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2 years ago

The sum of three consecutive even integers is 36 . find the smallest of them

Mathematics

1 answer:

bonufazy [111]2 years ago

7 0

Answer:

Step-by-step explanation:

You can get the three consecutive integers by using algebraic expressions.

Let's solve.

Let x be the smallest even integer.

Let x+2 be the second even integer.

Let x+4 be the largest even integer.

x+x+2+x+4 = 36

3x+6 = 36

3x = 36-6

3x = 30

x = $\frac{30}{3}$

x = 10

Therefore, 10 is the smallest even integer.

x+2 = 10+2 = 12

The second even integer is 12.

x+4 = 10+4 = 14

The largest even integer is 14.

Let's check by adding the three even integers.

10+12+14 = 36

36 = 36

It's correct. 

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2 years ago

If a coin is flipped 75 times, in how many ways could there be exactly two tails?

Dimas [21]

Answer:

2775 ways

Step-by-step explanation:

We have been given the case to choose exactly two tails when flipped 75 times means $^{75}C_2$

Since, $^nC_r$ is equal to $\frac{n!}{r!\cdot(n-r)!}$

Here n =75, r=2 substituting the values we will get

$\frac{75!}{2!(75-2)!}$

$n!=n\cdot (n-1)\cdot (n-2).....1$

After simplification we will get $\frac{75\cdot 74\cdot 73!}{2!\cdot73!}$

Cancel out the common term that is 73! we will get

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3 years ago

Read 2 more answers

Help!!!!!!!!!!!!!!!!

Andru [333]

Step-by-step explanation:

The area would be 9 times compared to the area of the original square. To test this, you can let the side of the original square be equal 1. By tripling this side, the side becomes three. Utilizing the area of a square formula, A= s^2, the area of the original square would be 1 after substituting 1 for s. Then, you do the same for the area of the tripled square. With the substitution, the area of the tripled square would be 9. This result displays the area of the tripled square being 9 times as large as the area of the original square. This pattern can be used for other measurements of the square such as:

let s = 2, Original Area= 2^2 = 4 Tripled Area= (2(3))^2 = 6^2= 36. 36/4 = 9

let s = 3, Original Area = 3^2 = 9 Tripled Area - (3(3))^2 = 9^2 =81. 81/9 = 9

let s = 4, Original Area = 4^2 = 16 Tripled Area - (4(3))^2 = 12^2 = 144. 144/16 = 9

let s = 5, Original Area = 5^2 = 25 Tripled Area - (5(3))^2 = 15^2 = 225. 225/25 = 9

let s = 6, Original Area = 6^2 = 36 Tripled Area - (6(3))^2 = 18^2 = 324. 324/36 = 9

let s = 7, Original Area = 7^2 = 49 Tripled Area - (7(3))^2 = 21^2 = 2,401. 2,401/49 = 9

You can continue to increase the length of the square and follow this pattern and it will be consistent.

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2 years ago

Read 2 more answers

The sum of three consecutive even integers is 36 . find the smallest of them​

The sum of three consecutive even integers is 36 . find the smallest of them