The inverse of the function f(x) = 4(x-3)² + 2 is
The given function is:
f(x) = 4(x - 3)² + 2
To find the inverse of the function:
Make x as the subject of the formula
Replace x by and replace f(x) by x
Therefore, the inverse of the function is:
Learn more here: brainly.com/question/17285960
Answer:
Step-by-step explanation:
Hello!
The objective is to test ESP, for this, a psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, square.
Be X: number of times the psychic identifies the symbols on the cards correctly is a size n sample.
p the probability that the psychic identified the symbol on the cards correctly
You have to calculate the sample size n to estimate the proportion with a confidence level of 95% and a margin of error of d=0.01
The CI for the population proportion is constructed "sample proportion" ± "margin of error" Symbolically:
p' ±
Where is the margin of error. As you can see, the formula contains the sample proportion (it is normally symbolized p-hat, in this explanation I'll continue to symbolize it p'), you have to do the following consideration:
Every time the psychic has to identify a card he can make two choices:
"Success" he identifies the card correctly
"Failure" he does not identify the card correctly
If we assume that each symbol has the same probability of being chosen at random P(star)=P(cross)=P(circle)=P(square)= 1/4= 0.25
Let's say, for example, that the card has the star symbol.
The probability of identifying it correctly will be P(success)= P(star)= 1/4= 0.25
And the probability of not identifying it correctly will be P(failure)= P(cross) + P(circle) + P(square)= 1/4 + 1/4 + 1/4= 3/4= 0.75
So for this experiment, we'll assume the "worst case scenario" and use p'= 1/4 as the estimated probability of the psychic identifying the symbol on the card correctly.
The value of Z will be
Now using the formula you have to clear the sample size:
To estimate p with a margin of error of 0.01 and a 95% confidence level you have to take a sample of 7203 cards.
I hope this helps!
The triangle pay $32 more for that day than it paid per day during the first period of time.
Step-by-step explanation:
The given is,
Triangle Construction pays Square Insurance $5,980
To insure a construction site for 92 days
To extend the insurance beyond the 92 days costs $97 per day
Triangle extends the insurance by 1 day
Step:1
Insurance per day from the 92 days period,
Where, Total insurance for 92 days = $ 5,980
Period = 92 days
From the values, equation becomes,
= $ 65 per day
Step:2
Insurance per day after the 92 days,
= $ 97
Amount Pay for that day than it paid per day during the first period of time,
= $32
Result:
The triangle pay $32 more for that day than it paid per day during the first period of time, if the Triangle Construction pays Square Insurance $5,980 to insure a construction site for 92 days and to extend the insurance beyond the 92 days costs $97 per day.