Toby's trucking company determined that on an annual basis the distance traveled per truck is normally distributed with a mean of 50.0 thousand miles and a standard deviation of 12.0 thousand miles.
a. what proportion of trucks can be expected to travel between 34.0 and 50.0 thousand miles in the year?

0.4082

Step-by-step explanation:

Data

mean () = 50,000 miles

standard deviation () = 12,000 miles

expected distance (X) = 34,000 miles

In the figure attached, standard normal distribution table can be seen. Z is computed as follows:

In standard table, the area between 0 and -1.33 is the sem as between 0 and 1.33. So, the proportion of trucks is 0.4082

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°