Answer:
Step-by-step explanation:
to solve this system of equations we will add them
x-3y=-12
2x+3y=3 now +3y-3y=0
3x=-12+3
3x=-9
x=-3
plug in the first equation
-3-3y=-12
-3y=-12+3
-3y=-9
y=3
4d=56
d=14. Ad a result, Dorothy is 14 years old. Hope it help!
Income of the first account after x years:

Income of the second account after x years:

Equating the above tw values we get the equation:

Solving the above equation for x:

Answer 8 years.
OK. I did it, and I have the solution.
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The length of the deck is (5 + 2x) .
The width of the deck is (4 + 2x) .
If the deck didn't have that big hole in the middle where the pool is,
then its area would be
(5 + 2x) · (4 + 2x) .
When you multiply that all out, you get Area = 4x² + 18x + 20
and the question tells us that the area of the whole big rectangle is 90 yds² .
So we can write
4x² + 18x + 20 = 90 .
Subtract 90 from each side: 4x² + 18x - 70 = 0
Divide each side by 2 : 2x² + 9x - 35 = 0
You can use the quadratic equation to solve that and find out that
x = 2.5 yards, and that's what the question is asking you.
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That makes the deck 10 yds high and 9 yds wide.
Total area of the whole big rectangle, (deck + pool ), = 90 yds².
Answer:
0.337 = 33.7% probability that one of the eight children has a food allergy.
Step-by-step explanation:
For each children, there are only two possible outcomes. Either they have a food allergy, or they do not. The probability of a child having food allergy is independent of any other child. This means that 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.
7% of U.S. children 4 years of age or younger have a food allergy.
This means that 
A day care program has capacity for 8 children in that age range.
This means that 
What is the probability that one of the eight children has a food allergy?
This is P(X = 1).


0.337 = 33.7% probability that one of the eight children has a food allergy.