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3 years ago

Find the ratio of the volume of one sphere to the volume of the right cylinder

Mathematics

1 answer:

yarga [219]3 years ago

5 0

Answer:

Step-by-step explanation:

<em>Let $r$ be the radius of one sphere.</em>

Volume of sphere is $V=\frac{4}{3}\pi r^3$

Since radius is r, the height of the cylinder will be $4r$

Also, the cylinder has the same radius as the sphere: $r$

Volume of Cylinder is $V=\pi r^2 h$

Plugging in the values we get: $V=\pi (r)^{2}(4r)=4\pi r^3$

<u>Ratio of volume of 1 sphere to volume of cylinder is</u>:

$\frac{\frac{4}{3}\pi r^3}{4\pi r^3}=\frac{\frac{4}{3}}{4}=\frac{4}{3}*\frac{1}{4}=\frac{1}{3}$

The ratio is 1:3

Answer choice B is right.

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Patrick wanted to gather data about the cost of joining a community pool in his area. He plotted the data and determined that th

ohaa [14]

Answer:

The y-intercept is 40. This is the cost of registration ⇒ last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- Patrick wanted to gather data about the cost of joining a community

pool in his area

- He plotted the data and determined that the average community

pool membership cost consists of a one-time registration fee and

a monthly fee

∴ The cost consists of two parts:

# Part A: one-time registration fee, it is a fixed amount not depend on

any other condition

# Part B: monthly fee, it depends on the number of months

- He modeled that by the equation y = 15 x + 40, where

# y is the cost for the membership

# 15 is the monthly fee

# x is the number of months

# 40 is the one-time registration

- The form of the equation is y = mx + c, where c is the y-intercept

∴ The y-intercept in the equation y = 15 x + 40 is 40

∴ The y-intercept is the one-time registration fee

* The y-intercept is 40. This is the cost of registration

4 0

3 years ago

John has a round swimming pool.The distance from the center of the pool to the edge is 3 meters.What is the diameter of John poo

shtirl [24]

Answer:

6 meters

Step-by-step explanation:

Th equation to find the diameter of a circle is,

radius * 2.

The radius of the swimming pool is 3, so 3 * 2 is 6.

Hope this helps!!

Let me know if I'm wrong...

8 0

3 years ago

If possible, draw a line of symmetry in each of the following figures or words. If it is not possible to draw a line of symmetry

Marrrta [24]

Answer:

a) none

b) vertical through the middle

c) horizontal through the middle

d) none

Step-by-step explanation:

a) A repeated asymmetrical pattern rarely has a line of symmetry. (I can't think of a case where it does.)

b) This figure has left-right symmetry about its centerline. (In general, a light bulb will not, because the screw threads are asymmetrical.)

c) Each of the letters is symmetrical about its horizontal centerline, so the word is as well.

d) The letter S is symmetrical about its center point, but not about any horizontal or vertical line. This word is not symmetrical about any line.

8 0

4 years ago

On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she ha

Sveta_85 [38]

Answer:

a. P(X=50)= 0.36

b. P(X≤75) = 0.9

c. P(X>50)= 0.48

d. P(X<100) = 0.9

Step-by-step explanation:

The given data is

x 25 50 75 100 Total

P(x) 0.16 0.36 0.38 0.10 1.00

Where X is the variable and P(X) = probabililty of that variable.

From the above

a. P(X=50)= 0.36

We add the probabilities of the variable below and equal to 75

b. P(X≤75) = 0.16+ 0.36+ 0.38= 0.9

We find the probability of the variable greater than 50 and add it.

c. P(X>50)= 0.38+0.10= 0.48

It can be calculated in two ways. One is to subtract the probability of 100 from total probability of 1. And the other is to add the probabilities of all the variables less than 100 . Both would give the same answer.

d. P(X<100)= 1- P(X=100)= 1-0.1= 0.9

8 0

3 years ago

Identify the equation of a line in slope-intercept form that is perpendicular to y = -1/3 x + 2 and passes through (2, 1)

Airida [17]

Answer:

Step-by-step explanation:

The slope of a line perpendicular to another line is the opposite reciprocal of the slope of the other line, meaning if the slope of the other line is $-\frac{1}{3}$ , then the slope of the line perpendicular is $3$ .