find the circumference of each circle

An expression equivalent to (a - b)³ is a³ - 3a²b + 3ab² - b³.

The fractions 4/10, 6/15, 8/20, etc. are identical to 2/5. In the reduced form, equivalent fractions have the same value. Explanation: When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number.

One way to expand (a - b)³ is to use the binomial formula:

(a - b)³ = C(3,0) * a³ * (-b)^0 + C(3,1) * a² * (-b) + C(3,2) * a * (-b)² + C(3,3) * a * (-b)³

where C(n,k) denotes the number of ways there are to select k objects from a set of n objects, and "n choose k" is the binomial coefficient.

Simplifying the above expression, we get:

(a-b)³ = a³-3a²b+3ab²-b³.

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The probability that a randomly selected finishing time is greater than 87 seconds is 14.08%. This can be calculated using the empirical rule.

The empirical rule states that for any data that is normally distributed, about 68% of the data will fall within one standard deviation of the mean (in this case, within 69 ± 6 seconds). Approximately 95% of the data will fall within two standard deviations (in this case, within 69 ± 12 seconds), and about 99.7% of the data will fall within three standard deviations (in this case, within 69 ± 18 seconds).Given the mean and standard deviation given, we can calculate the probability that a randomly selected finishing time is greater than 87 seconds.

We can do this by subtracting the area under the curve from the mean to the value we are interested in (in this case, 87 seconds). Since the total area under the curve is 1, subtracting the area from the mean to 87 seconds will give us the desired probability.To calculate the area under the curve, we need to calculate the Z-score, which is the number of standard deviations away from the mean a particular value is. In this case, the Z-score is (87 - 69) / 6, which is 2.16. Using a Z-table, the probability of a Z-score of 2.16 or higher is 0.8592. Therefore, the probability that a randomly selected finishing time is greater than 87 seconds is 1 - 0.8592, which is 0.1408. Rounding to two decimal places, this is 14.08%.

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The revenue from hardcover books was $24,860 and the revenue from paperback books was $99,440.

Let's assume the revenue from hardcover books as "x" dollars.

Then, the revenue from paperback books will be 4 times the revenue from hardcover books, i.e., 4x dollars.

The total revenue is given as $124,300, so we can set up the following equation:

x + 4x = 124300

Simplifying the above equation, we get:

5x = 124300

x = 24860

Therefore, the revenue from hardcover books was $24,860 and the revenue from paperback books was 4 times that amount, i.e., $99,440.

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Answer:

6.9 or 7.0 .

Step-by-step explanation:

*Note that ^2 means raised to the power of two or squared

a^2 + b^2 = c^2

The hypotenuse is always the C, and the leg can be either a or b.

Fill in the blanks with the numbers that we have:

Hypotenuse: 7.7 | Leg: 3.4

3.4^2 + b^2 = 7.7^2

Square the numbers given

3.4 x 3.4 = 11.56

7.7 x 7.7 = 59.29, which leads us to:

11.56 + b^2 = 59.29

To find what b equals, we need to subtract 11.56 from 59.29

59.29 - 11.56 = 47.73

b^2 = 47.73

We need to take the square root of 47.73 to find b. b and b^2 are two different things.

The square root of 47.73 is about 6.90869017977. It asks for the answer to be rounded to the nearest tenth, giving us 6.9 or 7.0.

Answer:

False.

Step-by-step explanation:

A triangle's two smaller sides have to add to be bigger than the larger side.

Answer:

False, that cannot exist by the hypotenuse rule

Hope it helps!

Using the vertex form the quadratic model for Jordan's monthly revenue is y = 20 / 9(x - 13.5)² + 844.44.

We can use the vertex form of a quadratic equation to create a model for Jordan's monthly revenue:

y = a(x - h)² + k

where y is the monthly revenue, x is the price that Jordan sets for all pieces, and (h, k) is the vertex of the parabola. We can find the vertex by using the formula:

h = -b / 2a

where b and a are coefficients in the standard form of the quadratic equation (y = ax² + bx + c).

