Angie and Kenny play online video games. Angie buys 2 software package and 2 months of gameplay. Kenny buys 1 software package and 3 month of game play. Each software package cost $20. If their total cost is $160, what is the total cost of one month of gameplay?

Hey there!

To solve this problem, we will take a look at the FOIL Method.

FOIL is a simple acronym that can be used to multiply binomials. It stands for:

F - Front

O - Outer

I - Inner

L - Last

See the image below for an example of how to use this in the given situation.

Front: Multiply the two terms out in the front.

[tex](-5a)(-4a) = 20a^2[/tex]

Outer: Multiply the two terms on the outsides.

[tex](-5a)(3)=-15a[/tex]

Inner: Multiply the two terms on the insides.

[tex](6)(-4a)=-24a[/tex]

Last: Multiply the two terms in the back.

[tex](6)(3)=18[/tex]

Now, we add all of our answers from above:

[tex]20a^2-15a-24a+18[/tex]

Simplify by combining like terms:

[tex]20a^2-39a+18[/tex]

There's our answer!

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The real or imaginary solutions of 2x² + 3 = 4x by factoring is x1 = (2 - √2) / 2 and x2 = (2 + √2) / 2

2x² + 3 = 4x

2x² + 3 - 4x = 0

2x² - 4x + 3 = 0

∆ = (-4)² - (4 × 2 × 3)

= 16 - 24

∆ = 8

√∆ = √8

= 2√2

x1 = -(-4) - 2√2 / (2 × 2)

or

x2 = -(-4) + 2√2 / (2 × 2)

x1 = 4 - 2√2 / 4

or

x2 = 4 + 2√2 / 4

x1 = (2 - √2) / 2

or

x2 = (2 + √2) / 2

Therefore, the real or imaginary solutions of 2x² + 3 = 4x by factoring is x1 = (2 - √2) / 2 and x2 = (2 + √2) / 2

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Answer: There are 12 volleyball players

Step-by-step explanation:

If the ratio of basket to volleyball players is 5:2 and there are 30 known basket ball players that means the ratio can be written as 30:x.

If 30 is 5 parts (5x) and volleyball players is 2 parts (2x)  we need to figure out the value of 1 part (x)

This can be done by

5x=30

x=6

Now we know what 1 part is, we can now use that two figure out 2 parts

2x or 2(6)

2(6) = 12

So the ratio is 30:12. This can be confirmed by dividing both sides of the radio by 6 to get 5:2

Mel should make 12 bracelets.

Here, we are given that Mel makes arm bracelets.

She is making a bracelet for each arm of her 6 friends.

We know that a humans by default have 2 arms each.

We will assume that all of her 6 friends have 2 arms each.

Thus, 6 of her friends will get 2 bracelets each, one for each arm.

This means that the total number of bracelets Mel should make will be given by-

2 + 2 + 2 + 2 + 2 + 2

or we can also write this as

2 × 6

6 times 2 is equal to 12.

Thus, Mel should make 12 bracelets.

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Answer:

yes it can be bc it is repeating

Answer:

33

Step-by-step explanation:

4+10+12+7

Part(A) Leslie's initial investment was $500 and

Part(B) The quarterly interest rate is 10.4 %

What is compound interest?

Compound interest is the interest calculated on the principal amount , which also considers all the accumulated interest of previous periods of deposit or loan.

If P is the principal amount and rate of compound interest is r  then after t years of time , the present amount (if the interest is compounded annually) will be = P(1+(r/100))^n

If the interest is compounded quarterly, then the present amount be A

Where A = [tex]P (1+\frac{r/4}{100} )^{4t}[/tex]

Given that Leslie invests in a bank that earns interest quarterly , and account balance after t years is given as 500(1.026)^(4t)

A= [tex]P (1+\frac{r/4}{100} )^{4t} = 500(1.026)^{4t\\[/tex]

Comparing both sides we get P = 500

And 1+(r/400)=1.026

(r/400)=1.026-1

(r/400)=.026

r=400(0.26) = 10.4 %

Therefore , Leslie's initial investment was $500 and the quarterly interest rate is 10.4 %

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Statistics on women in politics highlight that woman - who make up over 50 percent of the U.S. population - are substantially lag in high government positions.

