The marginal cost function is MC(x) = 5, the marginal revenue function is MR(x) = 8 - 0.002x, and the marginal profit function is MP(x) = MR(x) - MC(x). The quantity at which the marginal profit is zero is x = 1500.
Explanation:The marginal cost (MC) function represents the change in total cost when one additional unit is produced. It can be calculated by taking the derivative of the total cost function with respect to quantity (x). In this case, the total cost function is given as C(x) = 5x, so the marginal cost function is MC(x) = 5.
The marginal revenue (MR) function represents the change in total revenue when one additional unit is sold. It can be calculated by taking the derivative of the total revenue function (R(x)). In this case, the total revenue function is R(x) = 8x − 0.001x^2, so the marginal revenue function is MR(x) = 8 - 0.002x.
The marginal profit (MP) function represents the change in profit when one additional unit is produced and sold. It can be calculated by subtracting the marginal cost from the marginal revenue: MP(x) = MR(x) - MC(x).
To find all values of x for which the marginal profit is zero, set the marginal profit function equal to zero and solve for x: 0 = MR(x) - MC(x). In this case, 0 = (8 - 0.002x) - 5. Solving for x gives x = 1500, which is the quantity at which the marginal profit is zero.
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Which of these inequalities has no solutions?
use the geometric mean to find the 7th term in a geomtric sequence if the 6th term is 75 and the 8th term is 48.
Write an equation in slope-intercept form for the line that passes through (4, -4) and is parallel to 3 + 4x = 2y – 9.
what is the lcm of 4 and 10
The two shorter sides of a triangle are the same length. the length of the longer side is 5 m longer than each of the shorter sides. the perimeter of the triangle is 29 m
Maximum value of (log x)/x
Explain how unwrapping a present is used as an analogy for solving an equation. How do you "unwrap" with an equation?
...?
Solving an equation is likened to unwrapping a present because in both cases, you aim to uncover what's within by dealing with the outer layers systematically. Through an inverse process, you isolate the equation's variable and solve for it, just as the step-by-step unwrapping of layers reveals the gift within the package.
Explanation:Unwrapping a present is a great way to understand the process of solving an equation. If you consider the equation itself as being 'wrapped' in different operations such as multiplication, division, addition, and subtraction, you can begin to 'unwrap' it by systematically dealing with these operations in reverse from the order of operations. This would be like when you unpack the present by undoing the tape, then the paper, then the box, or whatever other layers might be present.
To use a direct example, let's consider the equation 3x + 7 = 22. You start unwrapping by isolating for the term with the variable. This means you handle the operation that does not involve the variable first. So, subtract 7 from both sides of the equation to get 3x = 15. Next, you handle the multiplication operation by dividing both sides by 3 and solving for x, which would be 5 in this case. Just like unwrapping a present, we aim to get to the 'inside' or the root of the equation.
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An audience of 450 people is seated in an auditorium. Each row contains the same number of seats and each seat in the auditorium is occupied. With three fewer seats per row, and five extra rows, the same audience could still be seated, occupying all seats. How many rows does the auditorium have? ...?
Answer with Step-by-step explanation:
Let there be r rows and s seats in every row.
An audience of 450 people is seated in an auditorium and each seat is occupied.
i.e. rs=450
or s=450/r
With three fewer seats per row, and five extra rows, the same audience could still be seated, occupying all seats.
i.e. (s-3)(r+5)=450
s(r+5)-3(r+5)=450
rs+5s-3r-15=450
450+5s-3r-15=450
Subtracting both sides by 450,we get
5s-3r-15=0
i.e. 5s-3r=15
5(450/r)-3r=15
Dividing both sides by 3 and multiplying by r, we get
750-r²=5r
r²+5r-750=0
r² + 30r - 25r - 750 = 0
r(r + 30) - 25(r + 30) = 0
(r + 30)(r - 25) = 0
either r+30=0 or r-25=0
either r= -30 or r=25
r can't be negative
Hence, number of rows in auditorium are:
25
Two cars, car X and car Y , start moving from the same point P on a cross intersection. Car X is travelling east and car Y is travelling north. Some time later car X is 60 km east of point P and travelling in an easterly direction at 80 km/h and car Y is 80 km north of point P and travelling in a northerly direction at 100 km/h. How fast is the distance between car X and car Y changing?
Lee Wong receives an annual salary of $65,000 from CVS Pharmacy. Today his boss informs his that he will be getting a $3,000 raise. The percent increase rounded to the nearest tenth percent is:
Lee Wong's annual salary raise of $3,000 represents a 4.6% increase from his original salary of $65,000 when rounded to the nearest tenth of a percent.