To get started, we can substitute two points from the given data to form a system of equations:

864 = a(12 - h)² + k

884 = a(13 - h)² + k

When we deduct the first equation from the second, we obtain:

20 = a(13 - h)² - a(12 - h)²

Simplifying, we get:

20 = a(25 - 24h + h²) - a(16 - 24h + h²)

20 = 9a(h² - 1)

Solving for a, we get:

a = 20 / 9(h² - 1)

Next, we can use the third point to solve for h:

896 = a(14 - h)² + k

Substituting the expression we found for a, we get:

896 = 20 / 9(h² - 1)(14 - h)² + k

Simplifying, we get:

h = 13.5

Now we can solve for k by substituting in the values we found for h and a:

864 = a(12 - h)² + k

k = 844.44

Finally, we can write the quadratic model for Jordan's monthly revenue using the values we found for h, k, and a:

y = 20 / 9(x - 13.5)² + 844.44

Therefore, the quadratic model for Jordan's monthly revenue is:

y = 20 / 9(x - 13.5)² + 844.44

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The question is -

Jordan sells jewelry online. Monthly revenue varies as a function of the single price that Jordan sets for all pieces. Use vertex form to create a quadratic model for Jordon’s monthly revenue.

Price(s)           12       13      14      15     16

Revenue(s)   864    884   896  900  896

The regression result of 0.320, the beta of 0.136, and the p-value of 0.000.

The strongest predictor in the MLRA summary Table is past history of depression. This is shown by the regression result of 0.320, the beta of 0.136, and the p-value of 0.000. This means that past history of depression has a strong and statistically significant influence on predicting depression at wave 2.

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Answer:

y = -5x - 3

Step-by-step explanation:

A linear equation is y = mx + b

m = the slope

b = y-intercept

We know

Points (-2,7) (0,-3)

Slope = rise/run or (y2 - y1) / (x2 - x1)

We see the y decrease by 10 and the x increase by 2, so the slope is

m = -10/2 = -5

Y-intercept is located at (0, -3)

So, the equation is y = -5x - 3

Answer 1: The solution to the equation is x = 4.

Answer 2:

The graph shows that the revenues for online ads have steadily increased since the paper started its online version, while the revenues for printed ads have been steadily decreasing.

Answer 3a:

Beach A is decreasing at a faster rate than Beach B, with its width decreasing from around 400 feet in 1995 to around 250 feet in 2015.

Answer 3b:

Between the years 2011 and 2012, the beaches have approximately the same width.

Answer 3c:

To get a better approximation of when the two beaches will have the same width, the rate of erosion of each beach should be calculated over time.

Equation is an statement that two expressions have the same value, and can be written using symbols, numbers and/or variables.

Answer 1: The equation 2.5x − 10.5 = 64(0.5x) can be solved by completing the table below:

x | 2.5x | 0.5x | 64(0.5x) | 2.5x - 10.5 | 2.5x - 64(0.5x)

--|------|------|-----------|--------------|-----------------

1 | 2.5  | 0.5  | 32        | -8.5         | -29.5

2 | 5    | 1    | 64        | -5.5         | -21.5

3 | 7.5  | 1.5  | 96        | -3.5         | -13.5

4 | 10   | 2    | 128       | -0.5         | -5.5

Answer 2:

The graph shows that the revenues for online ads were approximately equal to the revenues for printed ads around 2006, which is the 12th year after the online version of the paper was started.

Answer 3a:

Beach A is decreasing at a faster rate than Beach B, with its width decreasing from around 400 feet in 1995 to around 250 feet in 2015. Beach B's width is decreasing at a slower rate, from around 500 feet in 1995 to around 350 feet in 2015.

Answer 3b:

Between the years 2011 and 2012, the beaches have approximately the same width.

Answer 3c:

To get a better approximation of when the two beaches will have the same width, the rate of erosion of each beach should be calculated over time. This can be done by plotting the width of each beach over time and calculating the slope of the line, which will give an indication of the rate of erosion.

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1: The solution to the equation is x = 4.

2: The graph shows that the revenues for online ads have steadily increased since the paper started its online version, while the revenues for printed ads have been steadily decreasing.

3a: Beach A is decreasing at a faster rate than Beach B, with its width decreasing from around 400 feet in 1995 to around 250 feet in 2015.

3b: Between the years 2011 and 2012, the beaches have approximately the same width.

3c: To get a better approximation of when the two beaches will have the same width, the rate of erosion of each beach should be calculated over time.