In U.S. the population of Women are 50.8 percent. Approximately, 60 percent of women have their undergraduate degree, and 60 percent of women have their master's degree. They are very well educated. They earn almost 60 percent of law degrees.

But, when it comes to representation in high government positions, they substantially lag behind men. There are only 14.6 percent of executive officers, they hold only 24.2 percent of state legislative seats. They hold only 18.5 percent of congressional seats, and they are just 20 percent of U.S. senators.

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We need to use the concept of proprotionality for the given question.The value of y is 25.7, value of R is 1 and value of t is 144.

It is given that y varies directly as the square root of x which means that y is directly proportional to x, we can write it as

y∝[tex]\sqrt{x}[/tex] which can again be written as y=[tex]\sqrt{x} k[/tex] where k is a proportionality constant,we need to find the value of k inorder to find the value of y.We know that y=12 when x=49

12=[tex]\sqrt{49} k[/tex]=7k⇒12=7k⇒k=[tex]\frac{12}{7}[/tex]

when x=225 then y=[tex]\sqrt{225}[/tex]×[tex]\frac{12}{7}[/tex]=15×[tex]\frac{12}{7}[/tex]=25.7

R is inversely proportional to the cube of S,we can write it as

R∝[tex]\frac{1}{S^{3} }[/tex] ⇒R=[tex]\frac{k}{S^{3} }[/tex]

We need to find the value of k inorder to find the value of R, it is given that R=8 when S=3

8=[tex]\frac{k}{27}[/tex]

k=27x8=216

Value of R when S=6 will be

R=[tex]\frac{216}{6^{3} } =\frac{216}{216} =1[/tex]

It is given that n varies directly as the square root of t and inversely as l,we can write it as

n∝[tex]\frac{\sqrt{t} }{l}[/tex] which can be again written as n=[tex]\frac{\sqrt{t} }{l} k[/tex] where k is a proportionality constant,we need to find the value of k first to find the value of t

We know that n=5 when t=16 and l=2

5=[tex]\frac{\sqrt{16} }{2}k=\frac{4}{2} k=2k[/tex]

k=[tex]\frac{5}{2}[/tex]

We know that n=10,l=3 and k=[tex]\frac{5}{2}[/tex] substituting these values we can get the value of t

t=[tex](\frac{nl}{k} )^{2}[/tex]=[tex](\frac{10.3.2}{5} )^{2} =12^{2} =144[/tex]

Thus we can see that using the concept of proportionality we found out the values of y,R and t. Value of y is 25.7, R is 1 and t is 144.

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Answer:

Shorter piece: 5    Longer piece: 11

Step-by-step explanation:

(2x+1)+(x)=16

3x+1=16

3x=15

x=5

The total number of notebooks on Sasha's notebook is 2c - 6.

Unitary method:

The unitary method is used to solve problems by first determining the value of a single unit and then multiplying that value by the required value.

So, this method is basically used to find the value of a unit and then the value of a required number of units.

Given,

Sasha has c green notebooks.

She has 6 fewer red notebooks then green notebooks.

So, here we need to find how many notebooks does Sasha have in all.

We know that.

Sasha has c green notebooks.

The number of red notebooks on her is  

=> c − 6.

Here Sasha has either green or red notebooks.

The total number of notebooks on Sasha's notebook is  

=> c + c − 6

=> 2c - 6

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The cost of 420 grams of cherries is £1.47.

Cherries cost £3.50 per 1000 grams.

Therefore, the cost of 420 grams of cherries can be calculated as follows:

1000 grams of cherries  = £3.50

420 grams of cherries = ?

cross multiply

cost of 420 grams of cherries = 3.50 × 420 / 1000

cost of 420 grams of cherries =  1470 / 1000

cost of 420 grams of cherries = 147 / 100

cost of 420 grams of cherries = £1.47

Therefore, the cost of 420 grams of cherries is £1.47.

