Alex invests $2,000 in a company's stock. After a year, the value of Alex's stock has increased to $2,500. What rate of return has Alex received?

The rate of interest is 25%

Explanation:

Given:

Principal, P = $2,000

Amount, A = $2500

Time, t = 1 year

Rate of Interest, r = ?

We know:

On substituting the value we get:

Therefore, the rate of interest is 25%

Rate of return Alex has received is 25% .

Step-by-step explanation:

Here we have , Alex invests $2,000 in a company's stock. After a year, the value of Alex's stock has increased to $2,500. We need to find What rate of return has Alex received . Let's find out:

Alex initially invested $2000 in a company and after a year Alex's stock has increased to $2500 i.e. by :

⇒

⇒ $

So, rate of return Alex has received is given by :

⇒

⇒

⇒

⇒

Therefore , Rate of return Alex has received is 25% .

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.