Answer:
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Step-by-step explanation:
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Answer:
We have function,

Standard Form of Sinusoid is

Which corresponds to

where a is the amplitude
2pi/b is the period
c is phase shift
d is vertical shift or midline.
In the equation equation, we must factor out 2 so we get

Also remeber a and b is always positive
So now let answer the questions.
a. The period is


So the period is pi radians.
b. Amplitude is

Amplitude is 6.
c. Domain of a sinusoid is all reals. Here that stays the same. Range of a sinusoid is [-a+c, a-c]. Put the least number first, and the greatest next.
So using that<em> rule, our range is [6+3, -6+3]= [9,-3] So our range</em> is [-3,9].
D. Plug in 0 for x.





So the y intercept is (0,-3)
E. To find phase shift, set x-c=0 to solve for phase shift.


Negative means to the left, so the phase shift is pi/4 units to the left.
f. Period is PI, so use interval [0,2pi].
Look at the graph above,
Add it up then you will get answer
Answer:
A 95% confidence interval for the true mean minimum temperature that will damage an iPod is between 2.55°F and 7.45°F
Test statistic(Z) = 2.31
P-value = 0.0104
Step-by-step explanation:
Step 1
Null hypothesis: The average damaging temperature of nine iPods is 5°F
Alternate hypothesis: The average damaging temperature of nine iPods differs from 5°F
Step 2
Mean=5°F, Sd=3, df=n-1=9-1=8
The t-value corresponding to 8 degrees of freedom and 95% confidence level (5% significance level) is 2.306
Confidence Interval(CI) = (mean + or - t×sd/√n)
CI = (5 + 2.306×3/√8) = 5 + 6.918/2.828= 5+2.45=7.45°F
CI = (5 - 2.306×3/√8) = 5-2.45 = 2.55°F
Z = (sample mean - population mean)/(sd÷√n) = (5-2.55)/(3÷√8) = 2.45/1.061 = 2.31
Step 3
Using the standard distribution table, the cumulative area to the left of Z = 2.31 is 0.9896
P-value = 1 - 0.9896 = 0.0104
Step 4
Conclusion: A 95% confidence interval for the true mean minimum temperature that will damage an iPod is between 2.55°F and 7.45°F