please help with finding the answer

This is the absolute value function shifted to the left 2 units:

| x+2 | = {

x+2 if x >= -2,

-(x+2) if x < -2

}

In mathematics, a function is a relationship between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is a rule or a set of rules that assigns each input value exactly one output value. Functions can be represented using equations, graphs, or tables. They are used to model real-world phenomena and solve problems in various fields such as science, engineering, economics, and finance.

Here,

The absolute value function is defined as:

| x | = {

x if x >= 0,

-x if x < 0

}

To shift the function to the left 2 units, we can replace x with (x+2):

| x+2 | = {

x+2 if x+2 >= 0,

-(x+2) if x+2 < 0

}

Simplifying further, we get:

| x+2 | = {

x+2 if x >= -2,

-(x+2) if x < -2

}

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Complete question:

The absolute value function is defined as:

| x | = {

x if x >= 0,

-x if x < 0

}

Find the function when shifted to the left 2 units.

a) The standard error of mean for this data set is approximately 0.141.

b) The approximate 95% margin of error is approximately 0.282.

c) The approximate 95% confidence interval for the population mean age is 19.824 to 20.376.

a) The standard error of mean (SEM) is given by the formula: SEM = s / sqrt(n), where s is the sample standard deviation and n is the sample size. Plugging in the values given, we have:

SEM = 1.8 / sqrt(163) ≈ 0.141

So the standard error of the mean is approximately 0.141.

b) The approximate 95% margin of error (MOE) can be calculated using the formula: MOE ≈ 2 * SEM. Plugging in the SEM value from part 1, we get:

MOE ≈ 2 * 0.141 ≈ 0.282

So the approximate 95% margin of error is approximately 0.282.

c) The approximate 95% confidence interval (CI) for the population mean age can be calculated using the formula: CI = x ± (z*SEM), where x is the sample mean, z is the critical value from the standard normal distribution corresponding to the desired level of confidence (95% in this case), and SEM is the standard error of the mean. The critical value for 95% confidence is approximately 1.96. Plugging in the values, we get

CI = 20.1 ± (1.96 * 0.141) ≈ 19.824 to 20.376

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1. Time taken to fill one community pool is 2hours 24 minutes.

2. Time taken to audit 30 files is 4 hours 41 minutes.

3. The time taken to erect is 54/7 hours or 7 hours 43 minutes

Time and work is a branch of mathematics that deals with the calculation of the amount of time required to complete a job or task by a worker or a group of workers working at a certain rate.

1. Job: Fill one community pool       Rate        Time         Work Completed

  Reserve water tower                     1/6            x                  x/6

  City water pipes                             1/4            x                  x/4

Solution: Fill one community pool;   [tex]\frac{x}{6} + \frac{x}{4} = 1[/tex]

Simplify, x = 12/5 hours or 2hours 24 minutes

Time taken to fill one community pool is 2hours 24 minutes.

2. Job: Work together       Rate        Time         Work Completed

  Mr. Dupree                       12/5           x                  12x/5

  Ms. Carmichael                16/4           x                  16x/4

Solution: If they work together, time taken to audit one file is

[tex]\frac{12x}{5} + \frac{16x}{4} = 1[/tex]

Simplify, x = 5/32 hours

So, time taken to audit 30 file, (5/32)×30 = 75/16 hours or 4 hours 41 minutes

Time taken to audit 30 files is 4 hours 41 minutes.

3. Job: Work together            Rate         Time         Work Completed

  Macon Construction           100/8           x                100x/8

  Thomson Masonry              200/12        x                 200x/12

Solution: If they work together, time taken to complete a work

[tex]\frac{100x}{8} + \frac{200x}{12} = 1[/tex]

Simplify, x = 6/175

Macon Construction 2 hours before so,

remaining work = 250 - (100×2hour/8) = 225 feet

then, the time taken to erect 225 feet rock facing by together is

6/175 × 225 = 54/7 hours or 7 hours 43 minutes

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1. Time taken to fill one community pool is 2hours 24 minutes. 2. Time taken to audit 30 files is 4 hours 41 minutes. and 3. The time taken to erect is 54/7 hours or 7 hours 43 minutes.

An audit is an independent review of financial statements and related documents in order to confirm their accuracy and compliance with relevant regulations.

1. Job: Fill one community pool       Rate        Time         Work Completed
 Reserve water tower                     1/6            x                  x/6
 City water pipes                             1/4            x                  x/4
Solution: Fill one community pool;  
Simplify, x = 12/5 hours or 2hours 24 minutes
Time taken to fill one community pool is 2hours 24 minutes.

2. Job: Work together       Rate        Time         Work Completed
 Mr. Dupree                       12/5           x                  12x/5
 Ms. Carmichael                16/4           x                  16x/4
Solution: If they work together, time taken to audit one file is
Simplify, x = 5/32 hours
So, time taken to audit 30 file, (5/32)×30 = 75/16 hours or 4 hours 41 minutes
Time taken to audit 30 files is 4 hours 41 minutes.

3. Job: Work together            Rate         Time         Work Completed
 Macon Construction           100/8           x                100x/8
 Thomson Masonry              200/12        x                 200x/12
Solution: If they work together, time taken to complete a work
Simplify, x = 6/175
Macon Construction 2 hours before so,
remaining work = 250 - (100×2hour/8) = 225 feet
then, the time taken to erect 225 feet rock facing by together is
6/175 × 225 = 54/7 hours or 7 hours 43 minutes

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Answer:

b the solution is (3,5)

Step-by-step explanation:

look at the points where the lines intersect

Total number of steps taken by an average man in a year while walking with 7192 steps a day is equals to 2,625,080 steps/year.

Number of steps taken by average man in a day is equals to  7192

Then the total number of steps he takes in a year is equals to,

Calculate it by multiplying the average number of steps per day by the number of days in a year.

There are different ways to define a year,

But assuming a regular calendar year of 365 days, the calculation would be,

Total number of days in a year = 365 days

Total number of steps in a year

= 7192 steps/day x 365 days/year

= 2,625,080 steps/year

Therefore, on average the man would walk about 2,625,080 steps in a year.

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The given question is incomplete, I answer the question in general according to my knowledge:

If a man walks with random steps and the average man takes 7192 steps a day about how many steps does the average man take in a year?

Answer:

To write an exponential decay function for this situation, we can use the formula:

P(t) = P₀e^(rt)

where:

P(t) = the population at time t

P₀ = the initial population

r = the annual rate of decrease (as a decimal)

t = time in years

We are given P₀ = 3,846 and r = -0.0027 (since the population is decreasing).

To approximate the population in 2022, we need to find t, the number of years from 1996 to 2022. That is:

t = 2022 - 1996 = 26 years

Now we can plug in the values we have:

P(t) = 3,846 e^(-0.0027t)

To find P(2022), we plug in t = 26:

P(26) = 3,846 e^(-0.0027(26))

≈ 3,200.62

Therefore, we can approximate the population of the city in 2022 to be about 3,201 people.

Answer:

3,101

Step-by-step explanation:

Please hit brainliest if this helped!

To write an exponential decay function for the population of the city, we can use the formula:

P(t) = P₀e^(-rt)

where P(t) is the population at time t, P₀ is the initial population, r is the decay rate, and e is the base of the natural logarithm.

In this problem, P₀ = 3,846 and r = 0.0027 (0.27% expressed as a decimal). We want to find the population in 2022, which is 26 years after 1996.To use the formula, we need to convert 26 years to the same time units as the decay rate. Since the decay rate is per year, we can use 26 years directly. Therefore, the exponential decay function for the population is:

P(t) = 3,846e^(-0.0027t)

To find the population in 2022 (t = 26), we substitute t = 26 into the function:

P(26) = 3,846e^(-0.0027*26) ≈ 3,101

Therefore, the population in 2022 is approximately 3,101.

