Answer:
∑ₙ₌₁⁸ (3n − 9)
Step-by-step explanation:
This is an arithmetic series where the first term is -6 and the common difference is 3. The nth term can be written as:
aₙ = a₁ + d (n − 1)
aₙ = -6 + 3 (n − 1)
There are 8 terms in this series, so the sum is:
∑ₙ₌₁⁸ [-6 + 3 (n − 1)]
Simplified:
∑ₙ₌₁⁸ (3n − 9)
Answer:
so we get as,
let, y = 2 - 9i
so the absolute value is |y|
so we get as,
|y| =
2-9i
so the absolute value is |y|
|y|=√
2 to the 2nd power plus 9 to the second power
so we get as,
|y|=
√81+4=√85
so the value is √85
Example:
|
−
2
−
i
|
=
√
5
Explanation:
Absolute value of a complex number a
+
i
b is written as |
a
+
i
b
| and its value as √a
2
+
b
2
.
Hence, absolute value of −
2
−
i is √
(
−
2
)
2
+
(
−
1
)
2
=
√
4
+
1
=
√
5
.
Step-by-step explanation:
rotation, then translation, then reflection
Answer:
P = 0.0008 (non rounded answer is 0.000771605)
Step-by-step explanation:
You first need to determine how many different ways you can roll a 7 using 2 dice. You options are...
First Die Second Die
1 6
2 5
3 4
4 3
5 2
6 1
There are six different ways to roll a 7. If you do the same for all possible numbers, you will see that there are 36 total options when rolling two dice. The first die has six options, and the second die also has 6 options. 6x6 = 36. (This is the fundamental counting principal you have have leared in statistics)
So the chances of rolling a 7 one time with two dice is 1/6. Since repeated rolling of dice is an independent event (any roll has no effect on the next roll), you multiply the probabilities of each event.
So the probability of rolling a 7 four times in a row is
(1/6)(1/6)(1/6)(1/6), which simplifies to 1/6^4, or 1/1296,
Probability is written in decimal form, and usually rounded to 4 decimal places.
1/1296 = 0.000771605, or 0.0008 rounded to 4 decimals
