All categories

3 years ago

Which of the following equations represents a linear function?

Mathematics

1 answer:

Sphinxa [80]3 years ago

4 0

Answer:

Following equations represents a linear function:

y = 6x

y = 4x - √2

x – 4y = 6

Step-by-step explanation:

We know that a linear function is of the form

where m is the rate of change or slope and b is the y-intercept.

Please note that y = mx+b represents a straight line because the degree of a linear function is always 1.

Now, let us check whether the given functions represent the linear functions or not.

Checking y = 6x

y = 6x

You might be interested in

A falling rock produces a force of 250 Newtons from acceleration due to gravity alone. What is the rock's mass in kilograms? Ent

OlgaM077 [116]

Answer:

Convert 250 Newtons into Kilograms

25.5

7 0

3 years ago

What sample size would be required to estimate the true proportion of American female business executives who prefer the title "

monitta

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.05}{2.326})^2}=2164.1104$

And rounded up we have that n=2165

Step-by-step explanation:

Previous concepts

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 means 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.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p$ represent the real population proportion of interest

$\hat p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 98% of confidence, our significance level would be given by $\alpha=1-0.98=0.02$ and $\alpha/2 =0.01$ . And the critical value would be given by:

$z_{\alpha/2}=-2.326, z_{1-\alpha/2}=2.326$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.025$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

(b)

We can assume that the estimated proportion is 0.5 since we don't have other info provided to assume a different value. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.05}{2.326})^2}=2164.1104$

And rounded up we have that n=2165

7 0

3 years ago

The angle e lies in Quadrant II. sin 0 = 3/4 What is cos O?

Vilka [71]

Answer:

-√7/4

Step-by-step explanation:

Mathematically;

Sine is the ratio of opposite to hypotenuse

So here, hypotenuse is 4

The opposite is 3

To get the adjacent, we use the Pythagoras’ theorem which states that the square of the hypotenuse is equal the sum of the squares of the two other sides

Let the adjacent be x

4^2 = 3^2 + x^2

x^2 = 16-9

x^2 = 7

x = √7

The cosine is the ratio of the adjacent to the hypotenuse

Since we want to consider quadrant II

Cosine is negative here;

So the answer for Cos will be;

Cos theta = -√7/4

4 0

3 years ago

Is -7,964,837 × -7 positive or negative?

Inessa05 [86]

When using both negative symbols, and then multiplying them, this would mean that the numbers would be going up.

A negative (x's) a negative equals a positive.

Your answer: positive.

6 0

3 years ago

Read 2 more answers

A. 8 B. 12 C. 16 D. 18

oksian1 [2.3K]

18
Love you have a good night r

4 0

3 years ago