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2 years ago

Simplify i^41 (please help me)

Mathematics

2 answers:

ira [324]2 years ago

8 0

Answer:

Step-by-step explanation:

SOVA2 [1]2 years ago

8 0

Answer: Choice A) i

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Explanation:

Let's look at the pattern of powers of i

i^0 = 1
i^1 = i
i^2 = (sqrt(-1))^2 -1
i^3 = i*i^2 = i*(-1) = -i
i^4 = (i^2)^2 = (-1)^2 = 1

We loop back to 1, and the process starts all over again. The cycle is 4 units long. Ie, the pattern repeats every 4 terms.

What this means is that we can use remainders to quickly figure out something like i^41 without having to use a calculator or tons of paper.

Dividing 41/4 leads to a quotient of 10 and a remainder of 1. We only care about the remainder. The remainder 1 means i^41 = i^1 = i

Note how 41 and 1 lead to the same remainder when we divide by 4.

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. Following are the amounts measured in a

dlinn [17]

Answer:

The mean volume is 12 ounces.

Step-by-step explanation:

In this case we need to test whether the mean volume the machine fills the beverage cans with is 12 ounces or not.

The hypothesis for this test can be defined as:

H₀: The mean volume is 12 ounces. i.e. μ = 12 ounces.

Hₐ: The mean volume is not 12 ounces. i.e. μ ≠ 12 ounces.

As the population standard deviation is not known, we will use a t-test for single mean.

The sample mean and sample standard deviation is:

$\bar x=\frac{1}{n}\sum X\\=\frac{1}{8}\times [11.98+12.08+11.87+11.95+11.89+12.01+11.97+12.10]\\=11.98$

$\text{s} = \sqrt{\dfrac{\sum_{i=1}^{n}(x_i - \overline{x})^{2}}{n - 1}}\\=\sqrt{\dfrac{\sum_{i=1}^{n}(11.98 - 11.98)^{2}}{8 - 1}}+\sqrt{\dfrac{\sum_{i=1}^{n}(12.08- 11.98)^{2}}{8 - 1}}+...+\sqrt{\dfrac{\sum_{i=1}^{n}(12.10- 11.98)^{2}}{8 - 1}}\\=0.0815$ Compute the test statistic as follows: