Answer: P(100 ≤ x ≤ 130) = 0.43
Step-by-step explanation:
Since the scores are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = scores
µ = mean score
σ = standard deviation
From the information given,
µ = 100
σ = 20
We want to find the probability that the scores is between 100 and 130. It is expressed as
P(100 ≤ x ≤ 130)
For x = 100,
z = (100 - 100)/20 = 0
Looking at the normal distribution table, the probability corresponding to the z score is 0.5
For x = 100,
z = (130 - 100)/20 = 1.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.93
Therefore,
P(100 ≤ x ≤ 130) = 0.93 - 0.5 = 0.43
Answer:
A 30-degree angle is an acute angle. An angle is formed when two lines meet or intersect at a point. An acute angle is one in which the measure of the angle is less than 90 degrees.
Step-by-step explanation:
found this answer if its wrong im sorry :/
Answer:
x₁ = 1866.2 yd distance between ship and searchlight in C
x₂ = 2542.5 yd . distance between ship and searchlight in B
Step-by-step explanation:
The ship (point A) and the two searchlights points ( B and C) shape a triangle.
We have α = 38° ( opposite side x₁ or distance between ship and point C and β = 57 ° ( opposite side x₂ or distance between ship and point B then γ = 180 - ( α + β )
γ = 85°
Applying sin´slaw
x₁ / sin 38 = x₂/ sin57 = 3020 / sin 85
from sin table we find:
sin 38 = 0.6156
sin 57 = 0.8387
sin 85 = 0.9962
Then
x₁ / 0.6156 = 3020 / 0.9962
x₁ ( the opposite side to angle 38° ) / 0.6156 = 3031.5
x₁ = 3031.5*0.6156
x₁ = 1866.2 yd
x₂ = 3031.5 * 0.8387
x₂ = 2542.5 yd