To determine the number of copies made per minute, the total time of 4 minutes and 45 seconds is first converted to 4.75 minutes. Dividing the total copies (114) by the total time in minutes (4.75) gives us 24 copies per minute.
Calculating Copies Per Minute
To find out how many copies the machine makes per minute, we need to convert the total time into minutes. There are 4 minutes and 45 seconds. Since there are 60 seconds in a minute, we can convert 45 seconds into minutes by dividing by 60, which gives us 0.75 minutes. Therefore, the total time in minutes is 4 + 0.75 = 4.75 minutes.
Now, we use the given information that the copy machine makes 114 copies in 4.75 minutes to calculate the number of copies it makes per minute:
Copies per minute = Total copies / Total time in minutes
Copies per minute = 114 copies / 4.75 minutes
Copies per minute = 24 copies per minute (rounded to the nearest whole number)
What is 788 divided by 14 in a long division model?
Mrs. Curtis wants to buy online tickets for a concert. Two options are given here.
Option 1: $53 for each ticket plus a shipping fee of $10
Option 2: $55 for each ticket and free shipping
What is a system of equations to represent the costs of the tickets?
Express your equations in the form of y=mx+by=mx+b where x is the number of tickets purchased and y is the total cost.
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.
What is 324 divided by 6??
Your car gets 20 miles per gallon of gas. This is 4 more miles per gallon than your friend's car gets. How many miles per gallon does your friend's car get?
Answer:
Answer:
16 miles per gallon
Step-by-step explanation:
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
The linear function f(x) passes through the points (1,2) and (3,0).
A few values from the exponential function g(x) are shown in the table
What is the positive difference in the y-intercept of f(x) and g(x)?)
What is the lateral area of a pyramid with base edges 5ft and surface area 55ft^2? ...?
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
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 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
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
Where is the dependent variable plotted on a line graph?
What are prime numbers of 50?
What is the decimal expansion of the following fraction?
1/4
1.4
0.14
___
0.25
0.25
If $2500 is invested at an interest rate of 2.5% per year, compouded daily, find the value of the inevestment after 2 years
if 2tanA=3tanB,then prove that tan(A-B)=sin2B/(5-cos2B) ...?
What is 1,295.014 rounded to the nearest hundredth?
Find the distance between -422 and 166.
What is 2/3 times 26 but estimated ?
Solve and graph the absolute value inequality: |2x + 4| > 8. number line with open circles on negative 6 and 2, shading in between. number line with closed circles on negative 6 and 2, shading going in the opposite directions. number line with open circles on negative 6 and 2, shading going in the opposite directions. number line with open circles on negative 2 and 2, shading going in the opposite directions.
Final answer:
The inequality |2x + 4| > 8 is resolved by considering the inside expression being greater than 8 and less than -8, which leads to x > 2 and x < -6. The proper representation on a number line is with open circles on -6 and 2, shading away from these points, indicating the range of solutions.
Explanation:
To solve the absolute value inequality |2x + 4| > 8, we must consider the two scenarios that could make the inequality true: when (2x + 4) is greater than 8 and when -(2x + 4) is less than -8. Absolute values denote the distance from zero, so they are never negative. Since the inequality is strict (indicated by '>'), we will use open circles in the graph.
First, let's consider when the expression inside the absolute value is positive:
2x + 4 > 8
2x > 4
x > 2
This scenario corresponds to all x-values greater than 2.
Now for the negative scenario:
-(2x + 4) > 8
-2x - 4 > 8
-2x > 12
x < -6
This scenario corresponds to all x-values less than -6.
The correct graph of the solution set on a number line would have open circles on -6 and 2, with shading going in opposite directions away from these points, indicating all the numbers greater than 2 and all the numbers less than -6 satisfy the original inequality.
Based on this, the third choice is correct: A number line with open circles on negative 6 and 2, shading going in the opposite directions.
Goran is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges $93 and allows unlimited mileage. Company B has an initial fee of $65 and charges an additional $0.70 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m .
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.
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.
b-4/6=b/2. Solve for b.
2(b−4)=6(b) 2b - 8 = 6b 2b - 6b = 8 -4b = 8 Now you can solve.....
A steel plate has the form of a quarter of a circle with a radius of 49 cm. Two 2-cm holes are to be drilled in the plate. Let (X1,Y1) and (X2,Y2) be the coordinates of the centers of the holes. Find the coordinates for both holes.
The task is to determine the coordinates of two 2-cm holes in a quarter-circle steel plate, but there is insufficient information to provide a precise location without additional details or constraints.
Explanation:The question requires us to find the coordinates for the centers of two 2-cm holes to be drilled in a steel plate, which is shaped like a quarter of a circle with a radius of 49 cm. Assuming the plate is positioned with its corner at the origin (0,0), with the circular edge encompassed by the positive x-axis and positive y-axis, the holes should be placed in such a way that their centers within the quarter circle are equidistant from the axes and from the plate's circular edge.
However, the question does not provide sufficient information or constraints about the location of the holes within the quarter-circle plate. To determine the exact coordinates, we need more specifics, such as how far from the edges or any other centering constraints for the holes. Without this additional information, there are infinitely many possible coordinates for the holes that meet the given condition of being within the quarter-circle plate.
If the holes are to be evenly distributed and placed symmetrically, a possible choice could be to align the centers of the holes along the line y = x, which bisects the quarter-circle. Yet, without precise instructions, we cannot provide a definitive answer to the coordinates of the holes.
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What Rate Of Simple Interest Is Needed For $700 To Double,In 3 Years?
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.can u do this bro 100x7+8-678x56
Answer:
-37260
Step-by-step explanation:
did it in my head
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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