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Based on the given information, a hypothesis test was conducted at a significance level of 0.1. The resulting p-value is 0.044. To determine whether to reject or fail to reject the null hypothesis , we compare the p-value to the significance level.

In this case, the p-value (0.044) is smaller than the significance level (0.1). This means that the observed data is unlikely to occur under the assumption that the null hypothesis is true. As a result, we reject the null hypothesis.

Rejecting the null hypothesis indicates that there is evidence to support the alternative hypothesis. The alternative hypothesis typically represents the researcher's claim or the hypothesis they are trying to prove. In this context, rejecting the null hypothesis suggests that there is evidence to support the alternative hypothesis.

Therefore, the correct conclusion is that there is sufficient evidence to reject the null hypothesis and accept the alternative hypothesis. It implies that the observed data provides enough support to conclude that there is a significant relationship, effect, or difference, depending on the specific context of the hypothesis test.

It is important to note that rejecting the null hypothesis does not prove the alternative hypothesis to be true. It simply indicates that there is enough evidence to suggest that the alternative hypothesis is more likely than the null hypothesis. The conclusion should be interpreted in the context of the specific hypothesis being tested and the significance level chosen.

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there is a very loose positive correlation because they are all going in the positive direction but are also scattered.

Answer:

Yes, it is

Step-by-step explanation:

Ok sorry wish I can help promise

We have a dataset of 5 different engines, each with data on five parameters: Time, Miles, Load, Speed, and Oil. To estimate the time until the first engine overhaul as a function of all four predictor variables, we can use a regression model. To do this, we first create a scatter plot matrix of all possible combinations of features. However, since we only have 5 data points, we cannot say that our model is highly reliable.

It appears that the Time feature is somewhat linearly dependent on the Load feature, so we can use this relationship for the linear regression model:

Time = a*Load + b

We have a scatter plot matrix that we can use to make predictions based on a model, but we should bear in mind that the results may be unreliable due to the limited dataset. To fit a linear regression model to this dataset, we will use the sklearn library in Python. A code snippet is provided for this purpose, in which we import the necessary libraries and load the data into a pandas DataFrame. We then select the "Load" feature as the predictor variable (X) and the "Time" feature as the response variable (y). The linear regression model is then fitted to the data using the LinearRegression() function. The coefficients and intercept of the model are printed as output, which are 0.35 and 1.6019230769230759, respectively.

The slope of 0.35 is not very large, but we can still use it to make predictions for a given value of the "Load" feature. For instance, if we have a load of 23, we can substitute this value in the above model and predict the time for the engine to run before its first overhaul.

Thus, we can predict that the engine will run for 9.25 years until the first engine overhaul, as per the formula:

Time = 0.35*23 + 1.6 = 9.25.

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The dog's displacement given in vector notation is D = [-23.125 m, 18.25 m].

Given, First, the dog runs 9.75 m towards east,

So, the x-component of displacement is 9.75 m towards east.

Second, the dog runs 18.25 m towards north,

So, the y-component of displacement is 18.25 m towards north.

Third, the dog runs 23.125 m towards west.

Now, the x-component of the final displacement is negative as the dog is moving towards west.

Hence, the x-component is -23.125 m towards west.

Now, the displacement in vector notation can be given as:

Displacement vector D = [x-component, y-component]

Therefore, the dog's displacement in vector notation is D = [-23.125 m, 18.25 m]

Therefore, the dog's displacement given in vector notation is D = [-23.125 m, 18.25 m].

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Answer:

y = - 3x

Step-by-step explanation:

an equation involving direct proportion has the form

y = kx ← k is the constant of proportion

the only equation in this form is

y = - 3x ( with k = - 3  )

Answer:

awesome 100✓jjjjjjjjjjj

The empirical rule, also known as the 68-95-99.7 rule, provides a rough estimate of the percentage of values that fall within a certain number of standard deviations from the mean in a normal distribution.

According to the empirical rule, approximately 68% of the area under a normal curve is within 1 standard deviation of the mean, approximately 95% of the area is within 2 standard deviations of the mean, and approximately 99.7% of the area is within 3 standard deviations of the mean.

To match the probabilities to the range for the empirical rule, we can use the following table:

Within 1 standard deviation of the mean: 68%

Within 2 standard deviations of the mean: 95%

Within 3 standard deviations of the mean: 99.7%

It's important to note that the empirical rule is only an approximation and may not be accurate for all normal distributions.

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Therefore, the least-squares error in the least-squares solution of ax = b is e = ||b - A(A^T A)^(-1) A^T b||^2.

The least-squares solution of ax = b is given by x = (A^T A)^(-1) A^T b, where A is the matrix whose columns are the coefficients of the variables in the system of equations. The least-squares error is the sum of the squares of the residuals, which are the differences between the values of b and the values of ax predicted by the least-squares solution.

