All categories

2 years ago

Simplify i^38 ????????

Mathematics

1 answer:

stich3 [128]2 years ago

4 0

Answer:

i is defined as the square root of -1.

i^2 = -1

i^3 = -i

i^4 = 1

Following the pattern, we see that i^40 = 1, so i^38 is two above, or equal to -1.

So, i^38 = -1.

Let me know if this helps!

You might be interested in

February 12, 2009 marked the 200th anniversary of Charles Darwin's birth. To celebrate, Gallup, a national polling organization,

timurjin [86]

Answer:

$Z_{H0}$ = 2.83

Reject H₀

Step-by-step explanation:

Hello!

The objective of the poll is to compare the proportions of people who believe in the theory of evolution. For this, the investigator took a sample of 1018 and divided it into two groups using a criteria their level in college education.

Group 1 (people with some college education)

n₁= 325

x₁= 133

sample proportion ^ρ₁=x₁/n₁ = 133/325 = 0.409

Group 2 (college graduates)

n₂= 228

x₂= 121

sample proportion ^ρ₂=x₂/n₂ = 121/228 = 0.531

pooled proportion ^ρ= 0.459

The statistic test that corresponds to test if the proportions are equal or different is the difference of population proportions and you have to use the normal approximation for the proportions to calculate it.

The hypothesis is:

H₀: ρ₂=ρ₁

H₁: ρ₂≠ρ₁

α: 0.10

Z= (^ρ₂ - ^ρ₁) - (ρ₂ - ρ₁) ≈ N (0;1)

√(^ρ(1 - ^ρ)*(1/n₂+1/n₁)

The critical region is two-tailed, so you have a lower critrical value and an upper critical value:

$Z_{\alpha /2} = Z_{0.05} = -1.64$

$Z_{1-\alpha /2} = Z_{0.95} = 1.64$

If $Z_{H0}$ ≤ -1.64 or if $Z_{H0}$ ≥ 1.64 you reject the null hypothesis.

If -1.64 < $Z_{H0}$ < 1.64, the you do not reject the null hypothesis.

Z= (^ρ₂ - ^ρ₁) - (ρ₂ - ρ₁) = (0.531 - 0.409) - 0 = 2.83

√(^ρ(1 - ^ρ)*(1/n₂+1/n₁) √(0.459(1 - 0.459)*(1/228+1/325)

$Z_{H0}$ = 2.83

Since the calculated Z value is greater than the upper critical value, the decision is to reject the null hypothesis. In other words, there is significative enough evidence to say that there is a difference between the population proportion of people who believe in the evolution theory and graduated from college and the population proportion of people who believe in the evolution theory and have some college education.

I hope it helps!

5 0

3 years ago

Find m∠H. Put the answer below. m∠H =

Pavlova-9 [17]

Answer:

30°

Step-by-step explanation:

$\tan (m\angle H) = \frac{IJ}{JH} \\ \\ \implies \: \tan (m\angle H) = \frac{ \sqrt{10} }{ \sqrt{30} } \\ \\\implies \: \tan (m\angle H) = \frac{{1} }{ \sqrt{3} } \\ \\ \implies \: \tan (m\angle H) = \tan 30 \degree \\ \\ \implies \: m\angle H = \boxed{30} \degree$

6 0

2 years ago

Solve for Y -5y + 8 = -3y + 10?

lakkis [162]

Answer:

y=-1

Step-by-step explanation:

-5y+8=-3y+10

-5y-(-3y)+8=10

-5y+3y=10-8

-2y=2

y=2/-2

y=-1

7 0

3 years ago

SOLVE: 18x+103x-3x ill give brainliest

JulijaS [17]

Answer:

118x

Step-by-step explanation: hopes this helps

4 0

3 years ago

Could I solve this inequality by completing the square? How would I do so?

sammy [17]

Answer:

$\large\boxed{x>-2+\sqrt{14}\ \vee\ x$

Step-by-step explanation:

$x^2+4x>10\\\\x^2+2(x)(2)>10\qquad\text{add}\ 2^2=4\ \text{to both sides}\\\\x^2+2(x)(2)+2^2>10+4\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+2)^2>14\Rightarrow x+2>\sqrt{14}\ \vee\ x+2-2+\sqrt{14}\ \vee\ x$

8 0

3 years ago