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surface area of the triangular prism  =  area of square + area of square + area of square + area of triangle + area of triangle

We are given that the side length of each square is 2 units.

area of square  =  side length * side length

area of square  =  2 units * 2 units

area of square  =  4 square units

We are given that

area of triangle  =  1.5 square units

Once again,

surface area of the triangular prism  =  area of square + area of square + area of square + area of triangle + area of triangle

Can you figure out what to do next?

\(P[\text{at least 2 1's}] = 1 - P[\text{0 or 1 1's}]\\ P[\text{0 1's}] = \left(\dfrac 5 6\right)^3 = \dfrac{125}{216}\\ P[\text{1 1}] = \dbinom{3}{1}\left(\dfrac 1 6\right)\left(\dfrac 5 6\right)^2 = \dfrac{25}{72}\\ P[\text{at least 2 1's}] = 1 - \dfrac{125}{216}-\dfrac{25}{72} = \dfrac{2}{27}\)

@CPhill so the answer is 9.5 ^ 2?

This is a play with numbers exercise.  You can use a calculator.

The idea is that you try different combinations and see what happens (write down the question and answer each time, neatly underneath each other)

This will help teach you how numbers work together.

If we just hand you the answer then you will learn nothing.

Suggestion and hints:

1)  First put the numbers from smallest to largest.

2)  If you divide a number by something bigger than 1 then your number will get smaller.

3)  If you divide a number by something smaller than 1 then your number will get bigger.

              So if you want a big number which out of those 3 will you be dividing by? 

4) Division usually has more impact than addition.

Now thinking about what I have said and you can try your own combinations and tell us what you think the answer is.

Remember that this site is a calculator site.  

Please no one answer over the top of me.  I am trying to teach.

EDIT:

Oh dear I ahve missed out the absolute bit.   Another thing for you to play with.     

I also missed your comment about the 'book' answer. 

When you asked this question you would have been better off to tell us what answer you were trying to get and also tell us what the closest you had got so far was, with the working of course.   Then I would have formed a more appropriate answer for you because I would have understood better what you already knew and what you had tried already.

You can still tell us the closest you have got though.

\(t = \dfrac{20m}{c~m/s} = \dfrac{20}{c}s\\ c = \lambda \nu = 1.0m \cdot 2.0s^{-1} = 2m/s\\ \text{You finish}\)

I second CPhil's answer

It's correct.

The function isn't very well specified.  It's just fortunate that each expression produces the same value for 3.

This was a mistake so I just deleted the answer :/

∛ [ 4 (4)^4 (2)^5 ] +    [ 4 - (-5) ]

                                   _________ 

                                     (2 + -5)^2

∛  [ 4^5 * (2)^5]  +        9

                                  ______

                                   (-3)^2

4 (2) ∛ [ 4^2 * 2^2 ]  + 1

8 ∛[ 64] + 1

8 * 4 + 1

33

Sure can. Thx for your help.

sim shows 8/15 is correct.

Ok, it's not that big a deal.

You choose the first sock with probability 1 and the second unmatched sock with probability 4/5

For clarity let's say you chose (r,w) as the first pair.  We are left with (r,w,b,b)

For the third sock you can choose, either r or w, and be forced to choose b as the 4th, or

You can choose b, and then be forced to choose r or w as the 4th.  This is

2/4 x 2/3 + 2/4 x 2/3 = 2/3

I.e. there is a 2/3 probability you will choose a non-matching pair for the 3rd and 4th socks.

P[non-matching pair] = 4/5 x 2/3 = 8/15

Thanks g

x + x/4  = 13        multiply through by 4  to clear the fraction

4x + x = 52

5x = 52       divide both sides by  5

x = 52 / 5

An artist is using tiles and boards for a project. A tile has length one-half ft and width one-half ft. A board has length one-fourth yd and width one-fourth yd. What is the ratio of the length of the tile to the length of the board? What is the ratio of the area of the tile to the area of the board? The ratio of the length of the tile to the length of the board is???

We need to equate units ....we can do so in inches 

1/2 ft  = 6in

(1/4) yd = 9 in

Ratio of    length tile / length board = 6/9  = 2/3

Area of tile  = (6in)^2 = 36 in^2

Area of board = (9in)^2 = 81 in^2

Ratio of     tile area / board area  =  36 /81  =  4 / 9

(i - d)  = [ 3x^2 + 2 ] - [ 4x - 1 ]  =  [3x^2 - 4x + 3]

(i - d)(3) =  3(3)^3 - 4(3) + 3  =   27 - 12 + 3    =  18    means that

The rate at which the amount of liquid in the tank is changing at t = 3 hours is 18 gallons per hour

[At 3 hours.... It is entering at   3(3)^2 + 2  = 29 gallons/hr   and leaving at  4(3) - 1 = 11 gal/hr....so...the rate difference is 29 - 11  =  18 gal/hr ]

Thanks so much!

The second and third statements are false

f(x)  and g(x)  only intersect at one point = (2,0)

And  this a common x intercept

So....the last statement is true

Here's my best attempt

Assume that the only two integers are 1 and 3.......and.....the number of 3s is one more than the number of 1s 

So....

[3(n + 1) + 1(n) ]

______________     <   2.1

        2n + 1

4n + 3  <     4.2n + 2.1

.9  < .2n

9/2 < n

n = 5 

 1 1 1 1 1 3 3 3 3 3 3

We need 11 integers

0   isn't positive

[ 8(a) + b ] + 5[ a + b]  =  13a + 6b

13a + 6b  =  8b + a

12a = 2b

6a = b

a  cannot be an integer > 1   because this would make b at least 12....which is impossible in base 8

So...

a = 1        and b = 6

Proof

16₈  + 5 [ 1 + 6]   =  [  (1)*8  + 6]  + 5*7   =  [ 14 ] + 35  =  49

And

61₈   =  6(8) + 1   =  49

So

N  =  16₈

would it be 1.14???

-op

Sorry, didn't see that!.

I just put each of these equations into a graphing calculator and the two intersection points were at 2 and 3 if we're going for x values. 

n = 0.675675675....... x 814 = 550