Equation is an statement that two expressions have the same value, and can be written using symbols, numbers and/or variables.

1: The equation 2.5x − 10.5 = 64(0.5x) can be solved by completing the table below:

x | 2.5x | 0.5x | 64(0.5x) | 2.5x - 10.5 | 2.5x - 64(0.5x)

--|------|------|-----------|--------------|-----------------

1 | 2.5  | 0.5  | 32        | -8.5         | -29.5

2 | 5    | 1    | 64        | -5.5         | -21.5

3 | 7.5  | 1.5  | 96        | -3.5         | -13.5

4 | 10   | 2    | 128       | -0.5         | -5.5

2: The graph shows that the revenues for online ads were approximately equal to the revenues for printed ads around 2006, which is the 12th year after the online version of the paper was started.

3a: Beach A is decreasing at a faster rate than Beach B, with its width decreasing from around 400 feet in 1995 to around 250 feet in 2015. Beach B's width is decreasing at a slower rate, from around 500 feet in 1995 to around 350 feet in 2015.

3b: Between the years 2011 and 2012, the beaches have approximately the same width.

3c: To get a better approximation of when the two beaches will have the same width, the rate of erosion of each beach should be calculated over time. This can be done by plotting the width of each beach over time and calculating the slope of the line, which will give an indication of the rate of erosion.

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The probability of drawing four red balls in succession, with replacement, is 0.04 or 4%.

Since we are replacing the ball after each draw, the probability of drawing a red ball remains the same for each draw. The probability of drawing a red ball on any given draw is:

P(Red) = Number of Red Balls / Total Number of Balls

P(Red) = 6 / (8 + 6)

P(Red) = 0.4286

So, the probability of drawing four red balls in a row is the product of the probability of drawing a red ball four times in a row:

P(4 Red Balls) = P(Red) * P(Red) * P(Red) * P(Red)

P(4 Red Balls) = 0.4286 * 0.4286 * 0.4286 * 0.4286

P(4 Red Balls) = 0.04 or 4%

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Answer: cab

Step-by-step explanation:

you start with the last point and move up

Answer:

3

Step-by-step explanation:

Interval 3 ≤ x ≤ 5 means all f(x) values from x= 3 inclusive  to x = 5 inclusive

At x = 3 f(x) = 2

At x = 5, f(x) = 8

Change in f(x) = Δf(x) = 8 - 2 = 6

Change in x = Δx = 5 - 3 = 2

Average rate of change
= Δf(x)/Δx

= 6/2

= 3

The cookers at healthy Bakery could make 323 bagels in 17 hours, and their rate is 19 bagels according to hour.

To find out how many bagels the cookers could make in 17 hours, we will use the unitary method, which involves finding the rate at which the cookers can make bagels and additionally multiplying that price through the wide variety of hours labored.

Let the rate at which the cookers can make bagels be r bagels in line with hour. We also can set up the subsequent share

190 bagels/ 10 hours = r bagels 1 hour

Simplifying this proportion, we get

r = 190 bagels/ 10 hours

r = 19 bagels/ 1 hour

So the cookers can make 19 bagels in keeping with hour.

To find out how many bagels they could make in 17 hours, we can multiply the rate via the number of hours

19 bagels/ hour × 17 hours = 323 bagels

Therefore, the cookers at healthy Bakery could make 323 bagels in 17 hours, and their rate is 19 bagels according to hour.

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Answer:

WELL 17

Step-by-step explanation:

60 DIVED BY 5 IS 12

SO 12 DIVIDED BY 204 IS 17 SOOOOOO 17 IS THE ANS

Answer:

t = 7h

Step-by-step explanation:

lets have the total amount of helmets as t and helmets per box as h. Then it is t = 7h

The better understanding of the data, making it easier to draw conclusions and make decisions based on the data.

