Y = 7x + b
2 = 7 + b, b = -5
Y = 7x - 5
Theorem: If a function y = f(x) has a real root of b, then (x – b) is a factor of f(x).
As given in the problem, there are two roots: –2 and 1/2. The multiplicity of 1/2 is 2 meaning that the root 1/2 repeats twice. So the function f(x) can be written like this.
f(x) = k• (x – (–2))(x – 1/2)^2 = k•(x + 2)(x – 1/2)^2
We're supposed to find the coefficient k to complete the function.
Given that f(–3) = 5, we can plug –3 in for x and 5 in for f(x).
So 5 = k •(–3 + 2)(–3 – 1/2)^2
5 = k(–1)(–7/2)^2
5 = -k•49/4
Then 5 • 4/49 = -k
Or k = –20/49
So the function with the least degree is
f(x) = –20/49 (x + 2)(x – 1/2)^2.
Answer:
The probability is 40%
Step-by-step explanation:
a) There are ten pieces of paper with ten numbers
Probability of selecting four pieces of paper = 4/10 or 40%
Probability that the four numbers selected will have a sum greater than 82 = 82/205 = 40%
Therefore, the probability of selecting four numbers that have a sum greater than 82 out of ten numbers totalling 205 is 40%.
b) Probability is the ratio of the number of outcomes favourable for the event to the total number of possible outcomes. In other words, it is a measure of the likelihood of an event (or measure of chance).