Which set of numbers contains only rational numbers

The main idea behind statistical inference is that through the use of sample data, we are able to draw conclusions about the population from which the data was drawn (option c).

Statistical inference allows us to make inferences and draw conclusions about a larger population based on the analysis of a smaller representative sample.

By collecting data from a sample, we can use statistical methods to analyze and summarize the information. These methods include estimating population parameters, testing hypotheses, and making predictions.

The key assumption underlying statistical inference is that the sample is representative of the larger population, allowing us to generalize the findings to the population as a whole.

Statistical inference provides a way to make reliable and informed decisions, identify patterns and relationships, and make predictions about future observations based on the available data. It allows researchers, scientists, and decision-makers to make evidence-based conclusions and draw meaningful insights from limited observations.

To know more about statistical inference refer here:

https://brainly.com/question/30484842

#SPJ11

The standard error of the sample mean is 1.21.

Given;

Suppose a diet regimen for men results in an average weight loss of between 13. 4 and 18. 3 pounds, according to a 95% confidence interval. These findings were based on a group of 42 men who were classified as overweight at the beginning of the four-month trial.

A 95% confidence interval for a population mean is (13.4, 18.3)

Upper limit = 18.3

Lower limit = 13.4

Since population SD is unknown, this interval is constructed using the t distribution.

n = 42

c = 0.95

∴ α = 1 - c = 1 - 0.95 = 0.05

α/2 = 0.025

Also, d.f = n - 1 = 42 - 1 = 41

∴ ta/2.d.f =  ta/2.n-1  =  t0.025,41  =  2.02 . . . . use t table

Now,

The margin of error = (Upper limit - Lower limit)/2

                                 = (18.3 - 13.4)/2

                                 = 2.45

But,

Margin of error = ta/2.d.f-  * (s / \sqrt{} n)

Margin of error = ta/2.d.f-  * Standard error

2.45 = 2.02 * Standard error

Standard error = 1.2129

To learn more about Margin of error click here:

brainly.com/question/10501147

#SPJ4

Answer:

Step-by-step explanation:

The process here is to find out how far the tire travels in one rotation, then multiply that by 100. That means we need to find the circumference of the tire since the circumference tells us how far around the outside of the tire it is in inches.

C = πd where d is the diameter of the tire.

C = 3.1415(26) so

C = 81.679 inches. Multiply that by 100 to get

8167.9 inches, which in miles is a little over 1.5 miles

If there is at-least one-song liked by those two girls but disliked by the third, then the "different-ways" this is possible is 132 ways.

There are ⁴C₃ ways to choose the "3-songs" which are liked by "3-pairs" of girls.

There are 3! ways to find the three songs are liked by which pair of girls.

In total, there are ⁴C₃×3! possibilities for the first "3-songs".

There are "3-cases" for fourth song, let that song be "D".

Case 1: Song "D" is disliked by all three girls means there is only one possibility.

Case 2: Song "D" is liked by exactly one girl means there are three possibility.

Case 3: Song "D" is liked by exactly two girls means there are three pairs of girls to choose from.

However, there is an overlap when "other-song" is liked by "same-pair" of girl is counted as "fourth-song" at some point, in which "case-D" will be counted as one of first "three-songs" liked by same girls.

Counting the overlaps, there are "three-ways" to choose pair with overlaps and 4×3=12 ways to choose what the other "two-pairs" like independently.

In total, there are 3×12=36 over-lapped possibilities,

Therefore, there are ⁴C₃ × 3! ×(3+1+3)-36 = 132 ways for the songs to be likely by the girls.

Learn more about Different Ways here

https://brainly.com/question/13773260

#SPJ4

the boundary work done during the compression process is approximately -75,753 kJ.

To calculate the boundary work done during the compression process, we can use the formula:

Boundary work (W) = P * ΔV

Where:

P is the constant pressure during the compression process, and

ΔV is the change in volume.

