What additional information will allow you to prove the triangles congruent by the HL Theorem?
2 answers:
Answer:
The correct option is 3.
Step-by-step explanation:
The HL theorem states that 'if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.'
From the given figure it is noticed that triangle ABC and triangle EDC. In triangle ABC and triangle EDC, hypotenuses of triangles are AB and DE respectively.
To use HL hypotenuse and one leg of triangles must be equal.
(hypotenuse)
(leg)
(leg)
Therefore the additional information will allow you to prove the triangles congruent by the HL Theorem. Option 3 is correct.
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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!!!