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Answer:

Step-by-step explanation:

Cost of 420g cherries

147 ÷ 100

=1.47

therefore the cost of 420 of cherries

= £1.4

The original price of a computer was reduced by $250. If p = the computer's original price in dollars. p-250 is algebraic expression represents the reduced price.

The original price of a computer was reduced by $250

p = the computer's original price in dollars

reduced price = original price - reduction

algebraic expression can be written as:

p-250

The complete cost of purchasing an item is known as the original cost. The whole costs associated with purchasing and using an asset are taken into account when calculating its initial cost.

Listing price, also known as asking price, is the price at which a seller has placed a property on the market, but selling price is the price at which it actually sells. These days, properties that sell for significantly more than their asking or listed price receive a lot of media attention.

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Answer: No solution

Step-by-step explanation:

5r + 5 = 3(5r - 4) - 10r  Do multiplication

5r + 5 = 15r - 12 - 10r  combine like terms

5r + 5 = 5r - 12        This is impossible. 5r cannot equal 5 and 12 meaning there is no value of r that makes this equation true so there's No Solution.

You could continue

5r + 17 = 5r

-5r       =-5r

17=0 which is also not true

Answer:

To make AEH(triangle) do a vertical cut from A to H

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The sample proportion, p-hat, of engineers who have master's degrees is   68.5% out of 200 engineers.

p-hat proportion:

In this proportion,  "p" denotes the probability of a certain event occurring or a certain parameter being true for a certain population, but when a population is large, it may be impractical or impossible to measure it directly. So, we have used the proportion for that cases.

The general form for calculating p-hat proportion is,

[tex]\hat{p}=\frac{x}{y}[/tex]

where

x  is the number of successes in the sample, and

y is the size of the sample.

Given,

In a random sample of 200 engineers, 137 have a master's degree.

Here we need to find the the sample proportion, p-hat, of engineers who have master's degrees

According to the question,

x = 137 (number of successes in the sample)

and y = 200 (size of the sample)

Now apply the value on the formula then we get,

[tex]\hat{p}=\frac{137}{200}[/tex]

So, the value of p-hat is

[tex]\hat{p}=0.685[/tex]

The results are usually reported as a percentage, which in this case would be

=> 0.685 x 100 = 68.5%

Therefore, the sample proportion, p-hat, of engineers who have master's degrees is 68.5% out of 200 engineers.

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The value of an item is greater than or equal to 5. This statement is represented by the inequality [tex]x\geq 5[/tex] .

An inequality is a mathematical relation which compares the values of two different entities.

The various symbols used in expressing inequalities are

Linear inequalities in one variable are represented on the number line.

For example: a>100 represents all numbers greater than 100 along the number line

Linear inequalities in two variables are represented as a region in a cartesian plane.

For example: 2x+3y<6 represents a region below the straight line 2x+3y=6.

The given statement denotes that the value of the item is greater than or equal to 5.

Therefore the required inequality is : [tex]x\geq 5[/tex].

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The equation of the line from the given points marked on the graph is:

3. 3x+y+5=0

4. 3x+y+3=0

Given,

3.The points are:

(-1,-2) and (1,-8)

let the points be :

(-1,-2) = (x₁,y₁)

and (1,-8) = (x₂,y₂)

The equation of the line passing through the points (-1,-2) and (1,-8)

x - x₁/x₂-x₁ = y - y₁/y₂-y₁

For the given points, the equation is:

x-(-1)/1-(-1) = y-(-2)/-8-(-2)

x+1/2 = y+2/-6

-6(x+1) = 2(y+2)

-6x-6=2y+4

-6x-2y-6-4=0

-6x-2y-10=0

-2(3x+y+5)=0

3x+y+5=0 is the equation of the line.

4.The points are:

(-3,6) and (3,0)

let the points be :

(-3,6) = (x₁,y₁)

and (3,0) = (x₂,y₂)

The equation of the line passing through the points (-1,-2) and (1,-8)

x - x₁/x₂-x₁ = y - y₁/y₂-y₁

For the given points, the equation is:

x-(-3)/3-(-3) = y-6/0-6

x+3/6 = y-6/-6

-6(x+3) = 2(y-6)

-6x-18=2y-12

-6x-2y-18+12=0

-6x-2y-6=0

-2(3x+y+3)=0

3x+y+3=0 is the equation of the line

Hence we get the required equations of the line.

