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3 years ago

Use de moivre's theorem to write [2(cos 12 degrees + i sin 12 degrees)]^5 in standard form

Mathematics

1 answer:

Nuetrik [128]3 years ago

6 0

DeMoivre's theorem says

(2 (cos(12°) + i sin(12°)))⁵ = 2⁵ (cos(5×12°) + i sin(5×12°))

… = 32 (cos(60°) + i sin(60°))

… = 32 (1/2 + √3/2 i )

… = 16 + 16√3 i

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A demographer wants to measure life expectancy in countries 1 and 2. Let μ1 and μ2 denote the mean life expectancy in countries

Art [367]

Answer:

For this case we want to test if life expectancy in country 1 is more than 10 years lower than in country 2, (alternatibe hypothesis), so then the system of hypothesis are:

Null hypothesis: $\mu_1 \leq \mu_2 -10$

Alternative hypothesis: $\mu_1 > \mu_2 -10$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 \leq 10$

Alternative hypothesis: $\mu_1 - \mu_2 >10$

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Solution to the problem

For this case we want to test if life expectancy in country 1 is more than 10 years lower than in country 2, (alternatibe hypothesis), so then the system of hypothesis are:

Null hypothesis: $\mu_1 \leq \mu_2 -10$

Alternative hypothesis: $\mu_1 > \mu_2 -10$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 \leq 10$

Alternative hypothesis: $\mu_1 - \mu_2 >10$

7 0

3 years ago

The slope represents the ________ of a line.

Butoxors [25]

Answer:

Gradient

Step-by-step explanation:

The slope represents the gradient of a line

4 0

3 years ago

Which expression is equivalent to

fenix001 [56]

Answer:

$x {4}$

Step-by-step explanation:

easy math

6 0

3 years ago

Solve: negative 1 over 2x + 1 = −x + 8

marusya05 [52]

Equation: -1/2x + 1 = -x + 8

Work:

-x/2 + 1 = -x + 8

1 - x/2 = -x + 8

1 - x/2 = 8 - x

2 - x = 16 - 2x

-x = 16 - 2x - 2

-x = 2x + 14

-x + 2x = 14

x = 14

Final Answer:

x = 14

8 0

4 years ago

Please help me with questions 27 and 28

kondor19780726 [428]

Answer to Problem 27 is choice D) (x,y) --> (x+3, y-5)
Answer to Problem 28 is choice A) collinear

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Explanation for problem 27: Focus on point G. Notice how we shift it 4 units to the right and then 5 units down. So that's why the rule is (x,y) --> (x+3, y-5)

Explanation for problem 28: The term "collinear" means all points fall on the same line. Or put another way, its possible to draw a single straight line through all the points. The term "co" means "share" and "linear" means "line". So "collinear" translates to "sharing the same line". One axiom is that two points are always collinear no matter how you place them. Any more than 2, its not always guaranteed.

3 0

3 years ago