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Which simplifications of the powers of i are correct? There may be more than one correct answer.

fredd [130]

$\bf i^2=-1\qquad\qquad i^3=-i\qquad \qquad i^4=1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ i^{22}\implies i^{(4\cdot 5)+2}\implies i^{4\cdot 5}i^2\implies (i^4)^5 i^2\implies 1^5(-1)\implies -1~\dotfill \bigotimes \\\\\\ i^{11}\implies i^{(2\cdot 5)+1}\implies (i^2)^5 i\implies (-1)^5(i)\implies -i~\dotfill \checkmark$

$\bf i^{21}\implies i^{(4\cdot 5)+1}\implies (i^4)^5 i\implies 1^5(i)\implies i~\dotfill \checkmark \\\\\\ i^{12}\implies i^{3\cdot 4}\implies i^3 i^4\implies (-i)(1)\implies -i\dotfill \bigotimes \\\\\\ i^{20}\implies i^{4\cdot 5}\implies (i^4)^5\implies 1~\dotfill \checkmark \\\\\\ i^{26}\implies i^{(4\cdot 6)+2}\implies (i^4)^6 i^2\implies 1^6(-1)\implies -1\dotfill \checkmark \\\\\\ i^{27}\implies i^{(4\cdot 6)+3}\implies (i^4)^6 i^3 \implies 1^6(-i)\implies -i\dotfill \bigotimes$

6 0

3 years ago

Ill give u brainiest just tell me if i got any of those wrong!!! no links or i will report. ASAP

ololo11 [35]

Answer:

17 is what percent of 60? = 28.33.

what percent of 238 is 48 = 20.17

what percent of 365 is 40 = 10.96

Step-by-step explanation:

3 0

3 years ago

Sarah earns $10 per hour while babysitting and $20 per hour while cleaning houses. Sarah will need to earn $1000 during the summ

kozerog [31]

Why not just work for 50 hrs on house cleaning and get 1000$

4 0

3 years ago

Find the solution of the system of equations shown on the graph.

svlad2 [7]

Answer:

no solution

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

The 2 lines shown here are parallel and never intersect

Hence the system has no solution

8 0

4 years ago

survey on televisions requiring repairs within four years was conducted. Nineteen out of 200 televisions from company A and 25 o

Fudgin [204]

Answer:

$z=\frac{0.095-0.125}{\sqrt{0.11(1-0.11)(\frac{1}{200}+\frac{1}{200})}}=-0.959$

$p_v =P(Z$

Comparing the p value with the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to to FAIL to reject the null hypothesis, and we can't conclude that company A are more reliable than televisions from company B at 5% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=19$ represent the number of tvs who need a repair for A

$X_{2}=25$ represent the number of tvs who need a repair for B

$n_{1}=200$ sample 1 selected

$n_{2}=200$ sample 2 selected

$p_{1}=\frac{19}{200}=0.095$ represent the proportion estimated for the sample A

$p_{2}=\frac{25}{200}=0.125$ represent the proportion estimated for the sample B

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if company A are more reliable than televisions from company B (that means p1<p2) , the system of hypothesis would be:

Null hypothesis: $p_{1} \geq p_{2}$

Alternative hypothesis: $p_{1} < p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{19+25}{200+200}=0.11$

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.095-0.125}{\sqrt{0.11(1-0.11)(\frac{1}{200}+\frac{1}{200})}}=-0.959$

Statistical decision

Since is a left sided test the p value would be:

$p_v =P(Z$

Comparing the p value with the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to to FAIL to reject the null hypothesis, and we can't conclude that company A are more reliable than televisions from company B at 5% of significance.

4 0

3 years ago

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