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3 years ago

Solve each equation.

Mathematics

1 answer:

Andreyy893 years ago

3 0

Answer:

25)

v - 6(4v + 6) = - 82

v - 24v - 36 = - 82

v - 24v = - 82 + 36

- 23v = - 46

- v = - 46/23

- v = - 2

26)

- 96 = 4(6n - 6)

- 96 = 24n - 24

- 96 + 24 = 24n

- 72 = 24n

- 72/24 = n

- 3 = n

27)

- 2(- 5a - 2) = 84

10a + 4 = 84

10a = 84 - 4

10a = 80

a = 80/10

28)

7(7 + 3k) = 217

49 + 21k = 217

21k = 217 - 49

21k = 168

k = 168/21

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And that happens because we create linear transformations for the parts b and c and the linear transformation affects the mean.

And you have the same interpretation for the deviation, it is affected by the linear transformation as the mean.

Step-by-step explanation:

For this case we can use the following formulas for the mean and standard deviation:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

Part a

Data given: 42 36 48 51 39 39 42 36 48 33 39 42 45

And if we calculate the mean we got:

$\bar X = 41.538$

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Part b

For this case we know that each value present a 5% of rise so we just need to multiply each value bu 1.05 and we have this new dataset:

44.1, 37.8, 50.4, 53.55, 40.95, 44.1, 37.8, 50.4 ,34.65, 40.95, 44.1, 47.25

And if we calculate the new mean and deviation we got:

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The new dataset would be each value divided by 12 so we have:

3.5, 3, 4, 4.25, 3.25, 3.25, 3.5, 3, 4, 2.75, 3.25, 3.5, 3.75

And the new mean and deviation would be:

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