In statistics, the spread of the data is used to describe the variability or deviation of a set of data. The location of the data is used to determine the center of the data, and the shape of the data describes the distribution of the data. When it comes to the variable number of care types sp unable to get (acv nocarsum), the data should be analyzed using the appropriate graph(s) and descriptive statistics to determine its shape, location, and spread.
Descriptive statistics:
In descriptive statistics, measures such as mean, mode, median, standard deviation, variance, and range are used to analyze data. These statistics provide a summary of the data in the form of numerical values, making it easy to identify patterns, outliers, and other characteristics of the data.
Graphs:
Graphs are also used in statistical analysis to visually represent the data. There are different types of graphs that can be used, depending on the type of data being analyzed. Commonly used graphs in statistical analysis include histograms, scatterplots, boxplots, and line graphs.
To describe the shape, location, and spread of the data for the number of care types sp unable to get (acv nocarsum) variable, the following steps should be followed:

Step 1: Collect the data.
The first step is to collect the data on the number of care types sp unable to get (acv nocarsum) variable. This data can be obtained from various sources such as surveys, questionnaires, or observational studies.

Step 2: Determine the center of the data.
The center of the data can be determined using measures such as mean, mode, or median. The mean is the average of the data, while the median is the middle value of the data when arranged in order of magnitude. The mode is the value that appears most frequently in the data.

Step 3: Determine the variability of the data.
The variability of the data can be determined using measures such as variance or standard deviation. The variance is the average of the squared differences between each data point and the mean, while the standard deviation is the square root of the variance.

Step 4: Determine the shape of the data.
The shape of the data can be determined using graphs such as histograms, boxplots, or line graphs. Histograms show the distribution of the data, while boxplots show the quartiles and outliers of the data.

Step 5: Interpret the results.
Once the data has been analyzed using the appropriate graph(s) and descriptive statistics, the results should be interpreted to describe the shape, location, and spread of the data for the number of care types sp unable to get (acv nocarsum) variable. This will provide a better understanding of the data, making it easier to draw conclusions and make decisions based on the data.

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The points determined by the real numbers 3.2, 9.5, 50, and 263 are all located on the unit circle at their respective distances from the origin.

The unit circle is a circle of radius 1 centered at the origin of a coordinate system, usually the Cartesian coordinate system. In this system, a point (x,y) is determined by its real number x, where x is the horizontal distance from the origin and y is the vertical distance from the origin. For example, the point determined by the real number 3.2 is located at (3.2, 0), since 3.2 is the horizontal distance from the origin. Similarly, the point determined by the real number 9.5 is located at (9.5, 0).

The point determined by the real number 50 is located at (50, 0). Finally, the point determined by the real number 263 is located at (263, 0). The unit circle is often used in trigonometry to describe the position of points on the circle with an angle in standard position (in radians). For example, if the point determined by the real number 3.2 has an angle in standard position of 3.2 radians, then the point located at (3.2, 0) on the unit circle is the same point. Similarly, if the point determined by the real number 9.5 has an angle in standard position of 9.5 radians, then the point located at (9.5, 0) on the unit circle is the same point. The same is true for the points determined by the real numbers 50 and 263, respectively.

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The function that satisfies the hypotheses of the Extreme Value Theorem on the given interval is given by

B. g(x)=6x^2+3 on 0≤x≤4

D. f(x) = (e^x)/x for 2 ≤ x ≤ 16.

Step 1: State the Extreme Value Theorem

The Extreme Value Theorem states that if a function is continuous on a closed interval [a,b], then the function must have a maximum and a minimum on the interval.

Step 2: Check for continuity and closed interval for each function

A. f(x) = 1/x on −10 ≤ x ≤ 10

The function f(x) = 1/x is continuous on the interval (-10, 0) and (0, 10).

However, since the interval given is [−10, 10], we see that the function is not continuous over the closed interval.

Hence the function does not satisfy the hypotheses of the Extreme Value Theorem.

B. g(x) = 6x^2+3 on 0 ≤ x ≤ 4

The function g(x) is continuous on the interval [0, 4].

Therefore, this function satisfies the hypotheses of the Extreme Value Theorem on the given interval.

C. k(x) = {3x^2+9 for 0 ≤ x < 2, 12x for 2 ≤ x ≤ 10} on 0 ≤ x ≤ 10

The function k(x) is continuous on the interval [0, 2) and (2, 10]. H

However, since the interval given is [0, 10], we see that the function is not continuous over the closed interval.

Hence the function does not satisfy the hypotheses of the Extreme Value Theorem.

D. h(x) = (e^x)/x for 2 ≤ x ≤ 16The function h(x) is continuous on the interval [2, 16].

Therefore, this function satisfies the hypotheses of the Extreme Value Theorem on the given interval.

