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2 years ago

If the population of a country is growing at a rate of 2.2% compounded

1 answer:

4 0

It will take 31.9 years.

The general form of this equation is

y = a(1+r)ˣ, where y is the total population, a is the initial population, r is the growth rate as a decimal number, and x is the amount of time. For our problem, we have

120000 = 60000(1+0.022)ˣ

[The 120,000 is because we are doubling the 60,000 population]

Dividing both sides by 60,000,

120000/60000 = 60000(1+0.022)ˣ/60000
2 = 1.022ˣ

Using logarithms to solve this, we have
$log_{1.022}2=x
\\
\\31.85=x
\\
\\31.9\approx x$

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Josh had $10 more than Carly, so he gave Carly half of his money. Then Carly had more money than josh, so she gave Josh $4. Then

DedPeter [7]

each person starts with $8.

<u>Step-by-step explanation:</u>

Here we have , Josh had $10 more than Carly, so he gave Carly half of his money. Then Carly had more money than josh, so she gave Josh $4. Then they both had $13. We need to find How much money did each person start . Let's find out:

Suppose Carly had $x , Josh had $10 more than Carly i.e. $(x+10), so he gave Carly half of his money i.e.

⇒ $\frac{x+10}{2}$ ,Now , Josh have $ $\frac{x+10}{2}$ & Carly have $x + \frac{x+10}{2}$ .

Then Carly had more money than josh, so she gave Josh $4 . So ,

Josh now have $ $(4+\frac{x+10}{2})$ and Carly now have $ $(x+\frac{x+10}{2} -4)$ . Since both are equal :

⇒ $(x+\frac{x+10}{2} -4) = (4+\frac{x+10}{2})$

⇒ $x-4 = 4$

⇒ $x=8$

Therefore , each person starts with $8.

8 0

2 years ago

Samuel is solving the equation 3(x - 1) + 4 = 2 - (x + 3). Which equivalent equations might Samuel use? Select the TWO correct a

mote1985 [20]

A= 3, and 4. (c & d)

1. Solve the Equation: $3(x - 1) + 4 = 2 - (x + 3)\\$ , to get

------------------------------------------

1a. Use the distributive property to multiply 3 by x−1.

$3x−3+4=2−(x+3)$

1b. Add −3 and 4 to get 1.

$3x+1=2−(x+3)$

1c. To find the opposite of x+3, find the opposite of each term.

$3x+1=2−x−3$

1d. Subtract 3 from 2 to get −1.

$3x+1=−1−x$

1e. Add x to both sides.

$3x+1+x=−1$

1f. Combine 3x and x to get 4x.

$4x+1=−1$

1g. Subtract 1 from both sides.

$4x=−1−1$

1h. Subtract 1 from −1 to get −2.

$4x=−2$

1i. Divide both sides by 4.

$x=4−2$

1j. Reduce the fraction 4−2=−0.5 to lowest terms by extracting and canceling out 2.

$x=−21$ or x = -21

-------------------------------------

Now that you know the answers, solve the others:

2. A= 1, so this is wrong. How I solved it is shown below:

-----------------------------------

1a. Add −3 and 4 to get 1.

3x+1=2−x+3

1b. Add 2 and 3 to get 5.

3x+1=5−x

1c. Add x to both sides.

3x+1+x=5

1d. Combine 3x and x to get 4x.

4x+1=5

1e. Subtract 1 from both sides.

4x=5−1

1f. Subtract 1 from 5 to get 4.

4x=4

1g.Divide both sides by 4.

x=44

1h. Divide 4 by 4 to get 1.

x=1

----------------------------

3. A= .5, so it is Correct. Work below

-----------------------------

3a. Add x to both sides.

$3x+3+x=5$

3b. Combine 3x and x to get 4x.

$4x+3=5$

3c. Subtract 3 from both sides.

$4x=5−3$

3d. Subtract 3 from 5 to get 2.

$4x=2$

3e. Divide both sides by 4.

$x=42$

3f. Reduce the fraction 42=0.5 to lowest terms by extracting and canceling out 2.

$x=21$ (A = 1/2 or .5)

-----------------------------

4. A= .5, so it is correct. Work below. Now we have our 2, so we don't need to do it again.

-------------------------------

4a. Add −1 and 4 to get 3.

$3x+3=2−x+3$

4b. Add 2 and 3 to get 5.

$3x+3=5−x$

4c. Add x to both sides.

$3x+3+x=5$

4d. Combine 3x and x to get 4x.

$4x+3=5$

4e. Subtract 3 from both sides.

$4x=5−3$

4f. Subtract 3 from 5 to get 2.

$4x=2$

4g. Divide both sides by 4.

$x=\frac{2}{4}$

4h. Reduce the fraction 42=0.5 to lowest terms by extracting and canceling out 2.

$x=\frac{1}{2}$

7 0

3 years ago

The length of a rectangle is 4 in longer than its width. if the perimeter of the rectangle is 28 in , find its area.

ra1l [238]

The area is 45 inches squared

7 0

2 years ago

Evaluate u^2 -2u+4 when u= -3

OLga [1]

Answer:

Step-by-step explanation: Sub -3 into where all the u’s are. So it would be

(-3)^2 - 2(-3) + 4

Which would equal 19

6 0

2 years ago

A local restaurant is offering a special deal in which customers can receive one appetizer, one entree, and one dessert for a fi

Dmitriy789 [7]

There are105 different choices.
For 1 appetizer, there are 15 different combinations of entrees and desserts. 1 dessert has 5 entrees you can mix, and since there are 3 desserts, there are 15 choices. It goes the same for every appetizer until there is 7x15. 7Ax15choices equals 105 options.
The customer has 105 meal choices.

5 0

3 years ago