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4 years ago

What is the solution of the equation when solved over the complex numbers?

Mathematics

2 answers:

olga55 [171]4 years ago

5 0

Answer:

x = 5.2 or x = -5.2

Step-by-step explanation:

lyudmila [28]4 years ago

5 0

Answer:

The solution to the quadratic equations are:

$x=3\sqrt{3}i,\:x=-3\sqrt{3}i$

Step-by-step explanation:

Consider the provided quadratic equation.

$x^2+27=0$

Subtract 27 from both sides.

$x^2+27-27=-27$

$x^2=-27$

$x=\pm \sqrt{-27}$

$x=\pm 3 \sqrt{3}i$ ∴i=√-1

Hence, the solution to the equation are:

$x=3\sqrt{3}i,\:x=-3\sqrt{3}i$

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Researchers collected a simple random sample of the times that 81 college students required to earn their bachelor's degrees. Th

riadik2000 [5.3K]

Answer:

$t=\frac{4.8-4.5}{\frac{2.2}{\sqrt{81}}}=1.227$

$p_v =P(t_{(80)}>1.227)=0.1117$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is higher than 4,5 years at 1% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=4.8$ represent the sample mean

$s=2.2$ represent the sample standard deviation

$n=81$ sample size

$\mu_o =4.5$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 4.5, the system of hypothesis would be:

Null hypothesis: $\mu \leq 4.5$

Alternative hypothesis: $\mu > 4.5$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{4.8-4.5}{\frac{2.2}{\sqrt{81}}}=1.227$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=81-1=80$