Answer:
Raphael sells paintings for $200 each at a market, but has to pay $100 to reserve a table. :)
Step-by-step explanation:
The scenario that describes a proportional relationship is D; Raphael sells paintings for $200 each at a market but has to pay $100 to reserve a table.
What is directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex]where that middle sign is the sign of proportionality.
This inversely proportional relationship is denoted by;
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
Thus, the scenario that describes a proportional relationship is D; Raphael sells paintings for $200 each at a market but has to pay $100 to reserve a table.
Learn more about directly inversely proportional relationship variable here:
https://brainly.com/question/13082482
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A science fair poster is a rectangle 4 feet long and 3 feet wide. What is the area of the poster in square inches?
Be sure to include the correct unit in your answer.
in
in?
in?
G
Х
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1. If the total cost function for a product is C(x) = 200(0.02x + 6)3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?
2. A firm can produce only 3900 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total venue is given by R(x) = 450x-1/100x^2 dollars, how many items, x, should the firm produce for maximum profit?
3. If the profit function for a product is P(x) = 3600x + 60x2 ? x3 ? 72,000 dollars, selling how many items, x, will produce a maximum profit?.
Answer:
a. The number of units which will minimize average cost is approximately 5,130 units.
b. The firm should produce 12,500 items, x, for maximum profit.
c. The number of items, x, that will produce a maximum profit is 60 items.
Step-by-step explanation:
Note: This question is not complete as there are some signs are omitted there. The complete question is therefore provided before answering the question as follows:
1. If the total cost function for a product is C(x) = 200(0.02x + 6)^3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?
2. A firm can produce only 3900 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total venue is given by R(x) = 450x-1/100x^2 dollars, how many items, x, should the firm produce for maximum profit?
3. If the profit function for a product is P(x) = 3600x + 60x2 - x3 - 72,000 dollars, selling how many items, x, will produce a maximum profit?
The explanation to the answer is now given as follows:
1. If the total cost function for a product is C(x) = 200(0.02x + 6)3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?
Given;
C(x) = 200(0.02x + 6)^3 ……………………………………….. (1)
We first simplify (0.02x + 6)^3 as follows:
(0.02x + 6)^3 = (0.02x + 6)(0.02x + 6)(0.02x + 6)
First, we have:
(0.02x + 6)(0.02x + 6) = 0.004x^2 + 0.12x + 0.12x + 36 = 0.004x^2 + 0.24x + 36
Second, we have:
(0.02x + 6)^3 = 0.004x^2 + 0.24x + 36(0.02x + 6)
(0.02x + 6)^3 = 0.00008x^3 + 0.048x^2 + 7.20x + 0.0024x^2 + 1.44x + 216
(0.02x + 6)^3 = 0.00008x^3 + 0.048x^2 + 0.0024x^2 + 7.20x + 1.44x + 216
(0.02x + 6)^3 = 0.00008x^3 + 0.0504x^2 + 8.64x + 216
Therefore, we have:
C(x) = 200(0.02x + 6)^3 = 200(0.00008x^3 + 0.0504x^2 + 8.64x + 216)
C(x) = 0.016x^3 + 10.08x^2 + 1,728x + 43,200
Therefore, the average cost (AC) can be calculated as follows:
AC(x) = C(x) / x = (0.016x^3 + 10.08x^2 + 1,728x + 43,200) / x
AC(x) = (0.016x^3 + 10.08x^2 + 1,728x + 43,200)x^(-1)
AC(x) = 0.016x^2 + 10.08x + 1,728 + 43,200x^(-1) …………………………. (2)
Taking the derivative of equation (2) with respect to x, equating to 0 and solve for x, we have:
0.032x + 10.08 - (43,300 / x^2) = 0
0.032x + 10.08 = 43,300 / x^2
X^2 * 0.32x = 43,300 – 10.08
0.32x^3 = 43,189.92
x^3 = 43,189.92 / 0.32
x^3 = 134,968.50
x = 134,968.50^(1/3)
x = 51.30
Since it is stated in the question that x represents the number of hundreds of units produced, we simply multiply by 100 as follows:
x = 51.30 * 100 = 5,130
Therefore, the number of units which will minimize average cost is approximately 5,130 units.
