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djverab [1.8K]
2 years ago
15

I have a Lego model. The Lego model is a 1:25 scale. This means that 1 unit on the model is 25 units in reality. If my model is

14.5 inches tall, then how many units is this in reality?
Mathematics
1 answer:
Vera_Pavlovna [14]2 years ago
7 0
<h3>Answer:  362.5 inches</h3>

Explanation:

The scale 1:25 means "multiply by 25" in order to go from the scale model length to the actual length in reality.

If your model is 14.5 inches tall, then the actual height is 14.5*25 = 362.5 inches.

Side note: 362.5 inches = 362.5/12 = 30.20833 feet approximately

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I am Lyosha [343]

Equilateral triangle means each angle equals 60 degrees.

60 = 7x - 3

63 = 7x

x = 9

8 0
3 years ago
If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar
Oksana_A [137]

Answer:

n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}

Step-by-step explanation:

Lets divide it in cases, then sum everything

Case (1): All 5 numbers are different

 In this case, the problem is reduced to count the number of subsets of cardinality 5 from a set of cardinality n. The order doesnt matter because once we have two different sets, we can order them descendently, and we obtain two different 5-tuples in decreasing order.

The total cardinality of this case therefore is the Combinatorial number of n with 5, in other words, the total amount of possibilities to pick 5 elements from a set of n.

{n \choose 5 } = \frac{n!}{5!(n-5)!}

Case (2): 4 numbers are different

We start this case similarly to the previous one, we count how many subsets of 4 elements we can form from a set of n elements. The answer is the combinatorial number of n with 4 {n \choose 4} .

We still have to localize the other element, that forcibly, is one of the four chosen. Therefore, the total amount of possibilities for this case is multiplied by those 4 options.

The total cardinality of this case is 4 * {n \choose 4} .

Case (3): 3 numbers are different

As we did before, we pick 3 elements from a set of n. The amount of possibilities is {n \choose 3} .

Then, we need to define the other 2 numbers. They can be the same number, in which case we have 3 possibilities, or they can be 2 different ones, in which case we have {3 \choose 2 } = 3  possibilities. Therefore, we have a total of 6 possibilities to define the other 2 numbers. That multiplies by 6 the total of cases for this part, giving a total of 6 * {n \choose 3}

Case (4): 2 numbers are different

We pick 2 numbers from a set of n, with a total of {n \choose 2}  possibilities. We have 4 options to define the other 3 numbers, they can all three of them be equal to the biggest number, there can be 2 equal to the biggest number and 1 to the smallest one, there can be 1 equal to the biggest number and 2 to the smallest one, and they can all three of them be equal to the smallest number.

The total amount of possibilities for this case is

4 * {n \choose 2}

Case (5): All numbers are the same

This is easy, he have as many possibilities as numbers the set has. In other words, n

Conclussion

By summing over all 5 cases, the total amount of possibilities to form 5-tuples of integers from 1 through n is

n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}

I hope that works for you!

4 0
3 years ago
What's 486.12 fraction
melisa1 [442]
486.12 as fraction is 12153/25
HOPE THIS HELPS 
7 0
3 years ago
A triangle with three acute angles and no congruent sides
Sauron [17]
The answer should be an acute scalene triangle.

Hope this helped! ♡
8 0
3 years ago
what is the equation subtracting 7 from the product of 4 and a number results in the number added to 29
vitfil [10]

That would be:-

4x - 7 = x + 29

the solution:-

3x = 29 + 7

3x = 36

x = 12


7 0
3 years ago
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