Jumps has $55 in her savings account. This is $21 more than David. Write and solve an equation to find the amount David has in his savings account.

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.

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.

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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Answer:

kkkkkkk

Step-by-step explanation:

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.

Answer:

So, she spends 3 hours more sleeping than doing the activities.

Step-by-step explanation:

Consider the provided information.

According to the graph, Avery spends 33% of time in sleeping and 19% of time in doing "other" activities.

There are 24 h in a day.

According to Sleep category: 33% of 24 is:

33 % of 24=0.33×24=7.92 h ≈8 hours  

We are rounding to 8 hr because the solution should be in hours as per the question requirement.

Other category: 19% of 24 is:

19 % of 24=0.19×24=4.56 h ≈5 hours  

The difference of time is:

8h-5h=3h

So, she spends 3 hours more sleeping than doing the activities.

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.

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.

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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The number of weeks required to have $67 left in the account is 13 weeks

Given the Parameters :

To obtain the number of weeks to have $67 left in the account, we substitute y = 67 into the equation and solve for x :

y = - 24x + 379

67 = - 24x + 379

Collect like terms

24x = 379 - 67

24x = 312

x = 312 / 24

x = 13

Therefore, the Number of weeks required is 13 weeks

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