Given:

Initial volume (V1) = 0.447 m³

Final volume (V2) = 0.077 m³

Initial pressure (P1) = 204.9 kPa

First, we need to convert the pressure from kilopascals (kPa) to pascals (Pa) because the SI unit for pressure is the pascal.

P1 = 204.9 kPa = 204.9 * 1000 Pa = 204900 Pa

Next, we calculate the change in volume:

ΔV = V2 - V1

   = 0.077 m³ - 0.447 m³

   = -0.37 m³

Note that the change in volume is negative because the air is being compressed.

Now, we can calculate the boundary work:

W = P * ΔV

 = 204900 Pa * (-0.37 m³)

 = -75,753 kJ

The negative sign indicates that work is done on the system during compression.

To know more about negative visit:

brainly.com/question/29250011

#SPJ11

Answer:5 of those 6 numbers are divisors of 12. 1,2,3,4, and 6. 5/6 is 0.833... which is 83% of 6. So the probability of rolling divisors of 12 is 83%.

Step-by-step explanation:5 of those 6 numbers are divisors of 12. 1,2,3,4, and 6. 5/6 is 0.833... which is 83% of 6. So the probability of rolling divisors of 12 is 83%.

Answer:

33 R 19.8

1.6 goes into 52.8, 33 times, so write 33 while including the tens place.

↓ Subtract 52.8 by 33. ↓

\(52.8-33=19.8\)

Therefore, the answer is 33.

Answer:

5 b^2 + 4 b - 2116

Step-by-step explanation:

Simplify the following:

5 b^2 + 4 b - 46^2

| | 4 | 6

× | | 4 | 6

| 2 | 7 | 6

1 | 8 | 4 | 0

2 | 1 | 1 | 6:

Answer: 5 b^2 + 4 b - 2116

When the switch is closed, the potential difference across the resistor R connected to a secondary coil of a transformer is influenced by the turns ratio (n2 > n1). In this scenario, the number of turns in the secondary coil (n2) is greater than the number of turns in the primary coil (n1). This results in a step-up transformer, which increases the voltage across the resistor R in the secondary circuit.

When the switch is closed, a current flows through the primary coil of the transformer, which creates a changing magnetic field. This changing magnetic field induces a voltage in the secondary coil of the transformer, which is connected to resistor R. The ratio of the number of turns in the secondary coil to the number of turns in the primary coil is given by the turns ratio, which is represented by n2/n1.
Since the potential difference across a resistor is given by Ohm's law (V = IR), the potential difference across resistor R is proportional to the current flowing through it. Therefore, when the potential difference across resistor R connected to the secondary coil of the transformer is n2 > n1, it means that the current flowing through the secondary coil is greater than the current flowing through the primary coil. This is because the voltage induced in the secondary coil is greater than the voltage applied to the primary coil due to the turns ratio of the transformer.
When the switch is closed, the potential difference across the resistor R connected to a secondary coil of a transformer is influenced by the turns ratio (n2 > n1). In this scenario, the number of turns in the secondary coil (n2) is greater than the number of turns in the primary coil (n1). This results in a step-up transformer, which increases the voltage across the resistor R in the secondary circuit.

To learn more about ratio, click here:

brainly.com/question/13419413

#SPJ11

Answer:

8L - 2 = P

Step-by-step explanation:

Please, just one question per post.  I'll focus on #15

As a reminder, the formula for the perimeter of a rectangle is

P = 2L + 2W, where L is the length and W the width.

Next, we represent the width in terms of the length:  W = 3L - 1.

We want the perimeter of this rectangle in terms of the length, L, with the width, W, not appearing in the final result.

Here P = 2L + 2W = 2L + 2(3L - 1), or

P as a function of L = 2L + 6L - 2 = 8L - 2 = P

The remaining side is 16.9 and remaining angles are 83.1 and 34.9.

