day
= $10 each
Later he increased he increased the prices by 1 dollar and the number of necklaces he sold reduced by 2
Mathematically
18 necklaces = $11 each
Step 1
We find the Cost function C(x)
Let's assume that x = number of necklaces sold
If each material cost $6 , then
C(x) = 6 × x = 6x
Step 2
P(Profit) = R(x) - C(x)
R(x) = Revenue
Where Revenue = x × p(x)
Since p(20) = 10 and p(18) = 11
p(x) = -1/2x + 20
P(Profit) = x ( -1/2x + 20) - C(x)
C(x) = 6x
P = x(-1/2x + 20) - 6x
P = -1/2x² + 20x - 6x
P = -1/2x² + 14x
Step 3
We maximise the profit by differentiating P
P = Profit
P = -1/2x² + 14x
We differentiate P to find x
∆P/∆x = dp/dx = -x + 14
-x + 14 = 0
-x = -14
x = 14
Hence, we substitute 14 for x in the price function
p(x) = - 1/2x + 20
since , x = 14
p(14) = - 1/2 × 14 + 20
= -7 + 20
= $13
Therefore, the selling price function to maximize his profit is $13
Above question the given data:
Cost of material per necklace = $6 Terry sold 20 necklaces per day = $10 each Price increase by 1 dollar Number of necklaces sold reduced by 2
1.Cost function C(x)
Let's assume that x = number of necklaces sold
If each material cost $6 , then
C(x) = 6 × x
C(x) = 6x
2.P(Profit) = R(x) - C(x)
R(x) = Revenue ,Where Revenue = x × p(x)
Given data:
p(20) = 10
p(18) = 11
p(x) = -1/2x + 20
P(Profit) = R(x) - C(x)
P(Profit) = x ( -1/2x + 20) - C(x)
P = x(-1/2x + 20) - 6x
P = -1/2x² + 20x - 6x
P = -1/2x² + 14x
3.Maximise Profit
P = Profit
P = -1/2x² + 14x
We differentiate P to find x
∆P/∆x = dp/dx = -x + 14
-x + 14 = 0
-x = -14
x = 14
Now, we will substitute 14 for x in the price function
Now ,p(x) = - 1/2x + 20
since , x = 14
p(14) = - 1/2 × 14 + 20
p(14)= -7 + 20
p(14)= $13
Thus, the selling price function to maximize his profit is $13.
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