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.

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.

Answer:

Quadrant

Step-by-step explanation:

Final answer:

To solve the algebraic equation stated as 'six times the sum of a number and 7 equals 2,' we distribute, subtract 42 from both sides, and then divide by 6, leading to the solution x = -20/3 or approximately -6.67.

Explanation:

The question involves solving an algebraic equation to find an unknown number. When the problem states that six times the sum of a number and 7 equals 2, it can be represented mathematically as 6(x + 7) = 2. To find the value of x, you need to follow these steps:

First, distribute the 6 to both x and 7, which gives 6x + 42 = 2.

Next, to isolate the variable term (6x), you would subtract 42 from both sides of the equation, resulting in 6x = 2 - 42, which simplifies to 6x = -40.

Finally, to find the value of x, divide both sides by 6, giving x = -40 / 6, which simplifies to x = -20 / 3 or approximately x = -6.67.

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.

We want to make a table of ordered pairs for the given equation, and then graph two of these points to graph the equation.

We have the equation:

y = (-1/3)*x + 1

We can make the table:

[tex]\left[\begin{array}{ccc}x&y\\-1&\\0&\\1&\\3&\end{array}\right][/tex]

To complete the table, we just need to evaluate the given equation in these x-values. We will get:

y(-1) = (-1/3)*(-1) + 1 = 1/3 + 1 = 4/3

y(0) = (-1/3)*0 + 1 = 1

y(1) = (-1/3)*1 + 1 = 2/3

y(3) = (-1/3)*3 + 1 = 0

Now we just complete the table with the values that we got:

[tex]\left[\begin{array}{ccc}x&y\\-1&4/3\\0&1\\1&2/3\\3&0\end{array}\right][/tex]

Now to graph the equation, we can graph two of these points, for simplicity I will graph (0, 1) and (3, 0).

Once the points are graphed, we just need to draw a line that connects them. The graph can be seen below.

If you want to learn more, you can read:

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Graph is a representation of data by using the vertices and edges to convert the data in easily understandable form. Graph contains two axis, a vertical axis and a horizontal axis. These axis are also denoted as x axis and y axis.

In the given question we have to find the value of k using the points of graph on x axis and y axis.

Given

The graph passes through [tex]\rm\:A (4, -80)[/tex]

Value of [tex]\rm\;x= 4[/tex]

Value of [tex]\rm y=-80[/tex]

The value of k can be determined by the graphical intersection of the points on x axis and y axis. By putting the value of x and y in the given equation we got:

                                      [tex]\begin{aligned}\rm\;y&=kx\\\\k(4)&=-80\\\\k&=\dfrac{-80}{4} \\\\k&=-20\end[/tex]

Therefore by putting the values of x and y we found that the value of [tex]\rm\:k=-20[/tex]

Learn more about graphs here:

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The probability that it will snow and Amy will be late for school is found by multiplying the individual probabilities of each event, which are 60% and 10% respectively, resulting in 6%.

The probability that both events (it snowing and Amy being late for school) will occur is found by multiplying the probabilities of each independent event. As Amy states, there is a 60% chance of snow (which can be expressed as a probability of 0.60) and a 10% chance she will be late for school (expressed as a probability of 0.10). To find the probability that both events happen, we calculate:

Probability(snow and late) = Probability(snow) × Probability(late)

Probability(snow and late) = 0.60 × 0.10 = 0.06

Therefore, the probability that it will snow tomorrow and Amy will be late for school is 6%.

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.

Subtraction is a mathematical operation that reflects the removal of things from a collection.

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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average for 4 months total needs to equal 55*4 = 220 minutes

43 + 62 + 57 = 162

220-162 = 58

 58 minutes

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