Answer:
1430
Step-by-step explanation:
Given that a standard deck of cards is 52 cards, we have 13 Diamonds and we need 4 diamonds.
Hence, we have 13C4.
Also, we have 4 kings in a standard deck of cards, and in which we have 2 black kings but we need 1 king.
Hence we have a 2C1
Therefore:
13C4 * 2C1
=> 13! ÷ [4! (13 - 4)!] * 2! ÷ [1! (2-1)!]
=> 13! ÷ [4! (9)!]
=> (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13) ÷ [(1 x 2 x 3 x 4) (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9)]
=> (10 x 11 x 12 x 13) ÷ 24
=> (17160 ÷ 24) * (24 ÷ 6)
=> 715
2! ÷ [1! (2-1)!]
=> 2
Hence, we have 715 * 2
=> 1430
Hence, in this case, the correct answer to the question is 1430
Answer:
Step-by-step explanation:
Since the sequence is geometric (it multiplies the previous number each time). The nth term sequence would be 
Because the sequence multiplies by 3 each time, The base number in that equation would be 
.
So 
of the equation would be:
.
Compare the 2 equations:
4, 12, 36
3, 9 ,27
The difference between the 2 equations is: 1, 3, 9 which itself is a geometric sequence so the nth term of this new equation is: 
.
Combine these 2 equations together and you get:
.
Answer: x = {-1, -3, 2}
<u>Step-by-step explanation:</u>
x³ + 2x² - 5x - 6 = 0
Use the rational root theorem to find the possible roots: ±1, ±2, ±3, ±6
Use Long division, Synthetic division, or plug them into the equation to see which root(s) work <em>(result in a remainder of zero)</em>.
I will use Synthetic division. Let's try x = 1
1 | 1 2 -5 -6
|<u> ↓ 1 3 -2 </u>
1 3 -2 -8 ← remainder ≠ 0 so x = 1 is NOT a root
Let's try x = -1
- 1 | 1 2 -5 -6
|<u> ↓ -1 -1 6 </u>
1 1 -6 0 ← remainder = 0 so x = -1 is a root!
The coefficients of the reduced polynomial are: 1, 1, -6 --> x² + x - 6
Factor: x² + x - 6
(x + 3)(x - 2)
Set those factors equal to zero to solve for x:
x + 3 = 0 --> x = -3
x - 2 = 0 --> x = 2
Using Synthetic Division and Factoring the reduced polynomial, we found
x = -1, -3, and 2
