Answer:
C
Step-by-step explanation:
tanA = =
=
=
→ C
Points A, B, C, and D are on the same line segment. The length
1 answer:
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Answer:
5507.79 feet
Step-by-step explanation:
To find the height of the mountain, we can draw triangles as in the image attached.
Let's call the height of the mountain 'h', and the distance from the first point (31 degrees) to the mountain 'x'.
Then, we can use the tangent relation of the angles:
tan(34) = h/x
tan(31) = h/(x+1000)
tan(31) is equal to 0.6009, and tan(34) is equal to 0.6745, so:
h/x = 0.6745 -> x = h/0.6745
using this value of x in the second equation:
h/(x+1000) = 0.6009
h/(h/0.6745 + 1000) = 0.6009
h = 0.6009 * (h/0.6745 + 1000)
h = 0.8909*h + 600.9
0.1091h = 600.9
h = 600.9 / 0.1091 = 5507.79 feet
Answer:
It's the graph that its showed in the image
Answer:
a) Mean = 5800 hours
b) P(5000 ≤ L ≤ 6000) = 0.420
c) k = 4700 hours
Step-by-step explanation:
The full correct question is attached to this solution.
From the graph of the distribution of lifetime of bulbs presented, it is evident that this is a normal distribution.
(a) Write down the mean lifetime of the light bulbs.
From the normal distribution graph, the mean is at the very centre of the graph
Mean = μ = 5800 hours
(b) The standard deviation of the lifetime of the light bulbs is 850 hours.
Find the probability that 5000 ≤ L ≤ 6000, for a randomly chosen light bulb.
Mean = μ = 5800 hours
Standard deviation = σ = 850 hours.
The required probability = P(5000 ≤ L ≤ 6000)
To find this, we first normalize/standardize 5000 and 6000.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
For 5000
z = (L- μ)/σ = (5000 - 5800)/850 = -0.941
For 6000
z = (L- μ)/σ = (6000 - 5800)/850 = 0.235
The required probability
P(5000 ≤ L ≤ 6000) = P(-0.941 ≤ z ≤ 0.235)
We'll use data from the normal probability table for these probabilities
P(5000 ≤ L ≤ 6000) = P(-0.941 ≤ z ≤ 0.235)
= P(z ≤ 0.235) - P(z ≤ -0.941)
= 0.593 - 0.173 = 0.420
c) The company states that 90% of the light bulbs have a lifetime of at least k hours. Find the value of k. Give your answer correct to the nearest hundred.
P(L ≥ k) = 90% = 0.9
assuming that the z-score of k is z'
P(L ≥ k) = P(z ≥ z') = 0.90
P(z ≥ z') = 1 - P(z < z') = 0.9
P(z < z') = 0.1
Using the normal distribution table
z' = -1.282
z' = (k - μ)/σ
-1.282 = (k - 5800)/850
k = (-1.282 × 850) + 5800 = 4710.3 = 4700 hours to the nearest hundred.
Hope this Helps!!!
