what value of the correlation coefficient implies that there is no relationship between the two variables of a linear regression model?

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{Square inches formula is: }\\\\\large\boxed{\mathsf{l}\rm{ength}\times\mathsf{h}\rm{eight} = \mathsf{s}\rm{quare \ inches}}}}}}}[/tex]

[tex]\huge\text{So, your equation should look like:}[/tex]

[tex]\large\boxed{\mathsf{3\ inches \times 8\ inches \times 14\ inches = square\ inches^2}}}[/tex]

[tex]\huge\text{Now let us solve for your answer to this problem:}[/tex]

[tex]\large\boxed{\mathsf{3\ inches \times 8\ inches \times 14\ inches = square\ inches^2}}}[/tex]

[tex]\large\boxed{\mathsf{24\ inches\times 14\ inches = square\ inches^2}}[/tex]

[tex]\large\boxed{\mathsf{336 = square\ inches^2}}[/tex]

[tex]\huge\text{Therefore, your answer SHOULD be:}[/tex]

[tex]\huge\boxed{\mathsf{Option\ D. \ 336}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The height that will minimize the amount of tin that will be required to construct is 4 inches.

Given that,

It is necessary to build a cylindrical, open-top container with a 167 cubic inch volume.

To find : What height will result in the least amount of tin being used to make the can? ?

V = πr^2h. Eq1. And. A =2πr^2 +2πrh. Eq2

From Eq1 h = V/πr2. Eq3

Sub Eq3 into Eq2

Then A = 2πr^2 + 2πr ×(V/πr^2). And V =16π

So A = 2πr^2 + 32π/r

dA / d r = 4πr - 32π/r^2 = 0 at max/ min

r^3 -8 =0

r^3 =8

r= 2. sub into Eq3

h = 16π/ π×2^2

h=4 inches

Therefore, 4 inches is the height that will require the least amount of tin to build.

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a) The distance of the boat from its starting point is 20 km.

b. The nearest degree  is 63°

c. The bearing g that the boat should travel on to return to the starting point is 360° - 63° = 297°.

To find the distance of the boat from its starting point, we can use the Pythagorean theorem.

x^2 + y^2 = d^2

Substituting the values for x and y, we get:

12^2 + 16^2 = d^2

d^2 = 144 + 256

d^2 = 400

d = 20

Hence, the distance of the boat from its starting point is 20 km.

b) To find the bearing that the boat should travel on to return to the starting point, we must calculate the angle between the two legs of the journey.

b = arctan (y / x) = arctan (16 / 12) = 63.43°

To the nearest degree  is 63°.

c) The bearing that the boat should travel on to return to the starting point is the opposite direction of the angle formed by the two legs of the journey. Therefore, the bearing is 360° - 63° = 297°.

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When the potential costs of production are constant, the cost of creating one thing remains constant regardless of how much of that good is produced. This is also known as continuous returns to scale.

The term "constant" has several meanings in mathematics. It refers to non-variance as an adjective; as a noun, it has two meanings: A constant and well-defined integer or other mathematical object that does not change. A constant is a value or number whose expression never changes; it is always the same.

Here,

In this case, increasing the production of one good will result in a proportionate rise in the overall cost of production rather than an increase or decrease in the opportunity cost of producing that good. For example, if a corporation manufactures chairs and tables and the opportunity cost of manufacturing one chair is always two tables, the cost of making two chairs is four tables, the cost of producing three chairs is six tables, and so on.

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The following data which represent the test scores of a math class using frequency table of six classes are;

Based on the given task content; we are required to construct a frequency table using the given Data,

The frequency table must use 6 classes;

The class width or class interval = 15

Given Data: 26 29 37 37 46 62 64 68 71 73 74 80 86 92 94 97 100

11 - 25 0

26 - 40 4

41 - 55. 1

56 - 70 3

71 - 85 4

86 - 100 5

In conclusion, the data represented using frequency table of six classes starts from 11 and ends at 100

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A histogram is a graphical representation of data that uses bars of different heights to represent the frequency of a given variable.

It is used to display the distribution of a categorical variable by showing the number of data points that fall into each of several categories.

To calculate the heights of the bars in a histogram, you first need to determine the number of data points in each category. This is done by counting the number of data points that fall into each category, and then dividing by the total number of data points. This gives us the histogram of each category, which can then be used to calculate the height of the bar. The formula for this is:

Bar Height = Frequency of Category / Total Number of Data Points

For example, say there are 10 data points in the category “A” and 20 data points in the category “B”. The frequency of “A” is 0.5 (10/20), and the frequency of “B” is 0.5 (20/20). The height of the bar for “A” would be 0.5, and the height of the bar for “B” would be 0.5.

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The appropriate values to be used on the x and y axis are; w will represent the input values which will be on the x-axis while y will represent the output values which will be on the y-axis.

Usually, linear equation graphs are made up of the y-axis and x-axis values.

In this type of graph, the y-axis values are referred to as the range or output of the function while the x-axis values are referred to as the domain or input of the function.

Now, in the given question, we see that w is clearly the input function and as such will be represented on the x-axis while the output value will be represented on the y-axis.

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The proportion is solved to give s = 3

Proportion can simply be described as an equation made equal to each other.

Also, algebraic expression are defined as expression that are comprised of terms, variables, factors, coefficient and constants.

They are also made up of arithmetic operations, such as;

From the information given, we have that;

s + 1/4 = 4/8

cross multiply

8(s + 1) = 16

Divide both sides by 8, we get;

s + 1 = 2

collect like terms

s = 3

Hence, the value is 3

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The number of bracelets and earrings sold is 10 and 16.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

Bracelets = x

Earings = y

Cost of bracelets = $5.00

Cost of the earrings =  $3.00

Now,

One day she sold 6 more earrings than bracelets and her sales totaled $98.

We can make two equations as,

y = x + 6 _____(1)

5x + 3y = 98 ______(2)

Substituting (1) in (2)

5x + 3(x + 6) = 98

5x + 3x + 18 = 98

8x = 98 - 18

8x = 80

x = 10

And,

y = 10 + 6

y = 16

Thus,

Bracelets = 10

Earings = 16

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The correct response is d. 4.6 years. The company is replacing at most 10% of their toasters sold 4.6 years.

To handle problems using samples that have a normal distribution, utilize the z-score formula.

The z-score of a measure X in a collection with mean and standard deviation is given by:

Z= x−μ/σ

The measure's standard deviations from the mean are determined by the [tex]Z-[/tex]score. We examine the p-value linked with the [tex]Z-[/tex]score in the [tex]Z-[/tex]score table after computing the [tex]Z-[/tex]score. This p-value is the probability that the measure's value is smaller than [tex]X[/tex], or the percentile of [tex]X[/tex]. The likelihood that the value of the measure exceeds [tex]X[/tex] is calculated by deducting [tex]1[/tex] from the pvalue.

This issue involves that:

Mean, μ[tex]=5.8[/tex]

Standard deviation,σ[tex]=0.9[/tex]

Only those who rank in the bottom 10% will be replaced.

So, if Z has a p value of 0.10, the warranty is equal to the value of X.

So it is X when

[tex]Z=-1.28[/tex]

Z= x−μ/σ

x=Z∗σ+μ

[tex]x=-1.28*0.9+5.8\\x=4.6[/tex]

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Answer:

1/4 is the answer or one-fourth

Step-by-step explanation:

Answer:

0.25 or 1/4 is the answer.

Step-by-step explanation:

The transformations are composed so that the sides of triangles are in the ratio of 1/2 and the angles are equal.

Similarity transformations are a sort of mathematical transformation that preserves the length ratios of related lines in a figure. Among these transformations are:

A translation is the movement of a figure in a given direction without affecting its size or shape. The combination of two translations results in a single translation equal to the total of the distances travelled.

A rotation is a transformation that involves turning a figure around a fixed point known as the center of rotation. The combination of two revolutions results in a single rotation equal to the total of the angles of rotation.

A reflection is a transition that occurs when a figure is flipped over a line known as the line of reflection. The combination of two reflections is simply a single 180-degree rotation.

Dilation: A dilation is a transformation that enlarges or reduces a figure by a given scale factor, centered at a fixed point. The product of two dilations is a single dilation equal to the product of the scale factors.

Here,

The sides of triangles are in ratio.

4/8=6/3=1/2

The composition of transformations is the sides of triangles are in ratio of 1/2 and angles are equal.  

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A carousel with a 45-foot diameter makes 3 revolutions per minute. (a) The angular speed is 6π rad/minute. (b) The linear speed is 424 feet per minute.

