Answer:
Option 4). Machine with $8 per hour operating cost, producing 14 pounds of candy per hour.
Step-by-step explanation:
We have to find the most profitable investment for a candy shop that earns $1 per pound of candy.
We will take up each option one by one.
Option 1).
Producing eight pounds of candy per hours means profit = $1×8 = $8
But workers take $10 per hours so expenditure = $8 - $10 = -$2
There is a loss of $2 in this investment.
Option 2).
Production of 16 pounds candy per hour will make the profit = $1 × 16 = $16
But workers take $12 per hour so profit earned = 16 - 12 = $4
Option 3).
Machine produces 10 pound of candy per hour so profit will be = $1 ×10 = $10
Operating cost of the machine = $5 per hour
So profit generated = profit - Operating cost of machine
= 10 - 5 = $5
Option 4).
Profit earned by production of 14 pounds of candy per hour = $1 × 14 = $14
Operating cost of the machine = $8 per hour
Therefore, Total profit per hour = 14 - 8 = $6
Finally we can say that the maximum profit will be generated in option 4.
Therefore, Option 4) will be the best option to invest.
Final answer:
The most profitable investment for a candy shop is the machine with an $8 per hour operating cost, producing 14 pounds of candy per hour, yielding a net profit of $6 per hour.
Explanation:
The task is to determine the most profitable investment for a candy shop that makes $1 profit per pound of candy. To calculate the profitability of each option, we need to figure out the net profit per hour for each.
Worker at $10 per hour, producing eight pounds of candy per hour:
Profit = 8 pounds * $1 profit per pound - $10 wage per hour = $8 - $10 = -$2 per hour.
Worker at $12 per hour, producing 16 pounds of candy per hour:
Profit = 16 pounds * $1 profit per pound - $12 wage per hour = $16 - $12 = $4 per hour.
Machine with $5 per hour operating cost, producing 10 pounds of candy per hour:
Profit = 10 pounds * $1 profit per pound - $5 operating cost per hour = $10 - $5 = $5 per hour.
Machine with $8 per hour operating cost, producing 14 pounds of candy per hour:
Profit = 14 pounds * $1 profit per pound - $8 operating cost per hour = $14 - $8 = $6 per hour.
Comparing the net profit per hour for each option, the Machine with $8 per hour operating cost, producing 14 pounds of candy per hour, is the most profitable investment.
Please help me solve this word problem:
In a round-robin chess tournament, each player is paired with every other player once. The function shown below, models the number of chess games, "N", that must be played in a round-robin tournament with "t" chess players. In a round-robin chess tournament, 55 games were played. How many players entered the tournament?
N=t^2-t divided by 2.
Answer:
t = 11
Step-by-step explanation:
From the equation that gives, the number of games you can get the number t of players who participated in the ronund-robin tormeo, is:
[tex]N = \frac{t ^ 2-t}{2}[/tex]
[tex]55 = \frac{t ^ 2-t}{2}[/tex]
[tex]110 = t ^ 2-t[/tex]
[tex]t ^ 2-t -110 = 0[/tex]
[tex](t-11) (t + 10) = 0[/tex]. Then
[tex]t - 11 = 0\\t = 11\\t + 10 = 0\\t = -10[/tex]
Since t cannot take negative values, then t = 11.
A regular 24 sided polygon is rotated with this center of rotation at its center what is the smallest degree of rotation needed to map the polygon back onto itself
What is the surface area of a piece of pipe that is open at both ends, has a radius of 6 inches, and a height of 18 inches? (Use 3.14 for π.)
The surface area of an open-ended pipe with a radius of 6 inches and a height of 18 inches is 678.24 square inches. The calculation is based on the formula for the circumference of the circle, which is multiplied by the height of the cylinder.
To calculate the surface area of a pipe that is open at both ends, we need to find the area of the outer surface. Since the pipe is a cylinder without the top and bottom circles, the surface area is simply the circumference of the circle (which is the edge of the openings) times the height of the cylinder. The formula for the circumference of a circle is C = 2πr, where r is the radius.
The radius is given as 6 inches and the height is 18 inches, therefore:
Circumference (C) = 2πr = 2 × 3.14 × 6 inches = 37.68 inches.The surface area (SA) of the pipe is C × height = 37.68 inches × 18 inches = 678.24 square inches.What is 1,295.014 rounded to the nearest hundredth?