To calculate the percentage increase of Lee Wong's salary, we use the formula for percentage change: Percentage Change = (Change in Quantity / Original Quantity) × 100%. In this case, the change in quantity is the raised amount of $3,000, and the original quantity is the original salary of $65,000.
Percentage Increase = ($3,000 / $65,000) × 100% = 0.04615 × 100% = 4.615%. Rounded to the nearest tenth of a percent, Lee Wong's salary increase is 4.6%.
Jeanette wants to tile the floor of a room in her house. The square tiles measure 3/4 ft on each side. The room is 10 ft wide.
a. Write an inequality to describe how many tiles are needed to make one row of tiles across the width of the room.
b. Solve the inequality.
c. How many tiles should Jeanette buy to form one row?
Answer:
a. The inequality will be: [tex]\frac{3}{4}x\geq 10[/tex]
b. Solving the inequality: [tex]x\geq 13.333...[/tex]
c. Jeanette should buy 14 tiles to form one row.
Step-by-step explanation:
Suppose, the number of tiles needed to make one row [tex]=x[/tex]
Each square tiles measure [tex]\frac{3}{4}[/tex] ft on each side.
So, the total length of [tex]x[/tex] number of tiles [tex]=\frac{3}{4}x\ ft[/tex]
Given that, the room is 10 ft wide.
So, the inequality will be: [tex]\frac{3}{4}x\geq 10[/tex]
Solving the above inequality.....
[tex]\frac{3}{4}x\geq 10\\ \\ 3x\geq 4(10)\\ \\ 3x\geq 40\\ \\ x\geq \frac{40}{3}\\ \\ x\geq 13.333...\\ \\ x\approx 14[/tex]
So, Jeanette should buy 14 tiles to form one row.
A caterer has 5 rolls. He is ordering more rolls. He can order up to 9 packages of rolls and each package contains 12 rolls. The caterer cannot order partial packages. The function that models the number of rolls the caterer has is f(p)=12p+5f(p)=12p+5, where p is the number of packages the he orders.
What is the practical domain of the function?
A: all real numbers from 1 to 9, inclusive
B: {17, 29, 41, 53, 65, 77, 89, 101, 113}{17, 29, 41, 53, 65, 77, 89, 101, 113}
C: all integers from 1 to 9, inclusive
D: all real numbers
The practical domain of the function f(p) = 12p + 5 is all integers from 1 to 9, inclusive.
The practical domain of the function f(p) = 12p + 5 refers to the set of all possible values that p, the number of packages of rolls, can take given the constraints of the situation described. Since the caterer cannot order partial packages and can order up to 9 packages, p must be an integer from 1 to 9 inclusive.
Moreover, these are the only values that make sense in the context of this problem since ordering 0 packages will not change the quantity of rolls they already have and ordering more than 9 packages is beyond the caterer's limit.
A school conducts 27 test and 36 weeks assume the school conducts test at a constant rate what is the slope of the line that represents the number of tests on the Y axis and the time in weeks on the X axis
A: 3/4
B: 4/3
C: 3
D: 4
Answer:
3/4
Step-by-step explanation:
I got it right.
Which expression is equivalent to 6x−2(7x−3)?
a.)17x
b.) 14x
c.)−14x+12
d.)−8x+6
Identify the horizontal translation of the parent function. step by step
y=(x-4)^2
Suppose you note that there are congruent vertical angles in the triangles. Can you now use the ASA Postulate, the AAS Theorem, or both to prove the triangles congruent?
9% percent are in the band. the band has 180 members.how many people are in school
The correct answer is that there are 2000 people in the school.
To solve this problem, we can set up a proportion based on the information given. We know that 9% of the school's population is in the band, and the band has 180 members. We want to find the total population of the school, which we will denote as [tex]\( P \)[/tex].
The proportion can be written as:
[tex]\[ \frac{9}{100} = \frac{180}{P} \][/tex]
Now, we can solve for [tex]\( P \)[/tex] by cross-multiplying:
[tex]\[ 9P = 180 \times 100 \][/tex]
Divide both sides by 9 to isolate [tex]\( P \)[/tex]:
[tex]\[ P = \frac{180 \times 100}{9} \][/tex]
Simplify the right side of the equation:
[tex]\[ P = \frac{18000}{9} \][/tex]
[tex]\[ P = 2000 \][/tex]
Therefore, the total population of the school is 2000 people. This matches the correct answer given in the options.
Solve this: 9x-3=5x-15
Which is greater 20 5/6 or 20.8?
An equation for a line in the plane allows you to find the x- and y-coordinates of any point on that line.