2. A firm can produce only 3900 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total revenue is given by R(x) = 450x-1/100x^2 dollars, how many items, x, should the firm produce for maximum profit?
P(x) = R(x) - C(x) ……………. (3)
Where;
P(x) = Profit = ?
R(x) = 450x-1/100x^2
C(x) = 500 + 200x
Substituting the equations into equation (3), we have:
P(x) = 450x - 1/100x^2 - (500 + 200x)
P(x) = 450x - 0.01x^2 - 500 - 200x
P(x) = 450x - 200x - 0.01x^2 - 500
P(x) = 250x - 0.01x^2 – 500 …………………………………. (4)
Taking the derivative of equation (4) with respect to x, equating to 0 and solve for x, we have:
250 - 0.02x = 0
250 = 0.02x
x = 250 / 0.02
x = 12,500 items
Therefore, the firm should produce 12,500 items, x, for maximum profit.
3. If the profit function for a product is P(x) = 3600x + 60x2 – x^3 - 72,000 dollars, selling how many items, x, will produce a maximum profit?
Given;
P(x) = 3600x + 60x2 – x^3 - 72,000 …………………………. (5)
Taking the derivative of equation (5) with respect to x, equating to 0 and solve for x, we have:
3600 + 120x - 3x^2 = 0
Divide through by 3, we have:
1200 + 40x – x^2 = 0
1200 + 60x – 20x – x^2 = 0
60(20 + x) – x(20 + x) = 0
(60 – x)(20 + x) = 0
Therefore,
x = 60, or x = - 20
The negative value of x (i.e. x = - 20) will be will be ignored because it has no economic significance. Therefore, the number of items, x, that will produce a maximum profit is 60 items.
Points A and B are 200 mi apart.
Answer:
17*200/17+83
Step-by-step explanation:
Points A and B are 200 mi apart. A cyclist started from point A and a motorcyclist started from point B, moving towards each other. The speed of the cyclist was 17 mph, the speed of motorcyclist was 83 mph. At what distance from point A will they meet?
The distance under the question is 17*200/17+83= 17*2 = 34 miles.
17+83 = 100 mph in the denominator is the relative speed of the participants, the rate of decreasing the distance between them.
200/17+83=200/100= 2 hours is the time before they meet.
therefore 17*200/17+83 is the time before they meet
Casey wants to buy a gym membership. One gym has a $176 joining fee and costs $29 per month. Another gym has no joining fee and costs $51 per month.
Part 1 out of 2
In how many months will both gym memberships cost the same? What will that cost be?
Answer:
8 months for cost to be same, cost will be $408
Step-by-step explanation:
x = months
176 + 29x = 0 + 51x
176 = 22x
8 = x
176 + (29*8) = 408
0 + (51*8) = 408
How many ounces are equal to 7 pounds?
1) 112 ounces
70 ounces
84 ounces
56 ounces
My Progress >
Answer:
112
Step-by-step explanation:
16 ounce multiply that by 7. 112. This correct i googed it
The teacher has 5 cups or broth to share amoung 4 students. draw a model and explain your answer.
Answer:
1.25,but your teacher is prolly looking for a fraction so 1 1/4
Step-by-step explanation:
DO NOT PUT 20 THAT PERSON S WRONG
Find the quotient: 6)27L 600 mL
Answer:
27*1000=27000ml
600ml
Now, 27000ml+600ml=27600ml
Step-by-step explanation:
g(x) = -4x2 + 4x – 2
What is the maximum or minimum step by step
We want the maximun or minimum of [tex]g(x)=-4x^2+4x-2[/tex]
Firstly, notice that we have a leading coefficient of -4, wich means our parabola is concave down. Thus, our function will have a maximum.
