A rectangular room measures 9 feet by 12 feet. If carpeting costs $20.00 per square yard, what would it cost to carpet the room?
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The image of the point (1, -2) after a rotation of 180° about the origin is:
the base of a jewelry box is a square with a side length of 5 1/2 inches. the box is 2 inches high. what is the volume of the box?
An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 334 people living in East Vancouver and finds that 43 have recently had the flu. Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her 95% confidence interval to have a margin of error no larger than 0.03. How large a sample should she take to achieve this?
The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in.2. Which inequality can be used to find the possible lengths, x, of the base of the triangle?
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50 dozen donuts should be produced before your average cost per dozen drops to $2.45
Let x be the number of dozen donuts produced.
The total cost to produce x dozen donuts is:
Total cost = cost of raw materials + overhead costs
Total cost = 0.65x + 0.55x
Total cost = 1.20x
The average cost per dozen can be expressed as:
Average cost per dozen = Total cost / number of dozens
2.45 = 1.20x / x
To solve for x, we can cross-multiply and simplify:
2.45x = 1.20x
x = 50
Therefore, you must produce 50 dozen donuts before your average cost per dozen drops to $2.45.
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If x is the number of times the price is reduced by one dollar.
Find a function for total profit with respect to x. A negative value for x will mean the price is increased.
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given D = 21 when x = $16
21 = 16m + c ------------1) and also we know D = 24 unit, when x = $15,
24 = 15m + c ------------2)
subtract eqn 2) from eqn 1) we get
-3 = m , and plug this value of m in eqn 1) we get
21 = 16*(-3) + c => c = 69
hence demand function
D(x) = -3x + 69
Cost price is C = $1
Profit = Revenue - Cost price
P(x) = Demand*Selling price - Cost per unit* Demand
P(x) = (69 - 3x)*x - 1*(69 - 3x)
P(x) = 69x - 3x² - 69 + 3x ; or
P(x) = - 3x² + 72x - 69 -------------Answer
Differentiate profit function with respect to x (selling price)
dP/dx = -3*2x + 72 - 0
0 = 72 - 6x ; plug dP/dx = 0 for maxima minima
6x = 72
x = $12 per unit --------Answer
(Since d²P/dx² = -6 < 0 , hence profit will be maximum at x = $12 per unit
and Demand would be D(@12) = 33 unit
Revenue = 33*$12 = $396
Cost = $1*33 = $33
Max Profit = #396 - $33 = $363
B.rotation 180° about the origin
C.translation 10 units right
D.reflection across the y-axis
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Answer:
6-3/0-(-4)
=3/4
Step-by-step explanation:
Given two points of a line to find the slope, we use the formula.y2-y1/x2-x1 hence the answer above. Our xs are x2=0 x=-4 y2=6 y1=3
g(x) = x2 − 8x + 16
In which direction and by how many units should f(x) be shifted to obtain g(x)?
Left by 4 units
Right by 4 units
Left by 8 units
Right by 8 units
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Answer: The answer is (B) Right by 4 units.
Step-by-step explanation: The two functions f(x) and g(x) are defined as follows:
We are to check the correct transformation of the graph of f(x) to the graph of g(x).
We can rewrite the graph of g(x) as follows:
Comparing this with the equation of f(x), we can say that f(x) is shifted right by 4 units to obtain g(x).
The graphs of both the functions are shown in the attached figure.
Answer:
Left by 4 units
Step-by-step explanation:
I took it the first time and put Right 4 units and got it wrong. When i put left by 4 units i got it right.
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it needs to be 20 characters so here’s this ndnsoxid
Final answer:
The subject of this question is Mathematics and the grade level is High School. The relationship between the number of months and the total cost of having the account can be represented by the formula y = 4.95x, where y is the total cost and x is the number of months.
Explanation:
The subject of this question is Mathematics
- Joel's monthly service fee is $4.95, therefore, each month the total cost of having the account increases by $4.95
- In terms of variables, let x be the number of months and y be the total cost of having the account
- The relationship between x and y can be expressed as y = 4.95x, where 4.95 represents the monthly service fee and x represents the number of months
Thus, the formula y = 4.95x represents the relationship between the number of months and the total cost of having the account.
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