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3 years ago

Select all that apply.

Mathematics

1 answer:

Lelechka [254]3 years ago

8 0

Answer: The second option and the third option are true.

Step-by-step explanation:

The formula of the line in slope-intercept form is:

$y=mx+b$

Where m is the slope and b is the y-intercept.

By definition, the y-intercept in a direct variation is 0.

Therefore, substituting $m=-3$ and $b=0$ into the equation, you obtain:

$y=-3x+0$

Then, the equation is:

$y=-3x$

As this is a line, it is a linear function.

Therefore, the second option and the third option are true.

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If y varies inversely with 2.5x, and y=5.6 and x=30, write an equation to represent this relationship

klasskru [66]

Let the constant of variation be c.
We are given that y varies inversely with 2.5x, this means that:
y = (c) / (2.5x)
This can be written as:
2.5xy = c

Now, we a re given that y = 5.6 at x = 30.
Substitute with these values in the equation to get the value of c as follows:
2.5xy = c
2.5(30)(5.6) = c
c = 420

Therefore, the equation that describes the relation is:
2.5xy = 420

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What is the least common denominator of the fractions 2/3, 1/4, 1/8 and ?

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A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selec

VMariaS [17]

Answer:

$19.1-3.355\frac{1.5}{\sqrt{9}}=17.42$

$19.1+3.355\frac{1.5}{\sqrt{9}}=20.78$

And the best option would be:

C. [17.42,20.78]

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".

$\bar X=19.1$ represent the sample mean

$\mu$ population mean (variable of interest)

s=1.5 represent the sample standard deviation

n=9 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=9-1=8$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,8)".And we see that $t_{\alpha/2}=$