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3 years ago

Determine which expressions represent real numbers and which expressions represent complex numbers.

1 answer:

6 0

There seems to be a mistake in typing. You probably type the letter "i" as "1", so it is difficult to tell which numbers are complex numbers.

I will however explain what complex numbers look like, which will help you in determining which numbers are complex numbers, and the rest are real numbers.

Step-by-step explanation:

Complex numbers are numbers that include the square root of a negative number.

It is not possible to have a value for an expression with a square root of a negative number, then the letter j or i were introduced to help represent these kinds numbers.

√-1 = i or j (anyone is fine)

Knowing the square root of -1 is i, we can write the square root of any negative number with ease.

√(-6) = √(-1) × √6, right?

= i × √6

= i√6

And so on.

So, basically, the numbers that include the letter 'i', or √(-1) in them are the complex numbers. The rest are real numbers.

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There are 9 squares and 6 circles. What is the simplest ratio of circles to squares?

castortr0y [4]

Answer:

2:3, 2 to 3

Step-by-step explanation:

9 and 6 are both factors of three, so you have to reduce. 3 goes into 9 tree times, and 3 goes into 6 twice. Since it is circles to squares, the 2 comes first then 3.

Hope this helps!

6 0

2 years ago

3y- 3x + 3 =15 solve for y.

melisa1 [442]

Answer:

y=x+4 this should be the answer

6 0

3 years ago

What are he square roots of 36/100?

tiny-mole [99]

The square root of 36/100 is c. -6/10 and 6/10
You can get this by using a calculator.
@[email protected]

4 0

3 years ago

A random sample of 100 teletype operators indicates that their salaries fluctuate quite a bit. The sample Standard deviation of

ELEN [110]

Answer:

$\frac{(99)(10)^2}{123.225} \leq \sigma^2 \leq \frac{(99)(10)^2}{77.046}$

$80.341 \leq \sigma^2 \leq 128.495$

Now we just take square root on both sides of the interval and we got:

$8.963 \leq \sigma \leq 11.336$

Step-by-step explanation:

Data given and notation

s=10 represent the sample standard deviation

$\bar x$ represent the sample mean

n=100 the sample size

Confidence=90% or 0.90

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=100-1=99$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical values.