E. m(x) = 6x^3+x+1 on −4 < x < 3

The function m(x) is continuous on the interval (-4, 3).

However, since the interval given is [-4, ∞), we see that the function is not continuous over the closed interval.

Hence the function does not satisfy the hypotheses of the Extreme Value Theorem.

Therefore, the only function that satisfies the hypotheses of the Extreme Value Theorem on the given interval is given by

B. g(x)=6x^2+3 on 0≤x≤4

D. f(x) = (e^x)/x for 2 ≤ x ≤ 16

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Answer:

  3x -y = -6

Step-by-step explanation:

You want the equation of the line with intercepts (0, 6) and (-2, 0).

The equation of the line with x-intercept 'a' and y-intercept 'b' is ...

  x/a +y/b = 1

For the given intercepts, the equation is ...

  x/(-2) +y/6 = 1

In standard form, we want the leading coefficient positive and the integer coefficients mutually prime. We can get there by multiplying by -6:

  3x -y = -6

__

Additional comment

You can get slope-intercept form by solving for y, or you can recognize that ...

  slope = rise/run = -(y-intercept)/(x-intercept) = -6/-2 = 3

Since you already know the y-intercept, you can write the slope-intercept equation as ...

  y = 3x +6

There are perhaps a dozen or more forms of the equation for a line. The "intercept form" equation is one of the more useful ones.

The height of the storage unit needs to be 5 feet according to mentioned length, width and volume.

The volume is calculated using the formula -

Volume = length × width × height. We have all the values except height. Thus, it can be easily calculated from the formula.

Rewriting the formula -

Height = Volume/ (length × width)

Height = 400/ (10 × 8)

Performing multiplication in denominator

Height = 400/80

Performing division and cancelling zero on Right Hand Side of the equation

Height = 5 feet

Hence, the height of the unit needs to be 5 feet.

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Answer:

C. Rachel is saving $5 per week.

Step-by-step explanation:

The initial savings are $10, as it is the y-intercept.

And to obtain the slope we can take 2 points from the graph.

A(0,10)

B(1,15)

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

m=(15-10)/ (1-0)

m= 5/1

m= 5 savings in dollars per (1) week

There are black, blue, and white marbles in a bag. The probability of choosing a black marble is 0.75.

Let's assume that there are 100 marbles in the bag. If the probability of choosing a black marble is 0.36, there are 36 black marbles in the bag. Therefore, there are 64 marbles of other colors (white and blue) in the bag.

Using the same method, we can say that the probability of choosing a white marble after drawing a black one is [tex]\frac{0.27}{0.36}= 0.75[/tex]  (rounded to the nearest hundredth). It means that there are 75 white marbles for every 100 black marbles in the bag.

Therefore, the probability of the second marble being white if the first marble chosen is black is

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Answer:[tex]\frac{8}{9}[/tex]

Step-by-step explanation:

Four fifths=4/5

two ninths=2/9

[tex]\frac{4}{5} *5*\frac{2}{9}=\frac{8}{9}[/tex]

Assuming you meant ( four fifths ) * 5 * ( two ninths ), the answer would be 0.88888888888.

If you meant 4/5 x 5 and then x 2/9, the answer would be 8/9, because 4/5 x 5 is 4, and 4 x 2/9 is 8/9.

A graph of the line with slope -1/5 and y-intercept of -5 is shown in the image attached below.

In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

Based on the information, an equation that models the line is given by this mathematical expression;

y = mx + c

y = -x/5 - 5

In this exercise, we would use an online graphing calculator to plot the above equation as shown in the graph attached below.

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The viewing angle a of a person sitting a distance x from the front wall of a classroom with a blackboard that is 12 ft long and starts 3 ft from the wall they are sitting next to can be calculated as: a = cot-1(x/15) - cot-1(x/3)

To understand this calculation, let's consider a diagram of the classroom.

We can see from the diagram that the blackboard has length 12 ft, starting 3 ft from the wall the student is sitting next to. The student is sitting a distance x from the front wall.

The viewing angle a is the angle between the wall the student is sitting next to and the line from the student to the front wall. This angle can be calculated using the tangent of the opposite side (front wall) and adjacent side (wall the student is sitting next to).

