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2 years ago

1.(8x+3)(4x-5) 2.(10x-2)(3x+6) please show your work will mark brainliest

Mathematics

1 answer:

ANEK [815]2 years ago

8 0

Answer:

32x^2 - 28x - 15

30x^2 + 54x - 12

Step-by-step explanation:

(8x+3)(4x-5)

Using FOIL

= (8x)(4x) + (8x)(-5) + (3)(4x) + (3)(-5)

= 32x^2 - 40x + 12x - 15

= 32x^2 - 28x - 15

(10x-2)(3x+6)

Using FOIL

= (10x)(3x) + (10x)(6) + (-2)(3x) + (-2)(6)

= 30x^2 + 60x - 6x - 12

= 30x^2 + 54x - 12

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Consider a data set containing the following values: 70 65 71 78 89 68 50 75 The mean of the preceding values is 70.75. The devi

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If this is the sample data, the sample variance is 125.07 and the sample standard deviation is 11.18

If this is a population data, the population variance is 109.44 and the population standard deviation is 10.46

Step-by-step explanation:

We are given the following data-set:

70, 65, 71, 78, 89, 68, 50, 75

Deviations from the mean

–0.75, –5.75 , 0.25, 7.25, 18.25, –2.75, –20.75, 4.2

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$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

$s = \sqrt{\dfrac{875.5}{7}} = 11.18$

$\text{ Sample variance} = s^2 = 125.07$

Population:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

$\sigma = \sqrt{\dfrac{875.5}{8}} = 10.46$

$\text{ Population variance} = \sigma^2 = 109.44$

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