Pine trees and juniper trees are common to the San Bernardino mountains. Pine trees have a mean height of 52 meters with a

standard deviation of 3 meters. Juniper trees have a mean

height of 22 meters with a standard deviation of 5 meters.

(a) At the base of a trail, there is a 48-meter-tall pine tree and a

33-meter-tall juniper tree. Calculate the Z-score for each of

these trees.

If necessary, round your answers to the nearest 2 decimal

places. Write both answers in the text box below.

Z-score = 0.9450

Step-by-step explanation:

Step(i):-

 mean height of pine tree (x₁⁻) = 52

standard deviation of pine tree σ₁ = 3

Mean height of Jupiter tree ((x₂⁻) = 22

standard deviation of Jupiter tree  σ₂ = 5

Size of first sample n₁ = 48

size of second sample n₂ = 33

Step(ii):-

Z-score

             Z = 0.9450

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°

r = 78539458390583095803458309458039485093485 or just 3

step-by-step explanation: