In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider the following data set.
8, 16, 14, 8, 16

(a) Use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to four decimal places.)

(b) Add 8 to each data value to get the new data set 16, 24, 22, 16, 24. Compute s. (Enter your answer to four decimal places.)

(c) Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?

Adding the same constant c to each data value results in the standard deviation remaining the same.

Adding the same constant c to each data value results in the standard deviation increasing by c units.

Adding the same constant c to each data value results in the standard deviation decreasing by c units.

There is no distinct pattern when the same constant is added to each data value in a set.

Answer:

20/8

=2.5

14×2.5=35

[tex] \frac{20}{8} = \frac{x}{14} \\ x = \frac{20 \times 14}{8} \\ x = \frac{280}{8} \\ x = 35[/tex]

Answer:

Step-by-step explanation:

A

Answer:

[tex]g(h(1011)) = 2010[/tex]

Step-by-step explanation:

Given

[tex]g(x) = x - 4[/tex]

[tex]h(x) =2x - 8[/tex]

Required

[tex]g(h(1011)[/tex]

First, we calculate [tex]g(h(x))[/tex]

[tex]g(x) = x - 4[/tex]

Substitute h(x) for x

[tex]g(h(x)) = h(x) -4[/tex]

Substitute [tex]h(x) =2x - 8[/tex]

[tex]g(h(x)) = 2x - 8 -4[/tex]

[tex]g(h(x)) = 2x -12[/tex]

Substitute 1011 for x

[tex]g(h(1011)) = 2*1011 -12[/tex]

[tex]g(h(1011)) = 2022 -12[/tex]

[tex]g(h(1011)) = 2010[/tex]

Answer:

6

Step-by-step explanation:

just did it on egde 2021

Answer:

Step-by-step explanation:

3,969 = 4,000 rounded to nearest hundred

2,811=3,000 rounded to nearest hundred

therefore... the difference is 4,000 - 3,000 = 1,000 kilometers

Answer:1,100

Step-by-step explanation:

rounding 3,969 to the nearest hundreds is 4,000 and rounding 2811 to the nearest hundred is 2900. Now you subtract 4000-2900 = 1100.

Answer:

x = 9 , jk = 42 , kl= 78

Step-by-step explanation:

Explained in the paper.

Goodluck

Answer:

x = 9

Step-by-step explanation:

[tex](4x+6)+(7x+15)=120[/tex]

[tex](4(9)+6)+(7(9)+15)=120[/tex]

[tex](36+6) + (63+15)=120[/tex]

[tex](42)+(78)=120[/tex]

x = 9

JL = 42

KL = 78

Answer:16 degree is the answer.

Since r and m are parallel:

10x-3=7x+45

3x=48

x=16

Answer:

x < 30

Step-by-step explanation:

Given the inequality expression that denotes the statement as;

30x+100 < 1000

Subtract 100 from both sides

30x + 100 - 100 <1000 - 100

30x < 900

Divide both sides by 30

30x/30 < 900/30

x < 30

Hence the required solution is x < 30

The number of employee the manager can afford a day is x < 30.

The given parameters:

The inequality of the number of employee the manager can afford a day is calculated as follows;

30x + 100 < 1000

collect similar terms together;

30x < 1000 - 100

30x < 900

divide both sides of the equation by 30;

[tex]x <\frac{900}{30} \\\\x <30[/tex]

Thus, the number of employee the manager can afford a day is x < 30.

Learn more about solution to inequality here: https://brainly.com/question/24372553

Answer:

If you've more doubts you can ask :)

Step-by-step explanation:

If the centre of a circle is (a, b) and radius r, then the equation of the circle is :

[tex](x - x)^2 + (y-b)^2 = r^2[/tex]

First we will find the centre, (a , b):

[tex]a = \frac{3+(-1)}{2} = \frac{2}{2} = 1\\\\b = \frac{-2 + 4}{2} = \frac{2}{2} = 1[/tex]

Find radius:

[tex]Radius, r = \frac{Diameter}{2}[/tex]

Diameter is the distance between (-1, 4) and (3, -2)

[tex]diameter = \sqrt{(x_2 - x_1)^2 +(y_2-y_1)^2} \\\\[/tex]

             [tex]= \sqrt{(3-(-1)^2 + (-2-4)^2} \\\\=\sqrt{16 + 36}\\\\=\sqrt{52}\\\\=\sqrt{4 \times 13}\\\\=2\sqrt{13} \ units[/tex]

Therefore , [tex]r = \frac{2 \times \sqrt{13} }{2} = \sqrt{13} \ units[/tex]

Equation of the circle is :  

                                 [tex](x - 1)^2 +(y-1)^2 = 13[/tex]

Answer:

F(x) = -1/3 x^2 - 7x + C

Answer:

The answers are options d and e

The modified boxplot created for the distribution is boxplot E

Given the values :

