According to the Insurance Institute of America, a family of four spends between $400 and $3,800 per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts. If we select a family at random, what is the probability they spend less than $2,000 per year on insurance per year? (Round your answer to 4 decimal places.)

0.471

Step-by-step explanation:

Calculation for the probability that they spend less than $2,000 per year on insurance per year

First step is to find the base

Base =$2,000-$400

=$1,600

Second step is to find the probability using this formula

P=1/b+a×base

Where,

b represents $3,800

a represents $400

base represents $1,600

Let plug in the formula

P=1/$3,800-$400×$1,600

Hence,

P=1×$1,600/$3,800-$400

P=$1,600/$3,400

P=0.471

Therefore the probability that they spend less than $2,000 per year on insurance per year will be 0.471

∠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.