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The probability that the mean cost of 9 LCD computer monitors is less than $180 is 0.8186 or 81.86% and the probability that the mean cost of 36 LCD computer monitors is less than $180 is 0.9999 or 99.99%.

What is the Central Limit Theorem (CLT)?

The Central Limit Theorem (CLT) is a statistical concept that states that the sample mean of a large number of independent and identically distributed (iid) random variables will be approximately normally distributed, regardless of the underlying distribution of the individual random variables.The significance of the Central Limit Theorem is that it allows us to make inferences about the population mean based on a sample mean, even if the population is not normally distributed. This is because the distribution of the sample mean becomes approximately normal as the sample size increases.

Finding the given probabilities:

To find the probability that the mean cost of 9 LCD computer monitors is less than $180, we can use the formula for the standard error of the mean:

[tex]SE = \sigma / \sqrt{n}[/tex]

where SE is the standard error of the mean, [tex]\sigma[/tex] is the population standard deviation, and n is the sample size. Plugging in the given values, we get:

[tex]SE = 55 / \sqrt(9) = 18.33[/tex]

Next, we can calculate the z-score corresponding to a sample mean of $180:

[tex]z = (180 - 170) / 18.33 = 0.546[/tex]

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than 0.546, which is 0.7079. However, we are interested in the probability that the sample mean is less than $180, which is the same as the probability that a standard normal variable is less than the calculated z-score. Therefore, the probability that the mean cost of 9 LCD computer monitors is less than $180 is:

[tex]P(z < 0.546) = 0.7079[/tex]

Rounding to four decimal places, we get 0.8186 or 81.86%.

To find the probability that the mean cost of 36 LCD computer monitors is less than $180, we can use the same formula for the standard error of the mean:

[tex]SE = \sigma / \sqrt{n}[/tex]

Plugging in the given values, we get:

[tex]SE = 55 / \sqrt{36} = 9.17[/tex]

Next, we can calculate the z-score corresponding to a sample mean of $180:

[tex]z = (180 - 170) / 9.17 = 1.090[/tex]

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than 1.090, which is 0.8621. However, we are interested in the probability that the sample mean is less than $180, which is the same as the probability that a standard normal variable is less than the calculated z-score. Therefore, the probability that the mean cost of 36 LCD computer monitors is less than $180 is:

[tex]P(z < 1.090) = 0.8621[/tex]

Rounding to four decimal places, we get 0.9999 or 99.99%.

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Suppose you look by eye at a star near the edge of a dusty interstellar cloud. The star will look dimmer than it would if it were outside the cloud.

Interstellar clouds are vast, dense regions of dust and gas that exist between stars. These clouds contain tiny solid particles of dust, which scatter and absorb light as it passes through them.

When we observe a star that is located near the edge of an interstellar cloud, the light from that star has to pass through a greater amount of dust before it reaches our eyes or telescopes. The dust scatters and absorbs some of the light, causing the star to appear dimmer than it would if it were outside the cloud.

This effect is similar to how the sun appears dimmer when it is viewed through a thick layer of clouds or fog. In both cases, the amount of light that reaches us is reduced due to the presence of a barrier that scatters and absorbs some of the light.

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The length of arc AB is 7pi/3 yards is the area of the shaded region and the length of the arc AB.

what is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.

To find the area of the shaded region and the length of arc AB, we need to first find the measure of angle ZAB. Let's call this angle x.

Since angle ZAOB measures 110 degrees and angle ZAB and angle BOA are vertical angles, we know that angle BOA also measures 110 degrees. Therefore, angle ZAB + angle BOA = 180 degrees.

So, we can write:

x + 110 = 180

Solving for x, we get:

x = 70

Now, we can use the formula for the area of a sector to find the area of the shaded region. The sector is defined by the central angle ZOB, which measures 360 - 110 - 70 = 180 degrees. So, we have:

Area of shaded region = (180/360) * pi * 6^2 = 18pi

Therefore, the area of the shaded region is 18pi square yards.

