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If arithmetic....the difference between succesive terms would be  constant....this clearly isn't true

If geometric.....then this must be true

7/5  = 12/7   

1.4  = 1.7142857  

Not true....so.... not geometric, either

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

Using sequence differences, you have this:
 5, 7, 12, 20, 31
   2,  5,  8,  11
      3,  3,  3

From the above, we can formulate a "closed form" as follows:

a_n = 1/2 (3 n^2 - 5 n + 12), which will give you each term in your sequence as follows: 

5, 7, 12, 20, 31, 45, 62, 82, 105, 131, 160, 192, 227, 265, 306, 350, 397, 447, 500, ....etc.

I don't understand why this rules out the interval 4 to 5. How does it rule out (without a calculator) 2.2 +2.7 = 4.9 for example.

Your sequence has this closed form:

a_n = 7 n + 11 

a(9) =9*7 + 11

a(9) = 74

The mid-value is 62.

The amplitude is the y-distance from the mid-value to the maximum value (which is also the y-distance from the mid-value to the minimum value).  Can you find this?

The period is the x-distance from the first occurrence of the mid-value to the next occurrence of the mid-value. Can you find this?

The vertical shift is the mid-value.

Thanks for the A2A.

The answer is neither.

Cheers!

There are two possibilities:  HHTT  =  (0.60)(0.60)(0.40)(0.40)  =  a

                                      or:   THTT  =  (0.40)(0.60)(0.40)(0.40)  =  b

Calculate a and b and add them together.

Thanks for the A2A.

First, let's see how many ways there are for 4O, 4A, 1B, and 1AB.

If we use the compound permutation/combination formula, we can do 10!/(4!*4!). We get 6300 ways to sort the 10 people around. 

Now let's do \(\frac{{44}^{4}+{42}^4+{10}^{1}+{4}^{1}}{{10}^{10}}\).

Do it on your calculator and you get .0007.

Multiply 6300 and .0007 and you'll get 4.32%

In decimal form, I believe it will be .043.

Cheers!

what is 'it' ?

Please state the reason properly.

I intend to delete comments that say an answer is wrong without a reason being given.

Thanks for the A2A.

I believe the answer is C.

OK, young person. I wrote this short computer code just to solve your problem !!!

e=222222;a=4*e; c=round(log(a) / log(5)); d=sumfor(n, 1, c, int(a / (5^n)));if(d==e, goto end,0);a++;if(a<=5*e, goto3, 0);end:print"Integer is  =",a,"!";print"Trailing 0s=",d

OUTPUT =Integers are   = 888,900!, 888,901!, 888,902!, 888,903! and 888,904![All 5 integers end in 222,222 zeros!]
 

First you find the proportions used

78.94*x+71.94*(1-x)=73.94

78.94*x+71.94-71.94*x=73.94

78.94x-71.94x=73.94-71.94

7x=2

x=2/7

x=0.2857

Multiply this proportion with the overall amount (1000 litres)

and you get

285.714 liters of premium

and 1000-285.714 of regular.

Well we know there are 6 half inches in 3 inches. So that means it's 

50 * 6 = 300 miles.

So 300 miles between two towns.

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 

$665.50 is compound interest NOT simple interest(which says in the question!).

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 

Does simple interest rate mean it's not compounding?

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

10% interest rate would yield 665,5 so that's incorrect.

$650 - $500 =$150 simple interest earned over 3 years.

$150 / 3 =$50 simple interest earned in 1 year.

$50 / $500 = 10 % simple interest rate per year.

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

since when were candy bars triangular prisims???