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3 years ago

Which equation represents the graphed function?

Mathematics

1 answer:

andrew11 [14]3 years ago

7 0

Answer:

y = -⅓x + 3

Step-by-step explanation:

To find the equation of the graph in the form of y = mx + b (slope-intercept form), we have to find the slope (m) and the y-intercept (b) of the graph:

Slope (m) = change in y/change in x

Slope (m) using the two points on the line, (0, 3) and (3, 2):

m = (2 - 3)/(3 - 0) = -1/3

m = -⅓

y-intercept (b) = 3 (the y-axis is intercepted at this point)

✔️To write the equation, substitute m = -⅓ and b = 3 into y = mx + b:

Thus,

y = -⅓x + 3

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A professor wants to estimate the average time it takes his students to finish a computer project. Based on previous evidence, h

vova2212 [387]

Answer:

A sample size of 3 is required.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.96}{2} = 0.02$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.02 = 0.98$ , so Z = 2.054.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

Based on previous evidence, he believes that the standard deviation is approximately 3.6 hours.

This means that $\sigma = 3.6$

He would like to be 96% confident that his estimate is within 5 hours of the true population mean. Use RStudio to determine how large of a sample size is required without rounding any interim calculations.

The sample size needed is of n, and n is found when M = 5. So

$M = z\frac{\sigma}{\sqrt{n}}$

$5 = 2.054\frac{3.6}{\sqrt{n}}$

$5\sqrt{n} = 2.054*3.6$

$\sqrt{n} = \frac{2.054*3.6}{5}$

$(\sqrt{n})^2 = (\frac{2.054*3.6}{5})^2$

$n = 2.19$

Rounding up:

A sample size of 3 is required.

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3 years ago

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Elena L [17]

126
Explanation
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multiply 12 and -1
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