Final Answer:
The revenue function is R(x) = 150x.
The profit function is P(x) = -0.1x² + 141x - 3200.
To make a profit, Gymnast Clothing should manufacture between approximately 23.07 and 1386.93 pairs of cleats. Because they cannot manufacture a fraction of a cleat, they should manufacture at least 24 pairs and no more than 1386 pairs.
Explanation:
Let's start by defining the revenue and profit functions for Gymnast Clothing.
**Revenue Function:**
The revenue function, R(x), is calculated by multiplying the number of cleats sold, x, by the selling price per pair of cleats. Since Gymnast Clothing sells cleats at $150 per pair, the revenue function is:
R(x) = 150x
**Cost Function:**
The cost function, C(x), is given as:
C(x) = 3200 + 9x + 0.1x²
**Profit Function:**
The profit function, P(x), represents the money made after subtracting costs from the revenue. It's defined as the difference between the revenue function and the cost function:
P(x) = R(x) - C(x)
Substitute R(x) with the revenue function and C(x) with the cost function to get:
P(x) = 150x - (3200 + 9x + 0.1x²)
Simplify the profit function by combining like terms:
P(x) = -0.1x² + 141x - 3200
This is the profit function, which tells us how the profit varies with the number of x pairs of cleats manufactured and sold.
**Determining the Number of Cleats to Manufacture for Profit:**
To figure out how many cleats Gymnast Clothing should manufacture to make a profit, we need to determine when the profit P(x) is greater than zero:
P(x) > 0
In other words, we want to find the values of x for which:
-0.1x² + 141x - 3200 > 0
Solving this inequality for x gives us the interval within which manufacturing the cleats will be profitable. Based on the solution to the inequality, the number of pairs of cleats that Gymnast Clothing should manufacture to make a profit is between approximately 23.07 and 1386.93 pairs.
Summary:
- The revenue function is R(x) = 150x.
- The profit function is P(x) = -0.1x² + 141x - 3200.
- To make a profit, Gymnast Clothing should manufacture between approximately 23.07 and 1386.93 pairs of cleats. Because they cannot manufacture a fraction of a cleat, they should manufacture at least 24 pairs and no more than 1386 pairs.
Revenue: [tex]\( R(x) = 150x \)[/tex]. Profit: [tex]\( P(x) = -0.1x^2 + 141x - 3200 \).[/tex] Solve [tex]\(-0.1x^2 + 141x - 3200 > 0\)[/tex] for profit.
To find the exact values for the revenue and profit functions, we'll use the given cost function and selling price.
1. Revenue Function [tex](\(R(x)\))[/tex]: The revenue is given by the product of the number of units sold [tex](\(x\))[/tex] and the selling price per unit[tex](\$150):[/tex] [tex]\[ R(x) = 150x \][/tex]
2. Profit Function [tex](\(P(x)\)):[/tex] The profit is the difference between revenue and cost: [tex]\[ P(x) = R(x) - C(x) \][/tex]
Given that the cost function is [tex]\(C(x) = 3200 + 9x + 0.1x^2\),[/tex] we substitute this into the profit function: [tex]\[ P(x) = 150x - (3200 + 9x + 0.1x^2) \][/tex]
Simplify the expression:
[tex]\[ P(x) = -0.1x^2 + 141x - 3200 \][/tex]
So, the exact functions are:
1. Revenue Function: [tex]\[ R(x) = 150x \][/tex]
2. Profit Function: [tex]\[ P(x) = -0.1x^2 + 141x - 3200 \][/tex]
To find how many cleats Gymnast Clothing should manufacture to make a profit, we set the profit function greater than zero and solve for x: [tex]\[ -0.1x^2 + 141x - 3200 > 0 \][/tex]
Solving this inequality will provide the exact values of x for which the company makes a profit within the given range [tex]\(0 \leq x \leq 500\)[/tex]. This involves factoring, using the quadratic formula, or graphing to determine the valid range of x values for profit.
X Y
-2 5
-1 3
0 1
1 -1
2 -3
Find the explicit formula and the type of function
Lorelle pays someone $35 to clear her driveway when it snows. She wants to buy an electric snow blower for $689 so that she can clear her own driveway. If the area Lorelle lives in has an average of 5.2 snowfalls each season, how many seasons will it take her to break even on what she spends for the snow blower?
It would take 20 sessions to break even on what she spends for the snow blower.
The cost of the snow blower is $689, hence:
Cost = $689
Let x represent the number of sessions, Since $35 is paid to clear the driveway, hence:
Revenue = 35x
At breakeven:
Cost = Revenue
35x = 689
x = 20 (to nearest whole number)
Hence it would take 20 sessions to break even on what she spends for the snow blower.
