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3 years ago

How many years (to two decimal places) will it take $15000 to grow to $17500 if it is invested at 8% compounded semi- annually?

Mathematics

1 answer:

VLD [36.1K]3 years ago

3 0

Answer:

1.97 years

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 8/100

r = 0.08 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(17,500.00/15,000.00) / ( 2 × [ln(1 + 0.08/2)] )

t = ln(17,500.00/15,000.00) / ( 2 × [ln(1 + 0.04)] )

t = 1.965 years

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In 12 years, Janice will be 8 times as old as she was 2 years ago. How old is Janice<br> now?

Setler [38]

Janice is currently 4.

In 12 years, Janice will be 16, and 2 years ago she was 2. That being said, 16 is eight times more than 2, thus meaning she is currently 4 years old.

I hope this helps!

6 0

3 years ago

Find the zeros of y = x2 – 6x – 4 by completing the square.

katrin [286]

Answer:

The solutions to the quadratic equations are:

$x=\sqrt{13}+3,\:x=-\sqrt{13}+3$

Step-by-step explanation:

Given the function

$y\:=\:x^2\:-\:6x\:-\:4$

substitute y = 0 in the equation to determine the zeros

$0\:=\:x^2\:-\:6x\:-\:4$

Switch sides

$x^2-6x-4=0$

Add 4 to both sides

$x^2-6x-4+4=0+4$

Simplify

$x^2-6x=4$

Rewrite in the form (x+a)² = b

But, in order to rewrite in the form x²+2ax+a²

Solve for 'a'

2ax = -6x

a = -3

so add a² = (-3)² to both sides

$x^2-6x+\left(-3\right)^2=4+\left(-3\right)^2$

$x^2-6x+\left(-3\right)^2=13$

Apply perfect square formula: (a-b)² = a²-2ab+b²

$\left(x-3\right)^2=13$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

solve

$x-3=\sqrt{13}$

Add 3 to both sides

$x-3+3=\sqrt{13}+3$

Simplify

$x=\sqrt{13}+3$

now solving

$x-3=-\sqrt{13}$

Add 3 to both sides

$x-3+3=-\sqrt{13}+3$

Simplify

$x=-\sqrt{13}+3$

Thus, the solutions to the quadratic equations are:

$x=\sqrt{13}+3,\:x=-\sqrt{13}+3$

4 0

3 years ago

maggie spent half of the money in her savings account on a new computer if the computer was $345 how much was in her savings acc

dybincka [34]

690 is the answer (i think)

7 0

3 years ago

Read 2 more answers

In a rectangle, one side is twice as long as another side. The perimeter of this rectangle is how many times as long as his shor

Ede4ka [16]

Answer: 6 times

Step-by-step explanation:

Let the Length of the rectangle be L and the Width be W

Also , let us pick the Length as the longest side , then from the statement

L = 2W

The perimeter of a rectangle is given as :

P = 2 ( L + W )

substitute L = 2W into the formula , we have

P = 2 ( 2W + W )

P = 2 (3W)

P = 6W

Therefore the Perimeter is 6 times as long as the Width

3 0

3 years ago

What is the square number for 10

guajiro [1.7K]

10^2 equals 100

10 x 10=100

4 0

4 years ago