Silver scooter finds that it costs $300 to produce each scooter and the fixed costs are $750. The price is given by p=900-x, where p is the price in dollars at which exactly x scooters will be sold. Find the quantity of scooters that the company should produce and the price it should charge to maximize profit. Find the maximum profit. ...?
To maximize profit, the company should produce 300 scooters and charge a price of $600. The maximum profit is $88,500.
Explanation:The company should produce a quantity of scooters that maximizes profit. To find this quantity, we need to find the point where marginal revenue (MR) equals marginal cost (MC). In this case, MR is given by the derivative of the price equation, which is -1. So, we set -1 equal to the derivative of the cost equation and solve for x:
-1 = 300
This gives us x = 300. So, the company should produce 300 scooters to maximize profit. To find the price, we substitute this value of x into the price equation:
p = 900 - 300 = 600
Therefore, the company should produce 300 scooters and charge a price of $600 to maximize profit. The maximum profit can be calculated by subtracting the total cost from the total revenue. The total revenue is given by the price multiplied by the quantity sold, and the total cost is given by the fixed costs plus the cost per unit multiplied by the quantity sold. Using the given values, we have:
Total revenue = 600 * 300 = $180,000
Total cost = 750 + 300 * 300 = $91,500
Maximum profit = Total revenue - Total cost = $180,000 - $91,500 = $88,500
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Yolanda is finding 23,567-12,458. She added 2 to 12,458 before subtracting. Then she added it in again after she subtracted. Is her method correct? Explain.
Yolanda's method is incorrect because she should have subtracted the 2 she added before subtracting, not added it. Adding it before and after the subtraction alters the original values and results in an inaccurate subtraction.
Explanation:No, Yolanda's method is not correct. If you add a value to a number before subtracting, you have to subtract that same value after the subtraction, not add it again. This is because the addition of 2 alters the original value of 12,458, making it 12,460, and thus changes the result of the subtraction. However, by adding 2 again after subtracting, Yolanda incorrectly compensates for the initial addition. The correct approach would have been to subtract 2 after the subtraction, returning 12,458 to its original value and ensuring the accuracy of the subtraction.
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A function f satisfies the following conditions: f(5)=20, f'(5)=2, and f"(x)<0, for x>=5. Which of the following are possible values for f(7)? possible choices are 28, 20, 26, 24, 22
Given the function's conditions, the value of f(7) must be less than or equal to 24 due to the concave-down nature indicated by the negative second derivative, making 20, 22, or 24 possible values for f(7).
Explanation:The student asked about determining possible values for a function f(x) given a set of conditions: f(5)=20, f'(5)=2, and f"(x)<0 for x>=5. The negative second derivative indicates that the function is concave down for x>=5, meaning the rate of increase of f(x) is decreasing. Starting at x=5 with a value of 20 and a slope of 2, we can deduce that after moving 2 units to x=7, the value of f(7) cannot be greater than what it would be if f(x) were linear, since f"(x)<0 implies the function's rate of growth is decreasing. Therefore, f(7) must be less than or equal to 20 + 2*(7-5), which is 24.
Since the rate of increase is decreasing and the function cannot increase at a rate faster than the initial slope of 2, the possible values for f(7) among the given choices must be less than or equal to 24. Thus, the possible values for f(7) could be 20, 22, or 24.
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The value of f(7) is 24.
Given the function f with conditions f(5)=20, f'(5)=2, and f''(x)<0 for x ≥ 5, we need to find possible values for f(7) from the choices given: 28, 20, 26, 24, and 22.
Here is a step-by-step solution:
f(5)=20 indicates that at x=5, the value of the function is 20.f'(5)=2 tells us that the slope or the derivative at x=5 is 2, which implies the function is increasing at this point.f''(x)<0 for x ≥ 5 indicates that the function is concave down, meaning its slope is decreasing as x increases.Since the function is concave down, the rate of increase of the function will decrease as x moves from 5 to 7:
f(x) initially increases from 5 to 7 with a slope of 2, so f(7) cannot be lower than f(5): 7 − 5 = 2 * 2 = 4, thus the function increases by at most 4 from 5 to 7.So the maximum possible value considering the concavity is 20 + 4 = 24.Therefore, among the choices 28, 20, 26, 24, and 22, the possible value for f(7) given the conditions is 24.
16,000 rolls of paper were purchased and 12,500 were sold at $1.79, what is the total ending inventory?
Factorise this
72-6x
PLZZZ HELP ME!!
Edward’s recipe for salad uses a ratio of 2 1/4 cups of lettuce to 1/2 lb of tomatoes.
(a) Use a complex fraction to compare the amount of lettuce to the amount of tomatoes.
(b) Determine how many cups of lettuce Edward needs to mix with 1 lb of tomatoes. Show your work.
Answer:
4.5 cups of lettuce for 1 cup of tomatoes
Step-by-step explanation:
Paper cost $49 for 10 reams. How much for 1 ream?
To calculate the cost of 1 ream of paper from the total cost of 10 reams, divide $49 by 10 to get $4.90 per ream.
To find out how much it costs for 1 ream of paper when 10 reams cost $49, we simply divide the total cost by the number of reams. In this case:
Cost per ream = Total cost / Number of reams
Cost per ream = $49 / 10
Cost per ream = $4.90
Therefore, the cost for 1 ream of paper is $4.90.
How do I factorise 5a2 + 6ab
2 is squared
5. If p || q, which pair of angles must be congruent?
1 and 8
2 and 5
4 and 6
7 and 8
Answer:
1 and 8.
Step-by-step explanation:
Two angles will be congruent if both measure the same. Then, as p is parallel to q we have that the alternate external angles (pair of angles out of the parallel lines, one on the right of the transversal line and the other on the left of the transversal line) has the same measure. In this case, 1 and 8 are alternate external angles.
