Answer:
0.3085,0.2417,0.0045
Step-by-step explanation:
Given that X, the amount of money spent at shopping centers between 4 P.M. and 6 P.M. on Sundays has a normal distribution with mean $85 and with a standard deviation of $20.
X is N(85, 20)
To convert into std normal variate we use the following formula
a) the probability that he has spent more than $95 at the mall
=
b. the probability that he has spent between $95 and $115 at the mall
=
c. If two shoppers are randomly selected, what is the probability that both shoppers have spent more than $115 at the mall
=product of two probabilities since independent
=
Answer:
Vertex form: f(x) = -10(x − 2)^2 + 3
Standard form: y = -10x^2 + 40x - 37
Step-by-step explanation:
h and k are the vertex coordinates
Substitute them in the vertex form equation:
f(x) = a(x − 2)^2 + 3
Calculate "a" by replacing "f(x)" with -7 and "x" with 1:
-7 = a(1 − 2)^2 + 3
Simplify:
-7 = a(1 − 2)^2 + 3
-7 = a(-1)^2 + 3
-7 = a + 3
-10 = a
Replace a to get the final vertex form equation:
f(x) = -10(x − 2)^2 + 3
Convert to standard form:
y = -10(x − 2)^2 + 3
Expand using binomial theorem:
y = -10(x^2 − 4x + 4) + 3
Simplify:
y = -10x^2 + 40x - 40 + 3
y = -10x^2 + 40x - 37
2xy + 5x -12y -30
x(2y + 5) - 6( 2y + 5)
(2y+5) (x-6)
The solution as in where do they intersect? if so, it would be 0.0769 and -0.0769