3. When the line of best fit is found by hand, it is exact. O True O False

-4x+y=24 and -14x+2y=-30. Use the substitution method to determine the solution.

STatiana [176]

The answer is x=13 y=76

6 0

3 years ago

If you invested $500 at 5% simple interest for 2 years, how much interest do you earn? Show work and answer in

givi [52]

Answer:

$50

$30.88

I will invest in simple interest as the interest there is more.

Step-by-step explanation:

If I invested $500 at 5% simple interest for 2 years, then the interest that I will get will be given by the formula

$I = P \times \frac{rt}{100}$ , where P is the invested principal, r is the APR and t is the time in years.

So, in our case, $I = 500 \times \frac{5 \times 2}{100} = 50$ dollars. (Answer)

Now, if I invest $500 at 3% compound interest compounded monthly for 2 years.

Now, using the formula of compound interest we have

$I = P(1 + \frac{r}{n \times 100} )^{tn} - P$ , where r is the APR and n is the number of times in a year the principal is compounded.

In our case, $I = 500(1 + \frac{3}{12 \times 100} )^{2 \times 12} - 500 = 30.88$ dollars. (Answer)

Therefore, I will invest in simple interest as the interest there is more. (Answer)

3 0

3 years ago

A candy box is made from a piece of cardboard that measures 23 by 13 inches. Squares of equal size will be cut out of each corne

wolverine [178]

Answer:

2.67 inches.

Step-by-step explanation:

Assuming that we represent the size of the squares with the letter y, such that after the squares are being cut from each corner, the rectangular length of the box that is formed can now be ( 23 - 2y), the width to be (13 - 2y) and the height be (x).

The formula for a rectangular box = L × B × W

= (23 -2y)(13-2y) (y)

= (299 - 46y - 26y + 4y²)y

= 299y - 72y² + 4y³

Now for the maximum volume:

dV/dy = 0

This implies that:

299y - 72y² + 4y³ = 299 - 144y + 12y² = 0

By using the quadratic formula; we have :

$= \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}$