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Thanks BJ  

Yes you could be right Alan.

 0 = - 9.81/2 t^2 + 2     subtract 2 from each side

-2 = - 9.81/2 t^2           multiply both sides by 2

-4 = -9.81t^2                divide both sides by -9.81

0.4077471967380224 = t^2    since this looks like a Physics formula where you want a positive result for t, take the positve root of each side 

0.638550856814100908  = t

You used 2 black tiles in every row, except in the center where there is just one.

So....there were 44 rows where 2 black tiles were present and 1 row where 1 was present.

This make 45 rows.   And since we have a square, there are the same number of "columns."

So  ... 45^2  - 89 = 1936 white tiles.......

Adam, Ben, Cathy and Dana share some lollies. First Adam takes 3/5 of the lollies, then Ben takes 1/4 of the remainder, and then Cath takes1/3 of what is left. Dana gets all the rest. What fraction of the original number of lollies does Dana get ???

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After Adam takes 3/5 of them there are 2/5 left

Ben takes 1/4 of these, so that means that there are (3/4)(2/5) left = 6/20 = 3/10 left

Cath takes 1/3 of these, so there are (2/3)(3/10) l= 2/10  left for Dana

Check

Adam gets 3/5 = 6/10

Ben gets (1/4)(2/5)  = 1/10

Cath  gets (1/3)(3/10)  = 1/10

Dana gets 2/10

And these all sum to 1

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I'm going to answer this question....but I'm assuming an even spacing of the points  {I actually don't know if this makes a difference, or not  !!!!!  }

When the number of points is even, it is quite complicated to determine the number of intersecting points.

When the number of points is odd.....number theory shows that no more than two diagonals ever intersect at any one point !!!.... and we have the following "formula" for the number of intersections when the number of points is odd:

C(n, 4)  where n is the number of odd points on the circle

For instance, when n = 5, we have  C(5,4) = 5

When n = 7, we have  C(7,4)  = 35

So, when n= 9,  we have C(9,4) =126 points of intersection

BTW......

With 6 points, there are 13 points of intersection

By the "formula," 6 points should give us 15 points of intersection, but note that 3 diagonals actually meet in the center....thus...two "pair-wise" intersections are "lost"

And with 8 points, there are 47 points of intersection .... (if I counted correctly  !!!)

The number of possible hands of drawing any 6 cards from 60 = C(60,6) = 50063860

And from these possibilities we want to draw  2 red cards from 15 and 4 blue cards from 45

So, this gives us

C(15.2) * C(45, 4) = 15644475

So

15644475 / 50063860   = anout 31.25%

BJ.....I'm not sure what is wanted here.....notice that

sin^2x sin^2x   =

sin^4x

Or....this could equal

(1-cos^2x)(1-cos^2x)  =

1 - 2cos^2x + cos^4x

Other forms are possible......but the first answer of sin^4x   seems the most simple......(???)

Take the decimal part of a degree and multiply is by 60 to turn that part into minutes.

Example 17.812°  =  17° + (.812 x 60)'    =  17° + 48.72'  =  17° 49'.

I'm stuck -- all I can get is sin⁴x

or sin²x(1 - cos²x)

... but that's it ...

To get red-red-blue-blue-blue-blue would be 15/60 x 14/59 x 45/58 x 44/57 x 43/56 x 42/55.

But this is not the only arrangement; there are actually 15 ways to end with two reds and four blues, so take the above answer times 15.

I don't have a textbook lol. I believe using the "m" and "b" might be the better choice.

Not quite. x is any value that you can substitue for x while y represents the answers that you get.

Sometimes, the slope is called 'm', so, in this case, m = 2/3.

The y-intercept may be called either 'b' or 'k' (depending upon your textbook, so b = -4.

Never mind, I got this one! Thanks again :)

We can count them all; let's first consider only those created by moving to the right and up.

We could end at these points (10,0), (9,1), (8,2), ..., (2,8), (1,9), and (0,10). These are 9 points in the first quadrant and 2 points on the axes.

In each quadrant, we get 9 points (for a total of 36 points) plus 4 more points for the axes. Total = 40 points.

Thanks but I'm a little confused. The answer is x = 2/3 and y= -4  ??

After you subtract 1 tile for the middle, the remaining 88 tiles will be split with 1/2 of them in one diagonal and the other 1/2 in the other diagonal. Thus, each diagonal has 45 tiles (with the one in the middle being in both diagonals).

If the diagonal has an odd number of tiles, the diagonal will have as many tiles as each side has. (Check this out with 3 x 3 and 5 x 5 squares to convince yourself.

Since each side has 45 tiles, the total number of tiles will be 45 x 45 = 2025 tiles.

Of these tiles, 89 are black, so 2025 - 89 = 1936 are white.

50 ÷ (3/7)  =  116.67

Answer:  116 glasses (plus a little extra in case you spill).

The original price minus 15% of that price is $12.00.

Let p represent the original price; then we get:  p - 0.15p  =  12.00

Simplify:                                                                       .85p  =  12.00

Divide by 0.85                                                                    p  =  $14.12

2x - 3y  =  12

Solve for y:  -3y  =  -2x + 12     --->     y  =  2/3 x - 4

The slope is the coefficient of the x-term (2/3) and the y-intercept is the constant (-4).

Press (2nd) then (atan) then enter the value ...

If you have 3 points on a circle and connect them in all possible ways, you will have no internal points of intersection.

If you have 4 points, then you get 1 internal point of intersection = ₄C₀.

If you have 5 points, then you get 5 internal points of intersection = ₅C₁.

If you have 6 points, then you get 15 internal points of intersection = ₆C₂.

If you have 7 points, then you get 35 internal points of intersection = ₇C₃.

Etc. 

Can you take it from here?

If you want a circle with the center at (0,0) and a radius of r, use:  x² + y² = r².

For instance, a cricle with its center at the origin and a radius of 5:  x² + y² = 5²  or  x² + y² = 25.

If you don't want the center at (0,0) then use the formula (x - h)² + (y - k)² = r²  where the center is (h, k).

For instance, a circle with its center at (4, -3) and radius = 7:  (x - 4)² + (y - -3)² = 7² or:

(x - 4)² + (y + 3)² = 49.

You can use the definite integral to find the volume of a solid with specific cross sections on an interval, provided you know a formula for the region determined by each cross section. If the cross sections generated are perpendicular to the x‐axis, then their areas will be functions of x, denoted by A(x). The volume ( V) of the solid on the interval [ a, b] is