Answer:
Ava's share = $20
Charlotte's share = $16
Step-by-step explanation:
15x + 12x = 36 : multiply each girl's age by same amount and adding gives $36
27x = 36 : add x terms
x = 36 / 27 : divide both sides of equation by 27
x = 4 / 3
Ava's share = 15x = 15 * 4/3 = 20
Charlotte's share = 12x = 12 * 4/3 = 16
The factors of 50 are 1, 2, 5, 10, 25 and 50.<span> The factors of a number can be found by determining which numbers evenly divide into a given number.</span>
they are equal or congruent because if you look at it they both are right triangles
y - y₁ = m(x - x₁)
y - (-10) = -1⁴/₂₁(x - 6)
y + 10 = -1⁴/₂₁(x) + 1⁴/₂₁(6)
y + 10 = -1⁴/₂₁x + 7¹/₇
- 10 - 10
y = -1⁴/₂₁x - 3¹/₇
Let Xi be the random variable representing the number of units the first worker produces in day i.
Define X = X1 + X2 + X3 + X4 + X5 as the random variable representing the number of units the
first worker produces during the entire week. It is easy to prove that X is normally distributed with mean µx = 5·75 = 375 and standard deviation σx = 20√5.
Similarly, define random variables Y1, Y2,...,Y5 representing the number of units produces by
the second worker during each of the five days and define Y = Y1 + Y2 + Y3 + Y4 + Y5. Again, Y is normally distributed with mean µy = 5·65 = 325 and standard deviation σy = 25√5. Of course, we assume that X and Y are independent. The problem asks for P(X > Y ) or in other words for P(X −Y > 0). It is a quite surprising fact that the random variable U = X−Y , the difference between X and Y , is also normally distributed with mean µU = µx−µy = 375−325 = 50 and standard deviation σU, where σ2 U = σ2 x+σ2 y = 400·5+625·5 = 1025·5 = 5125. It follows that σU = √5125. A reference to the above fact can be found online at http://mathworld.wolfram.com/NormalDifferenceDistribution.html.
Now everything reduces to finding P(U > 0) P(U > 0) = P(U −50 √5125 > − 50 √5125)≈ P(Z > −0.69843) ≈ 0.757546 .