The least-squares error can be calculated as follows:

e = ||b - Ax||^2

= ||b - A(A^T A)^(-1) A^T b||^2

where ||.|| denotes the Euclidean norm.

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The main difference between the nation and the nationality is what each one represents, that is, each one represents a different element.

We have to:

In this sense, let us note that the nation refers to a group of people that make up a country, while nationality is a link between a person and the State.

¡Hope this helped!

Answer:

A=82

C=83

X+y=60

X=30+50+80

X=80

The standard matrix a for the linear transformation t. the image of v under the reflection in the y-axis is (-2,-5).

To find the standard matrix a for the linear transformation t, we need to apply the transformation to the standard basis vectors in R2. The standard basis vectors are (1,0) and (0,1).

Applying t to (1,0), we get t(1,0) = (-1,0). Therefore, the first column of a is (-1,0).

Applying t to (0,1), we get t(0,1) = (0,1). Therefore, the second column of a is (0,1).

So the standard matrix a for the linear transformation t is:

a = \begin{pmatrix}-1 & 0\\ 0 & 1\end{pmatrix}

This means that to apply the reflection in the y-axis to any vector in R2, we simply multiply the vector by this matrix. For example, if we have the vector v = (2,-5), we can apply the transformation as follows:

t(v) = a v = \begin{pmatrix}-1 & 0\\ 0 & 1\end{pmatrix} \begin{pmatrix}2\\ -5\end{pmatrix} = \begin{pmatrix}-2\\ -5\end{pmatrix}

So the image of v under the reflection in the y-axis is (-2,-5).

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The highest point on the graph of the normal density curve is located at its mean represented by μ.

The highest point on the graph of the normal density curve is located at its mean. The normal density curve or the normal distribution is a bell-shaped curve that is symmetric about its mean. The mean of a normal distribution is the measure of the central location of its data and it is represented by μ. It is also the balancing point of the distribution. In a normal distribution, the standard deviation (σ) is the measure of how spread out the data is from its mean.

It is the square root of the variance and it determines the shape of the normal distribution. The normal distribution is an important probability distribution used in statistics because of its properties. It is commonly used to represent real-life variables such as height, weight, IQ scores, and test scores.

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Whe you need to write a number in standard form, you normally write a number between the range of 1 and 10 and then multiply it by 10 raised to the power of ___.

So 400 becomes

4 x 100

4 x 10^2

Answer:

128

Step-by-step explanation:

Let, total number of T-shirts are x.

Number of blue T-shirts = (2/3)x = 2x/3 .

Number of blue shirts on sale = (3/5)(2x/3) = 2x/5 .

Number of medium sized blue shirts on sale = (1/5)(2x/5) = 2x/25 .

Fraction of the​ shop's T-shirts are blue​ T-shirts that are on sale and are size​ medium = \(\dfrac{2x/25}{x}\)= 2/25 . ( Number of medium sized blue shirts on sale divided by total number of T-shirts )

Hence, this is the required solution.

The value of x for this problem is given as follows:

x = 5.

Hence the angle measures are given as follows:

We have that angles A and D are congruent for this problem, meaning that they have the same measure.

Hence the value of x is obtained as follows:

7x - 3 = 5x + 7

2x = 10

x = 5.

Hence the angle measures are given as follows:

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a) To find the value of k, we use the given information that there are 5.5 pounds of salt in the barrel after 10 minutes.

By substituting these values into the equation Q(t) = 15(1 - e^(-kt)), we can solve for k. The rounded value of k is provided as the answer.

b) As t approaches infinity, the amount of salt in the barrel will reach a maximum value and stabilize. This is because the exponential function e^(-kt) approaches zero as t increases without bound. Therefore, the amount of salt in the barrel will approach a constant value over time.

a) We are given the equation Q(t) = 15(1 - e^(-kt)) to represent the amount of salt in the barrel at time t. By substituting t = 10 and Q(t) = 5.5 into the equation, we get 5.5 = 15(1 - e^(-10k)). Solving this equation for k will give us the desired value. The calculation for k will result in a decimal value, which should be rounded to four decimal places.

b) As t approaches infinity, the term e^(-kt) approaches zero. This means that the exponential function becomes negligible compared to the constant term 15. Therefore, the equation Q(t) ≈ 15 holds as t approaches infinity, indicating that the amount of salt in the barrel will stabilize at 15 pounds. In other words, the concentration of salt in the barrel will reach a constant value, and no further change will occur.

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Answer:

The amount of balls on each side would stay the same. The amount of balls would stay the same as long as both sides are throwing the same number of balls at the same time.

