Multiply. (−2/3)(5/4) Enter your answer as a fraction, in simplified form, in the box.

The base of a prism has n sides. Find the numbers of faces, edges, and

Harman [31]

Answers:

faces = n+2
edges = 3n
vertices = 2n

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Explanation:

Think of a hexagonal room with n = 6 walls, i.e. the floor is a hexagon with n = 6 sides. The floor and ceiling are parallel to each other, and congruent hexagons. That's 2 faces so far. Then we have another 6 faces to account for the walls. This gives 2+6 = 8 faces of a hexagonal prism.

In more general terms, a prism with a base of n sides will have 2 parallel and congruent base faces, and n walls or lateral faces. This gives n+2 total faces.

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Let's go back to the hexagonal prism. The floor has 6 sides to it, and so does the ceiling. We have 6+6 = 12 edges so far. Then we have another 6 edges where each of the rectangular walls meet up. That gives 12+6 = 18 edges total of this hexagonal prism room.

For any more general case, each base has n sides. That gives 2n sides so far for just the bases. Then add on another n for the lateral edges and we get 3n total edges.

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Once again lets revisit the room with the hexagonal floor and ceiling. The floor has 6 vertices and the ceiling has the same vertex count. Therefore, this prism has 6+6 = 12 vertices.

For the general case, each base has n vertices. There are 2 such identical bases giving 2n vertices total.

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One way to check the answer:

We could use Euler's Polyhedron Formula which is

F+V-E = 2

where,

F = number of faces
V = number of vertices
E = number of edges

For the hexagonal prism we found

F = 8
V = 12
E = 18

Then notice how

F+V-E = 2

8+12-18 = 2

20-18 = 2

2 = 2

This confirms the formula works for a hexagonal prism.

Now let's check it for the more general case

We found earlier that,

F = n+2
V = 2n
E = 3n

So,

F+V-E = 2

n+2+2n-3n = 2

3n-3n+2 = 2

0n+2 = 2

0+2 = 2

2 = 2

This helps confirm the answer for any prism with the base of n sides.

4 0

2 years ago

The quotient of m and 11 minus 3 as a algebraic expression

PilotLPTM [1.2K]

(m/11) - 3
Doing the quotient first so I put it in parenthesis, then subtract 3

3 0

3 years ago

100 POINTS! ANSWER NOW! I'm really slow so please explain this as thoroughly as possible.

Slav-nsk [51]

Step-by-step explanation:

a) The graph of a normal curve with a mean of 64" and a standard deviation of 3.5" is a bell-shaped curve with its

maximum value at x = 64.

Important points:

mean - 3 deviations: 64 - 3(3.5) = 64 - 10.5 = 53.5

mean - 2 deviations: 64 - 2(3.5) = 64 - 7 = 57

mean - 1 deviation: 64 - 3.5 = 60.5

mean: = 64

mean + 1 deviation: 64 + 3.5 = 67.5

mean + 2 deviations: 64 + 2(3.5) = 64 + 7 = 71

mean + 3 deviations: 64 + 3(3.5) = 64 + 10.5 = 74.5

b) If there are 3000 plants, approximately how many will be taller than 71"?

71" is 2 standard deviations above the mean. The region between two standard deviations below the mean and two standard deviations holds approximately 95% of the plants.

Therefore there will be approximately 5% of the plants divided equally between being taller than two standard

deviations above the mean and being shorter than two standard deviations below the mean. Thus, there will be

approximately 2.5% of the plants taller than 71": 0.025 x 3000 = 75 plants.

or

the z-score for 71

= (71-64)/35 = 2

going to your tables, or some other suitable source for standard deviation, we find

P(z < 2) = .9772

P(z > 2) = .0228

.0228(3000) = 68.4

or appr 68 plants

5 0

3 years ago

Help!!!!! please!!!!!

Marysya12 [62]

Answer: D) 85

Step-by-step explanation:

The area of a rectangular prism is length * width * height(5*3.4*5)

5 * 3.4 * 5 = 85

3 0

4 years ago

M- Determine whether or not the procedure described below results in a binomial distribution. If it is not binomial, identify a

Igoryamba

Answer:

A. Yes, the result is a binomial probability distribution.

Step-by-step explanation:

The experiment above depicts a binomial probability distribution because the 4 required conditions are met :

1.) The distribution is independent as the possible outcome of each trial is the same.

2.) There are two possible categories and the result of each trial is one of two outcomes : Yes or No

3.) The number of observation is fixed at sample size of 5500

4.) The probability of success and failure of each trial is the same for all trials in the sample.

Hence, we can conclude that the experiment depicts a binomial probability distribution.

7 0

3 years ago