Question

name jonathan francis

1. what type of function is represented in the table above
2. find p(a u b). assume that events a and b are not mutually - exclusive events. hint p(a u b)=p(a)+p(b)-p(a ∩ b)

p(a)=0.64
p(b)=0.57
p(a ∩ b)=0.49

1. a certain company wants to maximize profits. they need to price (x) the product to maximize profits (y). which of the following quadratic equations would be best for the job.

a) y = - 4x²+40x - 104
b) y=-4(x - 4)(x - 8)
c) y=-4(x - 4)²+24

1. use quadratic equation in factored form: f(x)=(x - 3)(x - 1)

a) what is the standard form of given equation?
f(x)=x²-4x + 3
b) what are the coordinates of the y - intercept? (0,3)
c) what are the coordinates of each of the x - intercepts? set each given factor to zero. answers here: 1) (1,0) 2) (3,0)
d) what is the x - coordinate of the vertex? 2
show work here:
x=-b/2a=-(-4)/(2×1)=4/2 = 2
e) what is the y - coordinate of the vertex?
show work here: f(x)=x²-4x + 3
f) sketch the graph on a separate sheet of paper of the given quadratic equation points and coordinates of the vertex, both x - intercepts, y - intercept and the l

Explanation:

Step 1: Solve for P(A ∪ B)

Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Substitute \(P(A) = 0.64\), \(P(B)=0.57\) and \(P(A\cap B)=0.49\).
\[P(A\cup B)=0.64 + 0.57- 0.49\]

Step 2: Calculate the result

\[P(A\cup B)=0.72\]

Answer:

The value of \(P(A\cup B)\) is \(0.72\)