To find the length of arc AB, we can use the formula:

Length of arc AB = (x/360) * 2 * pi * 6

Plugging in x = 70, we get:

Length of arc AB = (70/360) * 2 * pi * 6 = 7pi/3

Therefore, the length of arc AB is 7pi/3 yards.

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Using the concept of parabola, the quadratic inequality represented by the graph can be written as:

y = x² -2x +2.

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola.

The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix.

The general equation for a parabola is given as:

y = a(x-h) ² + k

Now here we have:

(x,y) = (2,5)

(h,k) = (1,1)

Putting these values in the equation,

5 = a (2-1) ² + 1

a = 5-1

=4

Substituting the values:

y = (x-1) + 1

y = x² -2x +2

Therefore, the quadratic inequality can be written as: y = x² -2x +2.

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Answer:

Let's call the unknown number "x".

According to the problem:

x - (-17) = 25x

Simplifying:

x + 17 = 25x

Subtracting x from both sides:

17 = 24x

Dividing by 24:

x = 17/24

Therefore, the unknown number is 17/24.

The coordinates of the point we are looking for are (2, -9).

What are the coordinates of the point ?

The origin is the point at which all lines in a coordinate system intersect. When x and y are both equal to zero, the axes intersect. The origin's coordinates are (0, 0).

To find the coordinates of the point that partitions the line segment from (-6, 6) to (2, -10) into a ratio of 1 to 3, we can use the following formula:

(x, y) = ((32 - 1(-6))/4, (3*(-10) - 1*6)/4)

Here, the ratio of 1 to 3 corresponds to the fact that we are partitioning the line segment into 4 equal parts, with the point we want to find being at the end of the first part (i.e., 1/4 of the way from (-6, 6) to (2, -10)).

Plugging in the values, we get:

(x, y) = ((32 + 6)/4, (3(-10) - 6)/4)

= (2, -9)

Therefore, the coordinates of the point we are looking for are (2, -9).

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The matches of Histogram, Bin, Descriptive Statistics, Mean, Median and Standard Deviation are C, E, D, A, F, G and B respectively.

The Match the definition are given.

Histogram - C). is a graph of the frequency distribution of a set of data

Bin - E). a group in a histogram

Descriptive Statistics - D). values calculated from a data set and used to describe some basic characteristics of the data set

Mean - A). The scatter around a central point

Median - F). the middle value of a sorted set of data

Mode - G). is the most commonly occurring value in a data set

Standard Deviation - B). is a measure of a data’s variability

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The function f(x,y) has only minimum value at (1,0) is -1 and maximum value does not exist.

The given function is f(x,y)=x²+y²-2x

First find the partial derivative with respect to x and y

f'(x)=2x-2

f'(y)=2y

f'(x)=0=f'(y)

2x-2=0

x=1

and y=0

Now we will cheak maxima and minima at (1,0)

f''(x,y)=2 and f"(x,y)=2 and f"(x,y)=0( derivative of first order of x with respect to y)

We know that

rt-s²≥0 and r positive then f is minimum and  r negative maximum

r=2 , t=2 and s=0

rt-s²≥0 and r is positive so f(x,y) is minimum at (1,0)

f(1,0)=1-2=-1

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Answer: 14,605 pieces.

Step-by-step explanation:

In the second quarter, the company produced 795 pieces more than in the first quarter.

So, the total pieces produced in the second quarter can be calculated as:

6905 + 795 = 7700

The total pieces produced in the first semester (two quarters) can be calculated as:

6905 + 7700 = 14,605

Therefore, the company produced 14,605 pieces in the first semester.

The number of pieces the company produced in the first semester was 14,605 pieces.

The question asks to calculate how many pieces a company produced in the first semester, considering the production of two quarters.

In the first quarter, the company produced 6,905 pieces, as indicated in the question.

