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2 years ago

What is the percent of increase in the rent for Bob's apartment if it went from $560 to $616?

Mathematics

2 answers:

son4ous [18]2 years ago

5 0

This is a two step problem. First, you need to find the difference (or increase) in the rent using subtraction.

616-560 = $56 increase

Now we need to figure what percent 56 is to the original amount (560)

We voice it like this:

56 is to 560 as x is to 100.

The equation looks like this:

56/560 - x/100

Cross multiply to cancel out the denominators.

56 x 100 = 560 x

5600 = 560 x

x = 10 percent.

Check it!

What is 10 percent of 560?

560 x .1 = $56

Was that your increase? ... yes.

Svetlanka [38]2 years ago

4 0

Answer:

10%

Step-by-step explanation:

Apply the formula for percent increase: 616-560/560 * 100 = 56/560*100=10%... ALL CREDIT GOES TO AOPS

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The system of equations

cupoosta [38]

Answer:

z = -12

Step-by-step explanation:

The given system of equations is:

xy/(x + y) = 1 ...........................(1)

xz/(x + z) = 2...........................(2)

yz/(y + z) = 3...........................(3)

From (1): x + y = xy

=> y = xy - x

y = x(y - 1)

x = y/(y - 1).......................................(4)

From (2): 2(x + z) = xz

=> 2x + 2z = xz

2x = xz - 2z

2x = z(x - 2)

z = 2x/(x - 2) ....................................(5)

From (3): 3(y + z) = yz

=> 3y + 3z = yz

3y = yz - 3z

3y = z(y - 3)

z = 3y/(y - 3)....................................(6)

Comparing (5) and (6)

2x/(x - 2) = 3y/(y - 3)

2x(y - 3) = 3y(x - 2)

2xy - 6x = 3xy - 6y

6(y - x) = xy .................................(7)

But from (1): xy = x + y

Using this in (7), we have

6(y - x) = x + y

6y - y - 6x - x = 0

5y - 7x = 0

5y = 7x

x = 5y/7................................................(8)

Using this in (4)

5y/7 = y/(y - 1)

1/(y - 1) = 5/7

(y - 1) = 7/5

y = 1 + 7/5

y = 12/5..........................................(9)

Using this in (8)

x = 5(12/5)/7 = 12/7 .......................(10)

Using (10) in (5)

z = 2x/(x - 2)

z = 2(12/7) ÷ (12/7 - 2)

= 24/7 ÷ -2/7

= 24/7 × (-7/2)

= -24/2 = -12

z = -12.

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2 years ago

Marley drives to work every day and passes two independently operated traffic lights. The probability that both lights are red i

madam [21]

Let event A be the first light being red.
Let event B be the second light being red.

P(A) = 0.48
P(A & B) = P(A) * P(B) = 0.35

P(B) = 0.35 / P(A)
P(B) = 0.35 / 0.48
P(B) = 0.73

Since the lights are independent, P(B|A) = P(B) therefore d is the correct answer.

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2 years ago

Read 2 more answers

Mia has a spool of ribbon that is 30.5 yards long. She will cut the ribbon into 5 equal pieces to make bows. What is the length

GenaCL600 [577]

Each piece of ribbon will be 6.1 yards long hope this helped ;D

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2 years ago

You have a budget of $48. You want to buy fruit and granola bars. Fruit costs $4 per pound, and the granola bars are $1 each. Yo

zzz [600]

1)Define the variables you will use in your model.

Let

x------->total pounds of the fruit

y-------> the total number of granola bars

TC----> total cost

Tf------> total cost of the fruit

Tg----> total cost of the granola bars

2) Write an inequality representing the total cost of your purchase. (3 points)

a. Each pound of fruit costs $4. Write an expression that shows the total cost of the fruit. Use the variable you identified in question 1

Tf=4*x

b. Each granola bar costs $1. Write an expression that shows the total cost of the granola bars. Use the variable you identified in question 1.

Tg=1*y--------> Tg=y

c. Combine the expressions from parts a and b to write an expression for the total cost. Then use this expression to write an inequality that compares the total cost with the amount you have to spend.

TC=Tf+Tg

TC=4*x+y

inequality-------> $4x+y \leq 48$

3. Write the inequality that models the number of granola bars you need to buy.

You need at least 10 granola bars

$y\geq 10$

4. Describe in words what each of your inequalities means

inequality 1

$4x+y \leq 48$

the total cost of fruits plus the total cost of granola bars must be less than or equal to 48 dollars

inequality 2

$y\geq 10$

5. Graph your system of inequalities.

using a graph tool

see the attached figure

6. Identify one point on the graph that represents a viable solution to the problem, and then identify one point that does not represent a viable solution.

Let

A-------> one point on the graph that represents a viable solution

B-------> one point on the graph that does not represent a viable solution

A(4,20)

x=4-------> total pounds of the fruit

y=20------> the total number of granola bars

check point A

substitute the values of x and y in the inequality 1

$4x+y \leq 48$

$4*4+20\leq 48\\ 36\leq 48$ -------> is ok

substitute the values of x and y in the inequality 2

$y\geq 10$

$20\geq 10$ --------> is ok

the point A represents a viable solution, because satisfies both inequalities

B(10,30)

x=10-------> total pounds of the fruit

y=30------> the total number of granola bars

check point B

substitute the values of x and y in the inequality 1

$4x+y \leq 48$

$4*10+30\leq 48\\ 70\leq 48$ -------> is not a viable solution

substitute the values of x and y in the inequality 2

$y\geq 10$

$30\geq 10$ --------> is ok

the point B is not a viable solution because does not satisfy the inequality 1

3 0

1 year ago

You wanted to join a booth fair, and you are aiming to get a profit that is twice as

sashaice [31]

You wanted to join a booth fair, and you are aiming to get a profit that is twice as your capital. Using the given information, your sample plan may be as follows:

Product Organic skincare products for women

Description An organic skincare cream and soap that brightens

and moisturizes your skin.

Goal To provide anti-aging skin for women and

maintaining their skin body.

Capital 15000

Fixed Cost 7000

Variable Cost 8000

Profit function 300(a) = 450a - 150a

To prove that the profit function will yield twice the capital.

This profit function: 300(y) = 450y - 150y will help achieve twice profit as your capital.

Profit function = revenue function r(y) - cost function c(y)

300(y) = 450y - 150y

where;

y = no of units produced and sold.
p = profit sold per unit

Cost function C(y) = fixed cost + (variable cost) × (amount of unit sold)

Assumption:

Cost function C(y) = 7000 + (80 × 100)

Cost function C(y) = 7000 + 8000

Cost function C(y) = 15000

Revenue function R(y) = price per revenue sold × no of sold units

R(y) = 450 × 100

R(y) = 45000

∴

Profit function = 45000 - 15000

Profit function = 30000

Therefore, can conclude that the profit function is revenue function r(y) - cost function c(y).

Hence the formula:

Profit function = revenue function r(y) - cost function c(y) (Proved)

Learn more about Profit function here:

brainly.com/question/16866047?referrer=searchResults

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2 years ago