Avendor converts the weights on the packages she sends out from pounds to kilograms (1kg approximately equals 2.2 pounds).
a. how does this affect the mean weight of the packages?
b. how does this affect the standard deviation of the weights?
c. if the vendor begins using heavier packages, which increases the weight of each package by 50 g; how much does this affect the mean weight of the packages?

a) b) the standard deviation and the mean is affected by the conversion factor as well

c)  the mean is displaced by b units

Step-by-step explanation:

for a new variable

Y=a*X  , where a= constant (conversion factor= 1 kg/2.2 pounds)

then

p(y)= p(a*X) = p(X)

a) mean =μ=E(Y)= ∑ a*X*p(y) = a ∑ X*p(x) = a* E(X)

mean =μ=a*μₓ

b) σ² = ∑ (Y-μ)²* p(y) =  ∑ (a*X-a μₓ)²* p(y) = a²*∑ (X-μₓ)²* p(x) = a²*σₓ²

then

standard deviation = σ= √σ²=√(a²*σₓ²) = a*σₓ

standard deviation = σ= a*σₓ

then the standard deviation and the mean is affected by the conversion factor as well

c) nevertheless for a displacement b

Y₂=X + b (b= constant= 50 gr)

p(Y₂)= p(X + b) = p(X)

then

mean =μ=∑ (X-b)*p(y)=∑ X*p(x)- b ∑ p(x) = E(X) -

mean =μ=μₓ - b

then the mean is displaced by b units

the circle graph is not a function.

step-by-step explanation:

the graph of the circle is not a function.

because for a graph to be a function, each value of x must give one value of y

in the circle, the values of x for -2< x< 2 each give 2 values of y.

hence this is not a function.

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2