Answer:

And we can find this probability using the normal standard table or excel and we got:

The figure shows the calculation for this case.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the hardness of a population, and for this case we know the distribution for X is given by:
Where
and 
We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability using the normal standard table or excel and we got:

The figure shows the calculation for this case.
Answer:
m = 54
Step-by-step explanation:
The secant- secant angle 20° is half the difference of the intercepted arcs, that is
(160 - 2m - 12) = 20° ( multiply both sides by 2 to clear the fraction )
- 2m + 148 = 40° ( subtract 148 from both sides )
- 2m = - 108 ( divide both sides by - 2 )
m = 54
Answer:
weeks or
weeks
Step-by-step explanation:
To do this we can set up a proportion

This will tell us how many weeks are in 2/5 of a year
Let's evaluate this
We cannot simplifiy this anymore, so we will leave it as an improper fraction, or a mixed number as shown below
weeks
Answer: 31
Step-by-step explanation:
179 - 148 = 31
Answer:
-5
Step-by-step explanation:
You can work backwards with this problem if that helps you.
so, what times 3 = -15
-5 times 3 = -15 so that would be the answer