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Answers all look good,  

The odd numbers  are 1, 3 and 5

1 comes up 11 times

3 comes up 14 times

5 comes up 13 times

So.....spinning an odd number   =    [ 11 + 14 + 13 ]  / 60   =  38 / 60   =  19 / 30

Spin an odd number

1  3  or 5

11 14 + 13 =  38

38/60   or   19/30

r /5 = 4/7   Multiply both sides by 5

5 (r/5) = 4/7 *5

r = 20/7

r / 5  = 4/ 7

cross-multiply

7 * r  =  4* 5 

7 * r   = 20   

divide both sides by 7

r  =  20 / 7

C. 180 degrees, because the terminal side is on the x-axis

OK....not as tough as it appears

4 / r  =  5 /7    cross-multiply

4 * 7  =  5 * r      

28 = 5*r   divide both sides by 5

28 / 5  =  r     [ and we are through  !!! ]

Thank you!!

Sorry I had to log off. Thank you so much for your help! I appreciate it very much.

That is what I was thinking but steps you provided helped me understand it more. Thank you

The answer to the second one is "B"....this will divide the larger right triangle into two smaller  similar  right triangles  which can be used to prove the P Theorem

For the last one......we have this relationship

y - 10.8         14.4

______  =  ______               cross-multiply

14.4             10.8

10.8 ( y - 10.8)  =  14.4 * 14.4

10.8 y - 116.64   = 207.36      add 116.64 to both sides

10. 8 y   = 324      divide both sides by 10.8

y  = 30

Got it! Thank you

Yep...[.as long  as we have an exponent  on "b"  and "a" is positive ]

So......

a (b)^x       is decay  if     0 < b < 1

And  growth   if  b > 1

4 * 6^3x=221

6^3x =221/4

Log (6^3x) = Log (221/4)

3x log 6 = log 221/4

3x = log 221/4  /  log 6

x = log(55.25)/(3 log 6)

It only matters about whether or not the number instead the parentheses is greater or less than 1 ? to determine the answer?

Note that   A = (4/3)^t  is still growth, too....b > 1

H=(7/2)(5/6)^t       decay     (  b  = 5/6   )

And as long as the last one  is   (4/9) (8)^t   it is still growth

Some of these were fraction, i put the choices in wrong would the answers change ?

here is the correct choices

g(x)=0.3(x)

H=7/2(5/6)^t

A=(4/3)^t

H=5.9(0.82)^t

y=0.8(3.6)^t

f(t)=0.72(15)^t

A=4/9(8)^t

Remember that in the form

a(b)^x       where  a > 0

When   b > 0  but < 1.....we have a decay function

When   b > 1.....we have a growth function

BTW..."a"  doesn't matter in the determination of these.....only the value of  b 

So

g(x)=0.3(x)      this  is neither ...we have no exponent [ it's linear ]

H=72(56)^t     growth  b  = 56

A=(43)^t        growth   b  = 43    [ "a" is an understood "1"  ]

H=5.9(0.82)^t      decay       b =  0.82

y=0.8(3.6)^t      growth   b = 3.6

f(t)=0.72(15)^t    growth    b  = 14

A=49(8)^t      growth  b  = 8

Does this make sense, Jenny   ???

thank you very much!

I just "eye-balled" it...and didn't have time to go through the sum-of-differences thing

Thanks for the answer, Rom....!!!

boo CPhill, enough of these have been done that I'd have thought you'd seen one by now.

You need to take successive adjacent differences of f(x)

\(\left( \begin{array}{c} \{30,0,-2,0,30,160,510\} \\ \{30,2,-2,-30,-130,-350\} \\ \{28,4,28,100,220\} \\ \{24,-24,-72,-120\} \\ \{48,48,48\} \\ \end{array} \right)\)

in the matrix above the first line is f.

successive lines are formed by taking the line above minus it shifted 1 place to the left

that we could do this 4 times before all the numbers were equal shows that f is degree 4