To find what is the maximum, let's firstly find on wich value of x it happens. We'll start by taking the first derivative of the function:
[tex]g'(x)=-8x+4[/tex]
To find the extremes of the function, we just need to find where the derivative equals zero. Setting g'(x)=0 we have
[tex]0 = -8x+4\\8x=4\\x=\frac{1}{2}[/tex]
So we found that the x coordinate of the maximum is x=1/2. To find the y coordinate we just need to substitute the value of x into the original function.
[tex]g(1/2)=-4(1/2)^2+4(1/2)-2\\g(1/2)=-1+2-2\\g(1/2) = -1[/tex]
Therefore, the maximum point [tex]M[/tex] of the function is
[tex]\boxed{M=(0.5,-1)}[/tex]
Glad to help! Wish you great studies.
If you found this helpful consider giving this answer brainliest ;)
Can someone please help me if you know! Thank you
Answer:
D
Step-by-step explanation:
the equation for Josh is 500 + 40x while the equation for Vanessa is only 60x
if josh's account balance is greater than it would be josh > vanessa or vanessa < josh
Help mehhhhhh please!!!!!!!!!!!!
log(5t)(5t + 1) * log(5x+1) (5t + 2) * log(5t+2 )(5t + 3)... log(5t+n)(5t +n +1)
I assume you're referring to the product,
[tex]\log_{5t}(5t+1)\cdot\log_{5t+1}(5t+2)\cdot\cdots\cdot\log_{5t+n}(5t+n+1)[/tex]
Recall the change-of-base identity:
[tex]\log_ab=\dfrac{\log_cb}{\log_ca}[/tex]
where c > 0 and c ≠ 1. This means the product is equivalent to
[tex]\dfrac{\log(5t+1)}{\log(5t)}\cdot\dfrac{\log(5t+2)}{\log(5t+1)}\cdot\cdots\cdot\dfrac{\log(5t+n+1)}{\log(5t+n)}[/tex]
and it telescopes in the sense that the numerator and denominator of any two consecutive terms cancel with one another. The above then simplifies to
[tex]\dfrac{\log(5t+n+1)}{\log(5t)}=\boxed{\log_{5t}(5t+n+1)}[/tex]
what is greater 9/3, 2 3/4
Answer:
9/3 is greater
Step-by-step explanation:
Convert it to decimals.
9/3=3
2 and 3/4= 2.75
in a company, 40% of the workers are women. If 1380 woman work for the company, how many total workers are there?
Answer:
Step-by-step explanation:
The total number of workers is our unknown. If 40% of this unknown number are women and the number of women is 1380, then the equation looks like this:
(remember that the word "of" generally means to multiply)
(also remember that we have to use the decimal form of a percent in an equation)
.40(x) = 1380 then divide to get the number of total workers:
x = 3450
Help please and show ya work
Answer:
D: 14.5
Step-by-step explanation:
4.1 = d - 10.4 add 10.4 to each side
14.5 = d
Answer:
14.5
Step-by-step explanation:
10.4 - 4.1 = 14.5
Solve -2(x-5) + 3x = 2(x+3) + 17 *
Answer:
x=-13
Step-by-step explanation:
Hope this helped :)
Answer:
x = -13
Step-by-step explanation:
-2x + 10 + 3x = 2x + 6 + 17
x + 10 = 2x + 6 + 17
x + 10 = 2x + 23
10 = 2x + 23 - x
10 = x + 23
10 - 23 = x
-13 = x
x = -13
The least common denominator of 3/2 and 2/3 is
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Multiply the 2 denominators which gives you 6. P.S make sure to do cross multiplication for the numerator cause if the rest of the question asks for the full answer then you would get it wrong if you don't.
3x+y=-8
-2x-y=6
Find X and Y By Substituting
(-2,-2) is the answer .............
What is 3(2+q)+15 simplified
Answer:
The Answer should be....
3q + 21
The perimeter of a rectangle,p, is given by p =2L + 2W , where L is its length and w is its width what is the perimeter of a rectangle of length 15ft and width 15ft ?
Answer:
60ft
Step-by-step explanation:
multiple the length by 2
15 times two equals 30
multiple the width by two
15 times two equals 30
add the total lengths and widths
30 plus 30 equals 60
ans=60
Can you help me with this question please
Answer:
x should be 101
Step-by-step explanation:
4x^2+x^3 factorised
How do you do this?...
