How many points need to be removed from this graph so that it will be a function?

A glass paperweight has a composite shape: a square pyramid fitting exacty on top of an 8 centimeter cube. The pyramid has a hei

ArbitrLikvidat [17]

Answer:

Part 1) The volume of the paperweight is $576\ cm^{3}$

Part 2) The total surface area of the paperweight is $400\ cm^{2}$

Step-by-step explanation:

Part 1) what is the volume of the paperweight?

we know that

The volume of the paperweight is equal to the volume of the square pyramid plus the volume of the cube

step 1

Find the volume of the pyramid

The volume of the pyramid is equal to

$V=\frac{1}{3}BH$

where

B is the area of the square base

H is the height of the pyramid

$B=8^{2}=64\ cm^{2}$

$H=3\ cm$

substitute

$V=\frac{1}{3}(64)(3)=64\ cm^{3}$

step 2

Find the volume of the cube

The volume of the cube is equal to

$V=b^{3}$

$V=8^{3}=512\ cm^{3}$

step 3

Find the volume of the paperweight

$64\ cm^{3}+512\ cm^{3}=576\ cm^{3}$

Part 2) what is the total surface area of the paperweight?

we know that

The total surface area of the paperweight is equal to the surface area of 5 faces of the cube plus the lateral area of the pyramid

step 1

Find the surface area of 5 faces of the cube

$SA=5b^{2}$

$SA=5(8^{2})=320\ cm^{2}$

step 2

Find the lateral area of the pyramid

$LA=4[\frac{1}{2}bh]$

$LA=4[\frac{1}{2}(8)(5)]=80\ cm^{2}$

step 3

Find the total surface area of the paperweight

$320\ cm^{2}+80\ cm^{2}=400\ cm^{2}$

8 0

3 years ago

Which expression is equal to p + (q + r)?

Svetach [21]

The answer should be a) (p+q)*r

7 0

3 years ago

A new television set was recently purchased for the common room in a residence hall for $436.80 including tax the tax rate is 4%

garri49 [273]

Answer:

The price of the television before taxes is $420

Step-by-step explanation:

* Lets explain how to solve the problem

- The purchased price = cost price + taxes

- A new television set was recently purchased for the common room

in a residence hall for $436.80

- This price including tax

- The tax rate is 4%

- We need to find the price of the television before taxes

* <em>Lets solve the problem</em>

- Assume that the price of the television before tax is 100%

∵ The tax rate is 4%

∵ The price after tax = price before tax + tax

∵ The price before tax = 100%

∴ The price after tax = 100% + 4% = 104%

∵ 104% equivalent to $436.80

∴ 100 ⇒ ?

104 ⇒ 436.80

- <em>By using cross multiplication</em>

∴ ? = $\frac{(436.80)(100)}{104}=420$

∴ The price of the television before taxes is $420

6 0

3 years ago

Cuantos lados tiene un polígono regular si su ángulo central mide 24 grados

jeka94

Answer:

D

Step-by-step explanation:

4 0

3 years ago

A baseball player hit 65 home runs in a season. Of the 65 home runs, 19 went to right field, 23 went to right-center field, 9

olchik [2.2K]

Answer:

a) 29.23% probability that a randomly selected home run was hit to right field

b) 29.23% probability that a randomly selected home run was hit to right field, which is not lower than 5% nor it is higher than 95%. So it was not unusual for this player to hit a home run to right field.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes. It is said to be unusual if it is lower than 5% or higher than 95%.

(a) What is the probability that a randomly selected home run was hit to right field?

Desired outcomes:

19 home runs hit to right field

Total outcomes:

65 home runs

19/65 = 0.2923

29.23% probability that a randomly selected home run was hit to right field

(b) Was it unusual for this player to hit a home run to right field?

29.23% probability that a randomly selected home run was hit to right field, which is not lower than 5% nor it is higher than 95%. So it was not unusual for this player to hit a home run to right field.

8 0

3 years ago