Please give the right answer and show work if possible

Mathematics

1 answer:

Step2247 [10]3 years ago

6 0

Answer:

Step-by-step explanation:

Sin(∅) = Opposite angle ÷ hypotenuse.

Sin (45) = 7 $\sqrt{2}$ ÷ hypotenuse

hypotenuse = 7 $\sqrt{2}$ ÷ sin(45)

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Keep in mind

sin(45) = √2÷2

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so we have: Hypotenuse = 7√2 ÷ (√2÷2)

Hypotenuse= 14.

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X + 7x = 56 + 8

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Answer:

a. The mean of the sample is M=35.

The variance of the sample is s^2=39.125.

The standard deviation of the sample is s=6.255.

b. z=-1.6

c. SEM = 2.212

Step-by-step explanation:

The mean of the sample is M=35.

The variance of the sample is s^2=39.125.

The standard deviation of the sample is s=6.255.

Sample mean

$M=\dfrac{1}{8}\sum_{i=1}^{8}(27+25+32+40+43+37+35+38)\\\\\\ M=\dfrac{277}{8}=35$

Sample variance and standard deviation

$s^2=\dfrac{1}{(n-1)}\sum_{i=1}^{8}(x_i-M)^2\\\\\\s^2=\dfrac{1}{7}\cdot [(27-(35))^2+(25-(35))^2+(32-(35))^2+(40-(35))^2+(43-(35))^2+(37-(35))^2+(35-(35))^2+(38-(35))^2]\\\\\\$

$s^2=\dfrac{1}{7}\cdot [(58.141)+(92.641)+(6.891)+(28.891)+(70.141)+(5.64)+(0.14)+(11.39)]\\\\\ s^2=\dfrac{273.875}{7}=39.125\\\\\\s=\sqrt{39.125}=6.255$