Given the parent function of f(x) = x3, what change will occur when the function is changed to f(x + 3)? A) Shift to the right 3
2 answers:
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<h3>Answer: y = x+1</h3>
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Explanation:
f(x) = x^3 - 2x + 3
f ' (x) = 3x^2 - 2 ..... apply the power rule
f ' (1) = 3(1)^2 - 2 ... plug in x coordinate of given point
f ' (1) = 1
If x = 1 is plugged into the derivative function, then we get the output 1. This means the slope of the tangent line at (1,2) is m = 1. It's just a coincidence that the x input value is the same as the slope m value.
Now apply point slope form to find the equation of the tangent line
y - y1 = m(x - x1)
y - 2 = 1(x - 1)
y - 2 = x - 1
y = x - 1 + 2
y = x + 1 is the equation of the tangent line.
The graph is shown below. I used GeoGebra to make the graph.
Answer:
a) 0.98% probability that 17 of the 29 people are men.
b) 3.86% probability that the first woman is reached on the 8th call
Step-by-step explanation:
For each person chosen by the agency, there are only two possible outcomes. Either it is a man, or it is a woman. The probability of selecting a man or a women in each trial is independent from other trials. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
(a) What is the probability that 17 of the 29 people are men?
This is P(X = 17) when . So
0.98% probability that 17 of the 29 people are men.
(b) What is the probability that the first woman is reached on the 8th call?
On the first 7 trials, all men, each with a 78% probability.
On the 8th trial, a women, with a 22% probability. So
3.86% probability that the first woman is reached on the 8th call