The length of time needed to complete a certain test is normally distributed with mean 62 minutes and standard deviation 8 minutes. find the probability that it will take less than 74 minutes to complete the test. a) 0.0668b) 0.5334c) 0.5000d) 0.4666e) 0.9332

the correct option is e

Step-by-step explanation:

Since the The length of time needed to complete a certain test is normally distributed, we would apply the the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = The length of time needed to complete a certain test

u = mean time

s = standard deviation

From the information given,

u = 62 minutes

s = 8 minutes

We want to find the probability the probability that it will take less than 74 minutes to complete the test. It is expressed as

P(x lesser than or equal to 74)

For x = 74,

z = (74 - 62)/8 = 1.5

Looking at the normal distribution table, the corresponding value for the z score is 0.9332

P(x lesser than or equal to 74) = 0.9332

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

22.83 repeating

step-by-step explanation:

137 ÷ 6 is 22.8333333 therefore we understand that 3 is repeating.

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