10. Joe borrowed $1000 and agreed to pay $1200 in settlement of the debt in 3 years and 3 months. What annual nominal rates compounded quarterly was charged on the debt?

1.2%

Step-by-step explanation:

A = P(1 + r/n)^nt

A = final amount

P = initial principal balance

R = interest rate

n = number of time interest per time period

t = number of time period elapsed

A = P(1 + r/n)^nt

1200 = 1000 (1 + r/4)^ 4*15

1200 = 1000 (1 + r/4)^60

1200 = 1000 (4 + r/4)^60

1200/1000 = (4+r/4)^60

1.2 = (4+r/4)^60

Take the 60 root of both sides

1.0030433 = (4+r/4)

4 * 1.0030433 = 4 + r

4.01217 = 4 + r

r = 4.01217 - 4

r = 0.012 = 1.2%

4096 bacteria

step-by-step explanation:

∠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.