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Manuela has two boxes. The larger of the two boxes has dimensions of 15cm by 25cm by 29 cm. The smaller of the two boxes is a cube with sides that are 10 cm long. If she were to put the smaller box inside the larger, what would be the remaining volume of the larger box?
When a number x is multiplied by 6, the result is 3/8 . What is the value of x? Drag and drop the correct number into the box so that the equation is true.
If a transformation moves points only up or down, how do the coordinates of the point change? What can you conclude about the coordinate nation for the transformation
Solve and find the measurement for angle B
3(x+1)^(4/3)=48
how do i solve this?
Drag a reason to each box to complete the flowchart proof.
From linear pair postulate, if two angles are in linear pair, then they are supplementary.
Also, the definition of supplementary angles states that the sum of the angles is 180 degrees.
Hence, the correct option is Definition of supplementary angles.
What is .04 as a mixed number
Help me asap!!
To the nearest percent, what is the probability of rolling a 4 on the number cube?
Deniz tried to subtract two polynomials. Her work is shown below.
5 rubber stamps cost $9.70 Which equation would help determine the cost of 11 rubber stamps?
For his parents’ anniversary, Danny spends $5.87 on a photo.He also buys a balloon for $2.49 and a box of strawberries for $4.50. How much money does he spend all together
The total amount of money spent by Danny is [tex]\fbox{\$12.86}[/tex].
Further explanation:
Given:
Danny spends $5.87 on a photo, $2.49 for balloon and $4.50 on strawberries.
Calculation:
Consider the total money spent as [tex]S[/tex], money spends on photo as [tex]x[/tex], money spends on balloons as [tex]y[/tex] and money spend on strawberries as [tex]z[/tex].
Total money spent [tex]S[/tex] is written as the sum of the money spent on photo [tex]x[/tex], balloons [tex]y[/tex] and strawberries [tex]z[/tex] as follows:
[tex]S=x+y+z[/tex] …… (1)
Substitute, 5.87 for [tex]x[/tex], 2.49 for [tex]y[/tex] and 4.50 for [tex]z[/tex] in equation (1) to obtain the total money spent by Danny as follows:
[tex]\begin{aligned}S&=5.87+2.49+4.50\\&=8.36+4.50\\&=12.86\\\end{aligned}[/tex]
Thus, the total amount of money spent by Danny is [tex]\fbox{\$12.86}[/tex].
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1. Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}
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2. A given line has the equation 10x + 2y = −2. what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y = ( )x + 12
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3. what are the domain and range of the function f(x) = 3x + 5?
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Answer Details :
Grade: Middle School
Subject: Mathematics
Chapter: linear equation
Keywords:
Money, Danny, anniversary, photo, balloon, strawberries, dollar, spent, x+y+z, function, substitution, direct substitution, elimination, graph, middle term factorization, scientific notation.
17. A local university accepted 2,300 students out of 4,500 applicants for admission. What was the acceptance rate, expressed as a percent? Show your work.
The acceptance rate of the students is 51.1%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a local university accepted 2,300 students out of 4,500 applicants for admission.
The acceptance rate will be calculated as,
Acceptance rate = ( 2300 x 100 ) /4500
Acceptance rate = 51.1 %
Therefore, the acceptance rate of the students is 51.1%.
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Is this a funtion? Explain.
84, 99, 88, 82, 95, 85
Myra's test scores are shown. She has one more test for the semester. What is the minimum score that she can make on her last test and have an average greater than 90?
Note: All scores are whole numbers and scores are not rounded
a. 95
b.96
c.97
d.98
Answer:
Option: d is the correct answer.
d. 98
Step-by-step explanation:
The scores of Myra's test are as follows:
84, 99, 88, 82, 95, 85
Let 'x' be the minimum score that is obtained by Myra in the last test so that the average is greater than 90 marks.
i.e.
[tex]\dfrac{84+99+88+82+95+85+x}{7}>90\\\\\\i.e.\\\\\\\dfrac{533+x}{7}>90\\\\\\i.e.\\\\\\533+x=90\times 7\\\\\\533+x>630\\\\\\x>630-533\\\\\\x>97[/tex]
Hence, the minimum score has to be 98.
( Since, the scores are in whole number )
If Susan subtracts 11 from one-fourth of her number she gets 11
Final answer:
Susan's number is found by solving the equation x/4 - 11 = 11, which after isolating the variable and multiplying both sides by 4 yields the answer x = 88.
Explanation:
If Susan subtracts 11 from one-fourth of her number, she gets 11. To solve this problem, we set up an equation where x represents Susan's number. The one-fourth of her number would be x/4, and subtracting 11 from one-fourth of her number yields: x/4 - 11 = 11.