What is the fifth root of -32?
The fifth root of -32 is -2. To find it, think of a number that, when raised to the power of 5, gives the original number.
The fifth root of -32 is -2. To find the fifth root of a number, we can think of it as finding a number that, when raised to the power of 5, gives us the original number. In this case, -2 * -2 * -2 * -2 * -2 = -32.
Use elimination to solve the system of equations.
2x+6y=-8 and 5x-3y=88
The formula for the circumference C of a circle with radius r is C = 2πr. Which of the following is a formula for π (pi) of the circle in terms of the circumference and radius?
A. PI=C+2r
B: C-2r
C: PI=2R/C
D: PI/C/2R
...?
Answer: D. [tex]\pi=\dfrac{C}{2r}[/tex]
Step-by-step explanation:
Given : The formula to find the circumference is given by :-
[tex]C=2\pi r[/tex], where r is the radius of the circle.
To find the formula for [tex]\pi[/tex] , we need to divide 2r on both of the sides in the above equation, we get
[tex]\pi=\dfrac{C}{2r}[/tex] , where r is the radius of the circle.
Hence, the correct formula for [tex]\pi[/tex] : Option D [tex]\pi=\dfrac{C}{2r}[/tex]
If ON is a midsegment of KLM, find LM.
A.2
B.3
C.4
D.5
Answer:
LM= 4
Step-by-step explanation:
In the triangle KLM, ON is the mid segment of KLM
WE use triangle Mid segment theorem
MN= twice of ON
MN= 2 times of ON
4x= 2(x+1)
distribute 2 inside the parenthesis
4x= 2x+2
Subtract 2x on both sides
4x-2x= 2x+2-2x
2x= 2
divide by 2 on both sides
x= 1
To find length of MN, we plug in 1 for x
MN= 4x= 4(1)= 4
what is the range of the relation. (–2,7) (7,2) (2,7)
A. {-2,2,7}
B. {-2,7}
C. {2,7}
D. {2}
Domain:{−2,7,2}
Range:{7,2}
if 2tanA=3tanB,then prove that tan(A-B)=sin2B/(5-cos2B) ...?
Convert to scientific notation: 0.000678
What is 2/3 times 26 but estimated ?
Find the greatest common factor of the monomials. 16x, 36x ...?
Final answer:
The greatest common factor of the monomials 16x and 36x is 4x, obtained by finding the common prime factors of 16 and 36 and including the variable x, which is present in both monomials.
Explanation:
To find the greatest common factor of the monomials 16x and 36x, we need to break each monomial into its prime factors and compare them.
Prime factors of 16 are 2 x 2 x 2 x 2.
Prime factors of 36 are 2 x 2 x 3 x 3.
Both 16 and 36 have two 2's in common.
Therefore, the GCF of 16 and 36 is 2 x 2 = 4. Since x is present in both monomials, x is also part of their GCF.
The greatest common factor of the monomials 16x and 36x is therefore 4x.
A)14 is 30 percent of what number?
B) 72 is what percent of 180?
the ratio of length to width in a rectangle is 3:1. If the perimeter of the rectangle is 112 feet, what is the length of the rectangle?
Length of the rectangle= 42 feet
Width of the rectangle =14 feet
What is rectangle?A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.
Given,
Ratio of length to width of rectangle = 3:1
Let width be x then length will be 3x
Perimeter of the rectangle = 112 feet
2(Length + Width) = 112
2(3x + x) = 112
2(4x) = 112
8x = 112
x = 112/8
Width x = 14 feet
length = 3x = 3×14 = 42feet
Hence, 42 feet is length and 14 feet is width of the rectangle.
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In a survey conducted by a union, members were asked to rate the importance of the following issues: (1) job security, (2) increased fringe benefits, and (3) improved working conditions. Five different responses were allowed for each issue. Among completed surveys, how many different responses to this survey were possible? ...?
Final answer:
To calculate the number of different responses in the survey, we multiply the number of potential responses for each issue. With 5 options for each of the 3 issues, there are 5 x 5 x 5 = 125 different possible combinations.