A. True
B. False
An equation for a line in the plane allows you to find the x- and y-coordinates of any point on that line.
Explanation:The statement is True.
An equation for a line in the plane, such as y = mx + b, allows you to find the x- and y-coordinates of any point on that line. The x-coordinate can be found by substituting a given y-value into the equation and solving for x. Similarly, the y-coordinate can be found by substituting a given x-value into the equation and solving for y.
Answer: TRUE!!!!!
Step-by-step explanation:
trust me
At the beginning of the season, MacDonald had to remove 5 orange trees from his farm. Each of the remaining trees produced 210 oranges for a total harvest of 41790 oranges.
Equations
and
Answer
Answer:
Equations: f(t) = 210(t-5)
Initial number of trees(t) = 204
Step-by-step explanation:
Let t represents the initial number of trees and f(t) represents the total number of oranges.
"Remove 5 orange trees from his farm" means (t-5)
" Each of the remaining trees produced 210 oranges" means [tex]210\cdot (t-5)[/tex]
so, the equation become [tex]f(t) = 210 \cdot (t-5)[/tex]
Also, it is given that total harvest of, 41790 oranges.
⇒f(t) = 41790
Substitute this in the above equation to get t;
[tex]41790 = 210(t-5)[/tex]
Divide both sides by 210 we get;
[tex]199 = t-5[/tex]
Add 5 both sides of an equation we get;
199 + 5 = t-5 + 5
Simplify:
204 = t
Therefore, there were initially 204 orange trees
#1: Jim, Jane, Ann, and Bill measure an object’s length, density, mass, and volume, respectively. Which student’s measurement might be in centimeters?
A. Bill’s
B. Jane’s
C. Jim’s
D. Ann’s
#2: How many centimeters are in 0.05 kilometers?
A. 50
B. 500
C. 5,000
D. 50,000
Ques 1)
The student whose measurement might be in centimeters is:
Jim
Ques 2)
C. 5,000
Step-by-step explanation:Ques 1)
We know that the standard unit centimeters or meters is used to represent the length of some object.
Here Jim measured an object's length.
Hence, he would represent his measurement in centimeters.
Ques 2)
We know that 1 m=100 cm
and 1 km=1000 m
Hence,
1 km=100000 cm
Hence,
0.05 km=0.05×100000 cm
Hence, we have:
0.05 km=5000 cm.
Hence, the correct answer is: Option: C
Answer:
#1. d. ann's
#2. 5,000
Step-by-step explanation:
Luis bought stock at $83.60. The next day, the price increased $15.35. This new price changed by -4 and 3/4 (mixed number) the following day. What was the final stock price? Is your answer reasonable? Explain.
After buying stock at $83.60, the price increased by $15.35 the next day, followed by a 4.75% decrease the day after. The final stock price was therefore $94.25, and this is a reasonable fluctuation in the stock market.
Luis purchased stock at an initial price of $83.60. On the next day, the stock price increased by $15.35, resulting in a new price of $83.60 + $15.35 = $98.95. The following day, the stock price experienced a decrease by 4 and 3/4 percent. To find the change in price, we multiply $98.95 by 4.75% (or 0.0475 in decimal form), which equals approximately $4.70. So, the final stock price after the decrease would be $98.95 - $4.70 = $94.25.
Is this answer reasonable? Yes, a price fluctuation in stock is common, and a change of $15.35 followed by a percentage decrease the following day is a typical scenario in the stock market.
find the slope of the line through each pair of points.
(1, -19), (-2, -7)
The slope of the line that passes through the points (1, -19) and (-2, -7) is calculated to be -4.
The slope of the line through the pair of points (1, -19) and (-2, -7), you can use the slope formula: slope (m) = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
Using the points given:
x₁ = 1, y₁ = -19
x₂ = -2, y₂ = -7
Substitute these values into the formula:
m = (-7 - (-19)) / (-2 - 1)
m = (12) / (-3)
m = -4
Therefore, the slope of the line through the points (1, -19) and (-2, -7) is -4.
Tarriq begins to solve the equation 50 + 2x = –190.
50 + 2x = –190
50 – 50 + 2x = –190 – 50
2x = –240
To finish solving the equation using the multiplication property of equality, which factor must Tarriq use?
A)-2
B)-1/2
C)1/2
D)2
Tarriq must use "2" as the Multiplication Property of equality.
What is the Multiplication Property of Equality?The Multiplication Property of Equality for any numbers a, b, and c, If we multiply both sides of an equation by the identical number, we always have equivalency.
