Step-by-step explanation:
We remeber that If we compose a function and it's inverse,
A invertible function is one to one so suppose that we have two inverse, g(x) and h(x). Let plug them in ,
and
Since f is a invertible function, it is one to one so if g and h are both inverse of f, then they are eqaul
Thus, a invertible function can have only one inverse.
Part a)
p = population proportion of correct guesses
Null Hypothesis: p = 0.5
Alternative Hypothesis: p > 0.5
The claim that people can tell the difference of the two drinks is in the alternative hypothesis p > 0.5 meaning that it's more than just luck at play here. Saying p = 0.5 is basically saying there's a coin toss to determine the guess.
x = 53, n = 80
phat = x/n = 53/80 = 0.6625
SE = sqrt(p*(1-p)/n) = sqrt(0.5*(1-0.5)/83) = 0.05488212999484
z = (phat-p)/(SE)
z = (0.6625-0.5)/(0.05488212999484)
z = 2.96089091322218
z = 2.96
Use a table or calculator to find that
P(Z < 2.96) = 0.9985
So,
P(Z > 2.96) = 1-P(Z < 2.96)
P(Z > 2.96) = 1-0.9985
P(Z > 2.96) = 0.0015
The p-value is approximately 0.0015. This value is less than many alpha values commonly used (such as 0.01 or 0.05) so we reject the null hyptohesis that p = 0.5 and accept that p > 0.5 is true. So the participants aren't randomly guessing. The results are significantly better than random guesses.
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Part b)
The p value 0.0015 is the probability of observing 53 or more claims out of 80 claims, under the assumption that the null hypothesis is true. This p value is very very small, so there is a small chance that the null hypothesis is correct. The smaller the p value, the more likely we reject the null. The general rule is that if the p value is smaller than the significance level alpha, we reject the null. Your textbook will state what alpha is equal to. If not, then the default is alpha = 0.05
Answer:
The graph of y = f(x) will shift left 6 units, as shown in figure a.
Step-by-step explanation:
A translation means we are able to move the graph of a function up or down - normally called Vertical Translation - and right or left - commonly called Horizontal Translation.
If we replace the graph of y = f(x) with the graph of y = f(x + 6). It means we have added 6 units to the input, meaning the graph y = f(x) will shift left by 6 units as 6 is being added directly to the x, so it is f(x + 6).
For example, if y = x² is the original function and of 6 is directly added to x i.e. f(x + 6), making it y = (x + 6)². So, we can easily observe that there will be a horizontal translation left of 8 units, as shown in figure a.
So, the graph of y = f(x) will shift left 6 units.
Keywords: graph shift, translation
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The computation shows that the distance will be 126 1/4 miles.
<h3>How to illustrate the information?</h3>
From the information given, it was stated that Mary tarvels 12 5/8 miles to work each day.
Therefore, the distance that she drives during the week will be:
= (12 5/8 × 2) × 5
= 126 1/4
Therefore, the distance will be 126 1/4 miles.
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