Step-by-step explanation:

Equation for east side: 20 (balls) -1 (thrown over to west) + 1 (thrown over from west) = 20 balls

Equation for west side: 40 (balls) -1 (thrown over to east side) +1 (thrown over by east side) = 40 balls

For the given order of units, the missing units are Deca, Kilo, Deci.

What is a unit?

In mathematics, a unit is a standard quantity that is used to measure or express other quantities. A unit provides a reference point that enables us to compare and quantify physical properties and quantities.

Units come in many forms, including length, mass, time, temperature, energy, and others. For example, the SI unit for length is the meter (m), while the unit for mass is the kilogram (kg), and the unit for time is the second (s).

Now,

The missing metric prefixes to complete the list are:

Deca-, Hecto-, Kilo-, Base Unit, Deci-, Centi-

The order of metric prefixes from largest to smallest is:

Kilo- (1000), Hecto- (100), Deca- (10), Base Unit (1), Deci- (0.1), Centi- (0.01), Milli- (0.001), Micro- (0.000001), Nano- (0.000000001), and so on.

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Domain: the smallest possible x-value to the largest possible x-value

In the case of this graph, we see the parabola starts at x = -3, and continues on forever.

Domain: [-3, infinity)

Range: the smallest possible y-value to the largest possible y-value

In the case of this graph, the parabola will continue to expand forever.

Range: (-infinity, infinity)

Therefore, while the domain has a restriction, the range does not and is all real numbers.

Hope this helps!

Answer:

$34.20

Step-by-step explanation:

P is the principal amount, $570.00.

r is the interest rate, 6% per year, or in decimal form, 6/100=0.06.

t is the time involved, 1....year(s) time periods.

So, t is 1....year time periods.

To find the simple interest, we multiply 570 × 0.06 × 1 to get that:

:) hope this helps

Answer:

√65

Step-by-step explanation:

The distance formula can be represented as

\(\sqrt{(x_{2} -x_1)^2 + (y_2-y_1)^2}\)

Taking (8,8) as (x₂, y₂) and (0,7) as (x₁, y₁), we have

\(\sqrt{(8 -0)^2 + (8-7)^2}\\= \sqrt{8^2 + 1^2}\\= \sqrt{65}\)

as our answer

9514 1404 393

Answer:

  (a) 6² +3² +1² +1² = 47

  (b) 5² +4² +2² +1² +1² = 47

  (c) 3³ +4² +2² = 47

Step-by-step explanation:

It can work reasonably well to start with the largest square less than the target number, repeating that approach for the remaining differences. When more squares than necessary are asked for, then the first square chosen may need to be the square of a number 1 less than the largest possible.

The approach where a cube is required can work the same way.

(a) floor(√47) = 6; floor(√(47 -6^2)) = 3; floor(√(47 -45)) = 1; floor(√(47-46)) = 1

__

(b) floor(√47 -1) = 5; floor(√(47-25)) = 4; ...

__

(c) floor(∛47) = 3; floor(√(47 -27)) = 4; floor(√(47 -43)) = 2

Answer:

3% of the figure is shaded

Fraction: 3/10

Decimal: 0.3

Hope this helped

Answer:

-0.86

Step-by-step explanation:

What is the slope of the line created by this equation? Round your answer out to two decimal places. 6x + 7y = 5

_____________________________________________

Slope intercept form solves for y:

y = mx + b when m = slope and b = y-intercept

First, solve for y:

6x + 7y = 5

subtract 6x from both sides:

6x + 7y - 6x = 5 - 6x

7y = 5 - 6x

divide both sides by 7:

7y/7 = (5 - 6x)/7

y = 5/7 - 6/7x

rearrange right side:

y =  - 6/7x + 5/7

Back to the equation: y = mx + b when m = slope and b = y-intercept

your slope is -6/7

in decimal form, rounded to two digits: -0.86

Answer:

\(\huge\boxed{\sf h \approx 7\ in}\)

Step-by-step explanation:

Volume = V = 2908.33 in³

Radius = r = 11.5 in.

π = 3.14

Height = h = ?

\(V= \pi r^2 h\)

Put the given data in the above formula.

2908.33 = (3.14)(11.5)²(h)

2908.33 = (3.14)(132.25)(h)

2908.33 = 415.265 (h)

2908.33/415.265 = h

\(\rule[225]{225}{2}\)

Answer:

..

...

Step-by-step explanation:

..

Answer:

x = 19

Step-by-step explanation:

Since C is between B and D , then

BC + CD = BD , substitute values

8x + 13 + 12x - 73 = 320 , that is

20x - 60 = 320 ( add 60 to both sides )

20x = 380 ( divide both sides by 20 )

x = 19