Rearrange unfamiliar terms to the left side of the equation then
2x = -190 - 50
Calculate the sum or difference
2x = -240
Divide both sides of the equation by the coefficient of variable 2, and we get
x = -240 [tex]$ \div[/tex] 2
Calculate the product or quotient then we get
x = -120
Therefore, the correct answer is option D) 2.
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Tarriq must use factor C) 1/2, as this represents dividing both sides of the equation by 2 to isolate x, resulting in x = –120.
To finish solving the equation 2x = –240 using the multiplication property of equality, Tarriq must divide both sides of the equation by 2, which is the coefficient of x.
This step can be shown as:
2x / 2 = –240 / 2
The division property of equality allows us to simplify by canceling out the 2s on the left, resulting in:
x = –240 / 2
Therefore, x equals:
x = –120
This shows that the factor Tarriq must use to finish solving the equation is C) 1/2 since that represents the inverse operation of multiplying by 2.
Samuel and Jason spend 3/4 of their combined earnings from Wednesday to buy a gift. How much do they spend? Is there enough left over from Wednesday's earnings to buy a card that costs $3.25? Explain.
Earnings:
Samuel - (12.5×0.40)
Jason - (7.1×0.40)
Answer:
they spend $ 5.88 to buy a gift but there is not enough money left to buy a card of $3.25
Step-by-step explanation:
The earnings form Wednesday of Samuel and Jason are:
Samuel earnings = 12.5x0.40 = $5
Jason earnings = 7.1x0.40 = $ 2.84
The combined earnings form Wednesday are:
Combined earnings = Samuel earnings + Jason earnings
Combined earnings= $5 + $ 2.84 = $ 7.84
The spended earnings are:
Spended earnings = combined earnings x ¾
Spended earnings = 7.84 x ¾ = $ 5.88
The left over is:
Left over = combined earnings – spended earnings
Left over = 7.84 – 5.88 = $ 1.96
So, they spend $ 5.88 to buy a gift but there is not enough money left to buy a card of $3.25
Solve for t. 3/4 t = 1/4
Andrea borrowed 2,240 at 15% apr for 18 months. how much interest will she pay?is the answer $336
Answer:
No, the answer is not $ 336
The interest that she will pay is $ 504.
Step-by-step explanation:
Given : Andrea borrowed 2,240 at 15% apr for 18 months.
We have to calculate the interest will she pay.
Using formula for Simple interest.
[tex]SI =P\times r\times t[/tex]
Where P is principal amount
r is rate of interest
t is time period.
Given : P = $ 2240
t = 18 months
In years , [tex]\frac{18}{12}[/tex]
r = 15% = 0.15
Substitute, we have,
[tex]SI=2240\cdot0.15\cdot\frac{18}{12}[/tex]
Simplify, we have,
SI = 504
Thus, The interest that she will pay is $ 504.
No, the answer is not $ 336
Andrea will pay $504 in interest on a loan of $2,240 at 15% APR over 18 months, not $336. The calculation involves converting the loan duration into years and applying the formula for simple interest.
To determine how much interest Andrea will pay on a loan of $2,240 at 15% APR for 18 months, we first need to understand that APR (Annual Percentage Rate) is the interest rate for a whole year (annual), rather than just a monthly fee or rate. Since APR is annual but our loan term is in months, we convert the duration into years to match the APR's annual nature. 18 months is equivalent to 1.5 years. Therefore, the interest calculation would be as follows:
Principal (the amount borrowed) = $2,240
Rate (APR) = 15%
Time = 1.5 years
Interest = Principal × Rate × Time
Interest = $2,240 × 15% × 1.5 = $2,240 × 0.15 × 1.5
Interest = $504
Therefore, Andrea will pay $504 in interest, not $336 as presumed. It's essential to accurately convert the time to years when dealing with APR to ensure the calculation is correct.
What is the average rate of change of the function f(x)=120(0.1)^x from x = 0 to x = 2?
The average rate of change of the function f(x)=120(0.1)^x from x=0 to x=2 is calculated as (f(2) - f(0)) / (2 - 0), which gives -59.4.
Average Rate of Change
The average rate of change of a function over an interval is calculated by the difference in function values at the endpoints divided by the difference in input values. For the function f(x) = 120(0.1)^x, we want to find this rate from x = 0 to x = 2. First, we find the function values:
f(0) = 120(0.1)⁰ = 120
f(2) = 120(0.1)² = 120(0.01) = 1.2
Then we use the formula for average rate of change:
Average rate of change = (f(2) - f(0)) / (2 - 0) = (1.2 - 120) / 2 = -118.8 / 2 = -59.4
Therefore, the average rate of change of the function on the interval from x = 0 to x = 2 is -59.4.
5t + 5 = 30 solve for t