For each comparison, write the corresponding percent. a. 7 out of 100 b. 76 out

Hi!

To convert numbers to percents, we can set up proportions and cross-multiply. 
I'm going to give you the answers for a, b, and c, but I want you to try to solve d! So make sure you pay attention to these instructions.

First, set up two fractions.
The first fraction will be the numbers you're turning to a percent. (for a, it is 7 and 100)
The second fraction will be x over 100. x is the percent we're trying to find. 

Pro tip: Numbers over 100 are pretty much already percents! 7 over 100 is the same as 7%. Don't understand how? Let me know. 

Okay, so let's set up our fractions. 



Now cross multiply and solve. (multiply the numerator of the first fraction by the denominator on the second fraction, then divide by the denominator on the first fraction) I hope that makes sense...

7 x 100 = 700
700/100 = 7

a. 7%

Now for b.



Psst. Remember the Pro tip? It applies for all of these! But I'm going to show you how to solve them anyway just for clarification. :)

76 x 100 = 7600
7600/100 = 76

b. 76%

And last but not least, c. 



430 x 100 = 43000
43000/100 = 430

c. 430%

Now I'm 100% positive (ha, see what I did there!) that you can solve d. Give it a go! Write me a message with your answer and I'll double check it for you. Good luck! :D

Hope this helps! :)

  6 +2√3 ft²

Step-by-step explanation:

Given a triangular pyramid with ...

an equilateral triangular baselateral edge length 2 ftlateral area 6 ft²

Find

total surface area

Solution

Since corresponding edges are the same length, the area of each of the three faces is (6 ft²)/3 = 2 ft². This can be computed by ...

  A = (1/2)s²·sin(α)

where s is the lateral edge length and α is the angle at the apex formed by the two edges that meet there. Filling in the given values, we find ...

  2 ft² = (1/2)(2 ft)²·sin(α)

  1 = sin(α)   ⇒   α = 90°

That is, each face of the pyramid is an isosceles right triangle with legs of length 2 ft. The hypotenuse of that triangle, the base edge of the pyramid, is then 2√2 ft.

So, the base is an equilateral triangle with edge lengths 2√2 ft. Its area can be computed from ...

  A = (√3)/4·s²

where s is the edge length of the equilateral triangle. That is, the base area is ...

  A = (√3)/4·(2√2)² = 2√3 . . . . square feet

So, the total surface area of the pyramid is ...

  (6 +2√3) ft² ≈ 9.4641 ft² . . . . . total surface area