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The linear equation in terms of the variable R is determined as x = R/10.

Given data:

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

The given equation is:

R = x + 9x

First, let's combine the like terms on the right side of the equation:

R = 1x + 9x

R = 10x

Now, we want to solve for x. To isolate x, divide both sides of the equation by 10:

R/10 = x

So, the solution for x is:

x = R/10

Hence, the expression for in terms of R is x = R/10.

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The value of x from the given linear function is 15

A linear function is a function hat has a leading degree of 1

Given the equation below;

2/5x +9 =15

Subtract 9 from both sides

2/5x + 9 - 9 = 15 - 9

2/5x = 15 -  9

2/5x = 6

Multiply both sides by 5

2/5x (5) = 6(5)

2x = 30

x = 15

Hence the value of x from the given linear function is 15

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Only (B) 4.72% of the couples polled have 5 or more children.

To find what number of children occurred the least frequently:

The percentage is as follows:

Therefore, only (B) 4.72% of the couples polled have 5 or more children.

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The complete question is given below;
A random sample of 1,250 couples was asked the question, "How many children presently reside in your household?"

Number of Children—Frequency

0——250

1——-112

2——560

3 ——201

5 or more ——59

What number of children occurred the least frequently? Calculate this percent

A) 2, 55.2%

B)5 or more, 4.72%

C)5 or more, 11.91%

D)4.21.67%

Answer:

B

Step-by-step explanation:

The slope of a line is written as a fraction of the vertical distance to the horizontal distance. The line drops down from (0,1) to (4,-2). This is a vertical distance of -3 and a horizontal distance of 4. The slope if the fraction -3/4.

Answer:

[tex] \sf \: b) \: \frac{ - 3 \: }{ 4} [/tex]

Step-by-step explanation:

The coordinates are,

→ x1 = 4, y1 = -2

→ x2 = -4, y2 = 4

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Now the required slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (4 -(-2))/(-4 - 4)

→ m = (4 + 2)/-8

→ m = 6/-8

→ [ m = -3/4 ]

Hence, the option (b) is correct.

Answer:

Step-by-step explanation:Answer:it Varys depending on the type of problem

Step-by-step explanation:Answer:

It Varys depending on what type of multi step problem

Step-by-step explanation:

if it has parentheses () then you do whatever problem is in the parentheses next is exponents which is the number of times a number is multiplied by itself the next thing you want to do is multiplication and division from left to right the last thing you will do for a multi step problem is Addition and subtraction from left to right always remember P. E.M.D.A.S for parentheses, exponents, multiplication, division, addition and subtraction.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{0}~,~\stackrel{y_1}{6})\qquad C(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +0}{2}~~~ ,~~~ \cfrac{ y +6}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE B}}{(5~~,~~-8)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x+0}{2}=5\implies \boxed{x=10} \\\\\\ \cfrac{y+6}{2}=-8\implies y+6=-16\implies \boxed{y=-22}[/tex]

The current percentage in comparison to in the year 2000 is 88.22%.

We are given the percentage of death in the year 2000, 2015 and the difference. Now, we have to find the percentage of donors between change and the original deaths in the year 2000.

To find this, we will use the following formula -

Percentage change = Difference between the percentage change in the year 2000 to 2015 ÷ Percentage of deaths in the year 2000 ×100

Now, keep the values in formula to find the percentage change.

Percentage change = [tex]\frac{8.24}{9.34} *100[/tex]

Performing division to find the percentage change

Percentage change = 0.882*100

Further performing multiplication to get the answer in the form of percentage

Percentage change = 88.22%

Hence, the comparison of difference with the percentage of donors dying from drug overdoses in 2000 is 88.22%.

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Answer:

12 1/2

1/6

Step-by-step explanation:

5/6 x 15/1

2/3 x 1/4