Question:
Choose an equivalent expression for 12^3 • 12^9 • 12^4 • 12^2
A. 12^4 B. 12^18 C. 12^35 D. 12^216
Answer:
Step-by-step explanation:
Given
Required
Determine the equivalent
Applying law of indices, we have:
Hence:
I assume you mean least. That would be 8.
Well, I don't know. Let's see . . . . .
First draw: One 'M' available out of 11 letters. Probability of picking it = 1/11.
2nd draw: Four 'I's available out of 10 letters. Probability of picking one = 4/10.
3rd draw: Four 'S's available out of 9 letters. Probability of picking one = 4/9.
4th draw: Three 'S's available out of 8 letters. Probability of picking one = 3/8.
5th draw: Three 'I's available out of 7 letters. Probability of picking one = 3/7.
6th draw: Two 'S's available out of 6 letters. Probability of picking one = 2/6.
7th draw: One 'S' available out of 5 letters. Probability of picking it = 1/5.
8th draw: Two 'I's available out of 4 letters. Probability of picking it = 2/4.
9th draw: Two 'P's available out of 3 letters. Probability of picking one = 2/3.
10th draw: One 'P' available out of 2 letters. Probability of picking it = 1/2.
11th draw: One letter left. It is an 'I'. Probability of picking it = 1 .
Probability of all of those draws in order =
(1/11) x (4/10) x (4/9) x (3/8) x (3/7) x (2/6) x (1/5) x (2/4) x (2/3) x (1/2) x (1) =
1,152 / 39,916,800 =
1 / 34,650 =
0.00002886 =
<em> 0.002886 percent</em> (rounded)
Not a good bet. (But better than the lottery.)
Answer:
720 employees
Step-by-step explanation:
Number of responded employees = 90% of 2000 employees = 1800 employees
Out of 1800 employees, if 60% answer yes, then the remaining 40% will answer "no". 72 employees did not respond to the survey.
Number of "no" answered employees = 40% of 1,800 employees = 720 employees( Answer)
Answer:
The solutions of the equation are -41.8° , 0.0° , 41.8°
Step-by-step explanation:
∵ 3 sin²Ф - 2 sinФ = 0 is a quadratic function
∵ The domain of the function is -90° ≤ Ф ≤ 90°
- Lets take sinФ as a common factor
∴ sinФ (3 sinФ - 2) = 0
- Two terms multiplied by each other = 0
∴ One of them must be equal zero
∴ sinФ = 0 or 3 sinФ - 2 = 0
- If sinФ = 0 ⇒ Ф = 0.0°
- If 3 sinФ - 2 = 0 ⇒ 3 sinФ = 2 ⇒ sin Ф = 2/3
∵ sinФ 2/3
∴ Ф = 41.8° ⇒ Ф ≤ 90° (in first quadrant)
∵ -90° ≤ Ф ≤ 90°
∴ Ф = -41.8° ⇒ Ф ≥ -90° (in fourth quadrant)
∴ The solutions of the equation are -41.8° , 0.0° , 41.8°
