CPhill

45 / 15 =  N / 9      where N is the number of apples

3  = N  / 9     multiply both sides by 9

27 = N  

(1)  1 + 3 + 5 + ....+  57

Note that the sum of the first 2 odd positive integers  = 2^2

And the sum of the  first  3 positive odds = 3^2

And 

2n  -1 =  57

2n = 58

n = 29

So 57 is the 29th positive odd

So.....the sum of  1 +3 + 5 + ....+ 57   is the sum of the first   29th odd numbers = 29^2  = 841

(2)  Sum of 1st n counting numbers =  n (n + 1)   / 2

So....the sum of the  first 28 counting numbers =   28 * 29 / 2  =  14 * 29  = 406

Let T  = price of  a box of truffles

Let P = priceof a  box of peanut brittle

So

58T  + 55P = 510

99T + 55P  = 715     subtract the first equation fro the second

41T  = 205      divide both sides by 41

T = 5  ( each box of truffles  = $5 )

And  using either  equation....

99 (5)  + 55P  = 715

495  +  55P  =715     subtract  495  from both sides

55P  = 220   divide  both sides by  55

P = 4 ( each box of  peanut brittle  = $4 ) 

Right....not compounding.....the interest earned each year  is on the original amount.....thus..it is constant 

Elsie made a snack mix using the following recipe. 1 1/2  cups of pretzels, 3/4 cup peanuts, 3/4 cup chocolate chips,1/4  cup bread crisps.  If she used 6 cups of pretzels and wanted to keep the ingredients proportional, how many cups of chocolate chips would she need to use?

In the new mixture, we need  6 / (1 1/2)    =   6 / ( 3/2)  =  6 * 2 / 3  =  12  /3   = 4   times as much of each of the  ingredients

So....the chocolate chips needed  =  4 (3/4)  = 3 cups 

Interst amount  earned  must have  been   650 - 500   = $150 

And   I  =  Prt

Where     I  = interest    P  = original amount     r =interest rate      t  = time in years

So

150 = 500 * r * (3)

150  = 1500 * r     divide both sides by  1500

150 /1500 =  1/10   = r   = .10   =  10% = interest rate

This makes sense.....the interst earned each year  =  .10 * 500  =   $50

So...at the end of 3 years....we have 3 * 50    = $150  more than what we originally deposited

A.  Height =    sqrt ( side lenth ^2 - (base/2)^2) =  sqrt (13^2  - 5^2)  = sqrt (169 - 25)   =sqrt ( 144)  =  12 cm

B.  Cardboard needed = Area  =  2* base area  + ( 20) ( 13 + 13 + 10)

2 *Base area  =  2*area of triangles at  both endes =   2* (1/2) (10)(12)  =  120

So...we have

120  + 20 ( 36) =

120  + 720  =

840 cm^2

                                    .02   (accident)

.90 (not distracted) 

                                    .98(no accident)

                                     .30(accident)

.10 (distracted)

                                     .70 (no accident)

a.  P(accident) =  P ( not distracted and accident)  + P ( distracted and  accident)  =

                                   (.90) (.02)  +  (.10) (.30)  =

                                         0.048  = 

                                          4.8%

b. P ( distracted and accident)  =   (.30)(.10)  = 0.03  = 3%

"Anchor"  April and May  in any two seats with a seat between them

We can seat them in 2 ways

For the person between them we have  C (6,1)   = 6  possibilities

And the other 5 people can  be seated in 5!  =120 ways

So.....the total possible arrangements  =

2 * 6 * 120  = 

12 * 120  = 

1440

-3 ( a - 7)  +  4a

-3a  + 21  + 4a

a + 21