The revenue function for Gymnast Clothing is R(x) = 150x, and the profit function is P(x) = 150x - (2750 + 7x + 0.1x^2). To make a profit, they need to produce and sell more than the breakeven number of cleats, which can be calculated by setting the profit function to zero and solving for x.
Explanation:When Gymnast Clothing sells soccer cleats at $150 per pair, the revenue function (R) would be the number of cleats, x, multiplied by the selling price. Therefore, R(x) = 150x. To find the profit function (P), we subtract the cost function (C(x)) from the revenue function, so P(x) = R(x) - C(x) or P(x) = 150x - (2750 + 7x + 0.1x2). A profit is made when P(x) > 0.
To determine the number of cleats needed to make a profit, we need to find the break-even point where P(x) = 0, and then any number greater than the break-even number of cleats would yield a profit. By setting the profit function equal to zero and solving for x, we can find the minimum number of cleats Gymnast Clothing should manufacture to begin making a profit.
Parallel lines p and q are cut by two non-parallel lines, m and n, as shown in the figure.
The value of the x and y are 78° and 115°
What are parallel lines?Parallel lines are coplanar infinite straight lines that do not intersect at any point.
Parallel planes are planes in the same three-dimensional space that never meet.
Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance.
Given is a figure of parallel lines, m and n, we need to find the values of x and y,
x = 180°-102° [alternate interior angles and linear pair]
x = 78°
y = 115° [corresponding angle]
Hence, the value of the x and y are 78° and 115°
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The product of 6 and the sum of 5 and k
product means multiply, sum means add
so add 5+k = (5+k)
now multiply that by 6 to get
6(5+k)
what does a negative net worth indicate
sarah teaches craft classes. she has 214 bags of beads. each bag has enough beads for 22 bracelets. she estimates tht since 200 x 20 = 4000 there are enough beads for at least 4000 bracelets. tell how you can critique sarahs reasoning
Final answer:
Sarah estimated that she could make at least 4,000 bracelets from 214 bags of beads by simplifying the calculation to 200 bags with enough beads for 20 bracelets each. Her estimate was conservative, as the calculation of 214 bags multiplied by 22 bracelets per bag totals 4,708 bracelets, which is greater than her estimate.
Explanation:
To critique Sarah's reasoning, we need to compare her estimate with the actual number of bracelets that can be made with the beads she has. She has 214 bags of beads, each with enough beads for 22 bracelets. To find the actual number of bracelets possible, we multiply the number of bags by the number of bracelets each bag can make:
214 bags × 22 bracelets per bag = 4,708 bracelets.
Sarah estimated that there were enough beads for at least 4,000 bracelets, based on the approximation that 200 bags with enough beads for 20 bracelets each would yield 4,000 bracelets. Although her estimation method simplifies the calculation by rounding down to manageable numbers, the actual total (4,708 bracelets) is greater than her estimate. By using this estimation method, Sarah has effectively ensured she will have more than enough beads for her classes, as her estimate is lower than the actual number.
A class is made up of 14 girls and 15 boys. Use the given information and give the example of the following:
a) Part-to-part ratio
b) part to whole ratio
c)Write the ratio of girls to the whole class in the form of 1:n
Answer:
i would say part to whole
Step-by-step explanation:
What is the maximum value of 13.7 when rounding to the nearest tenth
chase drew the number line below to show -4 + (-3). Is his model accurate? If not, tell what is wrong with his model.
Chase's model is only accurate if it shows starting at -4 on a number line and moving 3 units left to land at -7. Otherwise, the model requires correction to accurately portray the sum of -4 and -3.
The student's question relates to the operation of adding two negative numbers on a number line. When adding -4 and -3, you start at -4 on the number line and move 3 units to the left because you're adding another negative number. If Chase's model does not show starting at -4 and moving 3 units left to end at -7, then his model is inaccurate. To correct the model, ensure that the number line accurately reflects this movement and resulting position on the number line.
Describe the pattern you see when you move from a lesser place-value position to the next greater place-value position.
One number exceeds another by 1 the sum of the numbers is 29 what are the numbers
Final answer:
To find the two numbers, we set up two equations, solve for one variable, and find the other. The numbers that satisfy the condition of one exceeding the other by 1 with their sum being 29 are 14 and 15.
Explanation:
The student's question involves finding two numbers where one number exceeds the other by 1 and their sum is 29. To solve this, let's set up a system of equations. We'll call the first number x and the second number y. Based on the question:
x = y + 1 (one number exceeds the other by 1)
x + y = 29 (the sum of the numbers is 29)
Substituting the first equation into the second gives us:
(y + 1) + y = 29
2y + 1 = 29
2y = 28
y = 14
Now that we have the value of y, we can find x:
x = y + 1
x = 14 + 1
x = 15
Therefore, the two numbers are 14 and 15.
Find three consecutive even integers such that the sum of the least integer and the middle integer is 30 more than the greatest integer
Let the first integer be represented by: 2k
the second integer by: 2(k+1)
and the third by: 2(k+2)
Then, 2k + 2(k+1) = 2(k+2) + 30
2k + 2k + 2 = 2k + 4 + 30
4k + 2 = 2k + 34
2k = 32
k = 16
first integer: 2k = 2(16) = 32
second integer: 2(k+1) = 2(16+1) = 2(17) = 34
third integer: 2(k+2) = 2(16+2) = 2(18) = 36
Answer: 32, 34, 36
How do you write 3.125 expanded form
A random sample of 50 units is drawn from a production process every half hour. the fraction of nonconforming product manufactured is 0.02. what is the probability that ????̂0.04 if the fraction nonconforming really is 0.02
The probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02 can be calculated using the normal approximation to the binomial distribution.
