Evaluate: 2x - y for x = 3 and y =

Give an example of a point that is the same distance from (3, 0) as it is from (7, 0). Find lots of examples. Describe the confi

Artist 52 [7]

Supposse that the distance from the point $(x,y)$ to the point $(3,0)$ is equal to the distance from $(x,y)$ to the point $(7,0)$ . Then, by the formula of the distnace we must have

$\sqrt{(x-3)^2 + (y-0)^2}=\sqrt{(x-7)^2 + (y-0)^2}$

cancel the square root and the $(y-0)^2$ 's, and then expand the parenthesis to obtain

$x^2 - 6x + 9 = x^2 - 14x + 49$

then, simplifying we obtain

$8x = 40$

therfore we must have

$x=5$

this means that the points satisfying the propertie must have first component equal to 5. So we can give a lot of examples of such points: $(5,0), (5,7),(5,1/2), (5,-10),...$ . The set of this points give us a straight line and the points (3,0) and (7,0) are symmetric with respect to this line.

3 0

3 years ago

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.â Suppose a small group of 11 Allen's humming

alexira [117]

Answer:

$3.15-1.28\frac{0.38}{\sqrt{11}}=3.003$

$3.15+ 1.28\frac{0.38}{\sqrt{11}}=3.297$

So on this case the 80% confidence interval would be given by (3.003;3.297)

And the margin of error is given by:

$ME = 1.28\frac{0.38}{\sqrt{11}}= 0.147$

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".

$\bar X=3.15$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=0.38$ represent the population standard deviation

n=11 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 0.80 or 80%, the value of $\alpha=0.2$ and $\alpha/2 =0.1$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NOR.INV(0.1,0,1)".And we see that $z_{\alpha/2}=1.28$

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

$3.15-1.28\frac{0.38}{\sqrt{11}}=3.003$

$3.15+ 1.28\frac{0.38}{\sqrt{11}}=3.297$

So on this case the 80% confidence interval would be given by (3.003;3.297)

And the margin of error is given by:

$ME = 1.28\frac{0.38}{\sqrt{11}}= 0.147$

8 0

3 years ago

How many times do you apply the distributive property in this example: 2(x + 5) – 3(2x + 7) ?

Brut [27]

Answer:

Hi there!

Your answer is two times.

Step-by-step explanation:

The distributive property is multiplying the coefficient in front of parentheses into the parentheses. You have two sets of parentheses both with a coefficient that needs to be distributed.

The first time you use it is on 2(x+5), distributing the 2.

The second time you use it is on the -3(2x+7), distributing the -3

Please let me know if you have questions :)

6 0

3 years ago

The owner of a large restaurant is considering a new “no tipping” policy and wants to survey a sample of employees. The policy w

Stolb23 [73]

A) The strata to be used in this survey by the employer is; Type of Staff

B) Stratified Random Sampling will be preferred because the opinions of the staffs on the tipping policy may be the same within each type but differ across the different types of staffs.

A stratified random sampling is a type of sampling that divides a population into groups known as strata.

Now, from the question, we see that after adding a 20% to the cost of food and beverages, that the additional revenue will be distributed equally among the kitchen and server staffs.

This means the strata here will be the type of staff because the opinions of the staffs on the tipping policy may be the within each type but differ across both types of staffs.

Read more at; brainly.com/question/1954758

7 0

2 years ago

Write a real-world problem that is solved by an equation and then solve (show work).

ololo11 [35]

A company is selling books. It has to pay $500 to start printing the books, and once they have done that, the books sell at $14.99 each. How many books must they sell to make a profit?

First we would model an equation. X will be the amount of books sold, and Y will be profits (in dollars obv). They had to pay $500 before they could start selling, so we must account for that too.

This equation would be $y=14.99x-500$ because for every book sold, X increases by 1, increasing Y by 14.99

The answer would be 34 books sold in order to turn a profit. (500/14.99=

6 0

2 years ago

Evaluate: 2x - y for x = 3 and y = - 5