Already in the second quarter, the company produced 795 more pieces than in the first quarter, which means that the production in the second quarter was:

6,905 + 795 = 7,700 pieces.

To know the company's total production in the first semester, just add the productions of the two quarters:

6,905 + 7,700 = 14,605 pieces

Answer:

Loan term of the truck in years:

The loan term of the truck is 60 months. To convert this to years, we divide by 12 since there are 12 months in a year. Therefore, the loan term of the truck in years is:

60 months ÷ 12 months/year = 5 years

Monthly repayments including insurance:

The monthly instalment of the truck is R22,301.67 and the insurance cover is R500. Therefore, the total monthly repayment including insurance is:

R22,301.67 + R500 = R22,801.67

Total amount owed to the financer excluding insurance in June 2022:

Half of the monthly instalments have been made towards the truck in June 2022, which means that 5 months' worth of payments have been made. Therefore, the total amount owed to the financer excluding insurance in June 2022 is:

(R22,301.67 × 55) - R500 = R1,223,592.35

Significance of including insurance cover:

Including an insurance cover when purchasing the water tanker is important because it provides protection for the contractor against unforeseen events such as accidents, theft, or damage to the vehicle. In the event of an accident or theft, the insurance cover can help cover the costs of repairs or replacement of the vehicle, which can be a significant expense for the contractor. Additionally, having insurance can provide peace of mind for the contractor, knowing that they are covered in case of unexpected events.

Tanker driver's daily pay during weekdays:

The driver works for 5½ days per week and 9 hours per day on weekdays, which amounts to:

5.5 days/week × 9 hours/day = 49.5 hours/week

The rate per hour is R92.50, so the driver's pay per day during weekdays is:

49.5 hours/week × R92.50/hour ÷ 5 days/week = R909.75/day

The people who are included in the survey conducted by Bureau of Labor Statistics are (a) certain unpaid workers, (b) part-time workers and (c) workers on vacation, the correct option is (d).

The Bureau of Labor Statistics (BLS) is a unit of the US Department of Labor that is responsible for collecting, analyzing, and publishing data on labor market activity, working conditions, and price changes in the economy.

The Bureau of Labor Statistics (BLS) considers individuals to be employed if they meet any of the given criteria:

(i) Worked at least one hour as paid employees

(ii) Worked at least 15 hours as unpaid workers in a family-owned enterprise

(iii) Were temporarily absent from their regular jobs due to illness, vacation, strike, etc.

⇒ This means that certain unpaid workers, such as family members working in a family-owned business, would be considered employed by the BLS.

⇒ Part-time workers, who work less than 35 hours per week but are paid for their work, are also included in the employed category.

⇒ The Workers on vacation are considered employed by the BLS because they are temporarily absent from their job.

Therefore, all the options are correct , which is Option(d).

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The given question is incomplete, the complete question is

Who of the following are included in the Bureau of Labor Statistics "employed" category?

(a) certain unpaid workers

(b) part-time workers

(c) workers on vacation

(d) All of the above are correct.

Answer:

Step-by-step explanation:

Let x be the number of points scored by Team B.

Then, Team A scored twice as many points, or 2x.

The total number of points scored by both teams is 12, so we can set up the equation:

x + 2x = 12

Combining like terms, we get:

3x = 12

Dividing both sides by 3, we get:

x = 4

So Team B scored 4 points, and Team A scored twice as many, or 8 points.

Answer:

A system of equations is when two equations equal each other. In this case, f(x) and g(x) must equal each other.

f(x) - g(x) = 0

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

x^2 - 2x - 4 = 0

Using the Quadratic Formula:

x = (2 ± √20)/2

Therefore, the values for x are x = 2 and x = -3.

The Function of maximum or minimum for t is infinity.

While the principal subordinate can let us know if the capability is expanding or diminishing, the subsequent subsidiary. tells us in the event that the primary subsidiary is expanding or diminishing. On the off chance that the subsequent subsidiary is positive, the first.

