(3 + 2i)(5 + i)
15 + 3i + 10i + 2i^2
15 + 13i - 2
13 + 13i
Answer:
(a) [8, 14]
(b) 
(c)See attachment
Step-by-step explanation:
We want to choose a value of x within 3 units of 11.
(a)Now, 11-3=8 and 11+3=14
The possible values of x ranges is in the closed interval [8,14]
(b) Since x is within 3 units of 11., we have:

Solving the absolute inequality

(c)To draw the number line, we use a closed dot since we have the less than or equal to sign.
The answer would be 8x^4 + 16x^3y - 48x^2y^2
In order to find this, multiply 8x^2 by each term individually.
8x^2 * x^2 = 8x^4
8x^2 * 2xy = 16 x^3y
8x^2 * -6y^2 = -48x^2y^2
Now you can put them all in a row.
8x^4 + 16x^3y - 48x^2y^2
Must do multiplication first....
-2/5 - 3/7 x 7/10
-2/5 - 21/70 (I'll reduce 21/70)
-2/5 - 3/10
Now you have to find a common denominator and subtract
-35/50 = -7/10......is what I get
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.