The mean age of 12 women in an office is 35 years old. The mean age of 8 men in an office is 31 years old. What is the mean age (nearest year) of all the people in the office?

34

Step-by-step explanation:

μ₁ = mean age of women

w = age of women

wₙ = number of women

μ₂ = mean age of men

m = age of men

mₙ = number of men

∑w = sum of the ages of all the women

∑m = sum of the ages of all the men

∑(w + m) = sum of the ages of all men and women

μ₀ = mean age of all people in the office

(w + n)ₙ = number of men and women

Formula for mean:

μ₀ = ∑(w + m)/(w + m)ₙ

Sum of the ages of everyone divided by the number of people

∑(w + m) = ∑w + ∑m

μ₁ = 35

wₙ = 12

∑w = 35 × 12

= 420

μ₂ = 31

mₙ = 8

∑m = 31 × 8

= 248

∑(w + m) = 420 + 248

= 668

(w + m)ₙ = wₙ + mₙ

(w + m)ₙ = 12 + 8

= 20

μ₀ = ∑(w + m)/(w + m)ₙ

μ₀ = 668/20

μ₀ = 33.8 → 34 (to the nearest year)

a: 1/6, j: 1/4

step-by-step explanation: you are welcome

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.