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3 years ago

Find Values of X and Y for No. 19

Mathematics

1 answer:

Crazy boy [7]3 years ago

4 0

So you need to find y in terms of x. But later, since the 12x and -12x cancel each other out. X can be any real number. And y. Depends on what real number x is.

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The complex numbers corresponding to the endpoints of one diagonal of a square drawn on a complex plane are 1 + 2i and -2 – i.Wh

Musya8 [376]

On the complex plane, the number $a+bi$ is mapped onto the point with coordinates $(a,b)$ .

In other words, the x coordinate is the real part of the number, while the y coordinate is the complex part of the number.

Viceversa, if you start from a point $(x,y)$ , you can identify the number $x + iy$ .

So, the endpoints of the diagonal are the points $(1,2)$ and $(-2,-1)$ . These are points A and C in the attached figure.

This means that points B and D have coordinates

$B = (-2,2),\quad D = (1,-1)$

So, the correspondant complex numbers are

$B = (-2,2)\mapsto -2+2i,\quad D = (1,-1)\mapsto 1-i$

6 0

3 years ago

What would be the measure of the exterior angle for each<br> vertex of an equilateral triangle?

Mars2501 [29]

Step-by-step explanation:

The exterior angles of an equilateral triangle will always have a measure of 120°.

3 0

3 years ago

What is 7 / 2/3 in simplest form

galina1969 [7]

To do this we have to do 7 divided by 2/3

The first step to dividing fractions is to turn it into a mutipuacation sentence

7x2/3

Now we want to flip the second fraction over or make it a reciprocal

Our new equation is

7x 3/2 which is equal to 21/2

There are two ways. You may simplify it to 10 1/2 or just leave it as it is

hope this helped!! If you have questions, feel free to ask

4 0

2 years ago

A right cylinder has a radius of 3 and a height of 12. what is its surface area?

tester [92]

The surface area is 90pi

8 0

3 years ago

Read 2 more answers

Dr. Pagels is a mammalogist who studies meadow and common voles. He frequently traps the moles and has noticed what appears to b

Alina [70]

Answer:

Null hypothesis = H₀ = There food preferences among vole species are independent of one another.

Alternate hypothesis = H₁ = There is a relationship between voles and food preference.

Expected meadow vole/apple slices = 29.983051

Expected common vole/apple slices = 28.016949

Expected meadow vole/peanut butter-oatmeal = 31.016949

Expected common vole/peanut butter-oatmeal = 28.983051

Chi-square value = χ² = 2.154239

Degree of freedom = 1

Critical value = 3.841

χ² < Critical value

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.

Step-by-step explanation:

He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices.

So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.

Null hypothesis = H₀ = There food preferences among vole species are independent of one another.

Alternate hypothesis = H₁ = There is a relationship between voles and food preference.

Data collected by Dr. Pagels:

meadow voles common voles Row Total

apple slices 26 32 58

peanut butter-oatmeal 35 25 60

Column Total 61 57 118

Where 118 is the grand total.

The expected number is given by

Expected = (row total)×(column total)/grand total

Expected meadow vole/apple slices = 58×61/118

Expected meadow vole/apple slices = 29.983051

Expected common vole/apple slices = 58×57/118

Expected common vole/apple slices = 28.016949

Expected meadow vole/peanut butter-oatmeal = 60×61/118

Expected meadow vole/peanut butter-oatmeal = 31.016949

Expected common vole/peanut butter-oatmeal = 60×57/118

Expected common vole/peanut butter-oatmeal = 28.983051

The chi-square statistic value is given by

χ² = Σ(Observed - Expected)²/Expected

χ² = (26 - 29.983051)²/29.983051 + (32 - 28.016949)²/28.016949 + (35 - 31.016949)²/31.016949 + (25 - 28.983051)²/28.983051

χ² = 2.154239

The degrees of freedom is given by

DoF = (row - 1)×(col - 1)

For the given case, we have 2 rows and 2 columns

DoF = (2 - 1)×(2 - 1)

DoF = 1

The given level of significance = 0.05

The critical value from the chi-square table at α = 0.05 and DoF = 1 is found to be

Critical value = 3.841

Conclusion:

Reject H₀ If χ² > Critical value

We reject the Null hypothesis If the calculated chi-square value is more than the critical value.

For the given case,

χ² < Critical value

We failed to reject H₀

We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.

8 0

3 years ago