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Lilit [14]
3 years ago
9

Can someone please answer this question please answer it correctly please show work

Mathematics
1 answer:
netineya [11]3 years ago
7 0

Answer:

Actual mean: 223 pages

Predicted mean / estimate: 225 pages

Explanation below

Step-by-step explanation:

Mean = total amount ÷ # of numbers

155 + 214 + 312 + 198  + 200 + 170 + 250 + 260 + 215 + 256

Add

2,230

# of numbers = 10

2,230 ÷ 10 = 223

The exact mean is 223

If I were to predict the mean, I would say that a good estimation would be around 225, because I see that the highest number in the data set is 312, and the lowest is 155. If 312 is rounded down to 300, and 155 is rounded down to 150, the number exactly in the middle of 300 and 150 is 225.

Actual mean: 223 pages

Predicted mean: 225 pages

Hope this helps :)

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Given that x and y are positive integers, solve the equation x² - 4y² = 13​
zvonat [6]
<h3>Answer:  x = 7 and y = 3</h3>

=====================================================

Explanation:

Apply the difference of squares rule

x² - 4y² = 13

x² - (2y)² = 13

(x - 2y)(x + 2y) = 13

Since x and y are positive integers, this means x-2y and x+2y are both integers as well.

The value 13 is prime. Its only factors are 1 and 13

Since the above equation shows 13 factoring into x-2y and x+2y, then we have two cases:

  • A) x-2y = 1 and x+2y = 13
  • B) x-2y = 13 and x+2y = 1

----------------

Let's consider case A

We have this system of equations

\begin{cases}x-2y = 1\\x+2y = 13\end{cases}

Add the equations straight down

  • x+x becomes 2x
  • -2y+2y becomes 0y = 0 which goes away
  • 1+13 becomes 14

Therefore we have 2x = 14 solve to x = 7

From here, plug this into either equation to solve for y

x-2y = 1

7 - 2y = 1

-2y = 1-7

-2y = -6

y = -6/(-2)

y = 3

You should get the same result if you used x+2y = 13

----------------

Since we've found that x = 7 and y = 3, notice how case B is not possible

Example:  x-2y = 13 becomes 7-2(3) = 13 which is false.

Also, x+2y = 1 would turn into 7+2(3) = 1 which is also false.

-----------------

Let's check those x and y values in the original equation

x² - 4y² = 13

7² - 4*(3)² = 13

49 - 4(9) = 13

49 - 36 = 13

13 = 13

The answer is confirmed.

4 0
2 years ago
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