Find the solution of this system of equation 8x-4y=-32 -3x 4y=42

4 lines extend from point B. A line extends straight up from B to point A. Another line extends up and to the right to point C.

never [62]

The other line extends slightly down and to the right to point E

4 0

3 years ago

Item 16 A sphere has a radius of 8 centimeters. A second sphere has a radius of 2 centimeters. What is the difference of the vol

Zigmanuir [339]

Answer:

$672\pi \text{ cm}^3$ .

Step-by-step explanation:

We have been given that a sphere has a radius of 8 centimeters. A second sphere has a radius of 2 centimeters. We are asked to find the difference of the volumes of the spheres.

We will use volume formula of sphere to solve our given problem.

$\text{Volume of sphere}=\frac{4}{3}\pi r^3$ , where r is radius of sphere.

The difference of volumes would be volume of larger sphere minus volume of smaller sphere.

$\text{Difference of volumes}=\frac{4}{3}\pi(\text{8 cm})^3-\frac{4}{3}\pi(\text{2 cm})^3$

$\text{Difference of volumes}=\frac{4}{3}\pi(512)\text{ cm}^3-\frac{4}{3}\pi(8)\text{ cm}^3$

$\text{Difference of volumes}=\frac{4}{3}\pi(512-8)\text{ cm}^3$

$\text{Difference of volumes}=4\pi(168)\text{ cm}^3$

$\text{Difference of volumes}=672\pi\text{ cm}^3$

Therefore, the difference between volumes of the spheres is $672\pi \text{ cm}^3$ .

3 0

3 years ago

A group of individuals were surveyed about their plans for vacation. There were 21 individuals who said they were going to the d

Alexeev081 [22]

Answer:

140 individuals were surveyed

42 people are planning on going to the mountains

Step-by-step explanation:

The question is missing the information regarding the percentage of people who said that they were going to each of the possible destinations. After a quick google search I've found that, in the original question, 32% of individuals were going to the beach, 15% to the desert, 23% to major cities, and 30% to the mountains.

If 21 people said they were going to the desert, and that corresponds to 15% of the total number of people surveyed, the number of people surveyed is:

$21=n*0.15\\n=140\ individuals$