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user100 [1]
2 years ago
7

A square with an area of 4 in² is dilated by a factor of 7. What is the area of the dilated square?

Mathematics
1 answer:
antoniya [11.8K]2 years ago
3 0

Answer:

196 in²

Step-by-step explanation:

Given that the scale factor is a : b , then

the area factor is a² : b²

Here the scale factor is 1 : 7 , thus

area scale factor is 1² : 7² = 1 : 49

That is the area of the dilated square is 49 times the original square.

area of dilated square = 4 × 49 = 196 in²

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We have been given in a cohort of 35 graduating students, there are three different prizes to be awarded. We are asked that in how many different ways could the prizes be awarded, if no student can receive more than one prize.

To solve this problem we will use permutations.

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We know that formula for permutations is given as

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On substituting the given values in the formula we get,

{_{3}^{35}\textrm{P}}=\frac{35!}{(35-3)!}=\frac{35!}{32!}

=\frac{35\cdot 34\cdot 33\cdot 32!}{32!}\\
\\
=35\cdot 34\cdot 33=39270

Therefore, there are 39270 ways in which prizes can be awarded.


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