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Valentin [98]
3 years ago
5

Rachel has twice as much money as Paul. If I gave Rachel $250, she will then have three times as much as Paul. How much did each

of them have originally?
Mathematics
2 answers:
scZoUnD [109]3 years ago
5 0

Answer:

Paul have $250 and Rachel have $500 originally.

Step-by-step explanation:

Rachel: 2x

Paul: x

If I gave Rachel $250, then:

Rachel: 2x + 250

Paul: 3x

We have he equation:

2x + 250 = 3x

2x - 3x = -250

-x = -250

x = 250

melamori03 [73]3 years ago
3 0

Let's make "x" the amount of Paul.

2x = Rachel.

This means that 2x + 250 = 3x.

Solve:

2x + 250 = 3x

2x - 3x = 250

-x = 250

x = 250

So that means Paul had 250 dollars.

And Rachel had 500 dollars.

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In each of the following scenarios, determine if the data are paired.
zmey [24]

Answer:

1. Can be Paired or Not Paired

2. Paired

3. Not Paired

Step-by-step explanation:

Two sets of observations are paired if each observation in one set has a special correspondence or connection with exactly one observation in the other data set.

1. Can be Paired or Not paired

Reason -

We might look at testing the difference of means using a two sample t-test. However, we may also try running a paired t-test.

But its used in cases where the observations are usually from the same populations at different times or through different sources etc.

Hence can't conclude that it is paired or not paired.

2. Paired

Reason -

Each record is a price of the same item from different stores.

3. Not paired

Reason -

This is again a case of testing the difference of means of two-samples (2 independent samples precisely) that are not paired.

5 0
3 years ago
Write 5(6x+4)-2(5x-2) in the form a(bx+c) where a,b and c integers and a>1
Tamiku [17]

Answer:

<h2>4(5x + 6)</h2>

Step-by-step explanation:

5(6x+4)-2(5x-2)\qquad\text{use distributive property}\ a(b+c)=ab+ac\\\\=(5)(6x)+(5)(4)+(-2)(5x)+(-2)(-2)\\\\=30x+20-10x+4\qquad\text{combine like terms}\\\\=(30x-10x)+(20+4)\\\\=20x+24

20x=4\cdot5x\\\\24=4\cdot6\\\\20x+24=4(5x+6)

6 0
3 years ago
Alladin went grocery shopping for candy at Costco in Rego Park. He wants to buy the package of candy with the greatest percentag
Pavlova-9 [17]

We need to find what percentage represents the number of Hershey's Cookie Crème Candy Bars in each package, and then compare which one is better.

For package A.

It has 13 Hershey's Cookie Crème Candy Bars out of 25. To find which percentage is 13 out of 25 we do the following:

• Divide 100 by the total amount of candy 25, and multiply the result by 13:

\frac{100}{25}\times13

we get the following percentage:

\frac{100}{25}\times13=4\times13=52

Package A has 52% of Hershey's Cookie Crème Candy Bars.

For package B.

It has 11 Hershey's Cookie Crème Candy Bars out of 20. we do the same as before to find the percentage, only that this time, instead of dividing by 25, we divide 100 by 20, and intead of multiplying by 12, we multiply by 11:

\frac{100}{20}\times11

The result is:

\frac{100}{20}\times11=5\times11=55

Package B has 55% of Hershey's Cookie Crème Candy Bars.

Which package should Alladin buy? He should buy Package B because it has a greater percentage.

3 0
1 year ago
1. Annual sales for a fast food restaurant are $650,000 and are increasing at a rate of 4% per year
Zielflug [23.3K]

Answer:

The value after 7 years is $ 855355.65

Solution:

Given that, Annual sales for a fast food restaurant are 650000 and are increasing at a rate of 4% per year

To find:  exponential function to find the annual sales after 7 years

The exponential growth function is given as:

Where,

"a" is the initial amount

"y" is the future value

"r" is the rate of interest in decimal

"t" is the number of years

Here in this given question,

a = 650000

t = 7 years

Substituting the values in given formula,

Thus the value after 7 years is $ 855355.65

Step-by-step explanation:

4 0
3 years ago
Alex stocks up for winter. He buys 32 cans of vegetables. He pays 80 cent per can for tomatoes and 40 cents per can for corn, fo
lara31 [8.8K]
X = # of cans of tomatoes, y = # of cans of corn

x + y = 32.....y = 32 - x
0.80x + 0.40y = 18

0.80x + 0.40(32 - x) = 18
0.80x + 12.8 - 0.40x = 18
0.80x - 0.40x = 18 - 12.8
0.40x = 5.2
x = 5.2 / 0.40
x = 13 <=== 13 cans of tomatoes were bought

leaving (32 - 13) = 19 cans of corn bought
4 0
4 years ago
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