To analyze the function R(t) = 2501² / e(3t), we can take the first and second derivatives:

R'(t) = -7503 * 2501² / e(3t)

R''(t) = 22509 * 2501² / e(3t)

To find the inflection point, we can set R''(t) = 0 and solve for t:

22509 * 2501² / e(3t) = 0

t = ln(0) / -3 = undefined

Since there is no real solution to this equation, there is no inflection point for this function.

To find the maximum or minimum, we can set R'(t) = 0 and solve for t:

-7503 * 2501² / e(3t) = 0

t = infinity

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Step-by-step explanation:

2x + ay + 2 = 0

the gradient or slope of the line is the factor m of x in the form

y = mx + b

so let's transform the given equation into that form :

ay = -2x - 2

y = (-2/a)x - 2/a

we know that m = 1.

so,

-2/a = 1

-2 = a

When the group leader uses the skill of reframing, he/she is easing the group out of emotional interaction and into cognitive reflection.

Reframing is a technique that involves taking a situation or problem and looking at it from a different perspective. In the context of group dynamics, the group leader can use reframing to help shift the focus of the group from an emotional or reactive response to a more reflective and analytical one.

For example, if a group is discussing a contentious issue and emotions are running high, the group leader might use reframing to help the group reframe the issue in a different way. This could involve asking the group to consider the issue from a different angle, or to think about it in a broader context.

The skill of reframing can be particularly useful in situations where the group is struggling to make progress or where emotions are preventing productive discussion. By using reframing, the group leader can help the group to reorient their thinking and focus on finding solutions rather than getting bogged down in emotional responses.

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The steps for finding out the third derivative of y (given as y''') are explained and given below.

To find the third derivative of y (y'''), you would need to differentiate the function y three times with respect to the independent variable. Here are the steps:

Start by differentiating y once to get the first derivative, y'.

Differentiate y' again to get the second derivative, y''.

Finally, differentiate y'' to get the third derivative, y'''.

You can use the chain rule, product rule, quotient rule, and other differentiation rules as needed to find each derivative.

Here's an example of finding the third derivative of y for the function y = x^4 + 2x^3 - 5x:

y' = 4x^3 + 6x^2 - 5

y'' = 12x^2 + 12x

y''' = 24x + 12

So the third derivative of y is y''' = 24x + 12.

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The standard deviation for the given mean length x is found to be: 2.138.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Here, the standard deviation enters the picture; it gauges how variable a set of values is, or how dispersed they are from the average. The differential between each value and the group average serves as the basis for the standard deviation.

Given data:

mean μ = 86

standard deviation σ = 8

number of sample n = 14

average body length  x = 91.1

The population standard deviation is divided by that of the square root of both the sample size to calculate the standard deviation of the sampled distribution of the sample mean.

So,

σₓ = σ / √n

σₓ = 8 / √14

σₓ = 2.138

Thus, the standard deviation for the given mean length x is found to be: 2.138.

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The complete question is-

Deer mice (Peromyscus manicul.atus) are small rodents native of North America. Their adult body lengths (excluding tail) are known to vary approximately Normally, with mean 86 mm and standard deviation 8 mm. Deer mice are found in diverse habitats and exhibit different adaptations to their environment. A random sample of 14 deer mice in a rich forest habitat gives an average body length of x = 91.1 mm. Assume that the standard deviation σ of all deer mice in this area is also 8 mm.

What is the standard deviation of the mean length x?

we would expect a supervisor rating of approximately 6.61 if a person had a selection test score of 6.

A mathematical sentence with two equal parts and an equal sign is called an equation. An illustration of an equation is 4 + 6 = 10. 4 plus 6 can be seen on the equal sign's left side, and 10 can be seen on the equal sign's right side.

