

follows from the fact that the cosine function is

-periodic, which means

. Roughly speaking, this is the same as saying that a point on a circle is the same as the point you get by completing a full revolution around the circle (i.e. add

to the original point's angle with respect to the horizontal axis).
If you make another complete revolution (so we're effectively adding

) we get the same result:

. This is true for any number of complete revolutions, so that this pattern holds for any even multiple of

added to the argument. Therefore

for any integer

.
Next, because

, it follows that

is also true for any integer

. So we have

The rest follows from considering either case and solving for

.
Answer:
68% of the sample can be expected to fall between 28 and 32 cm
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 30
Standard deviation = 2
What proportion of the sample can be expected to fall between 28 and 32 cm
28 = 30-2
28 is one standard deviation below the mean
32 = 30 + 2
32 is one standard deviation above the mean
By the Empirical Rule, 68% of the sample can be expected to fall between 28 and 32 cm
Answer:
You should graph the numbers on the side then pin point the coordinates on the graph
Step-by-step explanation:
The greatest common factor is 1
Answer: Mean: 17.14 Range: 20.
Step-by-step explanation: 12+13+13+15+16+19+32 25+13+15+16+19+32 38+15+16+19+32 53+16+19+32 69+19+32 88+32 120/7 17.14
32-12 20