For each value of kk specified in parts (a)–(e), plot the set of points in the plane that satisfy the equationx2 / k − y2 = 1.
a. k = −1
b. k = 1
c. k = 2
d. k = 4
e. k = 10
f. k = 25
g. Describe what happens to the graph of
x2 / k − y2 = 1 as k → [infinity].

Answer:

3031

Step-by-step explanation:

8.25 percent of 28000 is 231 add that to 2800 is 3031

Answer:

The probability that all four aces will be received by the same player is approximately 0.01.

Step-by-step explanation:

Of the 52 cards the four  aces can be selected in ways.

If any one of the players receives all the four aces then that player can be selected in ways.

Now for the selected player to receive all the four aces, the four ace cards must be placed among the 13 cards the player receives. This can be done in ways.

Then the total number of ways such that all the four aces is received by one player is .

Then the probability that all four aces will be received by the same player is:

Thus, the probability that all four aces will be received by the same player is approximately 0.01.

Final answer:

The probability that all four aces will be received by the same player in a game of 52 card deck distributed among four players is given by the formula P(E) = 4 * C(48, 9) / C(52, 13), derived through principles of combinatorics.

Explanation:

This is a probability problem that can be solved using combination and permutation principles in mathematics. Specifically, the subject involves combinatorics.

First, we note that each of the four players is dealt 13 cards from a 52 card deck. Hence, for a single player, the total number of ways 13 cards can be chosen from 52 is given by the combination formula C(n, r) = n! / [(n-r)!r!], where ! denotes factorial. In our case, n=52, and r=13.

The total number of ways to deal these 13 cards is thus C(52, 13).

Next, we need to consider the specific case where all four aces end up with one player. This means this player has 9 other cards that are not aces, from the remaining 48 cards (52 total cards - 4 aces). This can happen in C(48, 9) ways.

Therefore, the probability that a specific player gets all four aces is P(E) = C(48, 9) / C(52, 13).

To find the probability that any of the four players gets all four aces, we multiply this result by 4, because there are four players.

So, the final probability is P(E) = 4 * C(48, 9) / C(52, 13).

Learn more about Probability here:

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Answer:

Hi,

Step-by-step explanation:

Find the sum 1 +3+5+7+.........................+47+49.