A $300 suit is marked down by %20. Find the sale price
2 answers:
You might be interested in
Answer:
6 years
Step-by-step explanation:
Here,
and we need to find .
So using the formula , we can find T by substituting the values
years
The function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2
<h3>How to convert sine of an angle to some angle of cosine?</h3>We can use the fact that:
to convert the sine to cosine.
<h3>Which trigonometric functions are positive in which quadrant?</h3>- In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.
- In second quadrant(π/2 < θ < π), only sin and cosec are positive.
- In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.
- In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.
(this all positive negative refers to the fact that if you use given angle as input to these functions, then what sign will these functions will evaluate based on in which quadrant does the given angle lies.)
Here, the given function is:
The options are:
Checking all the options one by one:
- Option 1:
(the last second step was the use of the fact that cos flips its sign after pi radian increment in its input)
Thus, this option is same as the given function.
- Option 2:
This option if would be true, then from option 1 and this option, we'd get:
which isn't true for all values of x.
Thus, this option is not same as the given function.
- Option 3:
The given function is
This option's function simplifies as:
Thus, this option isn't true since always (they are equal for some values of x but not for all).
- Option 4:
The given function simplifies to:
The given option simplifies to:
Thus, this function is not same as the given function.
Thus, the function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2
Learn more about sine to cosine conversion here:
Answer:
We cannot say that the mean wake time are different before and after the treatment, with 98% certainty. So the zopiclone doesn't appear to be effective.
Step-by-step explanation:
The goal of this analysis is to determine if the mean wake time before the treatment is statistically significant. The question informed us the mean wake time before and after the treatment, the number of subjects and the standard deviation of the sample after treatment. So using the formula, we can calculate the confidence interval as following:
Knowing that :
Note that so we cannot say, with 98% confidence, that the mean wake time before treatment is different than the mean wake time after treatment. So the zopiclone doesn't appear to be effective.