1) the ages of trees in a forest are normally distributed with a mean of 25 years and a standard deviation of 5 years. using the empirical rule, approximately what percent of the trees are between 20 and 30 years old?
2)pizza delivery times at pizza time are normally distributed with a mean time of 27 minutes and a standard deviation of 3 minutes. using the empirical rule, approximately what percent of pizzas are delivered between 24 and 30 minutes?

1) 68%

2) 68%

Step-by-step explanation:

We know the mean and the standard deviation.

The mean is:

The standard deviation is:

The Z-score formula is:

For x=20 the Z-score is:

For x=30 the Z-score is:

Then we look for the percentage of the data that is between deviations from the mean.

According to the empirical rule 68% of the data is less than 1 standard deviations of the mean.  This means that 68% of the trees are between 20 and 30 years old

First we calculate the Z-scores

We know the mean and the standard deviation.

The mean is:

The standard deviation is:

The z-score formula is:

For x=24 the Z-score is:

For x=30 the Z-score is:

Then we look for the percentage of the data that is between deviations from the mean.

According to the empirical rule 68% of the data is less than 1 standard deviations of the mean.  This means that 68% of pizzas are delivered between 24 and 30 minutes

x = 19 degrees

y = 84 degrees

Step-by-step explanation:

recall that for an isosceles triangle (which is pictured), the base angles have the same value.

In our case, we can see that the base angles are 48 deg and (3x-9) deg

if they are equal, we can equate them like this:

48 = 3x-9    (add 9 to each side)

48 + 9 = 3x

57 = 3x   (divide both sides by 3)

x = 57/3

x = 19 degrees  (answer)

also recall that the sum of the interior angles of a triangle add up to 180 deg, hence

48 deg + 48 deg + y deg = 180 deg

2(48) + y = 180

96 + y = 180

y = 180 - 96

y = 84 deg