25, 34, 46, 37, 33, 42, 40, 37, 34, 49, 73, 46, 45, 45, 5

The outliers in the values are : 5 and 73

Hence, the modified values are :

25, 34, 46, 37, 33, 42, 40, 37, 34, 49 , 46, 45, 45

Using a boxplot maker or excel, we could use the modified data to create a boxplot with the following properties as obtained from the boxplot shown below :

Median value = 40

Minimum = 25

Maximum =  49

First quartile = 34

Third quartile = 45.5

The modified boxplot has no outlier and it corresponds with the boxplot in option E

Learn more : https://brainly.com/question/1523909

Answer:

graph C

Step-by-step explanation:

Answer:

89

Step-by-step explanation:

341 ( total of previous 4 tests)   + 89= 430  

Divide 430 by 5 ( number of tests)

Answer:

hey I am not sure about the answer but I guess this is the right answer:

(x+3)+x

Answer:

it is simple just compare the ratios simple as that

but I will need to know all the formula s

i think the correct answer is 2 hours and 10 mins

Answer:

DF = 11

Step-by-step explanation:

From the question given above, the following data were obtained:

EH = 8

HG = 3

EF = DG

DF =?

Since, EF = DG, it also means that EG = DF.

Next we shall determine EG. This can be obtained as follow:

EG = EH + HG

EH = 8

HG = 3

EG = 8 + 3

EG = 11

Finally, we shall determine EF. This is illustrated below:

EG = DF

EG = 11

DF =?

11 = DF

Therefore,

DF = 11

Answer:

Solution given:

f(x) = x +1 and g(x) = x²,

now

(gºf)(x) =g(fx)=g(x+1)=(x+1)²

B) (gºf)(x) = (x + 1)^2

Answer:

jane is correct

Step-by-step explanation:

10⁻⁴ can be written as [tex]\frac{1}{10000}[/tex] and as 0.0001

Answer:

- (- (+) - ÷ )

+) (-) (+) (-)

= (+) (-)

Answer:

The right answer is "605 persons".

Step-by-step explanation:

Given that,

⇒ [tex]\frac{dP}{dt} \alpha P[/tex]

or,

⇒ [tex]\frac{dP}{dt} =RP[/tex]

⇒ [tex]\frac{1}{R} \int\limits^{PT}_{500} {\frac{dP}{P} } = \int\limits^{t}_{0} dt[/tex]

⇒ [tex]\frac{1}{R} [log PT-log500]=t[/tex]

⇒                  [tex]log[\frac{PT}{500} ]=Rt[/tex]

At t = 10 years,

⇒ [tex]PT=\frac{110}{100}\times 500[/tex]

          [tex]=550[/tex]

∴ [tex]log[\frac{550}{500} ]=R\times 10[/tex]

            [tex]R=\frac{log(1.1)}{10}[/tex]

At t = 20,

⇒ [tex]log{\frac{PT}{500} }=\frac{log \ 1.1}{10}\times 20[/tex]

        [tex]PT=500\times (1.1)^2[/tex]

              [tex]=605 \ persons[/tex]

9514 1404 393

Answer:

  (x +yi)²

Step-by-step explanation:

Comparing the given expression to the square of a binomial, we can determine the given expression to be a square.

  (a +b)² = a² +2ab +b²

Here, we have a=x and b=yi. Then the factorization is ...

  x² +2xyi +(yi)² = (x +yi)²

Answer:

use the arthmetic mean

Step-by-step explanation:

Answer:

An interval scale is one where there is order and the difference between two values is meaningful. Examples of interval variables include: temperature (Farenheit), temperature (Celcius), pH, SAT score (200-800), credit score (300-850).

Step-by-step explanation:

thank me later

Answer:3.31662479036.

Step-by-step explanation:To find the square root of 11, use the long division method to get the approximate value. Therefore, √11 = 3.31662479036. Register at BYJU'S to learn other interesting mathematical concepts.

Step-by-step explanation:

[tex]\cos 90 \cos 30 + \sec^2 45 \sin 30 - \cos 270 \sin 180[/tex]

But we know that

[tex]\cos 90 = \cos 270 = \sin 180 = 0[/tex]

and

[tex]\sin 30 = \dfrac{\sqrt{3}}{2} \:\:\text{and}\:\: \sec 45 = \sqrt{2}[/tex]

so this leaves us with just

[tex]\sec^2 45 \sin 30 = (\sqrt{2})^2 \left(\dfrac{\sqrt{3}}{2} \right)= \sqrt{3}[/tex]

Answer:

[tex] - 6x = 3 {x}^{2} + 9 \\ 3 {x}^{2} + 6x + 9 = 0 \\ {x}^{2} + 2x + 3 = 0 \\ so \\ ether \: x = - 2 \\ or \: x = 1 [/tex]

Answer:

1/4

Step-by-step explanation:

4 divide in half so should be 1/4

Answer:

The surface area of the figure is 452.2m2 (A)

Answer:

angle B=74°

Step-by-step explanation:

the shapes are similar