Answer:
X²(4+x)
Step-by-step explanation:
You pick out the common term
Greetings.
The answer is x²(4+x)
Explanation:
[tex]4x^2+x^3\\[/tex]
By using a common factor, we factor x-term out. We factor the x-term with least degree and that is 2-degree. So we factor x² out.
When factored out, It's similar to dividing. When x² is divided by itself, the result is 1. When x³ is divided by x², the result is x (From the property of exponent.)
Similar to dividing, but we pull x² out.
[tex]4x^2+x^3\\x^2(4+x)[/tex]
Therefore, the answer/factored form is x²(4+x)
Which solution would make this equation have infinitely many solutions?
A.-18
B.-9
C.9
D.18
Answer: -18
Step-by-step explanation:
the length of a rectangle is three times its width ,if the width is x cm. write down an expression of length in term of x
Answer:
L = 3x cm
Step-by-step explanation:
For this problem, let's consider the relation that is stated:
Length is 3 times as much as the width. The width is x cm.
Mathematically we can say the following:
L = 3W
W = x cm
So we can say the following about the length:
L = 3W
L = 3(x cm)
L = 3x cm
Cheers.
7, 12, 10, 18, 13, 23, 29, 15, 16, 18, 15, 12, 20
find the outlier. explain your answer.
Answer:
29
Step-by-step explanation:
the rest of the numbers are closer to each other but if you plot these you see that 29 doesnt belong
Help please! I need an explanation but I dont understand this!!!!!!!
Answer:
its to small
Step-by-step explanation:
Delta math needed!!!
Answer:
Parallel
Step-by-step explanation:
Slopes of the line
8(7q+6p+11) please help me
Answer:
56p + 48q + 88
Step-by-step explanation:
When you see parentheses in math, it usually means that you are distributing (multiplying).
So here you would multiply everything inside the parentheses by 8.
7q x 8 = 56q
6p x 8 = 48p
8 x 11 = 88
56q + 48p + 88
There are no like terms here so the answer cannot be simplified any further.
1) Given: H is the midpoint of EG
mZE = mZG
G
D
Prove: ADEH - AFGH
H.
E
F
It is E
Duhhhhhhhhhhhhh
A gas pump fills 2^-2 gallon of gasoline per second. how many gallons does the pump fill in one minute?
Answer:
The gas pump filling the gallons in 1 minute will be: 15
Step-by-step explanation:
Given that a gas pump fills 2^-2 gallon of gasoline per second.As there are 60 seconds in 1 minute.
Thus,
Gas pump filling the gallons in 1 minute will be:
[tex]60\:\times 2^{-2}[/tex]
[tex]=60\times \frac{1}{2^2}[/tex] ∵ [tex]a^{-b}=\frac{1}{a^b}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \:a\times \frac{b}{c}=\frac{a\:\times \:b}{c}[/tex]
[tex]=\frac{1\times \:60}{2^2}[/tex]
[tex]=\frac{60}{2^2}[/tex]
[tex]=\frac{2^2\times \:3\times \:5}{2^2}[/tex]
[tex]=3\times \:5[/tex]
[tex]=15[/tex] gallons in one minute
Therefore, the gas pump filling the gallons in 1 minute will be: 15
If mZMRT = 133º , then which equation can be used to find g?
Answer:
D
Step-by-step explanation:
We know that MRT = 133 which means that is the total. Angle MRN and NRT are what makes the total angle which is 133. To find what each angle is individually, we can add them both together.
(2g - 2) + (4q - 9) = 133
6q - 11 = 133
6q = 144
q = 24
Best of Luck!
D. (2g - 2)+(4g -9) = 133
Because,
Given, angle MRT = 133°
and MRN = 2g - 2 °
and NRT = 4g - 9°
and MRT = MRN + NRT .........(equation (i))
Placing values in equation (i) we get,
133° = (2g - 2)° + (4g - 9)°
=> 133 = (2g - 2) + (4g - 9)
=> (2g - 2) + (4g - 9) = 133