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well, thank you for the help! :)

Area of base x  height  =

(15cm^2)  x   (10 cm)  =    150cm^3

14 < 3n ≤ 21        divde through by 3

14/3 < n  ≤  7

The  next largest  integer  after  14/3   is 5

So.....the  integer solutions for n   are   5, 6 and 7

150 cm cubed

around 2925 i guess

only5 and 6

Look at the graph here :  https://www.desmos.com/calculator/ol0uvzvw4p

When x is an   integer....the result   =  0

When x is not an integer.....the result  is  =  -1

So....only two possible values ...  0  and - 1

They represent  a "floor" function

This means the  largest integer  less than or equal to a given number

Ex :

Floor  (2)  = 2

Floor (2.5)  = 2

Floor (2.9999)  = 2

Floor (0)   = 0

Floor (- 0.5)  = -1

Floor (-1)  = -1

Floor (-1.5)  = -2

And so on....

i dont get it, 15/25 is 0.6 but you wantto put in a calculator 15/25=0.6?

Question! What do those "L" symbols around the \(x\)s mean? Are they like absolute value symbols?

\(WY\) is simply double of \(AY\), so that's \(2 \cdot 14 = 28\) :D

We know that the sum of the angles in a quadrilateral (like a rhombus) is \(360^{\circ}\), and opposite angles are equivalent.

So, \(m\angle WXY = m\angle WZY\), and \(m\angle ZWX = m\angle ZYX\). 

We can use the pythagorean theorem to find \(XY\), because we know that \(XA = \frac{22}{2} = 11\) and \(AY = 14\). That will also be the length of \(WZ\). 

So, what will the measures of the angles be? :D

This seems difficult.......!!!

Let's see if we can find a pattern.....

floor [sqrt (1) ]  to floor [ sqrt (3)]  have the same result  = 1  ⇒ 3 occurences

floor [sqrt (4) ] to floor [ sqrt (8)] have the same result = 2  ⇒ 5 occurences

floor [ sqrt (9)] to floor [ sqrt (15)] have the same result = 3  ⇒ 7 occurences

floor  [ sqrt (16) to floor [sqrt (24)]  have the same result = 4 ⇒ 9 occurences

floor [sqrt (25)] to floor [sqrt (35)] have the same result = 5 ⇒ 11 occurences

So...it appears  that    2(result)  + 1  =  the number of occurences

And we need 137 occurences

So  we  need to solve this:

2 (result)  + 1  = 137      subtract 1 from both sides

2 (result) = 136      divide both sides by 2

result  = 68

But we need to square this to find   the first   "n"  = 68^2  = 4624

And  the last "n"  =  4624 + 136  = 4760

Check

floor [ sqrt (4623)]  = 67

floor [ sqrt (6084)]  = 68

floor [sqrt (4760)]  = 68

floor [ sqrt (4761)]  =  69

So  m   =  68

Thank you! it really helped

Pythagorean Theorem Time! \(a^2 + b^2 = c^2\) (a = length of one leg, b = length of second leg, c = hypotenuse length)

\(4^2 + 6^2 = c^2\)

\(16 + 36 = c^2\)

\(52 = c^2\)

\(c = \sqrt{52} = \fbox{$2\sqrt{13}$}\) is the slant height (the hypotenuse) :D

3x + 2 < 8

       -2   -2   subtract both sides by 2

= 3x < 6

3x/3 < 6/3    divide both sides by 3

= x < 2

Isolating the variable: 3x < 6

Divide by 3: x < 2 :D

The probability  =

1 -  the probability that Colin is not chosen at all  =

1 - P(that Colin isn't chosen the first time) *P(that Colin isn't chosen the second time)  =

1 - (9/10)(8/10)  =

1 -  72/100  =

1 - .72  =

.28

Great job showing your steps! Keep it up CentsLord!!!

Haha I know right! LOL!!!

THX, guys....

At least LuckyDucky and I got the same answer   >>>>LOL!!!!!

Note SpongeBob that

floor  [ sqrt (1)] , floor [ sqrt (2)], floor [sqrt(3)]  all = 1

And

floor  [ sqrt (4)]  through floor  [sqrt (8)]  =  2

And

floor [sqrt (9)] through floor [ sqrt (15)]  = 3

And floor [ sqrt (16) )]  = 4

So.....the sum is

3(1)  + 5(2)  + 7(3)  + 4  =

3 + 10 + 21  + 4  =

38

Thanks! in this solution I tried to put as many steps as possible so the guest can learn how to do it!

Cool! A perfect explanation for souls hoping to learn!