You measure the period of a mass oscillating on a vertical spring ten times as follows:

Period (s): 1.06, 1.31, 1.28, 0.99, 1.48, 1.37, 0.98, 1.31, 1.59, 1.55

Required:
What are the mean and (sample) standard deviation?

a. Mean: 1.228, Standard Deviation: 0.2135
b. Mean: 1.325, Standard Deviation: 0.1674
c. Mean: 1.292. Standard Deviation: 0.2211
d. Mean: 1.228, Standard Deviation: 0.2098
e. Mean: 1.292, Standard Deviation: 0.2135

Answers

Answer 1

Answer:

Step-by-step explanation:

Mean is the ratio of sum of the dataset to the sample size. Mathematically:

[tex]\overline x = \frac{\sum Xi}{N}[/tex]

Xi are the individual periods

N is the sample size

[tex]\sum Xi = 1.06+1.31+1.28+0.99+1.48+1.37+0.98+1.31+1.59+1.55\\\sum Xi = 12.92[/tex]

N = 10

Substitute

[tex]\overline x = \frac{12.92}{10}\\\overline x = 1.292[/tex]

hence the mean of the samples is 1.292

For the standard deviation:

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

[tex]\sum (x-\overline x)^2 = (1.06-1.292)^2+ (1.31-1.292)^2+ (1.28-1.292)^2+ (10.99-1.292)^2+ (1.48-1.292)^2+ (1.37-1.292)^2+ (0.98-1.292)^2+ (1.31-1.292)^2+ (1.59-1.292)^2+ (1.55-1.292)^2\\\sum (x-\overline x)^2 = 0.43996[/tex]

Substitute into the formula:

[tex]\sigma = \sqrt{\frac{0.43996}{10} }} \\\sigma = \sqrt{{0.043996}}} \\\sigma = 0.2098[/tex]

Hence the standard deviation is 0.2098


Related Questions

Please help me with this problem please ;(

Answers

9514 1404 393

Answer:

  -2

Step-by-step explanation:

The average rate of change on the interval [3, 9] is ...

  (f(9) -f(3))/(9 -3) = (41 -53)/(9 -3) = -12/6 = -2

Which expression is equivalent to -4(w-1)

4w-4
4w
-4w+4
-5w
None of the above

Answers

Answer:

-4w+4

Step-by-step explanation:

Answer:

-4w+4 Is te correct answer

Write and equation of a line perpendicular to y=-5x+8 and passes through (10,4)

Answers

im not sure just yet

I need to do this assignment but I need help on how to draw it and answer the questions because I am confused on how to do these things. Thank you

Answers

1) The domain is [0,300]. The range is [0,250]

2) The slope for the initial climb is 3.57. The equation of the line is

3) The rate of change of the second hill is -1.4

4) The rate of change of the third hill is -2.1

5) The blue hill is steeper

6) It is not a function

Step-by-step explanation:

1)

The domain of a function is the set of values of x (the input) for which the function itself is defined.

Instead, the range of a function is the set of values of y (the output) that the function can take.

To find the domain, we have to look at the x-axis and see for which values of x the function is defined. By looking at the graph, we see that the function is defined between

x = 0 and x = 300

So, the domain is [0,300].

To find the range, we have to look at the y-axis and see for which values of y the function has an output. By looking at the graph, we see that the function has values of y between

y = 0 and x = 250

So, the range is [0,250].

2)

The slope of a function in a certain range is given by

where

is the change in the y-coordinate

is the change in the x-coordinate

For the initial climb (pink line), we have:

Therefore, the slope in this part is

We can now write the equation of the line in the form

y = mx + b

where b is the y-intercept: since it is zero, the line has simply the form

3)

Again, to calculate the slope of the hill, we use:

where

is the change in the y-coordinate

is the change in the x-coordinate

For the green hill, we have:

So the rate of change is

4)

As before, the rate of change of the hill is

For the blue hill, we have:

So the rate of change is

5)

To know which hill is steeper, we need to compare the magnitude of their rate of change.

In fact, both hills have rate of change negative - because we are going down along the slope. Therefore, we have to consider the magnitude of their slope.

For the green hill:

For the blue hill:

We see that the blue hill has a greater slope (in magnitude): therefore, the blue hill is steeper.

6)

A function is defined as a mapping (operation between two sets of variables) in which to one value of x (the input) corresponds one and only one value of y (the output).

This means that a function cannot have multiple values of y for the same x (the input).

By looking at the graph, we see that this function does not respect this criterium: in fact, we see that certain values of x give multiple values of the output, y (for instance, at x=300 the function has two values). So, this is not a function.

Help I’ll mark you as the brainliest
No answer choice
parallel to y = 5x – 7 but contains (-1,-3)

Answers

Answer:

-3 = -12

Step-by-step explanation:

Have a great day

I hope that is the answer you are looking for :)

the first 5 multiples of 18 after 0 are?​

Answers

Answer:

18,36,54,72,90 are first five multiples of 18

Step-by-step explanation:

Answer:

18,36,54,72,90

Step-by-step explanation:

Which of the following represents this function written in intercept form
y= - x2 – x+ 6

A. v= - (x − 2)(x+3)
B. v= (-x+3)(x-4)
c. v= - (x + 2)(x+6)
D. v= - (1+2)(1-6)

Answers

Answer:

v=2(x - 1)(x-6)=2(x²-6x-x+6)=12x²-12x-2x+12

v = 12x²-14x+12  standard form

Step-by-step explanation:

Find x.... Figure is not drawn to scale.

Answers

Answer:

33.

Step-by-step explanation:

I assume that the 2 triangles are similar.

x/77 = 24/56

56x = 77*24

x = (77*24(/56

x = 33.

Solve the following equation
4(3-2x)=15

Answers

Answer:x= -3/8

Step-by-step explanation:

Answer:

-3/8

Step-by-step explanation:

4(3-2x)=15

-3/8

The centers of two small metal spheres with a charge of 7.4 × 10−8 C are 10 cm from each other. a) What is the electric force between them? b) One of the spheres touches another identical neutral one, what is now the electric force if they are kept at the same distance? The constant in the Coulomb's law expression is k = 9.0 × 109 Nm2C2.

Answers

Georgia Washington was the election compadre

Answer:

answer is 9 in th by form of the good answer is the to k=9.0 10á gd gd

△BCD≅△GEF . If BC=10 , CD=3x+8 and EF=4x+6 , then what is the measure of CD ?

Answers

Given :-

ΔBCD ≅ ΔGEF

Then :-

∠B <=> ∠G ( ∠B = ∠G )

∠C <=> ∠E ( ∠C = ∠E )

∠D <=> ∠F ( ∠ D = ∠F )

BC <=> GE ( BC = GE )

CD <=> EF ( CD = EF )

BD <=> GF ( BD = GF )

Using this let us find CD .

CD = EF

Which means :-

[tex] 3x + 8 = 4x + 6[/tex]

[tex]8 = 4x + 6 - 3x[/tex]

[tex]8 = 1x + 6[/tex]

[tex]1x + 6= 8[/tex]

[tex]1x = 8 - 6[/tex]

[tex]1x = 2[/tex]

[tex]x = 2[/tex]

Then :-

EF =

[tex]EF = 4x + 6 \\ = 4 \times 2 + 6 \\ = 8 + 6 \\ = 14[/tex]

CD =

[tex]CD = 3x + 8 \\ = 3 \times 2 + 8 \\ = 6 + 8 \\ = 14[/tex]

Therefore , CD = 14 .

△BCD≅△GEF

The measure of CD is 14

Given :

Two triangles are congruent

△BCD≅△GEF

When triangles are congruent then the sides are equal

[tex]BC=GE\\CD=EF\\DB=FG\\[/tex]

Given that CD=3x+8 and EF=4x+6

[tex]CD=EF\\3x+8=4x+6\\3x+8-3x=4x-3x+6\\8=x+6\\8-6=x+6-6\\x=2[/tex]

The value of x=2

Now we find measure of CD

[tex]CD=3x+8\\CD=3(2)+8\\CD=14[/tex]

The measure of CD is 14

Learn more :  brainly.com/question/18373823

How can you use the order of operation to explain why you cannot combine the variable terms before using the distributive property when solving the equation 7(x+5)-x=42

Answers

Answer:

Step-by-step explanation:

The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.

This standard is critical to simplifying and solving different algebra problems. Without it, two different people may interpret an equation or expression in different ways and come up with different answers. The Order of Operations is shown below.

Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.

Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.

Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.

Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.

Before we begin simplifying problems using the Order of Operations, let's examine how failure to use the Order of Operations can result in a wrong answer to a problem.

Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways

We cannot combine the variable terms before using the distributive property when solving the equation as it will results in wrong answer.

What is distributive property of multiplication over addition ?

If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.

Here the expression given is :

7(x+5)-x=42

The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.

Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.

Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.

Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.

Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.

Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways.

Read more about property of multiplication here :

https://brainly.com/question/14391436

#SPJ2

Molly’s hair was 20 inches long . Three years later it was 35 inches long

Answers

Answer:

Step-by-step explanation:

75

5d+1/2=d-4 section 2.04

Answers

Answer:  d = -9/8

Steps: 5d + ½ = d - 4

Subtract ½ from both sides: 5d + ½ - ½  = d - 4 - ½

Simplify: 5d = d - 9/2

Subtract d from both sides: 5d - d = d - 9/2 - d

Simplify: 4d = -9/2 ÷ 4

Simplify: d = -9/8

PLz mark brainliest:)

Point V is on line segment UW. Given VW = 5x - 4, UV = 2x, and

UW = 52, determine the numerical length of VW.

Answers

Answer:

VW = 36

Step-by-step explanation:

From the question, we are given:

VW = 5x - 4, UV = 2x,

UW = 52

Hence,

UV + VW= UW

2x + 5x - 4 = 52

7x = 52 + 4

7x = 56

x = 56/7

x = 8

VW = 5x - 4,

VW = 5(8) - 4

VW = 40 - 4

VW = 36

PLEASE HELP ASAP
IT AN EMERGENCY



Answers

Answer: E) Not enough information

We're given two pairs of congruent sides, and a pair of congruent angles. The angles are not between the two congruent sides. So we don't have enough information to know if the triangles are congruent or not. SSA is not a valid congruence theorem. This is because there are some cases where two triangles are possible leading to ambiguity.

If the marked angles were between the tickmarked sides, then we could use SAS.

In the past, patrons at a cinema spent an average of $ 2.50 for popcorn with standard deviation of $ 0.90. The amount of these expenditures is normally distributed . Following an intensive public campaign about the negative health effects of eating popcorn by a local medical school, the mean expenditures for a sample of 18 patrons is found to be $ 2.10. At 0.01 level of significance, does this recent experience suggest decline in spending

Answers

Answer:

There's no evidence to show that the recent experience suggests a decline in spending.

Step-by-step explanation:

We are given;

Population mean; μ = $2.5

Population Standard deviation; σ = $0.9

Sample mean; x¯ = $2.1

Sample size; n = 18

Significance level; α = 0.01

Let's define the hypothesis;

Null hypothesis; H0: μ ≥ $2.5

Alternative hypothesis; Ha: μ < $2.5

z-score formula is;

z = (x¯ - μ)/(σ/√n)

z = (2.1 - 2.5)/(0.9/√18)

z = -0.4/0.2121

z = -1.886

Using the p-value from z-score calculator attached and using z = -1.886; α = 0.01; one tail; we have;

P-value = 0.2965

This is more than the significance level. Thus, we will fail to reject the null hypothesis and conclude that there is no evidence to show that the recent experience suggests a decline in spending.

In 2 /3 ÷ 4 /5 the is 2/ 3 .

Answers

Answer:

5/9

Step-by-step explanation:

2/3 • 5/2 • 2/3

1/3 • 2/5 • 2/3

multiply 1/3 for 5/2

5

-----------

3 • 2

multiply 3 for 2

5/6 • 2/3

anular el factor común 2

5/3 • 1/3

multiply 5/3 for 1/3

5

------------

3 • 3

multiply 3 for 3

5/9

the result

5/9

form decimal

0.5

Is this a function or not a function? (Picture)

Answers

Answer:

Not a Function

Step-by-step explanation:

What are the similarities and differences between translations, reflections, and rotations? Describe a real-world transformation? Give examples of two different transformations.

Answers

Answer:

There are four main types of transformations: translation, rotation, reflection and dilation.Translation moves the object without rotating it or changing its size. Reflection flips the object about a line of reflection. Rotation rotates a figure about a fixed point. Dilation changes the size of a figure without changing its essential shape.When you reflect a point across the x-axis, the x-coordinate remains the same,but the y-coordinate is transformed into its opposite. a negative angle of rotation turns the figure in a clockwise direction.Transformation can be done in a number of ways, including reflection, rotation, and translation. ~When you reflect a point across the x-axis, the x-coordinate remains the same,but the y-coordinate is transformed into its opposite. a negative angle of rotation turns the figure in a clockwise direction.

Step-by-step explanation:

Transformation simply means changing the size and location of shapes, lines and points in the coordinate geometry

The similarities

Translations, reflections, and rotations are all rigid transformations

This means that, they do not change the side lengths and angle measure of the shape they transform.

The differences

Translation: can only change the position of shapes without rotating or flipping the shape.

Rotation: This means that a shape is to be turned around a center at a particular degree

Reflection: This simply means that, a shape is mirrored over a line

Real-world transformation

A scenario is when the blades of a fan rotates when the fan is powered on

Examples

Reflection

MirrorLeaves of a book

Rotation

Fan rotationWheels of vehicle

Translation

Movement Changing positions

Read more about transformations at:

https://brainly.com/question/13801312

f(x) = (2x² – 3)^(-2a? – 9)11

Answers

Answer:

-44ax^2-198x^2+66a+297

Step-by-step explanation:

there

A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of LaTeX: 50cm^3/hr. At what rate is it's diameter decreasing

Answers

Complete question is;

A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of 50 cm/hr. At what rate is its diameter decreasing?

Answer:

Diameter is decreasing at the rate of 5/(2πr) cm/hr

Step-by-step explanation:

We are told the stone is wearing away at a rate of 50 cm/hr. This means the volume is decreasing. Thus;

dV/dt = -50 cm/hr

Now, a grindstone is in the shape of a cylinder. Thus, volume of grindstone is;

V = πr²h

dV/dr = 2πrh

Now,to find the rate at which the diameter is decreasing, we'll write;

dr/dt = (dV/dt)/(dV/dr)

dr/dt = -50/(2πrh)

We are given;

Diameter = 200 cm

Radius; r = 200/2 = 100 cm

Thickness; h = 10 cm

Thus;

dr/dt = -50/(2π × r × 10)

dr/dt = -5/(2πr) cm/hr

The rate at which grindstone diameter decreases is [tex]-5/2\pi r \;{\rm cm/hr}[/tex] and this can be determined by using the given data.

Given :

A 10 cm thick grindstone is initially 200 cm in diameter and it is wearing away at a rate of 50 [tex]\rm cm^3/hr[/tex].

The following steps can be used in order to determine the rate at which grindstone diameter decreases:

Step 1 - According to the given data, the rate at which grindstone volume decreases is:

[tex]\dfrac{dV}{dt} = 50\;{\rm cm^3/hr}[/tex]        --- (1)

Step 2 -  The formula of the volume of the cylinder (grindstone) is given below:

[tex]V = \pi r^2 h[/tex]

Step 3 - Differentiate the above expression with respect to 'r'.

[tex]\dfrac{dV}{dr} = 2\pi r h[/tex]          --- (2)

Step 4 - So, using the expression (1) and (2) the rate at which grindstone diameter decreases is:

[tex]\dfrac{dr}{dt}=\dfrac{\frac{dV}{dt}}{\frac{dV}{dr}}[/tex]

[tex]\dfrac{dr}{dt}=\dfrac{-50}{2\pi r \times 10}\\[/tex]

[tex]\dfrac{dr}{dt} = -\dfrac{5}{2\pi r }\; {\rm cm/hr}[/tex]

So, the rate at which grindstone diameter decreases is [tex]-5/2\pi r \;{\rm cm/hr}[/tex].

For more information, refer to the link given below:

https://brainly.com/question/12748872

whats the answer of 3/4 + 1/4 =

Answers

Answer:

1

Step-by-step explanation:

3/4 + 1/4 since they both have a 4 as the denominator you only have to add the top since they made it easy. and since that would be 4/4 your answer would be 1 whole.

Kiran says “If I walk 3 miles per hour toward you, and you walk 3.4 miles per hour toward me, it’s the same as if you stay put and I jog 6.4 miles per hour.” What do you think Kiran means by this? Is he correct?

Answers

Answer:

Yes it is the same. Since the total distance left behind per time unit would be the same. Just that He would Do that by himself.

Answer:

yes

Step-by-step explanation:

THIS IS DUE TODAY! PLEASE ANSWER!: Find the value of 'X' in the triangle below

Answers

Answer:

Step-by-step explanation:

First find the angle in the lower left.

180 - 100 = 80

3x + 2x + 80 = 360

solve for x

5x = 280

5x/5 = 280/ 5

x = 56

Plug this in to make sure the equation is true

3(56) + 2(56) + 80 = 360

168 + 112 + 80 = 360

360 =360

Therefore x = 56

question 10 I mark as brainliest ​

Answers

Answer:

134 is the answer

Answer: 134

Step-by-step explanation:

54+ (48+72) x 2/3

54+120x2/3=134

if a number contains decimal places then it is an irrational number​

Answers

Answer:

sometimes true

Step-by-step explanation:

Write an equation in slope-intercept form for the line with slope 2/5 and y-intercept -6 .

Answers

Answer:

[tex] y = \frac{2}{3}x - 6 [/tex]

Step-by-step explanation:

Recall that the the equation of a line in slope-intercept form is given as [tex] y = mx + b [/tex].

m = the slope of the line

b = the y-intercept. This is the point at which the line intercepts the y-axis.

We are given:

slope (m) = ⅖

y-intercept (b) = -6

All you need to do to get an equation of the line is to simply substitute m = ⅔ and b = -6 into [tex] y = mx + b [/tex].

[tex] y = \frac{2}{3}x + (-6) [/tex]

[tex] y = \frac{2}{3}x - 6 [/tex]

The equation for the line is .[tex] y = \frac{2}{3}x - 6 [/tex]

Which of the following equations has exactly one solution?
O A. 4x - 4 + 2x = 6x - 4
O B. 2(4x + 5) = 8x + 10
C. 4x - 8 = 4(x - 4)
O D. 3x + 5 = 2x - 6

Answers

It would be b because

4(3x + 1)
What is the answer to 4(3x + 1)

Answers

12x + 4

Divide 12 by 4

X=3

Answer:

Answer is 12x+4. Hope that helped.

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