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1 year ago

Solve X-9+2wx=y for x

2 answers:

8 0

X - 9 + 2wx = y Add 9 to both sides x + 2wx = y + 9 Factor out the x x (1 + 2w) = y + 9 Divide both sides by (1 + 2w) x = (y + 9) / (1 + 2w)

EleoNora [17]1 year ago

5 0

Answer:

$x=\frac{y+9}{1+2w}$

Step-by-step explanation:

$x-9+2wx=y$

Add 9 to each side of the equation

$x+2wx=y+9$

Take out the common factor

$x(1+2w)=y+9$

And divide by (1+2w) at each side of the equation

$x=\frac{y+9}{1+2w}$

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Consider the following random sample from a normal population: 14, 10, 13, 16, 12, 18, 15, and 11. What is the 95% confidence in

seraphim [82]

Answer:

$13.625-2.365\frac{2.669}{\sqrt{8}}=11.393$

$13.625+2.365\frac{2.669}{\sqrt{8}}=15.857$

So on this case the 95% confidence interval would be given by (11.393;15.857)

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".

Data: 14, 10, 13, 16, 12, 18, 15, 11

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=13.625$ represent the sample mean

$\mu$ population mean (variable of interest)

s=2.669 represent the sample standard deviation

n=8 represent the sample size

Calculate the confidence interval

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:

$df=n-1=8-1=7$

Since the confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,7)".And we see that $t_{\alpha/2}=2.365$

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

$13.625-2.365\frac{2.669}{\sqrt{8}}=11.393$

$13.625+2.365\frac{2.669}{\sqrt{8}}=15.857$

So on this case the 95% confidence interval would be given by (11.393;15.857)

3 0

1 year ago

Two rectangular properties share a common side. Lot A is 33 feet wide and 42 feet long.

s344n2d4d5 [400]

Answer:

The width of lot B is 11 feet, so option A is correct.

Step-by-step explanation:

Given:

Two rectangular properties share a common side.

Lot A is 33 feet wide and 42 feet long.

The combined area of the lots = 1,848 square feet.

To find:

How many feet wide is Lot B?

Solution:

we know that, area of a rectangle is length x breadth

Then area of lot A = 33 x 42 = 1386 square feet.

And area of lot B = width x 42

Now, we are given that, total area = 1848

area of lot A + area of lot B = 1848

1386 + width x 42 = 1848

width x 42 = 1848 – 1386

width x 42 = 462

$width =\frac{42}{462}$

width = 11

Hence, the width of lot B is 11 feet, so option A is correct.

7 0

2 years ago

The parallel dotplots below display the girths (belly

liraira [26]

Answer:

The standard deviation for the distribution of girths is

about the same for both male and female pigs.

Step-by-step explanation:

Step 1

We will interprete the dotplots

For the Male pigs

24, 26, 26, 26, 26, 26, 26, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 30, 30, 30, 30, 30, 30, 32

Range

Maximum value - Minimum value

= 32 - 24

= 8

IQR = Interquartile range = Q3 - Q1

Q1 formula = 1/4(n + 1)th

=n = 25

= 1/4(25 + 1)

= 1/4(26)

= 26/4

= 6.5

This mean the value is between the 6th and 7th value

6th value = 26

7th value = 26

Q1 = 26 + 26/2

Q1 = 26

Q3 formula = 3/4(n + 1)th

=n = 25

= 3/4(25 + 1)

= 3/4(26)

= 78/4

= 19.5

This mean the value is between the 19th and 20th value

19th value = 30

20th value = 30

Q3= 30+ 30/2

= 30

IQR = 30 - 26

= 4

Standard deviation

Mean

First we find the mean

= 24+ 26+26+ 26+ 26+ 26+26+28+ 28+ 28+ 28+28+ 28+ 28+28+ 28+28+28+30+ 30+30+ 30+30+30+32/28

= 700/25

= 28

Standard deviation Formula = √(x - mean)²/n - 1

= √[(24-28)² + (26- 28)² + (26 -28)² + (26 - 28)² +................ (32 - 28)²]/25 - 1

= √(16 + 4 + 4+ 4+ 4+4+ 4+0+ 0+ 0+ 0+0+ 0+ 0+ 0+0+0+0+ 4+ 4+4+4+4+ 4+ 16)/25 - 1

= √80/25 - 1

=√3.333333333

1.825741858

Female Pigs

21, 23, 23, 23,23,23,23,25, 25, 25, 25, 25, 25, 25, 25, 25, 25,25, 27, 27, 27, 27,27, 27, 29

Range:

Maximum value - Minimum value

= 29 - 21

IQR

IQR = Interquartile range = Q3 - Q1

Q1 formula = 1/4(n + 1)th

=n = 25

= 1/4(25 + 1)

= 1/4(26)

= 26/4

= 6.5

This mean the value is between the 6th and 7th value

6th value = 23

7th value = 23

Q1 = 23 + 23/2

Q1 = 23

Q3 formula = 3/4(n + 1)th

=n = 25

= 3/4(25 + 1)

= 3/4(26)

= 78/4

= 19.5

This mean the value is between the 19th and 20th value

19th value = 27

20th value = 27

Q3= 27+ 27/2

Q3 = 27

IQR = 27 - 23

= 4

First we find the Mean

=(21+23+23+23+23+23+23+25+ 25+ 25+ 25+25+ 25+ 25+ 25+25+25+25+27+27+ 27+27+27+ 27+29)/25

= 625/25

= 25

Standard deviation Formula = √(x - mean)²/n - 1

= √[(21-25)² + (23- 25)² + (23 -25)² + (23 - 25)² +................ (29 - 25)²]/25 - 1

= √(16 + 4 + 4+ 4+ 4+4+ 4+0+ 0+ 0+ 0+0+ 0+ 0+ 0+0+0+0+ 4+ 4+4+4+4+ 4+ 16)/25 - 1

= √80/25 - 1

=√3.333333333

1.825741858

Looking at the calculation above and comparing both the girths from the male and female

We can conclude that: The standard deviation for the distribution of girths is

about the same for both male and female pigs which is 1.825741858

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2 years ago

Prof. okamoto selects 3 different students to report on 3 different current events. if there are 27 students in the class, in ho

kenny6666 [7]

Consider this option:
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2 years ago

on a piece of paper, graph this system of inequalities. Then determine which region contains the solution to the system. a pictu

slava [35]

C. Region D

Step-by-step explanation:

Just plug the equations into desmos the calculator will graph it and show you with colors where the solution is.

4 0

2 years ago