The cosine formula to find the side of the triangle is given by:

c = √[a² + b² – 2ab cos C] Where a,b and c are the sides of the triangle.

Given:

m∠B = 62°, a = 11, and c = 19

Now, b² = a² + c² - 2ac cos B.

b = √ a² + c² - 2ac cos B

b = √ 11² + 19² - 2x 11  x 19 cos 62

b= 16.9

Now. a/ sin A = b/ sin B= c/ sin C

So, <C = arc sin ( c sin B /b)

<C = arc sin ( 19 sin 62 /16.9)

<C = 83.1

and, <A = arc sin ( a sin B /b)

<A = arc sin ( 11 sin 62 /16.9)

<A = 34.9

Learn more about Cosine Formula here:

https://brainly.com/question/17171751

#SPJ1

Step-by-step explanation:

the answer is 3.142

\(3.142 \times 20 \times 18 \\ 2 = 1131.2 \times 3.142 \times 10^{2} = 628.4 \\ \\ = 1759.52\)

The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer:

-a square bc

Step-by-step explanation:

-ab(ac)

= - (a*a*b*c)

= - a to the power 2 and bc

= -a square bc

Answer:

-a square bc

Step-by-step explanation:

trust

Answer:

14.84

Step-by-step explanation:

20*(6%+1)*(1-30%)

20*(0.06+1)*1-0.3)

20*1.06*0.7

14.84

It is important to check for multicollinearity in a regression model and take steps to reduce it, such as removing one of the highly correlated independent variables or using regularization techniques.

Multicollinearity is a statistical phenomenon where two or more independent variables in a regression model are highly correlated with each other. This can cause problems in the regression model as it becomes difficult to distinguish the individual effects of the independent variables on the dependent variable.
When multicollinearity is present in a regression model, the p-values of the slopes of the independent variables are affected. The p-value measures the probability of obtaining a result as extreme or more extreme than the observed result, assuming that the null hypothesis is true. The null hypothesis in a regression model is that the slope of the independent variable is zero, meaning that there is no relationship between the independent variable and the dependent variable.
Multicollinearity can cause the standard errors of the slopes to increase, leading to inflated p-values. In other words, the significance of the relationship between the independent variable and the dependent variable may be underestimated. This is because the highly correlated independent variables are both trying to explain the same variation in the dependent variable, leading to an unreliable estimate of the effect of each independent variable on the dependent variable.
Therefore, it is important to check for multicollinearity in a regression model and take steps to reduce it, such as removing one of the highly correlated independent variables or using regularization techniques. This can help to ensure that the regression model produces reliable estimates of the effects of the independent variables on the dependent variable.

for more questions on multicollinearity

https://brainly.com/question/17216244

#SPJ11

Answer:

63.43

Step-by-step explanation:

For this I'll be using tangent, which is an easier way.

tan x = 22/11

x = \(tan^{-1}\) (22/11)

Plug into calculator, you get 63.43.

Answer: 69.9

Step-by-step explanation:

According to the given data 47% of the fans that attend the event, purchase the peanuts.

The sample collected was among 200 fans which means total fans = 200

out of which 94 fans purchased peanuts which means

Percentage of Fans purchased Peanuts  = \(\frac{94}{200}\)  X 100

                                                                     = 47 %

Not exactly the half of the fans purchased the peanuts but approximately half that is 3% less than 50 % fans puchased the peanuts which implies => 47 % fans purchased peanuts.                

#SPJ4

Answer : 20.95cm³

Step-by-step explanation:

Volume of cone,V = ⅓πr²h

Radius,r = 2cm

Height,h = 5cm

π = 22/7

V = ⅓*²²/7*(2)²*5

= 20.95cm³

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=5\\ r=2 \end{cases}\implies V=\pi (2)^2(5)\implies V=20\pi \implies V\approx 62.83 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=5\\ r=2 \end{cases}\implies V=\cfrac{\pi (2)^2(5)}{3}\implies V=\cfrac{20\pi }{3}\implies V\approx 20.94\)

Answer:

Point Form: (- 1/4, 5/4)

Equation Form: x = - 1/4, y  = 5/4

Step-by-step explanation:

The equation "Sixty-four reduced to a number is forty-eight" can be expressed algebraically or as algebra expression as: 64 - x = 48

In this equation, the variable "x" represents the unknown number that we are trying to find. By subtracting "x" from 64, we are reducing the value to 48.