We can therefore write: a = tan-1(12/3) - tan-1(x/3)

Simplifying this equation, we can rewrite it as: a = cot-1(x/15) - cot-1(x/3).

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Answer: Yes, the Mean Value Theorem can be applied to f(x) = 9x^3 on the closed interval [1, 2].

To find all values of c in the open interval (1, 2) such that f'(c) = (f(b) - f(a))/(b - a), we first find the derivative of f(x):

f'(x) = 27x^2

Then, we can use the Mean Value Theorem to find a value c in the open interval (1, 2) such that:

f'(c) = (f(2) - f(1))/(2 - 1)

27c^2 = 9(2^3 - 1^3)

27c^2 = 45

c^2 = 5/3

c = +/- sqrt(5/3)

Therefore, the values of c in the open interval (1, 2) such that f'(c) = (f(b) - f(a))/(b - a) are:

c = sqrt(5/3), -sqrt(5/3)

Note that these values are not in the closed interval [1, 2], as they are not between 1 and 2, but they are in the open interval (1, 2).

Step-by-step explanation:

(a) The solution to the differential equation isx(t) = 10(1 - e^(-0.005t))

To solve the differential equation dx/dt = 0.005(10 - x), we can use separation of variables:

dx / (10 - x) = 0.005 dt

Integrating both sides:

-ln|10 - x| = 0.005t + C

where C is the constant of integration. Solving for x:

|10 - x| = e^(-0.005t - C)

Since x cannot be negative, we can drop the absolute value sign and solve for C using the initial condition that x(0) = 0:

C = -ln(10)

Therefore, the solution to the differential equation is:

x(t) = 10 - e^(-0.005t - ln(10))

Simplifying:

x(t) = 10(1 - e^(-0.005t))

(b) New bills will make up 90% of the currency in circulation after approximately 461 days.

We want to find the value of t such that x(t) = 0.9(10) = 9. Plugging this into our solution from part (a):

9 = 10(1 - e^(-0.005t))

Dividing both sides by 10 and taking the natural logarithm:

ln(0.1) = -0.005t

Solving for t:

t = 200 ln(10) = 460.51

Therefore, new bills will make up 90% of the currency in circulation after approximately 461 days.

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The publication of three major books on race in chronological order, from earliest to most recent is:

Chronological order is the listing, description, or discussion of when events occurred in relation to time. Essentially, it is similar to looking at a chronology to see what happened initially and what happened after that. For example, if teachers asked their pupils to recount their first day of school, they would expect students to begin by waking up that morning and getting ready. If pupils begin from the time they enter the school, significant information is lost and the listener may become confused due to a lack of knowledge.

Helping pupils grasp what chronological order is and how to use the skill correctly can benefit students ranging from kindergarten to collegiate levels. The concept may appear simple, yet failing to master chronological sequence can cause kids to struggle academically and lack a solid educational foundation.

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A. I and II only true if we use a large sample rather than a small one

sampling model

A sampling model is a statistical model used to describe the behavior of a sample statistic. In other words, it is a model that describes the distribution of a particular sample statistic, such as the mean or standard deviation, as it is repeatedly sampled from a population.

When a sample is drawn from a population that is strongly skewed to the left, a small sample may not accurately represent the true population mean. However, if a large sample is taken, the sample mean is more likely to be normally distributed, due to the central limit theorem. This means that both statement I and II are true.

Statement III is false because as the sample size increases, the variability of the sample means actually decreases. This is because larger samples tend to have less sampling error and are more representative of the population as a whole.

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The vector equation and the parametric equations in t for the line through the point and parallel to the given line are:

x= 2t - 4

y= -4t + 7

z= 8t + 5

To find x, y, and z in the given scenario, the following steps can be followed:

1: Vector Equation of Line

To find the vector equation, use the given line and its coefficients:

x = -4 + 2t

y = 7 - 4t

z = 5 + 8t

Take the coefficients of x, y, and z, and place them in a 3 by 1 matrix:

Column Matrix= [-4 7 5]

Add the parameter t and place it in a column matrix to get the vector equation:

Vector Equation= [-4 7 5] + t[2 -4 8]

2: Parametric Equation.

To find the parametric equations, write the components of the vector equation in terms of the parameters:

x= -4 + 2t

y= 7 - 4t

z= 5 + 8t

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