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:
a=(2/5), b = (-2,6)
Step-by-step explanation:
well slope formula is rise/run. So for the first one you start at the point rise 2 run 5 and you reach the endpoint. That is how you know you got the correct slope. (2/5)
For the second one you start at the first point and you cannot go up because it is a negative slope you run 6 till you hit the other point go down 2. Since you go down 2 that would make it -2. (-2,6)
Answer:
4
Step-by-step explanation:
y=8x+4
y=mx+b where m=slope and b=y-intercept
b=4
Answer:
15 km
Step-by-step explanation:
3 cm on the map = 5 km
3 x 3 = 9 cm
5 x 3 = 15 km
So, 9 cm on the map = 15 km