I need help with these 4 problems

Answer:

(a) [tex]\sigma = 7.04[/tex]

(b) [tex]\sigma = 14.1[/tex]

(c) The population standard deviation is multiplied by k

Step-by-step explanation:

Given

[tex]Dataset: 12, 7, 18, 23, 24, 27[/tex]

Solving (a): The population standard deviation

Start by calculating the mean

[tex]\mu = \frac{\sum x}{n}[/tex]

[tex]\mu = \frac{12+7+18+23+24+27}{6}[/tex]

[tex]\mu = \frac{111}{6}[/tex]

[tex]\mu = 18.5[/tex]

The population standard deviation is:

[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]

This gives:

[tex]\sigma = \sqrt{\frac{(12-18.5)^2 + (7 - 18.5)^2 + (18-18.5)^2 + (23-18.5)^2 + (24 - 18.5)^2 + (27 - 18.5)^2}{6}}[/tex]

[tex]\sigma = \sqrt{\frac{297.5}{6}}[/tex]

[tex]\sigma = \sqrt{49.5833}[/tex]

[tex]\sigma = 7.04[/tex]

Solving (b): Double the dataset and calculate the new population standard deviation

The new dataset is:

[tex]Dataset: 24, 14, 36, 46, 48, 54[/tex]

Start by calculating the mean

[tex]\mu = \frac{\sum x}{n}[/tex]

[tex]\mu = \frac{24+ 14+ 36+ 46+ 48+ 54}{6}[/tex]

[tex]\mu = \frac{222}{6}[/tex]

[tex]\mu = 37[/tex]

The population standard deviation is:

[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]

This gives:

[tex]\sigma = \sqrt{\frac{(24-37)^2 +(14-37)^2 +(36-37)^2 +(46-37)^2 +(48-37)^2 +(54-37)^2}{6}}[/tex]

[tex]\sigma = \sqrt{\frac{1190}{6}}[/tex]

[tex]\sigma = \sqrt{198.33}[/tex]

[tex]\sigma = 14.1[/tex]

Solving (c): What happens when the dataset is multiplied by k

In (a), we have:

[tex]\sigma = 7.04[/tex]

In (b), when the dataset is doubled,

[tex]\sigma = 14.1[/tex]

This implies that when the dataset is multiplied by k, the population standard deviation will be multiplied by the same factor:

i.e.

[tex]New \sigma = k * \sigma[/tex]

Answer:

75 : 225

Step-by-step explanation:

[tex]\frac{\frac{1}{4} }{\frac{3}{4} } :\frac{75}{y}[/tex]

0.25 × y = 0.75 × 75

0.25y = 56.25

0.25y ÷ 0.25 = 56.25 ÷ 0.25

y = 225

The number of hours does each group member work on the project is 4 hours. Therefore, the correct answer is option B.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is x+45/4=4x.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

4x-x=45/4

3x=45/4

x=15/4

x=3.75

x≈4 hours

Therefore, option B is the correct answer.

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Answer:

[tex]v=480 ~in^3[/tex]

Step-by-step explanation:

[tex]v=1/3 Bh[/tex]

[tex]1/3(12)^210=[/tex]

[tex]480 ~in^3[/tex]

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hope it helps...

have a great day!!!

Answer:

It is best to solve a system of equations using substitution when one of the equations isolates one of the variables, or when the coefficient of one of the variables is 1 or -1.

Step-by-step explanation:

This makes it easier to substitute one variable for the other, allowing you to solve for the remaining variable. It is also a good idea to check the solution back in the original equations just to make sure it is a valid solution

Answer:

Answer Below

Step-by-step explanation:

It is best to use substitution if one of the variables is isolated or has a coefficient of 1 or -1.

Answer:

160 in³

Step-by-step explanation:

Volume of rectangular pyramid, V = (Length * width * height) / 3

Length = 10 in ; width = 8 in ; height = 6 in

V = (10 * 8 * 6) / 3

V = 160 in³

Answer:

yes it is

Step-by-step explanation:

a) The degree of the polynomial is 5.

b) The second difference is -726        -126        -6        114         714

c) The difference when they are constant is 480.

What is a polynomial?

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.

y values:      -999           -140          -7          0           1         116          945

1st difference        859           133          7           1          115         829

2nd difference               -726        -126        -6        114         714

3rd difference                           600      120      120       600

4th difference                                  -480      0         480

5th difference                                           480     480

The degree of a polynomial is the number of difference where it is constant.

The degree of the polynomial function is 5.

The constant is the 5th difference which is 480.

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Answer:

A

Step-by-step explanation:

Hi I don't usually upload pictures but I was too lazy to type so I did it on paper. I had to get the numbers in the parenthesis out so I multiplied the + by everything in the parenthesis following the negative and positive multiplication rules. Then, I combined and subtracted like terms.

Hope this helps !!

-Ketifa

Answer:

The answer is C

Step-by-step explanation:

You have to divide both numerators then the denominater.

