All Answers 358524 Answers

EF is the hypoteneuse and we're trying to find the side adjacent to angle E, i.e., DE

So, we can use the cosine for this....we have

cos(68) = DE/11   mutiply both sides by 11

11* cos (68) = DE = about 4.12

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The second one is just like the first...we know the hypoteneuse XY and we're trying to find the adjacnt side to angle Y, i.e., ZY

So we have

cos (15) = ZY / 14

14 * cos (15) = ZY = about  13.52

Thanks for those kind words......I'll recommend that Melody use your answer in her "Daily Wrap"....

Ln uses base "e" ≈ 2.718 .......this number occurs naturally in many "growth" and "decay" situations

Log uses 10 as the base

Thank You CPhill. I have learned a lot from you, Melody and Alan!

I didn't run the numbers 7UP, but it looks good....well done !!!

If the diameter of the photo is 18, then the radius  = 9

And the area of the circle is

A = pi * r^2   =  pi * (9)^2  = 81* pi

And the area of the frame is just (20)^2 = 400

So, the ratio of the area of the photo to the area of the frame is just .... [ 81 * pi ] : 400

sin^2(0) = sin(0) * sin(0) = 0 * 0 = 0

ncr(20,5)= 15504 ----Total number of ways to select 5 of twenty.

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A.) Solution for at least 4 women

ncr(11,5)*ncr(9,0) = 462 Number of ways to select 5 of 11 females and select 0 of 9 males

ncr(11,4)*ncr(9,1) = 2970 Number of ways to select 4 of 11 females and select 1 of 9 males

Sum of combinations total = 3432. So there are 3432 ways to select this group of 5 where 4 or more are women.

(3432/15504 = 22.1%) Incidental probability of this occurring.

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B.) Solution for no more than 2 men.

ncr(11,5)*ncr(9,0)= 462 Number of ways to select 5 of 11 females and select 0 of 9 males.

ncr(11,4)*ncr(9,1) = 2970 Number of ways to select 4 of 11 females and select 1 of 9 males.

ncr(11,3)*ncr(9,2) = 5940 Number of ways to select 3 of 11 females and select 2 of 9 males.

Sum of combinations total = 9372. So there are 9372 ways to select this group of 5 where 2 or less are men.

(9372/15504 = 60.4%) Incidental probability of this occurring.

I doubled checked this, but Melody, CPhill, or Alan should verify the answers. 

PS This assumes males are men and females are women. My dad says it is not easy to tell any more. So far, I don’t seem to have a problem. LOL

~7UP~

The general form is

y = a ( x -  h)^2 + k     where (h, k) is the vertex  and (x, y) is the y intercept

Since we know the y intercept is a point (0, b), we can plug this into the "formula" to find "a"

Example......suppose we have a parabola whose vertex lies at (2, -2) with a y intercept of (0, 0)

Then we have

0 = a (0 - 2)^2  - 2   add 2 to both sides

2 = a(-2)^2

2 = a(4)    divide both sides by 4

2/4 = 1/2 = a

So...our equation is  y = (1/2)(x - h)^2 + k  =  

y = (1/2)(x - 2)^2 - 2

The arc length, S, is given by

S = rΘ  where Θ is in radian measure

An alternative formula is

S = (Θ / 360) * 2 * pi * r    where Θ is in degrees

Using the Pythagorean Theorem, we have

Hypoteneuse = √[(6.1)^2 + (9.3)^2 ] = √123.7 = about 11.12 units

(-8 - 4 / -6 - -2) =

-12 / (-6 + 2) =

-12 / -4  =  3

This function will be undefined wherever the denominator = 0

So, setting (r - 1)^2 + (r + 1)^2 = 0  (and expanding)  we have

r^2 - 2r + 1 + r^2 + 2r + 1 = 0

2r^2 + 2 = 0     divide through by 2

r^2 + 1 = 0

And this never = 0

So this is defined everywhere, i.e., ( -∞, ∞ )

Area of photo divided by the area of the frame. Be sure to use the same area unit in both areas.

Good luck!

333333333!

You follow the formula:

(θ/360) x πr^2

So, data divided by 360 times pi x radius squared.

Sorry I meant -27

First, distribute the -2. So -6a-24-3. Combine like terms. -6a-47. That is your answer

The answer is 

-6a-27

CPhill you helped me before. Is the answer 1 1/3 or is there more to it? Thank you

nevermind, I got it. Thank you CPhill!

0,272727

I assume you'd like to write this as a fraction

Ignoring the decimal, write the repeating part (27) over a denominator that has the same number of 9's as the number of digits in the repeating part . In this case, we have two repeating digits, so we will have two 9's. Thus, we have....

27 / 99

Check for yourself that this is .272727.......

I assume we have....

x^2+px+qx+pq     ....if so.....

x(x + p) + q(x + p) =    (factor out the common factor x + p )

(x + p)(x + q)

I should have said Reinout, it is really good to see you on the forum.  :))

Reinout, can the constant be negative.

I know it is not here but it can be can't it?

Also why can't m=g=-60 ?