Margo borrows $1000, agreeing to pay it back with 5% annual interest after 15 months. How much interest will she pay?

Put the following statements into order to prove that if 3n+4 is even then n is even. Put N next to the 3 statements that should

Alinara [238K]

Answer: 7, 2, 1, 5, 6, 4, 8

Step-by-step explanation:

1. Then, 3n+4=3(2k+1)+4=6k+7=2(3k+3)+1.

2. By definition of odd, there exists integer k such that n=2k+1.

N 3. Thus, if n is odd then 3n+4 is odd or by contradiction, if 3n+4 is even then n is even, .

4. Therefore, by definition of odd, 3n+4 is odd.

5. Since k is an integer, t =3k+3 is also an integer.

6. Thus, there exists an integer t such that 3n+4=2t+1.

7. Suppose n is odd.

8. Thus, if n is odd then 3n+4 is odd or by contraposition, if 3n+4 is even then n is even, .

N 9. Suppose 3n+4 is even.

N 10. By definition of odd, n=2k+1.

Right order:

7. Suppose n is odd.

2. By definition of odd, there exists integer k such that n = 2k+1.

1. Then, 3n+4 = 3(2k+1)+4 = 6k+7 = 2(3k+3)+1.

5. Since k is an integer, t = 3k+3 is also an integer.

6. Thus, there exists an integer t such that 3n+4 = 2t+1.

4. Therefore, by definition of odd, 3n+4 is odd.

8. Thus, if n is odd then 3n+4 is odd or by contraposition, if 3n+4 is even then n is even.

4 0

3 years ago

Brainliest is given to the correct answer!

OlgaM077 [116]

Answer:

a. $p = 2\pi r + 8r$

b. $r = \frac{p}{2\pi + 8}$

Step-by-step explanation:

a. Radius of semicircle (r) = r

Diameter of semicircle (d) = 2r

Length of rectangle (l) = 2*diameter of semicircle = 2*2r = 4r

Distance around the track (p) = circumference of circle + 2(l)

Note: the two semicircles of the track = 1 full circle

Circumference of full circle = πd = π*2r = 2πr

Distance around the track:

p = 2πr + 2(4r)

p = 2πr + 8r

b. Rewriting the formula to make radius, r, the subject of the formula in terms of distance around the track.

$p = 2\pi r + 8r$

Factor out r

$p = r(2\pi + 8)$

Divide both sides by (2π + 8)

$\frac{p}{2\pi + 8} = \frac{r(2\pi + 8)}{2\pi + 8}$

$\frac{p}{2\pi + 8} = r$

$r = \frac{p}{2\pi + 8}$

6 0

3 years ago

There are 156 people taking a boating safety course. The ratio of adults to students is 9 to 4. How many adults are taking the c

iren [92.7K]

108 adults and 48 students.

4 0

3 years ago

320% of 69 is what number?

DENIUS [597]

Answer:

220.8

Step-by-step explanation:

I believe 220.8

sorry if I am wrong.

3 0

3 years ago

Read 2 more answers

Find the product of the roots of the equation<br> xl-5x - 36 = 0

Marat540 [252]

Answer:

Step-by-step explanation:

Hello, I assume that you mean

$x^2-5x-36$

The product is -36.

$x_1 \text{ and } x_2 \text{ are the two roots, we can write}\\\\(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1\cdot x_2$

So in this example, it means that the sum is 5 and the product is -36.

Thank you

5 0

3 years ago