Information available in the problem:

diameter of the carousel = d = 45 feet

The carousel makes 3 revolutions per minute.

a) 1 revolution = 360⁰ = 2π radians

angular speed = 3 rev/minute

angular speed = 3 x 2π radians/minute = 6π rad/minute

b) the distance travelled in a revolution is equal to the circumference of the carousel.

Circumference of carousel = πd = 45π feet

Linear speed = 3 rev/minute = 3 x 45π  feet/minute

Linear speed = 424 feet per minute.

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$6,820 is the total tax owned by William.

percentage, a relative value indicating hundredth parts of any quantity.

Given that William earned $52,000 last year.

he first $30,000 is taxed at 11%

Let us find the 11% of 30000

30000×11/100

$3,300.

The tax owed on 30000 amount is $3,300.

The balance amount is 52000-30000

$22000

The above amount has a tax of 16%.

Now let us find the 16% of 52000

16/100×52000

$3520

The total tax owed by William is $3,300 + $3,520 = $6,820.

Hence, $6,820 is the total tax owned by William.

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Answer: -2(x+5)

Step-by-step explanation:

The correct response is B. Because respondents were self-selected, the findings cannot be extrapolated to the general population.

All citizens of a country, whether they live there permanently or are only passing through, are considered to be part of the "population." Regularly, this indicator shows the local population in a specific location. Growth rates are the yearly changes in population brought on by births, deaths, and net migration. The complete student body at a school is an illustration of a population. At the time of data collection, it would include every student enrolled in that institution. Each of these pupils' data is gathered, depending on the issue statement. Whether they are a part of a nation or a group of people who share a given quality, all of the individuals in a group are considered to be a population.

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A fashionable deck of cards trendy deck of playing cards carries fifty two playing cards, of which 26 are crimson and 26 are black, thirteen are of every match. The probablity of selecting two spades in a row = 3

A wellknown deck of cards incorporates 52 cards and consequently there are 52 feasible outcomes.

# of viable outcomes =

52

four of the 52 cards in a standard deck of cards are aces and accordingly there are 4 favorable results.

# of favorable outcomes

=

four

# of favorable consequences=4

The opportunity is the wide variety of favorable results divided by using the variety of possible outcomes:

�(Ace)=

# of favorable effects =4

# of feasible consequences =52

P(Ace)=

# of viable outcomes

# of favorable results =

fifty two

4​

=

13

1

​

The anticipated variety of aces is then acquired through multiplying the variety of draws via the opportunity.

Prediction = range of attracts × (Ace) = 39 × 1 = 39

=three Prediction = wide variety of draws×P(Ace)

13* 1 = 13

39×1 = 39

=3

thus we expect that three of the drawn cards will be aces.

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The true mean of the population (the true mean of all high school students spending an average of how many hours each week doing sports) is between 22.6 and 29.0 hours.

The 95% Confidence Interval for the mean of the sample of 8 high school students spending an average of 25.8 hours each week doing sports is calculated by using the formula:

CI95 = (X ± (2*Standard Error))

Where X is the sample mean (25.8 hours) and the Standard Error is calculated as the standard deviation (3.2 hours) divided by the square root of the sample size (8).

Therefore, the 95% Confidence Interval is calculated as:

CI95 = (25.8 ± (2*(3.2/√8)))

CI95 = (25.8 ± 3.2)

CI95 = (22.6, 29.0)

This means that we are 95% confident that the true mean of the population (the true mean of all high school students spending an average of how many hours each week doing sports) is between 22.6 and 29.0 hours.

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The 85% confidence interval for the mean time at lunch is (31.84, 39.36) minutes.

In a random sample of fourteen people, the mean time at lunch was 35.6 minutes.

Standard deviation of 8.2 minutes.

A common method to calculate the confidence interval for the mean of a normal distribution is to use the Z-score. For a 85% confidence interval, the Z-score is 1.44. Therefore, the confidence interval can be calculated as:

The confidence interval formula in statistics is used to describe the amount of uncertainty associated with a sample estimate of a population parameter.

Where,

n= Number of terms

[tex]$\overline{\mathrm{x}}[/tex]= Sample Mean

[tex]$\sigma[/tex]=Standard Deviation

[tex]$z_{\alpha / 2}[/tex]= Value corresponding to a2 in z table

[tex]$t_{\alpha / 2}[/tex]= Value corresponding to a2 in t table

[tex]$\alpha[/tex]=(1 - Confidence Level /100)

So for the given data, the confidence interval would be:

35.6 ± 1.44 * 8.2 / √14

35.6 ± 1.44 * 8.2 / 3.74

35.6 ± 3.76

Therefore, the 85% confidence interval for the mean time at lunch is (31.84, 39.36) minutes.

