1. A college newspaper, The College Spy, has a fixed production cost of $70 per edition and it costs 40¢ per copy to print and distribute. The College Spy sells for 50¢ per copy.
a. What is the cost expression for the newspaper?
b. What is the revenue expression for the newspaper?
c. Put the cost and revenue expressions into an inequality that would represent a successful newspaper.
d. How many copies should be sold to make a profit? Show all work! An answer with no work will receive 0 points.
e. Now go back to your answer for d. On every line of your solution write what property of math you would use to justify the transformation that occurred.
a. What is the cost expression for the newspaper?
The cost would be the sum of fixed cost and the variable cost. The fixed cost
is 70 while the variable cost is 0.40 x, where x stands for the number of
copies made. That is:
Cost = 70 + 0.40 x
where x = number of copies made
b. What is the revenue expression for the newspaper?
The revenue would simply be the product of selling price and number of copies sold or made, that is:
Revenue = 0.50 x
c. Put the cost and revenue expressions into an inequality that would represent
a successful newspaper.
To have a successful newspaper, the difference of revenue and cost must be
greater than 0, that is:
Revenue – Cost > 0
0.50 x – (70 + 0.40 x) > 0
d. How many copies should be sold to make a profit? Show all work! An answer
with no work will receive 0 points.
From the above equation, we solve for x.
0.50 x – (70 + 0.40 x) > 0
0.50 x – 70 – 0.40 x > 0
0.10 x > 70
x > 700
Number of copies made should be more than 700 copies
e. Now go back to your answer for d. On every line of your solution write what
property of math you would use to justify the transformation that
occurred.
0.50 x – (70 + 0.40 x) > 0 Distribution property
0.50 x – 70 – 0.40 x > 0 Addition property
0.10 x > 70 Addition property
x > 700 Division property
Final answer:
The cost expression for the newspaper is $70 + $0.40c. The revenue expression is $0.50c. A successful newspaper would have $0.50c > $70 + $0.40c. To make a profit, 700 copies should be sold.
Explanation:
a. The cost expression for the newspaper can be calculated by adding the fixed production cost per edition to the cost of printing and distributing each copy. So the cost expression is:
Cost = $70 + $0.40c
where 'c' represents the number of copies.
b. The revenue expression for the newspaper can be calculated by multiplying the selling price per copy by the number of copies sold. So the revenue expression is:
Revenue = $0.50c
c. To represent a successful newspaper, the revenue should be greater than the cost. So the inequality would be:
$0.50c > $70 + $0.40c
d. To calculate the number of copies needed to make a profit, we need to find the point where the revenue is equal to or greater than the cost. So we set the inequality from part c to equality and solve for 'c':
$0.50c = $70 + $0.40c
$0.10c = $70
c = $700
e. At every step in the solution, we used the property of equalizing the equation by adding or subtracting the same value on both sides, and also dividing by the same value on both sides.
Marley bought a sandwich for $3.50, a soda for $1.95, and a pack of chips for $0.95. She used a coupon for 1/2 off on the sandwich. What was Marley's total cost before tax was added?
What number equals 100 when it is squared
2) ½ b – 39 = 101 please show your work
Answer:
kkkkkkk
Step-by-step explanation:
HELP!! Triangle A′B′C′ is the image of triangle ABC after a dilation.
What is the scale factor of the dilation?
Ted picks 6 flowers with 4 petals on each flower. Bill picks 3 flowers with 8 petals on each flower. Jon picks 2 flowers with 12 petals on each flower. Ted says they all have the same amount of petals. Is Ted correct?
The line that passes through the point (4,9) and is parallel to y=3/4x+1
Whitney conducted a survey of grocery store customers to determine the most popular brand of bread. Of the 72 people she surveyed, 11 customers liked Moonbeam, 24 customers liked Dora Lee, 17 customers liked Wondrous Loaf, and 8 customers liked Mostess. Identify the sample size in the situation above.
Evaluate the expression 4a^2 - 2b ÷ 4 for a = 2 and b = 4.
A. 2
B. 8
C. 14
D. 16
clayton climbed down 50 meters. He climbed down in 10 meter intervals.In how many intervals did clayton make his climb?
which is bigger a milliliter or a centimeter
A fish tank is in the shape of a cube. Its volume is 125 ft 3. what is the area of one face of the tank
{-2x-3y=-18 and x-6y=-6
What is 11/12 + (-7/12) in simplest form?
The simplest form of adding the given fractions is [tex]\frac{1}{3}[/tex]
Given :
[tex]\frac{11}{12} +\frac{-7}{12}[/tex]
We need to add the fractions and write it in simplest form
To add any two fractions the denominators should be same
Here the denominators are same
so we combine the numerators
[tex]\frac{11}{12}+\frac{-7}{12}\\\frac{11-7}{12}\\\frac{4}{12}[/tex]
divide both sides by 4
so simplest for is [tex]\frac{1}{3}[/tex]
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Over which interval is the graph of f(x) = –x2 + 3x + 8 increasing?
(–∞, 1.5)
(–∞, 10.25)
(1.5, ∞)
(10.25, ∞) pls help
A barber cuts 3 people hair in 35 min . Each hair cut takes at least 10 min, and the first haircut takes the most time .list one way the barber could cut 3 people's hair given this information
One way the barber could cut 3 people's hair in 35 minutes is by spending 15 minutes on the first haircut and 10 minutes each on the second and third haircuts.