Explanation:
To determine the number of different responses to the survey conducted by a union, we need to calculate the total possible combinations that can occur when members are asked to rate the importance of three issues: (1) job security, (2) increased fringe benefits, and (3) improved working conditions. Since there are five different responses allowed for each issue, we would use a combination formula.
Each member can choose from 5 different responses for each of the 3 issues. This is a situation where we use the 'fundamental counting principle' where you multiply the number of options for each independent choice to get the total number of possibilities:
For job security: 5 possible responsesFor increased fringe benefits: 5 possible responsesFor improved working conditions: 5 possible responsesThe total number of different responses to the survey is 5 x 5 x 5, which equals 125.
So, members have 125 different ways to respond to the survey based on how they rate the importance of each issue.
If AZ is a midsegment of WXY, find XZ
A.7
B.9
C.12
D.14
A hole is poked in a balloon so that every minute the balloon loses 3/10ft 3 of air. What is the total change in the number of cubic feet of air in the balloon after 5/9 min?
Cory earns $20 for every lawn he mows and $9 for every hedge he trims. He uses the expression 20x + 9y to keep track of his earnings.
Part A: Identify the coefficients and variables in the expression.
Part B: How many terms are in the expression, what are they, and how do you know?
Part C: Which term in the expression shows the total earned from trimming hedges?
please help.
Rite cut riding lawnmower obeys the demand equation p=-1/20x+1060. The cost of producing x lawnmowers is given by the function c(x)=120x+5000
a)Express the revenue R as a function of x
b)Express the profit P as a function of X
c)Fine the value of x that maximizes profit. What is the maximum profit?
d)What price should be charged to maximize profit? ...?
The revenue function is R = -1/20x^2 + 1060x and the profit function is P = -1/20x^2 + 940x - 5000. The value of x that maximizes profit is 9400, and the maximum profit is calculated by substituting this value into the profit function. The price to charge to maximize profit is $590.
Explanation:a) To express revenue (R) as a function of x, we multiply the price (p) by the quantity (x):
R = p * x
Substituting the demand equation (p = -1/20x + 1060):
R = (-1/20x + 1060) * x
Simplifying:
R = -1/20x^2 + 1060x
b) Profit (P) is given by subtracting the cost (c(x)) from the revenue (R):
P = R - c(x)
Substituting the expressions for R and c(x):
P = (-1/20x^2 + 1060x) - (120x + 5000)
Simplifying:
P = -1/20x^2 + 940x - 5000
c) To find the value of x that maximizes profit, we take the derivative of the profit function with respect to x and set it equal to zero:
dP/dx = -1/10x + 940
Solving for x:
-1/10x + 940 = 0
x = 9400
d) To find the price that maximizes profit, we substitute the value of x (9400) into the demand equation:
p = -1/20(9400) + 1060
simplifying:
p = 1060 - 470
p = $590
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a) First, we must express the revenue, denoted as 'R'. Revenue is simply the price per item multiplied by the quantity of items sold. Given the demand equation 'p', we can express the revenue as follows:
R = p * x = ( -1/20 * x + 1060 ) * x
This simplifies to:
R = x * (1060 - 0.05*x)
b) Profit is revenue minus cost. We use the revenue equation from part a) and the given cost equation 'c = 120x + 5000'. Plug these into the profit equation:
P = R - c = ( x * (1060 - 0.05*x) ) - ( 120x + 5000 )
This simplifies to
P = x * (1060 - 0.05*x) - 120*x - 5000
c) To maximize profit, we need to find the derivative of the profit function and then solve for x when this derivative is equal to zero (this will find the quantity that maximizes profit). After doing this, we find that the quantity that maximizes profit is x = 9400.
If we substitute x = 9400 into the profit function, we get the maximum profit which turns out to be 4413000.
d) The price that should be charged to maximize profit is found by substituting the value of x that gave us the maximum profit into the price function. In this case, substituting x = 9400 gives us the price = 590.
Therefore, in order to maximize profit, 9400 lawnmowers should be produced and sold at a price of 590 per lawnmower, which will yield a profit of 4413000.
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What is the area of 74.8 and 22.6?
HELP!! Not hard, just confusing.. ΔABC is reflected across the x-axis and then translated 4 units up to create ΔA′B′C′. What are the coordinates of the vertices of ΔA′B′C′ ?
