CPhill

Re: randomly choosing 1 of 6 R's from a bag of 100 letter tiles

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(6C1) / (100C1) = 6 / 100  = 6%

why is cos(90)=0? (degrees)

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Think about this.....on a unit circle, the "x" value at pi/2 (90 degrees)  = 0 and the value of "r" always = 1.

Since the cos(θ) = x / r      then cos(90) = 0 / 1   =  0

Also, look at the cosine graph......notice at pi/2 that the curve crosses the x axis at that point, i.e., the value of the cosine at that point = 0

Thanks, Bertie.....I see where I made my error  (being in too much of a hurry!!)

Let's take it from here.....

log (10)(a^b) = log a^x       by a property of logs, we have

log 10 + log a^b = log a^x   and we have, using another log property

1 + (b) log a = (x) log (a)    

(b) log (a) = [ (x) log (a) - 1]     divide both sides by log (a)

b = [x - (1 / log (a)) ]    ≠   x/10

Thanks again, Bertie, for your sharp eyes!!!....I forgot that the "b" exponent wasn't being applied to the "10" (I hope I got it right this time !!!)    

what points would (2,3),(4,6) and (6,3) be after a rotation of 90 degrees counter clockwise

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The coordinates "reverse" and the "x" becomes "negative"...i.e..... (2,3) ⇔ (-3,2)

if sadia picked 2/5 of a basket of berries, Tashi picked 1/3 of a basket, shafma picked 4/7 of a basket and marzuk picked 4/5 of a basket do all of their berries fit into 2 baskets?

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OK......if we add all the fractions and we get a number less than "2" they will

Start by adding the 4/5 and the 2/5 = 6/5

To this add 1/3    so we have

6/5 + 1/3   and getting a common denominator, we have

18/15 + 5/15 = 23/15

To this add the remaining 4/7

So we have

23/15 + 4/7      and getting a common denominator, we have

161/105 +  60/105 =   221/105 = 2.1

So the berries won't all fit into 2 baskets  

Thanks, kitty <3 !!!

Here's another way to do this....it's a "trick" I used to use when I tutored...

Take the points and "reverse" them.....we have (2, -1) and (3, 3)

Line them up like this and draw a line under them

(2 , -1)

(3 ,   3)

______      Now just "subtract" the "underneath" things from the things "overhead" - individually - like this

(2 , -1)

(-3 ,  - 3)

________

-1  ,  -4

Now.......put the thing in the first column "over" the thing in the second column   (-1) / (-4)  = 1 / 4 and Voila!!.......there's the "slope" 

what is the slope of the line that contains the points (-1,2) and (3,3)

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Slope is defined as  ⇒  "Change in y"  /   "Change in x" 

Here's a "non-technical" way to figure this....

How much did  "y" change by from the  first point to the second ???.....Answer... (+1) ....it increased from 1 to 2

How much did "x" change by from the first point to the second ???.....Answer... (+4).....it increased from -1 to 3

Therefore ..... Change in y"  /   "Change in x"   ⇒  (+1) / (+4)  = 1 / 4   ....and that's the "slope"

If either "x" or "y" had decreased (but not both), our slope would have been negative....

how do i find the inverse matrix?

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Describing how to do this by hand is a lengthy process that can sometimes be very "messy"........

Here's a website that covers it.......

Renaldo is making purple paint using red and blue paint. The ratio of red paint to blue paint is 5 to 4. If Reynaldo has 6 quarts of blue paint, how much red paint does he need?

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Let's set this up as a ratio......

5 /4 = (quarts of red paint) / (quarts of blue paint)       so we have

5 / 4  = x / 6          where "x" is the number of quarts of red paint we're looking for

Cross-multiplying, we have

30 = 4x         divide both sides by 4

x = 7.5

-z+2z-7=0

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OK......first, let's  multiply both sides by (-1) just to make everything look "nicer"   we have

1z - 2z + 7 = 0

The quadratic formula is given by

And, in our equation b = -2  a = 1 and c = 7

So we have

x = (-(-2) ± SQRT[(-2)² - (4)(1)(7)] ) / [2(1)]  = 

[ 2 ± SQRT [4 -(28)] ]/ 2 =

[ 2 ± SQRT ( -24 ) ] / 2

Since the SQRT (-24) is not a real number, we don't have any real solutions..........

Here's a website that also might help you......

http://www.mathsisfun.com/algebra/quadratic-equation.html