Answer:
DE = 20units
Step-by-step explanation:
In Δ ABC,
angle A is congruent to angle B.... (given)
therefore, ΔABC is an isoceles triangle.
therefore, CA = CB..... (side opposite to congruent angles are congruent in an isoceles triangle)
therefore, CB = 4 units
In ΔCDE,
angle D is congruent to angle E.... (given)
therefore, ΔCDE is an isoceles triangle.
therefore, CD = CE
therefore, CD = 8 units
ΔCDE ~ ΔCBA
therefore,

Answer:
25% probability that all three residents will choose the same plumbe
Step-by-step explanation:
For each resident, there are only two possible outcomes. Either they choose the first plumbe, or they choose the second. The plumbers are chosen independent of each other. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Each resident randomly chooses one of the two plumbers.
This means that 
Three residents:
This means that 
What is the probability that all three residents will choose the same plumb
This is P(X = 0)(all choose the second pumble) or P(X = 3)(all choose the first pumble). So

25% probability that all three residents will choose the same plumbe
Since both equations are equal to y you can just make them equal to each other, like this 3x + 7 = x - 9. From there isolate the varible x on one side so that the solution will be on the other side of the equation. I'll do the steps too for you.
3x + 7 = x - 9
2x + 7 = -9
2x = -16
x = -8
Hope this helps :)
Step-by-step explanation:
2(4x + 1) < 3(2x - 3)
8x + 2 < 6x - 9
8x - 6x < -9 -2
2x < -11
x < -11/2
If they get unexpected results they could note what they could've done wrong or what they could change in a next trail of experiments. Or look back and see what different happened to they could've hypothesized. There could be many different courses on what to do next.