If the public debt of a country in 2009 was $12,752,000,000,000 and the budget for 2010 was in deficit by $201,645,000,000, what was the public debt in 2007?
Answer:
$ 12953645000000
Step-by-step explanation:
To find the public debt in 2007, subtract the deficit for 2008 from the public debt in 2007.
Explanation:To calculate the public debt in 2007, we need to work backwards from the given information. We know that the public debt in 2009 was $12,752,000,000,000 and the budget for 2010 was in deficit by $201,645,000,000. We can assume that the deficit for each year is equal to the change in the public debt from the previous year. So, we subtract the deficit for 2010 from the public debt in 2009 to find the public debt in 2010. Then, we subtract the deficit for 2009 from the public debt in 2010 to find the public debt in 2008. Continuing this process, we can subtract the deficit for 2008 from the public debt in 2007 to find the answer.
To summarize, we can find the public debt in 2007 by subtracting the deficit for 2008 from the public debt in 2007.
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a 6 feet tall boy cast a shadow of 9 feet at the same time of the day if the shadow of a tree measures 21 feet what is the height of the tree
Which equation represents the line that passes through (–6, 7) and (–3, 6)?
Answer:
Equation of line become [tex]y= \frac{- 1 *x}{3}+ 5[/tex].
Step-by-step explanation:
slope of the line
we know that the formula to calculate the slope between two points is equal to
Slope (m) = [tex]\frac{y_{2}- y_{1} }{x_{2}-x_{1}}[/tex].
substitute the values
(m) = [tex]\frac{6 - 7} }{ -3 - (-6)}[/tex].
(m) = [tex]\frac{-1} }{3}[/tex].
With the slope m and the point (-6, 7) find the equation of the line
we know that
the equation of the line in the point-slope form is equal to
[tex](y - y_{1}) = m ( x - x_{1})[/tex].
substitute the values
[tex](y - 7) = \frac{-1}{3} (x - ( -6))[/tex].
[tex](y - 7) = \frac{-1}{3} (x + 6)[/tex].
[tex](y - 7) = \frac{-x}{3} +2 )[/tex].
On adding both sides by 7.
[tex]y= \frac{-x}{3} - 2 + 7 [/tex].
[tex]y= \frac{-x}{3}+ 5[/tex].
Therefore, equation of line become [tex]y= \frac{-1 *x}{3}+ 5[/tex].
Two rooms in a house are similar rectangles. Room A is 12 ft by 16 ft. The longer side of Room B is 4 ft shorter than twice the length of the shorter side of Room A. What are the dimensions of Room B?
The triangles are similar. Find the value of a. Picture shown below.
A country's population in 1991 was 114 million. In 1997 it was 120 million. Estimate the population in 2014 using exponential growth. ...?
Mary baked 21 cookies on Saturday and twice that many on Sunday for a school fundraiser. 4 cookies fell on the ground and had to be thrown out. If she packaged 3 cookies to a bag, how many cookies were left over?
A) 0
B) 1
C) 2
D) 3
-8 ( 3-s) = 32 what is s
how do you solve (x3 + 6x2 + 3x + 1 ) ÷ (x - 2)
The product of (1/2 3/4i) and(1/2-3/4i) divided by (2-3i)
If f(x) = x3 – 2x2, which expression is equivalent to f(i)?
–2 + i
–2 – i
2 + i
2 – I
Answer:
It's D
2-i
Step-by-step explanation:
Put these numbers in order from least to greatest.
-15-26/40, -15, 18/25, 15.85
Translate the algebraic expression 3x+5 into a word phrase
solve 7n 6 4n-2=2n 2(4n 6)
Identify the degree of the polynomial 8x^3y^2 – 10xy + 4x^2y^2 + 3.
Answer:
The degree of the polynomial is 5
Step-by-step explanation:
A snake is slithering toward you at 1.5 m/s. If you start walking when it is 5.0 m away, how fast must you go in order that the snake not overtake you when you have gone 40.0 m?
At wild thing zoo, you can rent a motorized cart to tour grounds for a $3 initial charge and $7 per hour. at safari zoo, you can rent the same cart for a $7 initial charge and $6 per hour. for how many hours is the total charge the same?
Order the numbers from least to greatest.
0.21,1/5 , 0.18, 24%
The arrangement from least to greatest is 0.18 < 0.20< 0.21< 0.24.
What is Ascending Order?Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.
Given:
0.21,1/5 , 0.18, 24%
Now, writing each fraction in decimal form
1/5 = 0.2
24% = 24/100 = 0.24
So, we have the following numbers
0.21, 0.20, 0.18, 0.24
Hence, the arrangement from least to greatest is 0.18 < 0.20< 0.21< 0.24.
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what is the angular velocity of a 6-foot pendulum that takes 3 seconds to complete an arc of 14.13 feet?
A^2 + 4^2 = 5^2
A = __
the number of roses was 15 greater than twice the number of prunes. if the roses and prunes totaled 255, how many roses were there?
The problem is a simple algebraic equation that, when solved, shows there were 175 roses.
To solve the problem given by the student, we need to set up an equation based on the information provided. We are told that the number of roses was 15 greater than twice the number of prunes, and together they totaled 255.
Let the number of prunes be p. Then the number of roses can be represented as 2p + 15. Adding these amounts must total 255, so we can write the following equation:
2p + 15 + p = 255
Combining like terms:
3p + 15 = 255
Subtracting 15 from both sides of the equation:
3p = 240
Dividing both sides by 3:
p = 80
Now that we have the number of prunes, we can find out the number of roses:
Roses = 2p + 15 = 2(80) + 15 = 160 + 15 = 175
Therefore, the student had 175 roses.