If a barber cuts 3 people's hair in 35 minutes and each haircut takes at least 10 minutes, the timing could look as follows: The first haircut, taking the most time, could be 15 minutes. The second haircut could take 10 minutes, which is the minimum time per haircut. The third haircut would also take 10 minutes. This allocation adheres to the conditions that the first haircut takes the most time, and each haircut takes at least 10 minutes.
Total time spent would be 15 minutes + 10 minutes + 10 minutes, which equals 35 minutes.
what is 6.25 divided by 2.5
To divide 6.25 by 2.5, you can multiply both numbers by 10 to make it 62.5 divided by 25, which equals 2.5. Thus, 6.25 divided by 2.5 is 2.5.
To find this, we divide 6.25 by 2.5. First, we can make the divisor a whole number by multiplying both the divisor and dividend by 10, which will not change the value of the quotient:
6.25 × 10 = 62.5
2.5 × 10 = 25
Now, we divide 62.5 by 25:
62.5 ÷ 25 = 2.5
Therefore, 6.25 divided by 2.5 is 2.5.
Josiah, the manager of a pet store, bought 72 oz of water conditioner to use in his fish tanks. His small tanks would require 2 oz of conditioner and his large tanks would require 6 oz of conditioner. He made a sketch to show the line representing the different combinations of tanks he could put the water conditioner into. The x-axis represented the number of small tanks and the y-axis represented the number of large tanks. The manager labeled only the intercepts.
Which points did the manager label?
a. (0, 6) and (2, 0)
b. (6, 0) and (0, 2)
c.(0, 12) and (36, 0)
d(0, 36) and (12, 0)
Mrs. Carmen made $250 for a 20-hour work week. Last week she began making 7% more. How much does she make now?
Solve x^2+6x+15=0 using the quadratic formula
What is 3.993 rounded to the nearest hundredth
5°, 5¹, 5²
What comes next in the pattern?
Question 4 options:
5
25
5³
50
A culture started with 1,000 bacteria. After 3 hours, it grew to 1100 bacteria. Predict how many bacteria will be present after 17 hours. Round your answer to the nearest whole number. P=Ae^kt
If the polygon is translated 3 units down and 4 units left, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates.
Final answer:
To translate a polygon 3 units down and 4 units left, subtract 4 from the x-coordinate and 3 from the y-coordinate of each vertex. For example, the vertex (3, 0.4) would become (-1, -2.6) in prime notation after the translation.
Explanation:
If a polygon is translated 3 units down and 4 units left, the coordinates of the new image would change respectively. To find the new coordinates after the translation, the x-coordinate of each vertex will decrease by 4 (since it is moving left) and the y-coordinate will decrease by 3 (since it is moving down). For example, if the coordinates of a vertex are (x, y), after the translation, the new coordinates will be (x - 4, y - 3), which we denote using prime notation as (x', y').
So, if we are given the initial coordinates of the first vertex as (3, 0.4), then after the translation, the new coordinates will be:
x' = 3 - 4 = -1
y' = 0.4 - 3 = -2.6
Therefore, the new coordinates are (-1, -2.6), using prime notation to represent the translated vertex.
What is the volume of the cylinder
Given cylinder has diameter 16ft and height 10ft.
Radius of the cylinder = 16/2 = 8 ft.
We need to find the volume of cylinder.
Volume of the cylinder (V) = [tex]\pi r^2h[/tex]
Where r is the radius of the cylinder and h is the height of the cylinder.
Plugging values of r=8 and height h=10 in above formula, we get
V = [tex]\pi (8)^2(10)[/tex]
V= [tex]\pi 64 \times 10[/tex]
V=[tex]\pi \ times 640[/tex]
Plugging π =3.142
V= 3.142 × 640
V ≈2010.88.
In the given options it's nearly equal to 2010.62.
Therefore, Volume is 2010.62 ft^3.A ball is rolling at 4.80m/s over level ground when it encounters a ramp, which gives it an acceleration of -0.875m/s^2. If the ramp is 0.750m long, what is the final velocity of the ball when it reaches the top of the ramp?
In a parking lot there630 cars 270 convertibles 360 minivans what is the ratio of cards to convertibles reduce your fraction to the lowest term
1)When adding two negative numbers, _________ the absolute value of the numbers and keep the negative sign.
add, subtract, or change
2)When adding two different signed numbers, ________ the absolute values of the numbers and keep the sign of the number with the larger absolute value.
add, subtract, or change
3)When subtracting, change the subtraction to addition and _______ the sign of the number being taken away.
add, subtract, or change
Subtraction is a mathematical operation that reflects the removal of things from a collection.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
The given blanks can be written as,
1)When adding two negative numbers, add the absolute value of the numbers and keep the negative sign.
2)When adding two different signed numbers, subtract the absolute values of the numbers and keep the sign of the number with the larger absolute value.
3)When subtracting, change the subtraction to addition and change the sign of the number being taken away.
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solve the equation
5/13t = -9
5/13t = -9
Isolate the t. Multiply 13/5 to both sides
5/13t(13/5) = -9(13/5)
t = -9(13/5)
t = -117/5
Simplify.
t = -23.4
t = 23.4 is your answer
hope this helps
During last year's baseball season, Quinn pitched 3 less than 4 times the number of games that Derrick pitched. Let g represent the number of games Derrick pitched.