Answer:
a) 0.03
b) 0.68
c) 0.32
Step-by-step explanation:
We are given the following in the question:
B: companies in the area of biotechnology
I: companies in the area of information technology
P(B) = 0.2
P(I) = 0.15
The two events are given to be independent.
a) P(both companies become profitable)
0.03 is the probability that both companies become profitable
b) P(neither company becomes profitable)
0.68 is the probability that neither company becomes profitable.
c) P(at least one of the two companies become profitable)
0.32 is the probability that at least one of the two companies become profitable
The slope of XY is the same as the slope of AB because XY is parallel to AB. Parallel lines have the same slope.
Answer:
To satisfy the hypotheses of the Mean Value Theorem a function must be continuous in the closed interval and differentiable in the open interval.
Step-by-step explanation:
As f(x)=2x3−3x+1 is a polynomial, it is continuous and has continuous derivatives of all orders for all real x, so it certainly satisfies the hypotheses of the theorem.
To find the value of c, calculate the derivative of f(x) and state the equality of the Mean Value Theorem:
dfdx=4x−3
f(b)−f(a)b−a=f'(c)
f(x)x=0=1
f(x)x=2=3
Hence:
3−12=4c−3
and c=1.
Answer:
Height should be ≤ 9 inches.
Step-by-step explanation:
Given:
Frank is making a pennant in the shape of a triangle for his senior class photo.
Base of triangle = 6 in
Area of triangle ≤ 27 
Let height of the triangle be h
Now we now that,
Area of triangle = 
Hence the height of the triangle must be at most or ≤ 9 inches.
