Alice has just discovered base 10 cake! She is delighted with how powerful it is. One day, after nibbling on the cake, Alice realizes she is 1 mile tall. Having her head in the sky makes her think about space travel. She decides she wants to visit the moon, which is about 239,000 miles from the earth. How many more ounces of base 10 cake should Alice eat so the top of her head just touches the moon? Give your answer to the nearest hundredth of an ounce.

5.38 ounces

Step-by-step explanation:

Given that :

Alice height = 1 mile

Distance of earth to moon = 239000 miles

Number of base 10 cakes required so they Alice's head just touches the moon ;

Using the relation :

Distance = height per ounce * 10^number of ounces

Height per ounce = 1 mile ;

Let number of ounces = n

Hence,

239000 = 1 * 10^n

239000 = 10^n

Take log of both sides

Log(239000) = n

5.3783979 = n

5.3784 = n

Hence, Alice should take 5.38 ounces of base 10 cakes

∠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.

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3