Therefore, it can be translated into an algebraic equation:

64 - x = 48

Solving the equation allows us to determine the value of the variable "x," which represents the number we are looking for. The use of variables in algebraic expressions allows us to generalize problems and find solutions for different scenarios.

Learn more about algebra here:

https://brainly.com/question/4344214

#SPJ11

===================================================

Work Shown:

Use the slope formula to get

m = (y2 - y1)/(x2 - x1)

m = (0 - (-3))/(9 - 0)

m = (0 + 3)/(9 - 0)

m = 3/9

m = 1/3

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

Basically we subtract the y coordinates, and do the same for the x coordinates as well (subtract in the same order). Afterward, divide the two results. Reduce the fraction as much as possible.

A slope of 1/3 means we move up 1 unit each time we move to the right 3 units.

The slope being positive means the line goes uphill as you read from left to right.

Answer:

$260

Step-by-step explanation:

164 to the nearest tenth is 160 then 95 to the nearest tenth is 100 so then you have to add 100 and 160 together to get $260.

Answer:

100+170= 270 round 164 and 95 to the nearest 10th

Step-by-step explanation:

You are welcome may I please get brainliest?:)

Answer:

2

Step-by-step explanation:

Alice paid $25 for her pair of jeans, and Jeff paid $4 for the steaks.

Let's calculate the final amount paid by Alice and Jeff for their purchases.

Alice:

Jeff:

So, Alice paid $25 for her pair of jeans, and Jeff paid $4 for the steaks.

Learn more about discount here https://brainly.com/question/15319179

#SPJ4

To compute the values of (r) and (x) for the different states of the harmonic oscillator, we need to consider the wavefunction solutions for each state.

The wavefunctions for the harmonic oscillator are given by Hermite polynomials multiplied by a Gaussian factor. The energy eigenvalues for the harmonic oscillator are given by (n + 1/2) * h * ω, where n is the quantum number and ω is the angular frequency of the oscillator. (a) Ground State: The ground state of the harmonic oscillator corresponds to n = 0. The wavefunction for the ground state is: ψ₀(x) = (mω/πħ)^(1/4) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₀) is equal to 1/2 * h * ω. Therefore, for the ground state: (r) = 0 (since n = 0). (x) = √(ħ/(2mω)). (b) First Excited State:The first excited state corresponds to n = 1. The wavefunction for the first excited state is: ψ₁(x) = (mω/πħ)^(1/4) * √2 * (mωx/ħ) * exp(-mωx²/2ħ), where m is the mass of the oscillator. In this state, the energy (E₁) is equal to 3/2 * h * ω. Therefore, for the first excited state: . (r) = 1. (x) = √(ħ/(mω)). (c) Second Excited State:The second excited state corresponds to n = 2. The wavefunction for the second excited state is: ψ₂(x) = (mω/πħ)^(1/4) * (2(mωx/ħ)^2 - 1) * exp(-mωx²/2ħ)  where m is the mass of the oscillator. In this state, the energy (E₂) is equal to 5/2 * h * ω.

Therefore, for the second excited state: (r) = 2. (x) = √(ħ/(2mω)). In summary: (a) Ground State: (r) = 0, (x) = √(ħ/(2mω)). (b) First Excited State: (r) = 1, (x) = √(ħ/(mω)). (c) Second Excited State: (r) = 2, (x) = √(ħ/(2mω)).

To learn more about harmonic oscillator click here: brainly.com/question/13152216

#SPJ11