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Cool! #lets let this post to 1 MIll hearts 

Agreed! A very efficient way.

Let's break this up :D

There's \(3a^{-3}\), \(b^2\), \(2a^{-1}\) and \(b^0\), where \(a = -2\) and \(b=-3\).

\(3a^{-3} = 3((-2)^{-3}) = 3(\frac{1}{(-2)^3}) = \frac{3}{-8} = -\frac{3}{8}\)

\(b^2 = (-3)^2 = 9\)

\(2a^{-1} = 2((-2)^{-1}) = 2(\frac{1}{-2}) = \frac{2}{-2} = -1\)

\(b^0 = 1 \) :D

So, our expression is:

\((\dfrac{-\frac{3}{8} \cdot 9}{-1 \cdot 1})^2\)

Which is: 

\((\dfrac{-\frac{27}{8}}{-1})^2\)

Which makes:

\((\frac{27}{8})^2\) 

Which equals:

\(\fbox{$\frac{729}{64}$}\)

Which is the last option :D

Wow your answer was very short and efficient nice work!

81

Solution:

Step 1 : Find the smallest and largest 3 digit numbers

The smallest 3-digit number = 100

The largest 3 digit number = 999

Step 2 : 

Let us find number of numbers divisible by 11 from 1 to 999

999/11 = 90.82

Therefore number of numbers divisible by 11 from 1 to 999 = 90

Step 3 :

Let us find number of numbers divisible by 11 from 1 to 99

99/11 = 9

Therefore number of numbers divisible by 11 from 1 to 99 = 9

Step 4:

Number of numbers divisible by 11 (1 to 999) = 90

Number of numbers divisible by 11 (1 to 99) = 9

Number of numbers divisible by 11 (100 to 999)

                                            = 90 - 9

                                            = 81    

Therefore, the number of three-digit numbers (100 to 999) which are divisible by 11 is 81.

The first one divisible by 11 is  110

And the last one divisible  by 11  is 990

So....the total number  =

[ 990 - 110] / 11   +  1  =

80  +  1   =

81

Thanks Melody!

Note that  at the top of the figure we have a right triangle with two legs  of  10 and 20

So the area of this  right triangle  = (1/2) (10)(20)   = 100

And the base of this triangle  = sqrt  [ 10^2 + 20^2]  =  sqrt [ 500] =  10sqrt(5)

So......we can find the height of this triange as

100  = (1/2) (10sqrt (5) ) height

20 / sqrt (5)  =  height  =  4sqrt (5)

And using similar triangles  the height  of the small right triangle  on the top left  =  1/2  of this  = 2sqrt (5) = sqrt (20)

And the base  of this triangle  =  sqrt [ 10^2 - (sqrt(20))^2 ]  =  sqrt [ 100 - 20]  = sqrt (80) 

So  the area of this small right triangle  =  (1/2)sqrt (20)sqrt(80) = (1/2)sqrt(1600) = (1/2) 40  = 20

And we have two of these triangles in the larger right triangle at the top

So....the area of the remaining   trapezoid  = 100 - 2(20)  = 60

So....we have   4 smaller right triangles and  4 trapezoids....so their combined areas  =

4 ( 20 + 60)  = 4 (80)  = 320      (1)

So....the area  of the white  square  =  

area of the square  -  (1)   =

20^2  - 320  =

400 - 320  =

80   (m^2)

The distance between Mytown and Little Village is 65 miles.

That is because I didn't post a full answer on mine, I left the rest up to you :D

I can't show an estimate (I didn't even make one)! It is up to you. You make the estimate, does some external source command you to be exact? :D

plz show your estimate

i tried plz show your estimate

Are you sure? Hmm. With scatter plots, you can never really be accurate.

Isn't an exponential function different from a geometric sequence?  Or is an exponential function one type of geometric sequence?  I can't find the answer to this on the internet... they all dance around it.  Thanks to anyone for helping me understand this. 

_.

quetion c has to be accurate

For the first one:

So it looks like as the age of a car goes up, its price and value come down. Logical, right? :D

a) We know that each point represents a car. Its x-value (i.e. how far away to the left or right it is from 0) is its age, and its y-value (i.e. how far away to the north or south it is from 0) is its cost. 

If a car is 4 years old (it has an x-value of 4) and its price is 2,600 pounds (it has a y-value of 2600), where will the point representing the car go? Put the point there :D

b) When looking at a relation between the x and y values (in this case, the age and price of the car) in a scatter plot, we don't need to find some equation. We are looking for a correlation.

There are 3 situations: 

1. There is a positive correlation (every time x increases, y increases too). 
2. There is a negative correlation (every time x increases, y decreases)
3. There is no correlation (RANDOM!!!)

In this problem, it looks like the price of a car comes down when its age increases (as we wrote in the first sentence xD). 

Basically, every time x (the age) increases, y (the price) decreases. Now, what correlation does this remind you of? :D 

c) I trust you can do this on your own, now that you know about correlations! Here, your answer doesn't need you to be specific: You can make up a value! Just make sure it doesn't too strongly resist the correlation you set in part (b) :D

Edit: oops, didn't know it was only question (c). Oh well, the more you know! xD

Force (weight) is proportional to the mass of the planet and inversely proportional to the square of its radius, so

new weight = 800*2/2²  = 400N

There are many, many integer solutions. Here are just a few:

       x                     y

1559776320    400320
1559776527    897777
1559777240    1740760
1559779200    3024000
1559779759    3299759
1559781204    3923796
1559781248    3941248
1559784960    5207040
1559786700    5704500
1559791656    6928344
1559792340    7080660
1559794176    7474176
1559796000    7845600
1559799360    8487360
1559800800    8748000
1559808144    9971856
1559812480    10628480
1559818890    11530890
1559821680    11902320
1559821752    11911752
1559827584    12652416
1559832000    13185600
1559852640    15435360
1559855241    15696009
1559859120    16076880
1559866026    16733526
1559869892    17090108
1559875968    17635968
1559891700    18976500
1559896380    19357380
1559906208    20133792
1559907840    20259840
1559925000    21540600
1559937120    22401120
1559952000    23414400
1559963440    24164560
1559970000    24584400
1559977920    25081920
1559998080    26305920
1559999083    26365333

Same! I technically "joined" about a month before, but I was inactive until I decided to become active. You were the first person I met, and we both share the same interests alongside all the wonderful people on this forum! :D TY Everyone!

Let there be k students in front of Reim.

So there is  k students in front + 3k students behind + Reim = 4k+1 students

Let N be the number of students in front of Bindu. 

So there is N students in front + 4N students behind + Bindu = 5N+1 students

4k+1=5N+1

4k=5N

So the number of students is a product of both 4 and 5 + 1 more

20 is the only such product that is less than or equal to 30

So there are 21 students in the line.

Bindu is 5th and Reim is 6th.

Hey Alan, Thanks for the link. I really don't understand the explanation that was provided. I haven't learned most of the terms that were used in the explanation. Do you know if you could answer it in a more simplified form? Thanks for your help!

Sum =(102, 109, 120, 129, 190, 192, 201, 209, 210, 219, 290, 291, 901, 902, 910, 912, 920, 921) =7728

There are 18 integers. So, the mean =7728 / 18 =429 1/3 - the mean.

This is a Geometric Sequence. 3 is the common ratio. So: a(n) =3^n. The first term=3^1. Second term=3^2. Third term=3^3. Fourth term=3^4.........10th term=3^10........1000th term =3^1000.....and so on.

U.S. Gallon = 3.7854 Liters

British Gllaon =4.546 Liters.