To find the supervisor rating we would expect for a person with a selection test score of 6, we can plug 6 in for X in the regression line equation:

[tex]$$\hat{Y} = 1.7656 + 0.8073X$$[/tex]

So:

[tex]$$\hat{Y} = 1.7656 + 0.8073(6)$$[/tex]

Simplifying

[tex]$$\hat{Y} = 1.7656 + 4.8438$$[/tex]

[tex]$$\hat{Y} = 6.6094$$[/tex]

Therefore, we would expect a supervisor rating of approximately 6.61 if a person had a selection test score of 6.

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Answer: y=3x+0

Step-by-step explanation: rise (y) over run (x) would be 3/1, which is 3. The line passes through the origin (0,0) so its 0.

Answer:

The given function is an exponential growth function, not an exponential decay function because as the exponent x increases, the value of y also increases instead of decreasing.

To describe its end behavior using limits, we need to find the limit of the function as x approaches infinity and as x approaches negative infinity.

As x approaches infinity, the exponent -x approaches negative infinity, and the base (1/6) is raised to increasingly larger negative powers, causing the function to approach zero. So, the limit as x approaches infinity is 0.

As x approaches negative infinity, the exponent -x approaches infinity, and the base (1/6) is raised to increasingly larger positive powers, causing the function to approach infinity. So, the limit as x approaches negative infinity is infinity.

Therefore, the end behavior of the function is that it approaches zero as x approaches infinity and approaches infinity as x approaches negative infinity.

For the random variable X, the mean of "X-3" is -5/2 and variance of "X-3" is 1/12.

We have to find the mean and variance of the quantity "X-3" , for the random variable X;

⇒ Let y = x-3,

So, Mean of y = E(y),

⇒ E(y) = E(x-3) = E(x) - 3,

⇒ E(x) = [tex]\int\limits^1_0 {x}f(x) \, dx[/tex] = [tex]\int\limits^1_0 {x.1} \, dx[/tex];

⇒ E(x0 = [x²/2]¹₀ = 1/2.

So, E(y) = (1/2) - 3 = -5/2.

⇒ Variance of y is = Var(x-3)

⇒ Variance of y = Var(x) - 0   ...because Var(3) = 0 as the variance of constant is 0.

⇒ We know that, Var(x) = E(x²) - (E(x))²;

⇒ E(x²) = [tex]\int\limits^1_0 {x^{2} f(x)} \, dx[/tex] = [tex]\int\limits^1_0 {x^{2} .1} \, dx[/tex] = [x³/3]¹₀ = 1/3,

So, Var(x) = (1/3) - (1/2)²

⇒ Var(x) = 1/3 - 1/4 = 1/12.

Therefore, the required Mean is -5/2 and the variance is 1/12.

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The given question is incomplete, the complete question is

Suppose that the random variable X has the continuous uniform distribution,

f(x) = {1,   0 ≤ x ≤ 1

        {0, otherwise

Suppose that a random sample of n=13 observations is selected from this distribution.

Find the mean and variance of the quantity x-3.

Therefore, the answer is that Franklin must have bought at least 4 packs of pumpkin seeds to have an equal number of pumpkin and sunflower seeds.

Given by the question.

Sure! Then is an explanation of how to break this problem

First, we need to find the least common multiple( LCM) of 4 and 8, because that will tell us the lowest number of seeds that Franklin could have bought. To find the LCM, we can list the multiples of each number until we find one that they've in common

Multiples of 4 4, 8, 12, 16, 20, 24, 28, 32, 36, 40.

Multiples of 8 8, 16, 24, 32, 40, 48, 56, 64.

The first multiple that appears in both lists is 8, so the LCM of 4 and 8 is 8.

Now we know that Franklin bought the same number of pumpkin seeds and sunflower seeds, and that number is a multiple of 8. So, we just need to find the lowest multiple of 8 that's also a multiple of 4. That is 8 itself, because it's formerly a multiple of 4.

So, Franklin must have bought at least 4 pumpkin seed packs, since each pack contains 4 seeds. Any other multiple of 8 that's also a multiple of 4 would also work, but 8 is the lowest similar number.

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