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The number of zeros/roots it will have is 3

From the question, we have the following parametes that can be used in our computation:

P(x) = x^3 - 5x^2 − 2x + 24

The degree of the polynomial is 3

So, the number of roots is 3

Using a graphical calculator, we have the roots to be

Roots = -2, 3 and 4

To do this, we set x = 0

So, we have

P(0) = 0^3 - 5(0)^2 − 2(0) + 24

This gives

P(0) = 24

The end behaviour of the function is:

as x approaches negative and positive infinity, the function is positive

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Answer:

60.83 percent hope it helps

The probability of any one person visiting a particular station is 1/3. Since there are three people in the family, the probability that they would all visit the same station is 1/3 x 1/3 x 1/3, which is equal to 1/27.

The probability that all three members of the family visit the same station at the medical clinic is 1/27 (1/3 x 1/3 x 1/3). This is because each person has an equal chance of being assigned to any of the three stations and since there are three people in the family, the probability that they would all visit the same station is 1/3 multiplied by itself three times, which is equal to 1/27. The experiment is recording the station number for each member and since the incoming individuals are assigned to any of the three stations randomly, the probability that all three members visit the same station is 1/27.

The complete question is :

A family consisting of three persons—a, b, and c—goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. during a certain week, each member of the family visits the clinic once and is assigned at random to a station. the experiment consists of recording the station number for each member. suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability that all three members visit the same station?

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The probability that both cards are aces is 0.45%.

Given that,

A standard 52-card deck is used to deal two cards. In other words, two cards are uniformly and randomly sampled without being replaced.

There are four aces in the deck of 52 cards. The likelihood of drawing an ace when you draw a card is 4/52=1/13.

There are only 51 cards left when the second card is drawn, and since an ace has already been drawn, just 3 of those cards are still in the deck. Therefore, there is a 3/51 chance of drawing the second ace. The likelihood that both of these events occur is 1/13 x 3/51 = 0.00452. (approx). Thus, there is a 0.45% chance of drawing two aces.

Combinations and permutations offer a different perspective on this. There are 52C2 different methods to choose two cards from a deck. The entire sample space is shown here.

Therefore, the probability that both cards are aces is 0.45%.

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The area of the sector is 12π square units.

Given data:

To find the area of the sector, use the formula:

[tex]\text{Area of Sector} = \frac{\text{Central Angle} }{ 360^\circ} * \pi * r^2[/tex]

Given that the central angle is 120° and the radius is 6 units.

Substitute these values into the formula:

[tex]\text{Area of Sector} = \frac{120^\circ }{ 360^\circ} * \pi * 6^2[/tex]

[tex]A = \frac{1}{3} * \pi * 36[/tex]  square units

A = 12π square units

Hence, the area of the sector is 12π square units.

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Based on the information, she can infer that the children meet at 7:00 pm EST to play video games. Additionally, the best flight ticket for Morgan is Sunset airline since it is $12 cheaper than Autumn airline.

According to the information, Joey is in Ohio and Grayson is in Oregon. These two states have different time zones, in the case of Ohio it is (-5) and in the case of Oregon it is (-8). Therefore, they connect to play at 7:00 pm EST because when Grayson arrives at his house at 4:00 pm, in Ohio it is 7:00 pm. However, Joey is already connected since 4:20 pm that he arrived at his house.

To identify which is the best ticket for Morgan, we must add all the services that she wants to include in her plane trip and then find the difference between the value of the two tickets.

Sunset airline:

$219 + $80 + $30 = $329

Autumn airlines:

$261 + $40 + $40 = $341

$341 - $329 = $12

According to the above, Sunset airlines ticket is cheaper.

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Converting the binary (base-10) number 77₁₀ to decimal (base-2) gives 1001101₂.

In Mathematics, there are four (4) main types of number system and these include the following:

In this exercise, you're required to convert the given number in base 10 to base 2 and this can be done as follows:

2 | 77

2 | 38 R 1

2 | 19 R 0

2 | 9 R 1

2 | 4 R 1

2 | 2 R 0

2 | 1 R 0

2 | 0 R 1

Next, you would read the decimal number (base-2) upward and this gives:

77₁₀ = 1001101₂.

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