Explanation:To find the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02, we can use the normal approximation to the binomial distribution.
1. Calculate the mean of the sampling distribution using the formula:
μ = np = 50 * 0.02 = 1
2. Calculate the standard deviation using the formula:
σ = sqrt(npq)
where q = 1 - p = 1 - 0.02 = 0.98
σ = sqrt(50 * 0.02 * 0.98) ≈ 0.99
3. Convert p(hat) to a z-score using the formula:
z = (p(hat) - μ) / σ
z = (0.04 - 1) / 0.99 ≈ -0.96
4. Look up the z-score in the standard normal distribution table to find the corresponding probability.
P(z < -0.96) ≈ 0.166
Therefore, the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02 is approximately 0.166.
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Complete question:
A random sample of 50 units is drawn from a production process every half hour. The fraction of non-conforming product manufactured is 0.02. What is the probability that p(hat) < 0.04 if the fraction nonconforming really is 0.02?
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The answer and how to get it correctly on my own
Every 3 days Seth goes to the grocery store. His best friend Brian goes every 5 days. On what day will they both go to the store on the same day???
PLEASE HELP! number 18
Express (0.0006) in engineering notation.
Is this better? Its all.. There is no book to read it over so its confusing
find the value of x so that f( x ) = 7
The value for x so that f(x) = 7 is at x = -3.
Using the equation of slope-intercept form (y = mx + b), where m is the gradient and b is the constant, we can find the value of x at which f(x) is equal to 7 as follows:
By observation on the graph, when x = 1, y = 3 and when x = 2, y = 2.
3 = m + b...(1)
2 = 2m + b...(2)
we multiply equation (1) by 2 and subtract equation (2) from the result;
6 - 2 = 2m - 2m + 2b - b
4 = b
putting 4 for b in equation (1) gives;
m = -1
Thus we have the equation for f(x) as
f(x) = (-1)x + 4
For f(x) = 7;
-x + 4 = 7
x = 4 - 7
x = -3.
Therefore, for f(x) to be equal to 7, the value of x is equal to -3.
which expression has a value of 15 when p=12 18/p 3p. 18-p p+3
The required expression that has a value of 15 is given as P + 3.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Substitute the value of p in the expression,
= P + 3
= 12 + 3
= 15
When the value of p is put on another expression there output value is not 15.
Thus, the required expression that has a value of 15 is given as P + 3.
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Dominic earns 285 per week plus an 8% commission rate on all his sales. If dominic sell 4213 worth of merchandise in one week how much will his total earnings for the week be?
Dominic's total earnings for the week are calculated by adding his fixed salary of $285 to his commission, which is 8% of his sales. The commission on $4,213 worth of sales is $337.04, resulting in total earnings of $622.04.
Explanation:The question requires us to calculate Dominic's total earnings for the week based on his fixed salary and the commission he makes from sales. Dominic earns a fixed amount of $285 per week plus an 8% commission from his sales. To find his total earnings, we need to calculate his commission from the $4,213 worth of merchandise he sells.
Firstly, we convert the 8% commission rate into decimal form by dividing by 100, which gives us 0.08. Then, we multiply the total sales amount by this decimal to find the commission amount:
Commission = Total Sales × Commission RateCommission = $4,213 × 0.08Commission = $337.04Next, we add the commission to Dominic's fixed salary to get his total earnings for the week:
Total Earnings = Fixed Salary + CommissionTotal Earnings = $285 + $337.04Total Earnings = $622.04Therefore, Dominic's total earnings for the week will be $622.04.
Write the number with the same value as 32 tens
Write the following ratio using two other notations
3/2
what is the written form of 7.007?
The written form of 7.007 is "seven and seven thousandths." It is derived from the digit 7 representing the units place, and the last digit 7 representing the thousandths place.
The written form of 7.007 is "seven and seven thousandths." To understand the structure of this decimal:
The digit 7 before the decimal point represents the units place, or 'seven'.
The first digit 0 after the decimal point represents the 'tenths' place, which is zero in this case.
The second digit 0 after the decimal point represents the 'hundredths' place, which is also zero.
The third digit 7 after the decimal point is in the 'thousandths' place, which means we have seven thousandths.
Combining these, we get the phrase "seven and seven thousandths," which is the written form of the number 7.007.
solve the following problem correctly 6+6²÷(3+6) x 3
29,998 round to place underline digit which is 9
The minimum sustained wind speed of a category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour. Write an absolute value equation that represents the minimum and maximum speeds. Let V represent the wind speed.
The absolute value equation that represents the range of a category 1 hurricane's wind speed is |V - 84.5| ≤ 10.5. 84.5 is the average of the range and 10.5 is the difference from the range's center to the end.
Explanation:The absolute value equation that represents the minimum and maximum sustained wind speeds of a category 1 hurricane can be written as |V - 84.5| ≤ 10.5. Here, V stands for the wind speed. The middle value of 74 and 95 is 84.5 (the average of 74 and 95). And the distance from 84.5 to either end of the range (74 or 95) is 10.5. So, the range of speeds is represented by the absolute difference from the center of the range is less than or equal to 10.5.
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Given CA=3x-4, AT=4x+1, and CT=32, find AT
Theo mom bought an 8 pack of juice boxes at the store for four dollars. Find the unit rate for the juice boxes
How many atoms of Oxygen (O) are in H3OClO4
what is -1.3 ≥ 2.9 -0.6r graph the solution