A′(-3, 3), B′(-1, 1), C′(-2, 3)
A′(3, -3), B′(1, -1), C′(2, -3)
A′(3, -5), B′(1, -7), C′(3, -5)
A′(-3, 3), B′(-1, 1), C′(-2, -3)
Answer:
1st one : A′(-3, 3), B′(-1, 1), C′(-2, 3)
Step-by-step explanation:
below
You work at a dog food factory. The factory makes 10,600 kilograms of dog food a day. How many metric tons of dog food does the factory make a day?
What Rate Of Simple Interest Is Needed For $700 To Double,In 3 Years?
Judy has a sugar cone and wants to know how many cubic inches of ice cream it will hold if it is filled completely to the top of the cone and no more. the cone has a height of 4.5 inches and a radius of 1.5 inches.
The cone of dimension 4.5 inches height and 1.5 inches radius can hold 9.425 inches^3 of ice cream.
A sugar cone can be seen as a three-dimensional object, specifically a cone, which has a known formula for calculating its volume.
Volume of a cone: (1/3) x π x radius2 x height
Substituting the given values: (1/3) x π x 1.52 x 4.5 = 9.425 inches^3.
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the first equation is substituted into the second equation.
12x – y = –4
4x – 3y = –6
Answer
4x – 3(–12x – 4) = –6
4(12x + 4) – 3y = –6
4(–12x – 4) – 3y = –6
4x – 3(12x + 4) = –6
...?
Answer:
the answer to this question is 4x - 3(12x + 4) = -6 hope this helps
For a circle of radius 4 feet, find the arc length s subtended by a central angle of 26 degrees.
Answer:
The arc's length is 1.8 ft
Step-by-step explanation:
For calcaulate the arc length S we used the formula below:
[tex] S=\frac{\pi.\alpha(\º)}{180}*R[/tex]
Here alpha is the arc angle in degrees and R is the circle radius. Thus, if alpha is equal to 26 and R equals to 4 ft:
[tex] S=\frac{\pi.26}{180}\ *\ 4ft[/tex]
[tex] S=0.45\ *\ 4ft[/tex]
[tex] S=1.8\ ft[/tex]
(2s+5)/(s^2+6s+34) inverse Laplace transform
The inverse Laplace transform of (2s+5)/(s^2+6s+34) is found by completing the square in the denominator and then matching the result to a known form in the Laplace transform table.
Explanation:The question asks for the inverse Laplace transform of the function (2s+5)/(s^2+6s+34). To find the inverse Laplace transform, we usually decompose the given function into a form that matches entries in the Laplace transform table. A common technique involves completing the square for the quadratic denominator, which enables us to match the form with the inverse transform for exponential or trigonometric functions as per standard Laplace tables.
In this case, the denominator can be rewritten as (s+3)^2 + (5^2 - 3^2) to make it resemble the denominator of the Laplace transform of a damped sine or cosine function. Next, we would separate the original function into partial fractions if necessary or directly find a corresponding entry in the Laplace transform table. Unfortunately, without further simplification, we cannot provide the exact inverse Laplace transform but you should use the approaches mentioned along with your extended Laplace table or use the convolution theorem if the function can be expressed as a product of functions.
Find the distance between -422 and 166.
What is the inverse of the function f(x) = 2x + 1?
h(x) = 1/2 x – 1/2
h(x) = 1/2 x + 1/2
h(x) = 1/2 x – 2
h(x) = 1/2 x + 2
What is the exact answer?
Answer:
[tex]h(x)=\frac{x}{2}-\frac{1}{2}[/tex]
Step-by-step explanation:
Hello
Step1
Let f(x)=y
f(x) = 2x + 1
(1)y= 2x + 1
to find the inverse of f(x)
Replace every x with a y and replace every y with an x
y= 2x + 1
replacing
x=2y+1
Step 2
Now solve the equation for y
x=2y+1
subtract 1 on both sides
x-1=2y+1-1
x-1=2y
divide boths dies by 2
(x-1)/2=2y/y
[tex]\frac{x-1}{2} =\frac{2y}{2} \\y=\frac{x-1}{2}[/tex]
let this last equation h(x)= inverse of f(x)
[tex]h(x)=\frac{x-1}{2}\\h(x)=\frac{x}{2}-\frac{1}{2}[/tex]
Have a great day