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Where is your "figure below" ??!

Here is my attempt:
Each person gets: 9 / 3 =3 cards

 Person 1 draws their first card, then their second card and their 3rd card. Then, person 2 draws their first card, then their second card and their 3rd card. Finally, person 3 draws their first card, then their second card and their 3rd card. That gives us 9 separate draws, of which 3 are red. That means that there are  (9 C 3) ways for 3 red card to be drawn overall.

How many ways are there for every person to get a red card? The number of red cards is the same as the number of people, so each gets exactly 1 red card. For person 1, that could be their first card or their 2nd  or their 3rd . So there are 3 ways for person 1 to have 1 red card. That is true for person 2 and person 3 as well. 

Therefore, the number of ways for everyone to have a red card is: 3 * 3 * 3 =27

 Therefore, the probability is: 27 / (9 C 3)=27 / 84 =9 / 28

With 3 red cards, 3 yellow cards, and 3 blue cards, there are a total of 9 cards. Since each person is dealt the same number of cards, and the number of red cards is less than the total number of cards, the probability that everyone gets a red card is 1/3.

How much work have you done it? Can you show us?

Your answers are incorrect. Can you try again, please?

im sorry, but I made a mistake when writing the question, you answered the question which was unedited. May I plase get an answer to the new edited question?

Presumably by "outer circle" you mean a circumscribing circle that just touches the four corners of the square.

If the area of the square is 196 decimeters squared, then the side length is \(\sqrt{196}\) or 14 decimeters, which means the diagonal of the square is \(14\sqrt2\)decimeters, which means half the diagonal is \(7\sqrt2\) decimeters.  Since the radius of the circumscribing circle is equal to half the square diagonal, I'm sure you can work out the circle area from here.

Still don't know what method you're expected to use, so I'll just take you through the easiest, (leaving you to fill in the detail).

To begin with though ignore answers #2 and #4, both are incorrect.

#2 is from one of the sites dimwits and #4 is just simply incorrect, beginning with AC = 5, and then ignoring the point P, which is needed to determine the plane CPQ.

Basically, the method is 3D co-ordinate geometry, find the equation of the plane passing through C P and Q, substitute the two known co-ordinates of R, and out pops the third.

So, let A be the origin of the co-ordinate system with AD as the x-axis, AB the y-axis and AE the z-axis. You should then be able to write down the co-ordinates of the points P Q and C. (P will be (0, 2, 0) for example).

The equation of a plane in 3D can be written as ax + by + cz = 1. Substitute the co-ordinates of  P Q and C to determine the values of a b and c and then, having done that, substitute the two known co-ordinates of R. The third co-ordinate of R (the one that you need), drops out.

Post your answer if you wish.

If you like the method (and like to play with it), you could repeat it with different co-ordinate axes. For example, let B be the origin with BA BC and BF as the axes, the arithmetic will be different but you should arrive at the same result. Any of the cubes corners could be used as the origin of the co-ordinate system.

a) tan(alpha) = AB/BC, tan(beta) = BC/AC, and tan(beta + gamma) = (BC/AC)+(AC/AB) = (BC/AC)+(BC/BC) = (BC/AC) + 1.

b)tan(alpha+beta) = (AB/BC)+(BC/AC) = (AB/AC), tan(gamma) = AC/AB, tan(alpha+beta+gamma) = (AB/BC)+(BC/AC)+(AC/AB) = 1. Note that we used the fact that angle alpha,beta, and gamma are the angle opposite to the side length AC, BC, AB respectively and are in the triangle ABC.

So the answers are:

tan (alpha) = 7/3

tan (beta) = 2/5

tan (beta + gamma) = 1/2

tan (alpha + beta) = -8/3

tan (gamma) = 1/4

tan (alpha + beta + gamma) = -17/12

To find the length of DR, we can use the Pythagorean theorem. We know that the length of AC is 5 and the length of AQ is 1. Using the Pythagorean theorem, we can find that the length of CQ is 4. Now we know that CR is a right triangle, we can use the Pythagorean theorem again. We know that the length of CQ is 4 and the length of DR is unknown. Applying the Pythagorean theorem, DR = sqrt(5^2-4^2) = sqrt(9) = 3. so, DR = 3.

I'm sorry, both of your answers are incorrect. Can you provide a correct solution? Thanks!

CD/AB = 6.

Angle CBE is 18 degrees.

The answer is 7/10.

The smallest possible value of a is 245.

\(\theta = \dfrac{2 \pi }{3}\)

There are 443 possible paths.

The number of paths is 73.

The possible values of k are -16 and 20.

\((r_1, r_2, s_1, s_2) = (-3/5, 4/5, -24/25, 7/25)\)

\((t_1, t_2, u_1, u_2) = (144/145, -7/145, 9/41, -40/41)\)

Expand (sqrt(t) + 3t + 1)^3 + (sqrt(t) - 3t + 1)^3.

54 t^(5/2) + 2 t^(3/2) + 54 t^2 + 6 t + 6 sqrt(t) + 2