What is the volume of a rectangular prism with a length of 12ft, a width of 10ft, and a height of 18ft?

Please help me with this. Use the combination method of substitution to solve. Please show and explain work. Thanks.

Artemon [7]

Answer:

x = 25.35 (or 2129/84) and y = 4334.04 (or 121353/28)

Step-by-step explanation:

The given equations are set up and ready to go with substitution. Simply just plug in the first equation to the second equation as both are equal to y.

Step 1: Replace y in y = 87x + 2129 with 171x

171x = 87x + 2129

Step 2: Subtract 87 x on both sides

84x = 2129

Step 3: Divide both sides by 84 to get x

x = 2129/84 or 25.35 (rounded)

To get y, simply plug in x into one of the 2 original equations. In this case, I will use the first equation:

y = 171 (25.35)

y = 121353/28 or 4334.04 (rounded)

You can check your work by plugging both solutions into the calculator and see if they equal each other. The values for these answers are solely based on the equations, so if you write the equations wrong themselves, then that means you have the values wrong as well.

6 0

3 years ago

A survey is conducted to find out whether people in metropolitan areas obtain their news from television (Event T), an newspaper

MrMuchimi

Answer:

e) P ( R' | T ) = 0.62857

f) P ( T' | N ) = 0.32258

g) P ( R' | N ) = 0.70968

h) P ( T' | N&R ) = 5/6

Step-by-step explanation:

Given:

- The probability of Television as news source P ( T ) = 0.7

- The probability of Newspaper as news source P ( N ) = 0.62

- The probability of Radio as news source P ( R ) = 0.46

- The probability of Television & Newspaper as news source P (T&N) = 0.42

- The probability of Television & Radio as news source P (T&R) = 0.26

- The probability of Radio & Newspaper as news source P (R&N) = 0.18

- The probability of all 3 as news source P ( T & R & N ) = 0.03

Find:

Given that TV is a news source, what is the probability that radio is not a news source?

Given that newspaper is a news source, what is the probability that TV is not a news source?

Given that newspaper is a news source, what is the probability that radio is not a news source?

Given that both newspaper and radio are news sources, what is the probability that TV is not a news source?

Solution:

- We will first compute the individual probability of each event occurring alone.

P (Television is the only news source) = P(T) - P(T&R) - P(T&N) + P(T&N&R)

P ( Only Television ) = P ( only T ) = 0.7 - 0.42 - 0.26 + 0.03 = 0.05

P (Newspaper is the only news source) = P(N)-P(N&R)-P(T&N)+P(T&N&R)

P ( Only Newspaper ) = P ( only N ) = 0.62 - 0.18 - 0.42 + 0.03 = 0.05

P (Radio is the only news source) = P(R) - P(T&R) - P(N&R) + P(T&N&R)

P ( Only Radio ) = P ( only R ) = 0.46 - 0.26 - 0.18 + 0.03 = 0.05

- Now for part e)

We are asked for a conditional probability of the form as follows:

P ( R' | T ) = P ( R' & T ) / P ( T )

First compute the probability that next news source is not Radio provided it is already a source of TV.

P ( R' & T ) = P( only T ) + P ( only T & N ) = 0.05 + 0.42 - 0.03 = 0.44

Hence,

P ( R' | T ) = 0.44 / 0.7

P ( R' | T ) = 0.62857

- Now for part f)

We are asked for a conditional probability of the form as follows:

P ( T' | N ) = P ( T' & N ) / P ( N )

First compute the probability that next news source is not TV provided it is already a source of Newspaper.

P ( T' & N ) = P( only N ) + P ( only R & N ) = 0.05 + 0.18 - 0.03 = 0.2

Hence,

P ( T' | N ) = 0.2 / 0.62

P ( T' | N ) = 0.32258

- Now for part g)

We are asked for a conditional probability of the form as follows:

P ( R' | N ) = P ( R' & N ) / P ( N )

First compute the probability that next news source is not Radio provided it is already a source of Newspaper.

P ( R' & N ) = P( only N ) + P ( only T & N ) = 0.05 + 0.42 - 0.03 = 0.44

Hence,

P ( R' | N ) = 0.44 / 0.62

P ( R' | N ) = 0.70968

- Now for part h)

We are asked for a conditional probability of the form as follows:

P ( T' | N&R ) = P ( T' & N & R) / P ( N & R )

First compute the probability that next news source is not TV provided it is already a source of both radio and Newspaper.

P ( T' & N & R) = P ( only N & R ) = 0.18 - 0.03 = 0.15

Hence,

P ( T' | N&R ) = 0.15 / 0.18

P ( T' | N&R ) = 5/6

6 0

3 years ago

The floor of the cage measures 11 yardyard wide by 66 feetfeet long. One bag of shavings covers 55 square feetfeet. How many bag

bazaltina [42]

Answer:

3 3/5 bags

Step-by-step explanation:

We have to find the surface area of the floor of the cage first.

The cage measures 1 yard wide by 6 feet long.

1 yard = 3 feet

The floor of the cage is rectangular, so, the surface area of the floor of the cage is therefore:

3 * 6 = 18 square feet

One bag of shavings covers 5 square feet.

To find the number of bags we need to cover the floor, we divide the surface area of the floor by the number of bags per square feet.

The number of bags needed for the floor of the cage is therefore :

18 / 5 = 3 3/5 bags

5 0

3 years ago

A membership committee of three is formed from four eligible members. Let the eligible members be represented by A, B, C, and D.

yKpoI14uk [10]

The correct statement is:

There are four ways to choose the committee.
There are three ways to form the committee if person D must be on it.
If persons B and C must be on the committee, there are two ways to form the committee.

It is given that:

A membership committee of three is formed from four eligible members.

1) There are four ways to choose the committee.

This statement is true.

Since we have to choose 3 members out of the 4 members so we can use the method of combination.

2) There are three ways to form the committee if person D must be on it.

This statement is also true.

Since D has to be in the committee, this means we have to choose 2 more people out of the three people to form the committee.

3) If seven members are eligible next year, then there will be fewer combinations.

This statement is wrong.

Since we have to choose 3 members out of 7 members so the number of possible combinations will be:

There are 35 combinations possible.

4) If persons B and C must be on the committee, there are two ways to form the committee.

If B and C have to be in the committee then we have to choose just one person out of the two people left.

Hence, the statement is true.

5) If persons A and C must be on the committee, then there is only one way to form the committee.

If A and C have to be on the committee then as in the last option we have to choose any one of the two-person left.

So possible number of ways is 2.

Hence, the statement is false.

Learn more about committee here: brainly.com/question/425830

#SPJ4

Your question is incomplete. Please read below to find the missing content.

A membership committee of three is formed from four eligible members. Let the eligible members be represented by A, B, C, and D. The possible outcomes include S = {ABC, ABD, ACD, BCD}.

Which statements about the situation are true? Check all that apply.

There are four ways to choose the committee.

There are three ways to form the committee if person D must be on it.

If seven members are eligible next year, then there will be fewer combinations.

If persons B and C must be on the committee, there are two ways to form the committee.

If persons A and C must be on the committee, then there is only one way to form the committee.

8 0

2 years ago

What does 1/8+1/9 equal

slavikrds [6]

The solution is 17/72

4 0

3 years ago