Answer:
look at the picture i have sent
Answer:
3y² + 8y + 4
Step-by-step explanation:
To multiply binomials (multiplying two equations that each have two terms), use FOIL. This means from each of the binomials, multiply the first terms, inside terms, outside terms, then the last terms. This helps you keep track that you have multiplied every term you need to.
Use FOIL twice in this expression because you are multiplying the first two binomials (2y-3) (y+2), multiplying two more binomials (y+5) (y+2)
, then adding them together.
(2y-3) (y+2) + (y+5) (y+2) Expand using FOIL twice
= (2y² + 4y - 3y - 6) + (y² + 2y + 5y + 10) Remove the brackets
= 2y² + 4y - 3y - 6 + y² + 2y + 5y + 10 Rearrange with like terms
= 2y² + y² + 4y - 3y + 2y + 5y - 6 + 10 Collect like terms
= 3y² + 8y + 4 Expanded answer
Like terms are terms that have the same variables and exponents.
There are three types of like terms in this question:
No variables
y
y² You only see them after expanding with FOIL
Since they are alike, then can be combined with adding or subtracting.
Answer:4
Step-by-step explanation:
Answer:
-6 ± √5i
Step-by-step explanation:
Answer:
a) 0.3226
b) 0.9340
c) 0.5257
d) mean=1.68 workers , standard deviation=1.15 workers
Step-by-step explanation:
since each worker's gender is independent from the others , then defining the random variable X= getting x male workers out of the sample of 8 workers , we know that P(X) has a binomial distribution , where
P(X)=n!/((n-x)!*x!)*p^x*(1-p)^(n-x)
where
n= sample size = 8
p= probability that a worker is male = 0.21
x= x workers are male
then
a) P(X=1) = 8!/((8-1)!*1!)*(0.21)^1*(1-0.21)^(8-1) = 0.3226
b) P(X<4) = P(X=0) + P(X=1)+ P(X=2)+ P(X=3) + P(X=4)
in order to avoid doing the calculus for each term we can use the cumulative probability distribution , whose results can be found in tables. Then
P(X<4)= F(4) = 0.9340
c) P(X>2) = 1- P(X≤1) = 1- F(1) = 1- 0.4743 = 0.5257
d) the mean for a binomial distribution is
E(X)= n*p = 8*0.21 = 1.68 workers
and the standard deviation is
σ(X)= √[n*p*(1-p)]= √[8*0.21*0.79]= 1.15 workers