What is the distance between the points (4,3) and (1,-1) on the coordinate plane

Mathematics

2 answers:

spayn [35]3 years ago

8 0

Answer:

5 units

Step-by-step explanation:

All that you have to do is use the pythagorean theorem. You can tell that the distance on the x-axis is 3 and on the y-axis is 4, just by subtracting (1,-1) from (4, 3). Then, square the sides, add them, and find the square root of the answer.

4x4 = 16

3x3 = 9

16 + 9 = 25

The square root of 25 is 5. Your answer is 5.

Mariulka [41]3 years ago

7 0

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

We have the points (4, 3) and (1, -1). Substitute:

$d=\sqrt{(1-4)^2+(-1-3)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5$

<h3>Answer: The distance between the points (4, 3) and (1, -1) is equal 5 units.</h3>

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Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee a

rusak2 [61]

Answer:

We would have to take a sample of 62 to achieve this result.

Step-by-step explanation:

Confidence level of 95%.

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

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

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.

Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.

This means that $\sigma = 2$

If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result?

We would need a sample of n.

n is found when $M = 0.5$ . So