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3 years ago

Find the Distance between the points (-6,5)and(8, -3)

Mathematics

1 answer:

marusya05 [52]3 years ago

7 0

Answer:

$d=16.1245$

Step-by-step explanation:

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

Simply plug in your 2 coordinates into the formula to find distance d:

$d=\sqrt{(8-(-6))^2+(-3-5)^2}$

$d=\sqrt{(8+6)^2+(-8)^2}$

$d=\sqrt{(14)^2+64}$

$d=\sqrt{196+64}$

$d=\sqrt{260}$

$d=16.1245$

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In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour

Lesechka [4]

Answer:

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

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".

$\bar X=54$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=21$ represent the sample standard deviation

n=16 represent the sample size

Solution to the problem

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

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

Since the Confidence is 0.90 or 90%, the value of $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

Now we have everything in order to replace into formula (1):

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

4 0

3 years ago

Please help me with questions 21 and 22

valentina_108 [34]

I’m not sure abt 21 but 22 is the second one and the 4th one. So 2,4.

3 0

3 years ago

According to a recent study, the average woman's leg hair grows an eighth of an inch per month. A new drug company believes that

Afina-wow [57]

Answer:

Step-by-step explanation:

Null hypothesis should be: The average woman's leg hair grows an eighth of an inch per month: u = eighth of an inch

Alternative hypothesis: The average woman's leg hair growth is not an eighth of an inch per month after treatment: u ≠ eighth of an inch

This test after carrying out its treatment will be able to determine if the drug was effective or not

5 0

3 years ago

Logan is going to invest in an account paying an interest rate of 3.1% compounded continuously. How much would Logan need to inv

skad [1K]

Answer:

yessir

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

PLEASE HELP ME

balandron [24]

Answer:

The sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis.

Explanation:

By inspection (watching the figure), you can tell that to transform the triangle XY onto triangle X"Y"Z", you must slide the former 5 units to the left, 1 unit down, and, finally, reflect it across the x-axys.

You can check that analitically

Departing from the triangle: XYZ

Translation 5 units to the left: (x,y) → (x - 5, y)

Vertex X: (-6,2) → (-6 - 5, 2) = (-11,2)

Vertex Y: (-4, 7) → (-4 - 5, 7) = (-9,7)

Vertex Z: (-2, 2) → (-2 -5, 2) = (-7, 2)

Translation 1 unit down: (x,y) → (x, y-1)

(-11,2) → (-11, 2 - 1) = (-11, 1)

(-9,7) → (-9, 7 - 1) = (-9, 6)

(-7, 2) → (-7, 2 - 1) = (-7, 1)

Reflextion accross the x-axis: (x,y) → (x, -y)

(-11, 1) → (-11, -1), which are the coordinates of vertex X"

(-9, 6) → (-9, -6), which are the coordinates of vertex Y""

(-7, 1) → (-7, -1), which are the coordinates of vertex Z"

Thus, in conclusion, it is proved that the sequence of transformations that maps triangle XYZ onto triangle X"Y"Z" is translation 5 units to the left, followed by translation 1 unit down, and relfection accross the x-axis.

7 0

3 years ago