11-6=5 ounces. She doesn’t have enough for both of the recipes. She will need 11 more ounces to be able to make the recipes. 5+11=16 and 16 ounces are in a pound.
The distributive property: a(b + c) = ab + ac
12(6k + 3) + 4(7 - 5k) = 12(6k) + 12(3) + 4(7) + 4(-5k)
= 72k + 36 + 28 - 20k = 52k + 64
That's impossible. unless you cut the apples in half
Answer:
The mean is also increased by the constant k.
Step-by-step explanation:
Suppose that we have the set of N elements
{x₁, x₂, x₃, ..., xₙ}
The mean of this set is:
M = (x₁ + x₂ + x₃ + ... + xₙ)/N
Now if we increase each element of our set by a constant K, then our new set is:
{ (x₁ + k), (x₂ + k), ..., (xₙ + k)}
The mean of this set is:
M' = ( (x₁ + k) + (x₂ + k) + ... + (xₙ + k))/N
M' = (x₁ + x₂ + ... + xₙ + N*k)/N
We can rewrite this as:
M' = (x₁ + x₂ + ... + xₙ)/N + (k*N)/N
and (x₁ + x₂ + ... + xₙ)/N was the original mean, then:
M' = M + (k*N)/N
M' = M + k
Then if we increase all the elements by a constant k, the mean is also increased by the same constant k.