To find x, we first isolate the variable on one side by adding 11 to both sides of the equation, so we have x/4 = 22. Next, we multiply both sides by 4 to solve for x: x = 22 * 4. Therefore, Susan's number is 88.
When is the sum to two negative mixed numbers an integer?
This has really gotten confuzzing for me. SOS
let number of hours = x
1st equation is 15.54+0.11x
2nd equation is 16.14-0.09x
now calulate x so the 2 equations are equal:
15.54+0.11x=16.04-0.09x
mutiply evrything by 100 to get rid of the decimal points andmake the calculations a little easier
1554+11x=1604-9x
add 9 x to both sides:
1554+20x=1604
subtract 1554 from both sides:
20x=50
divide 50 by 20 for x
x=50/20 = 2.5
x = 2.5
so they were the same after 2.5 hours
Find the equation of the line (3,-2) and parralel to the line containing the points (-2,4) and (-4,-2).
Use the graph of f to estimate the local maximum and local minimum. (5 points)
Answer:
Local maximum: (0,1)
Local minimum: [tex](-\pi,-1)\text{ and }(\dfrac{3\pi}{2},-1)[/tex]
Step-by-step explanation:
To estimate the local maximum and local minimum using graph.
Local maximum: It is largest value of function for all other values of function near by.
Local minimum: It is smallest value of function for all other values of function near by.
A function has two extrema maxima or minima.
Please see the attachment for graph.
In graph highest point only 1, Only one local maximum at x=0
Local maximum: (0,1)
In graph two lowest point at [tex]x=-\pi\text{ and }x=\dfrac{3\pi}{2}[/tex]
Local minimum: [tex](-\pi,-1)\text{ and }(\dfrac{3\pi}{2},-1)[/tex]
Hence, Local maximum: (0,1) ; Local minimum: [tex](-\pi,-1)\text{ and }(\dfrac{3\pi}{2},-1)[/tex]
A rectangular pool is 30 1/3 feet long and 12 1/2 feet wide what is the area of the pool
7x-4d use x = 8 and d = have (simplify algebraic exression)
A rectangle has a perimeter of 16 inches.
What dimensions (length, width) could be the dimensions of the sides?
A. (8, 0)
B. (2, 12)
C. (6, 2)
D. (13, 3)
E. (3, 10)
option C: (6, 2).
The student has asked for the possible dimensions of a rectangle given that its perimeter is 16 inches. To find the dimensions that are correct, we need to remember that the perimeter of a rectangle is calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. We must check each pair of dimensions provided and see if they satisfy this equation when the perimeter is 16 inches.
A. (8, 0) - This would give us a perimeter of 2(8) + 2(0) = 16 inches, which is correct, but it is not a possible dimension for a rectangle, as having a side of length 0 inches does not make a rectangle.B. (2, 12) - The perimeter here would be 2(2) + 2(12) = 28 inches, which is not equal to 16 inches.C. (6, 2) - Checking this option, we get 2(6) + 2(2) = 12 + 4 = 16 inches. This one is correct and is a possible dimension for a rectangle.D. (13, 3) - The perimeter in this case would be 2(13) + 2(3) = 26 + 6 = 32 inches, clearly more than 16 inches.E. (3, 10) - This would give us a perimeter of 2(3) + 2(10) = 6 + 20 = 26 inches, which also does not equal the 16-inch perimeter required.Therefore, the only possible dimensions for the rectangle given the choices provided and where both dimensions are greater than zero is option C: (6, 2).
6/10 in simplest form
2. AB and DE are parallel. Angle BAC = 30 , angle CDE = 50. What is the measure of angle ACD?
A. 100
B. 90
C. 80
D. 70
E. cannot be determined from the information
what is y=-3x+4 and y=3x-2
by using transitive property
Multiply: 3x4(4x4 − x5 + 2) 7x8 − 3x9 + 6x4
number of different 5 digit combinations if successive digits msut be different
The permutations formula is applied to determine the number of different 5-digit combinations where successive digits must be different, resulting in a total of 30,240 combinations.
Permutations are used when the order of elements matters. In this case, the number of different 5-digit combinations where successive digits must be different can be calculated using the permutations formula.
Identify that we need to use permutations due to the order of elements being important.Calculate the number of possibilities for each digit decreasing by 1 with each selection. For a 5-digit number, it would be 10 choices for the first digit, 9 for the second, 8 for the third, 7 for the fourth, and 6 for the fifth.Calculate the total number of combinations by multiplying the number of choices for each digit together: 10 x 9 x 8 x 7 x 6 = 30,240.can 50 go into 100 and 250
yes:
100/50 = 2
250/5 = 5