So, it would look like:  160 over 90 x 100 over 290

160x100=16   90x290=25     16/25

Answer:

y=2x+2

Step-by-step explanation:

you have to substitute x and y in the given equations and which one works

for y=x+3 , 4=1+3 true , 6=2+3 false

for y=3x+1, 4=3*1+3 false

for y=2x+2, 4= 2*1+2 true, 6= 2*2+2 true, 8= 2*3+2 true, 10=2*4+2 true

for y=4x, 4=4*1 true, 6= 4*2 false

Answer:

Years = {log(total) -log(Principal)} ÷ log(1 + rate)

Years = [log (200,000) -log (20,000)] / log (1.09)

Years = [5.3010299957 -4.3010299957] /  0.037426497941

Years = 1 / 0.037426497941

Years = 26.7190374471

*************************************************

Finding Doubling Time : (We'll calculate $100 becoming $200)

Years = {log(total) -log(Principal)} ÷ log(1 + rate)

Years = log (200) -log (100) / log(1.09)

Years =  (2.3010299957 -2) / 0.037426497941

Years = .3010299957 / 0.037426497941

Years 8.0432317278

It takes 8.0432317278 years for money to double at 9% per year.

Source:

http://www.1728.org/compint2.htm

Step-by-step explanation:

Answer:

550 lattes he sold this week

Step-by-step explanation:

$275÷$0.50= 550

Answer:

40.5 m²

Step-by-step explanation:

Area of the shaded = area of the square - area of the triangle

Area of square = s²

s = 9 m

Area of square = 9² = 81 m²

Area of triangle = ½*b*h

b = 9 m

h = 9 m

Area of triangle = ½*9*9 = 40.5 m²

Area of the shaded = 81 - 40.5 = 40.5 m²

Answer:

Infinity (∞)

Step-by-step explanation:

Graph the function and observe that the function P(t) increases without bound as x increases.

Here we go...

= 2x² - y² = 17

= 2x² = 17 + y²

= x² = 17 + y²/2

= x = √17+y²/2

= x + 2y = 1

= x = 1 - 2y

___________________

Sry,if i misunderstood the question.. do let me know in the comment section

Answer:

40 quarters are in $10

Step-by-step explanation:

Answer:

40 quarters i think cause there's 4 quarters in a dollar and then 10 x 4 equals 40...

Step-by-step explanation:

Answer:

yeah it's true

Step-by-step explanation:

............THANKS.........

Answer:

2019

Step-by-step explanation:

2010: 450,000

2011: (5% of 450,000) + 450,000 = 472,500

2012: (5% of 472,500) + 472,500 = 496,125

2013: (5% of 496,125) + 496,125 = 520,931.25

2014: (5% of 520,931.25) + 520,931.25 = 546,977.8125

2015: (5% of 546,977.8125) + 546,977.8125 = 574,326.703125

2015: (5% of 574,326.703125) + 574,326.703125 = 603,043.038281

2016: (5% of 603,043.038281) + 603,043.038281 = 633,195.190195

2017: (5% of 633,195.190195) + 633,195.190195 = 664,854.949705

2018: (5% of 664,854.949705) + 664,854.949705 = 698,097.69719

2019: (5% of 698,097.69719) + 698,097.69719 = 733,002.582049

Basically, take five percent of the population of the year and add it to the population of the previous year. This is the long way of doing it, but you get the population count for each year.

The nearest integer that is a solution, gotten through graphing of the quadratic function x² + 2x - 2 = 5, is x = -4

Quadratic equations when plotted on a graph follows a parabolic path.

To plot the functions there will be table of values that is used in making the graph. The table of values is solved as follows

x² + 2x - 2 = 5 rearranging the equation will result to x² + 2x - 7 = 0

For x = -20,  y = (-20)² + 2 * -20 - 7 = 353

For x = 0,  y = (0)² + 2 * 0 - 7 = -7

For x = 20,  y = (20)² + 2 * 20 - 7 = 433

x      y

-20  353

0      -7

20    433

The graph is plotted and attached. From the graph the solution is

x = -3.828, to the nearest integer = -4

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Sales Tax = $3.00

The total amount paid by the group was $48.15

The amount of the sales tax can be calculated by multiplying the pre-tax bill of $37.50 by the sales tax rate of 8%:

Sales tax = $37.50 * 8% = $3.00

The total amount paid including tax and tip can be calculated by adding the amount of the sales tax to the pre-tax bill and then calculating the tip on the new total:

Total = $37.50 + $3.00 + ($37.50 + $3.00) * 18% = $37.50 + $3.00 + $7.65 = $48.15

So the total amount paid by the group was $48.15.

Answer:

add the 3 and 4

Step-by-step explanation:

Answer:

110 in.²

Step-by-step explanation:

The figure is composed of a parallelogram and a rectangle

Therefore, the area of the figure = area of rectangle + area of parallelogram

= Length*Width + base*height

Length = 10 in.

Width = 6 in.

base = 10 in.

height = 5 in.

Area of the figure = 10*6 + 10*5

= 60 + 50

= 110 in.²

Answer:

14.1 inches

Step-by-step explanation:

The formula to be used to find the arc length is Ф = s(arc length) / r(radius)

First we rearrange the formula to find the arc length which would be s = Ф * r

This formula only works in radians so the first step is converting 135° to radians so we would do 135° * π radians/180° which would give us 3π/4

We would then multiply 3π/4 * 6 and get 18π/4,  plugging that value into a calculator returns us a value of ≈ 14.137

We then round to the nearest tenth and get an answer of 14.1 inches for the arc length of the circle below

Answer:

pi  3.1415926535897932384626433832795

20 beacuse you need hiking boots to hike

Answer:

25

Step-by-step explanation:

let x = # of participants on the hike

(.80)x = 20

x = 20/0.80 = 25

Answer:

commutative property of addition

Step-by-step explanation:

commutative property of addition

The commutative property of addition allows you to change the order of the numbers in an addition.

For example, 1 + 2 = 2 + 1

Answer:

35

Step-by-step explanation: