the table below represents gerry's trip to school and back home. if the total time is 45 minutes, how far does gerry leave from school?

Answer:

"The Theory of Evolution"

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The values of g(-4), g(-2), and g(3) are -5, undefined, and -11, respectively. The function g is defined differently for x = -2 and other real numbers, resulting in different output values.

Given the function g(x) = {(-4/1)(x-2) - (1/1)(x+2), if x ≠ -2; undefined, if x = -2}, we can evaluate g(-4), g(-2), and g(3) as follows:

1. g(-4):

Since -4 ≠ -2, we use the first part of the definition of g(x). Plugging in x = -4, we have:

g(-4) = (-4/1)(-4-2) - (1/1)(-4+2)

      = (-4/1)(-6) - (1/1)(-2)

      = 24 + 2

      = 26

Therefore, g(-4) = 26.

2. g(-2):

Since x = -2 matches the condition in the second part of the definition of g(x), g(-2) is undefined.

3. g(3):

Since 3 ≠ -2, we use the first part of the definition of g(x). Plugging in x = 3, we have:

g(3) = (-4/1)(3-2) - (1/1)(3+2)

     = (-4/1)(1) - (1/1)(5)

     = -4 - 5

     = -9

Therefore, g(3) = -9.

In summary, g(-4) = 26, g(-2) is undefined, and g(3) = -9. The function g(x) has different output values depending on whether x is equal to -2 or not.

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The inequality 6x - 13 < 6 (x - 2) is always true. 0 < 1 is always true so, the inequality is always true for any value of x.

When we simplify the inequality, we have 6x - 13 < 6x - 12.

6x - 13 < 6x - 12

or, 6x - 6x < 13 - 12

or, 0 < 1

Notice that the x-terms cancel out, resulting in 0 < 1.

In the comparison 0 < 1, the left side 0 is indeed less than the right side 1, making the inequality true. This holds true for all values of x.

Since the inequality is true regardless of the value of x, we can conclude that the original inequality 6x - 13 < 6 (x - 2) is always true.

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The Mean Absolute Percentage Error (MAPE) for a four-month moving average method applied to the given patient data is 13.7196%.

To calculate the MAPE using a four-month moving average method, we need to find the average of the absolute percentage errors for each month's forecasted value compared to the actual value.

First, we calculate the four-month moving average for each month using the provided data:

Moving Average for Month 1 = (593 + 464 + 618 + 765) / 4 = 610

Moving Average for Month 2 = (464 + 618 + 765 + 553) / 4 = 600

Moving Average for Month 3 = (618 + 765 + 553 + 731) / 4 = 666.75

Moving Average for Month 4 = (765 + 553 + 731 + 647) / 4 = 674

Moving Average for Month 5 = (553 + 731 + 647) / 3 = 643.67

Moving Average for Month 6 = (731 + 647) / 2 = 689

Moving Average for Month 7 = 647

Next, we calculate the absolute percentage error for each month's forecasted value compared to the actual value:

APE for Month 1 = |(610 - 593) / 593| = 0.0287

APE for Month 2 = |(600 - 464) / 464| = 0.2927

APE for Month 3 = |(666.75 - 618) / 618| = 0.0789

APE for Month 4 = |(674 - 765) / 765| = 0.1183

APE for Month 5 = |(643.67 - 553) / 553| = 0.1630

APE for Month 6 = |(689 - 731) / 731| = 0.0575

APE for Month 7 = |(647 - 647) / 647| = 0

Finally, we find the average of the absolute percentage errors and multiply it by 100 to obtain the MAPE:

MAPE = (0.0287 + 0.2927 + 0.0789 + 0.1183 + 0.1630 + 0.0575 + 0) / 7 * 100 ≈ 13.7196%

Therefore, the value of MAPE (in percent) for the four-month moving average method applied to the given patient data is approximately 13.7196%.

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(a) Forecast: Linear regression  the next year is approx 191.6007.

(b) MSE: Mean Squared Error is approximately 249.1585.

(c) MAPE: Mean Absolute Percent Error is approximately 10.42%.

(a) (a) Forecast using linear regression:
To forecast the number of disk drives for the next year, we can use linear regression to fit a line to the given data points. The linear regression equation is of the form y = mx + b, where y represents the number of disk drives and x represents the year.

Calculating the slope (m):
m = (Σ(xy) - n(Σx)(Σy)) / (Σ(x^2) - n(Σx)^2)

Σ(xy) = (1)(140) + (2)(160) + (3)(190) + (4)(200) + (5)(210) = 2820
Σ(x) = 1 + 2 + 3 + 4 + 5 = 15
Σ(y) = 140 + 160 + 190 + 200 + 210 = 900
Σ(x^2) = (1^2) + (2^2) + (3^2) + (4^2) + (5^2) = 55

m = (2820 - 5(15)(900)) / (55 - 5(15)^2)
m = (2820 - 6750) / (55 - 1125)
m = -3930 / -1070
m ≈ 3.6729

Calculating the y-intercept (b):
b = (Σy - m(Σx)) / n
b = (900 - 3.6729(15)) / 5
b = (900 - 55.0935) / 5
b ≈ 168.1813

Using the equation y = 3.6729x + 168.1813, where x represents the year, we can predict the number of disk drives for the next year. To do so, we substitute the value of x as the next year in the equation. Let's assume the next year is represented by x = 6:

y = 3.6729(6) + 168.1813
y ≈ 191.6007

Therefore, according to the linear regression model, the predicted number of disk drives for the next year is approximately 191.6007.

(b) Calculation of Mean Squared Error (MSE):

To calculate the Mean Squared Error (MSE), we need to compare the predicted values obtained from linear regression with the actual values given in the data.

First, we calculate the predicted values using the linear regression equation: y = 3.6729x + 168.1813, where x represents the year.

Predicted values:

Year 1: y = 3.6729(1) + 168.1813 = 171.8542
Year 2: y = 3.6729(2) + 168.1813 = 175.5271
Year 3: y = 3.6729(3) + 168.1813 = 179.2000
Year 4: y = 3.6729(4) + 168.1813 = 182.8729
Year 5: y = 3.6729(5) + 168.1813 = 186.5458
Next, we calculate the squared difference between the predicted and actual values, and then take the average:

MSE = (Σ(y - ŷ)^2) / n

MSE = ((140 - 171.8542)^2 + (160 - 175.5271)^2 + (190 - 179.2000)^2 + (200 - 182.8729)^2 + (210 - 186.5458)^2) / 5

MSE ≈ 249.1585

The Mean Squared Error (MSE) for the linear regression model is approximately 249.1585.

This value represents the average squared difference between the predicted values and the actual values, providing a measure of the accuracy of the model.

(c) Calculation of Mean Absolute Percent Error (MAPE):

To calculate the Mean Absolute Percent Error (MAPE), we need to compare the predicted values obtained from linear regression with the actual values given in the data.

First, we calculate the predicted values using the linear regression equation: y = 3.6729x + 168.1813, where x represents the year.

Predicted values:

Year 1: y = 3.6729(1) + 168.1813 ≈ 171.8542
Year 2: y = 3.6729(2) + 168.1813 ≈ 175.5271
Year 3: y = 3.6729(3) + 168.1813 ≈ 179.2000
Year 4: y = 3.6729(4) + 168.1813 ≈ 182.8729
Year 5: y = 3.6729(5) + 168.1813 ≈ 186.5458

Next, we calculate the absolute percent error for each year, which is the absolute difference between the predicted and actual values divided by the actual value, multiplied by 100:

Absolute Percent Error (APE):

Year 1: |(140 - 171.8542) / 140| * 100 ≈ 18.467
Year 2: |(160 - 175.5271) / 160| * 100 ≈ 9.704
Year 3: |(190 - 179.2000) / 190| * 100 ≈ 5.684
Year 4: |(200 - 182.8729) / 200| * 100 ≈ 8.563
Year 5: |(210 - 186.5458) / 210| * 100 ≈ 11.682
Finally, we calculate the average of the absolute percent errors:

MAPE = (APE₁ + APE₂ + APE₃ + APE₄ + APE₅) / n

MAPE ≈ (18.467 + 9.704 + 5.684 + 8.563 + 11.682) / 5 ≈ 10.42

The Mean Absolute Percent Error (MAPE) for the linear regression model is approximately 10.42%.

This value represents the average percentage difference between the predicted values and the actual values, providing a measure of the relative accuracy of the model.

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Each employee earns $33.50. Since there are 4 employees and they earn a total of $134, dividing the total by the number of employees gives us $33.50 per employee.

To determine how much each employee earns in a store where there are 4 employees in total, and they all earn the same amount, we can divide the total amount earned by the number of employees.

Given that the total amount earned by the 4 employees is $134, we need to divide this amount equally among them to find the individual earnings.

Let's calculate the amount earned by each employee:

Amount earned by each employee = Total amount earned / Number of employees

Amount earned by each employee = $134 / 4

Dividing $134 by 4, we find that each employee earns $33.50.

Therefore, each employee in the store earns $33.50.

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Answer (25-30 words): In point 7 and 8, the concept of surveys is repeated because research techniques refer to the overall approach, while data collection specifically focuses on the method used to gather data.

In research methodology, point 7 refers to the research techniques employed, which in this case is surveys. Surveys are a common method for gathering data in quantitative research. Point 8, on the other hand, specifies the data collection process, which again involves the use of surveys. While it may seem repetitive to mention surveys twice, it is important to differentiate between the broader research technique (point 7) and the specific method used to collect data (point 8).

The research technique, surveys, encompasses the overall approach of using questionnaires or interviews to collect data from respondents. It represents the methodology chosen to gather information. On the other hand, data collection focuses on the actual process of administering the surveys and collecting responses from the target population.

By including both points, the outline or concept map reflects the distinction between the research technique (surveys) and the specific step of data collection using surveys. This ensures clarity and precision in describing the methodology.

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If a triangle is equilateral, then it is equiangular.

The statement "Equilateral triangles are equiangular" is already in if-then form.

In if-then form, the statement can be written as "If a triangle is equilateral" (the "if" part), followed by "then it is equiangular" (the "then" part).

An equilateral triangle is a triangle in which all three sides are equal in length. Equiangular refers to a triangle having all three angles equal. The statement asserts that if a triangle is equilateral (the "if" condition), then it is also equiangular (the "then" consequence). This relationship holds true for equilateral triangles, making the statement accurate.

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Answer:

$30

Step-by-step explanation:

17+13

The dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

Let's assume that the width of the rectangle is x meters. According to the given information, the length of the rectangle is 3 meters less than double the width, which can be expressed as 2x - 3.

The area of a rectangle is given by the formula: Area = Length × Width. In this case, the area is given as 14 m². Therefore, we can write the equation:

(x)(2x - 3) = 14

Expanding the equation:

2x² - 3x = 14

Rearranging the equation to standard form:

2x² - 3x - 14 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 2, b = -3, and c = -14. Plugging in these values into the quadratic formula:

x = (-(-3) ± √((-3)² - 4(2)(-14))) / (2(2))

x = (3 ± √(9 + 112)) / 4

x = (3 ± √121) / 4

x = (3 ± 11) / 4

Simplifying further:

x = (3 + 11) / 4 or x = (3 - 11) / 4

x = 14 / 4 or x = -8 / 4

x = 7/2 or x = -2

Since the width cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is 7/2 meters.

Now, we can substitute the value of x into the expression for the length:

Length = 2x - 3

Length = 2(7/2) - 3

Length = 7 - 3

Length = 4 meters

Thus, the dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

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The difference between solving |x+3|>4 and |x+3|<4 lies in the direction of the inequality and the resulting solution set.

In the first inequality, |x+3|>4, we are looking for values of x that make the absolute value of x+3 greater than 4. In the second inequality, |x+3|<4, we are looking for values of x that make the absolute value of x+3 less than 4. When solving |x+3|>4, we consider two cases: one where x+3 is positive and one where x+3 is negative. For x+3 > 0, we solve x+3 > 4, which gives x > 1.

For x+3 < 0, we solve -(x+3) > 4, which gives x < -7. Combining these two cases, the solution to |x+3|>4 is x < -7 or x > 1. On the other hand, when solving |x+3|<4, we consider two cases as well. For x+3 > 0, we solve x+3 < 4, which gives x < 1. For x+3 < 0, we solve -(x+3) < 4, which gives x > -7. Combining these two cases, the solution to |x+3|<4 is -7 < x < 1.

The difference between solving |x+3|>4 and |x+3|<4 lies in the direction of the inequality and the resulting solution set. The former involves values of x that make the absolute value greater than 4, while the latter involves values that make the absolute value less than 4. The solution set for |x+3|>4 is x < -7 or x > 1, while the solution set for |x+3|<4 is -7 < x < 1.

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The tenth term of the sequence 4, 5, 6, 7, 8, ... is 13.

Using this formula, we can find the tenth term as follows:

a10 = a1 + (10-1)

= 4 + 9

= 13

The given sequence is an arithmetic sequence where each term is obtained by adding 1 to the previous term. The first term, a1, is 4. To find the nth term, we use the explicit formula an = a1 + (n-1), which represents the pattern of the sequence.

By substituting the value of n as 10, we can calculate the tenth term, which is 13. This means that the tenth term in the sequence is obtained by adding 9 to the first term, 4.

Therefore, the tenth term of the sequence is 13.

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From the question that we have;

1) P(t) = Po[tex]e^{rt}[/tex]

2) After seven hours we have 5003

3) The rate is 0.23

Exponential growth is a type of growth in which a quantity or population grows over time at an ever-increasing rate.

We have that;

P(t) = Po[tex]e^{rt}[/tex]

P(t) = Population at time t

Po = Initial population

r = rate of growth

t = time taken

Thus;

2(1000) = 1000[tex]e^{3r}[/tex]

2 = [tex]e^{3r}[/tex]

r = ln2/3

r = 0.23

After seven hours;

P(t) =1000[tex]e^{7(0.23)}[/tex]

= 5003

The rate of growth at seven hours;

5003 = 1000[tex]e^{7r}[/tex]

5003/1000 = [tex]e^{7r}[/tex]

r = 0.23

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The profit of a perfectly competitive firm is calculated using the production function. The firm should adjust capital employment based on marginal returns and costs to maximize profits.

To calculate the profit, substitute the given values of labor, capital, and input prices into the production function and subtract the total cost from total revenue.

The profit-maximizing quantity of capital can be determined by taking the derivative of the profit function with respect to capital and setting it equal to zero.

This will provide the optimal capital level that maximizes profits. Comparing the profit at the current capital level to the profit at other potential capital levels can indicate whether increasing or decreasing capital employment will result in higher profits.

This decision should be based on evaluating the marginal returns of capital, considering factors such as diminishing returns and the cost of additional capital units.

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For θ = π/6 radians, cosθ = √3/2 and sinθ = 1/2 is obtained by using trigonometric functions.

The measure θ of an angle in standard position is π/6 radians. To find the exact values of cosθ and sinθ for this angle measure, we can use the unit circle.

Step 1: Draw the unit circle, which is a circle with a radius of 1 centered at the origin (0, 0) on the coordinate plane.

Step 2: Locate the angle θ = π/6 radians on the unit circle. This angle is formed by the positive x-axis and a line segment from the origin to a point on the unit circle.

Step 3: To find the exact value of cosθ, look at the x-coordinate of the point where the angle intersects the unit circle. In this case, the x-coordinate is √3/2. Therefore, cos(π/6) = √3/2.

Step 4: To find the exact value of sinθ, look at the y-coordinate of the point where the angle intersects the unit circle. In this case, the y-coordinate is 1/2. Therefore, sin(π/6) = 1/2.

So, for θ = π/6 radians, cosθ = √3/2 and sinθ = 1/2.

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In the function g(x) = f(x + 1), the value of h is 1. This means that the graph of g(x) is shifted 1 unit to the left compared to the graph of f(x).

A horizontal translation of a function is a transformation that moves the graph of the function to the left or right by a certain number of units. In this case, the function g(x) is defined as f(x + 1). This means that for every input value x, the output value of g(x) is the same as the output value of f(x), but shifted one unit to the left.

For example, if x = 0, then g(0) = f(1). This means that the point (0, g(0)) on the graph of g(x) is the same point as the point (1, f(1)) on the graph of f(x).

The graph of g(x) is therefore shifted one unit to the left compared to the graph of f(x). This is because the input value x = 0 on the graph of g(x) corresponds to the input value x = 1 on the graph of f(x).

In conclusion, the value of h in g(x) = f(x + 1) is 1. This means that the graph of g(x) is shifted 1 unit to the left compared to the graph of f(x).

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The rule for how many significant figures you are able to get using a measuring instrument is that the number of significant figures is equal to the number of digits that are certain plus one digit that is estimated.

For example, if you measure a length with a ruler that has marks every millimeter, then you can report the length to two significant figures, such as 3.5 cm. The 3 is certain because it is a whole number that is marked on the ruler. The 5 is estimated because it is the value between the 4 and 6 marks on the ruler.

* The number of significant figures in a measurement is determined by the least precise digit.

* The least precise digit is the digit that is estimated.

* The other digits in the measurement are certain.

* For example, in the measurement 3.5 cm, the least precise digit is the 5. This digit is estimated because it is the value between the 4 and 6 marks on the ruler. The 3 is certain because it is a whole number that is marked on the ruler.

* Therefore, the measurement has two significant figures.

It is important to report the correct number of significant figures in a measurement. This is because it is a way of communicating the uncertainty of the measurement. If you report too many significant figures, you are giving the impression that your measurement is more precise than it actually is. If you report too few significant figures, you are not giving enough information about the uncertainty of your measurement.

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For n = 50, the standard deviation of the sampling distribution is σY/√n = 7.21. So, Pr(ˉY<91) = 0.8365, and for n = 166, the standard deviation of the sampling distribution is σY/√n = 2.82. So, Pr(91<ˉY<94) = 0.5987.

The central limit theorem states that the sampling distribution of the sample mean, ˉY, will be normally distributed with mean μY and standard deviation σY/√n, where n is the sample size.

The theorem states that, as the sample size increases, the sampling distribution of the sample mean will approach a normal distribution, regardless of the shape of the population distribution.

This means that we can use the normal distribution to calculate probabilities about the sample mean, even when we don't know the shape of the population distribution.

In this problem, we were able to use the central limit theorem to calculate the probability that the sample mean would be less than 91 and the probability that the sample mean would be between 91 and 94. These probabilities were calculated using the standard normal distribution, which is a table of probabilities for the normal distribution.

In this problem, we are given that μY = 90 and σY2 = 52. We are asked to find Pr(ˉY<91) and Pr(91<ˉY<94) for two different sample sizes, n = 50 and n = 166.

For n = 50, the standard deviation of the sampling distribution is σY/√n = 7.21. So, Pr(ˉY<91) = 0.8365.

For n = 166, the standard deviation of the sampling distribution is σY/√n = 2.82. So, Pr(91<ˉY<94) = 0.5987.

In conclusion, the central limit theorem allows us to use the normal distribution to approximate the sampling distribution of the sample mean, even when the population distribution is not normally distributed.

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Angle HLI is equal to 180 - 2x degrees.

The given information states that angle GLH is congruent to angle ILM. Let's denote angle ILM as x.

Therefore, angle GLH is also x. We are also given that angle KLM is 5 times angle ILM, so angle KLM is 5x. Additionally, it is stated that angle GLI is twice angle GLH, which means angle GLI is 2x.

To find angle HLI, we need to subtract angle GLI from 180 degrees since the sum of angles in a triangle is 180 degrees. Therefore, angle HLI is equal to 180 - 2x.

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There are 30° between every two consecutive numbers on an analog clock.

Given that on an analog clock, the minute hand moved 128° in an hour we need to find the numbers it has pass next,

On an analog clock, the minute hand completes a full revolution of 360° in 60 minutes.

This means that each minute corresponds to a movement of 360°/60 = 6°.

The minute hand has moved 128° from the hour, we can determine the number of minutes it has traveled by dividing 128° by 6°:

128° / 6° = 21.33 minutes

Since the minute hand has moved beyond 21 minutes, it will pass the next number on the clock.

If we consider the current number to be n, then it will pass the number (n+1) next.

To find the number of degrees between every two consecutive numbers on an analog clock, we divide the total degrees in a circle (360°) by the number of divisions on the clock face (12 numbers):

360° / 12 = 30°

Therefore, there are 30° between every two consecutive numbers on an analog clock.

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The expression √-24 can be simplified using the imaginary unit i as 2i√6.

To simplify √-24, we can break it down into two parts: the square root of -1 (which is represented by the imaginary unit i) and the square root of 24.

The square root of -1 is i, and the square root of 24 can be simplified as 2√6.

Combining these two parts, we get 2i√6 as the simplified form of √-24.

The imaginary unit i is defined as the square root of -1. It is used to represent imaginary numbers, which are numbers that involve the square root of a negative number. In this case, the expression involves the square root of -24, which is a negative number. By using the imaginary unit i, we can simplify √-24 as 2i√6, where 2 is the coefficient and √6 is the remaining radical term.

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The equation y = -x² + 9 accurately represents the path of the ball as it moves back and forth between you and your friend, with the ball's height at each horizontal position governed by the parabolic trajectory of the equation.

The equation that models the path of the ball in standard form is y = -x² + 9. This equation represents a downward-opening parabola that accurately represents the trajectory of the ball as it moves back and forth between you and your friend at a height of 3 feet.

The reasoning behind this equation is as follows:

Since the ball is being tossed back and forth at waist level, the height of the ball can be represented by the y-coordinate. The x-coordinate represents the horizontal distance from the person throwing the ball. We can assume that the ball is initially thrown from a position of x = 0.

To model the trajectory, we consider that the ball starts at a height of 3 feet and then follows a parabolic path. The negative coefficient in front of the x² term indicates that the parabola opens downward.

The constant term, 9, represents the maximum height of the ball. Since the ball is being tossed at waist level (3 feet), the maximum height reached by the ball is 3 + 6 = 9 feet. The additional 6 feet accounts for the vertical displacement of the ball from its starting height of 3 feet.

Therefore, the equation y = -x² + 9 accurately represents the path of the ball as it moves back and forth between you and your friend, with the ball's height at each horizontal position governed by the parabolic trajectory of the equation.

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Bailey's season batting average is approximately 0.317, while Janson's season batting average is approximately 0.314.

To determine each player's batting average for the entire season, we can use the formula for batting average, which is calculated by dividing the number of hits by the number of at-bats. Let's calculate the batting averages for Bailey and Janson based on the data provided in the table.

For Bailey:

In the first half of the season, Bailey had 17 hits and 56 at-bats, resulting in a batting average of 17/56 ≈ 0.304.

In the second half of the season, Bailey had 85 hits and 265 at-bats, giving a batting average of 85/265 ≈ 0.321.

To find Bailey's season batting average, we can add up the total hits and total at-bats from both halves of the season:

Total hits = 17 + 85 = 102

Total at-bats = 56 + 265 = 321

Bailey's season batting average = Total hits / Total at-bats

= 102 / 321 ≈ 0.317.

For Janson:

In the first half of the season, Janson had 107 hits and 345 at-bats, resulting in a batting average of 107/345 ≈ 0.310.

In the second half of the season, Janson had 50 hits and 155 at-bats, giving a batting average of 50/155 ≈ 0.323.

To find Janson's season batting average, we can add up the total hits and total at-bats from both halves of the season:

Total hits = 107 + 50 = 157

Total at-bats = 345 + 155 = 500

Janson's season batting average = Total hits / Total at-bats

= 157 / 500 ≈ 0.314.

In summary, Bailey's season batting average is approximately 0.317, while Janson's season batting average is approximately 0.314.

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Questions:The table shows the number of hits and at bats for two baseball players during the first and second halves of the season.

First half of season| Second half of season

Player & Hits & At bats & Batting average| Hits & At bats & Batting average

Bailey &17 & 56 & 0.304| 85& 265 &0.321

Janson & 107 & 345 & 0.310|50& 155 &0.323

Click to download the data in your preferred format. Crunch It! CSV Excel JMP Mac Text Minitab PC Text R SPSS TI Calc Batting average is determined by dividing the number of hits by the number of at-bats. Use the number of hits and at bats from the proceeding table to determine each player's batting average for the entire season. Enter the values in the following table. Give your answers precise to three decimal places. Player| Season batting average

Bailey |  

Janson|  

P(B∣A) is approximately 0.310, rounded to three decimal places.

To find the probability P(B∣A), we can use Bayes' theorem:

P(B∣A)= P(A) / P(A∣B)⋅P(B)

Given information:

P(B)=0.2

P(A∣B)=0.9

P(B')=0.8 (probability of not B)

P(A∣B′)=0.5 (probability of A given not B)

First, we need to calculate

P(A), the probability of event A. We can use the law of total probability to express P(A) in terms of the probabilities related to B and not B:

P(A)=P(A∣B)⋅P(B)+P(A∣B′)⋅P(B′)

Substituting the given values:

P(A)=0.9⋅0.2+0.5⋅0.8=0.18+0.4=0.58

Now, we can substitute the known values into Bayes' theorem:

P(B∣A)= P(A)/ P(A∣B)⋅P(B)

= 0. 9.0.2 / 0.58

Calculating this expression:

P(B∣A)≈ 0.5 80.18 ≈0.310

Therefore, P(B∣A) is approximately 0.310, rounded to three decimal places.

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The value of x is approximately 9.8.

In this question, we are given an equation, and we need to find the value of x in the equation.

The equation that is given to us is as follows: 19 cos 20° + x = 29

To find the value of x, we need to isolate it on one side of the equation.

First, we will subtract 19 cos 20° from both sides of the equation.

This gives us: x = 29 - 19 cos 20°Now we can use a calculator to evaluate the right-hand side of the equation.

Rounding to the nearest tenth, we get: x ≈ 9.8

Therefore, the value of x is approximately 9.8.

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Answer:

[tex]\text{g}^{-1}(x)=\boxed{\dfrac{x-13}{2}}[/tex]

[tex]\left(\text{g}^{-1} \circ \text{g}\right)(-4)=\boxed{-4}[/tex]

[tex]h^{-1}(9)=\boxed{-3}[/tex]

Step-by-step explanation:

To find the inverse of function g(x) = 2x + 13, begin by replacing g(x) with y:

[tex]y=2x+13[/tex]

Swap x and y:

[tex]x=2y+13[/tex]

Rearrange to isolate y:

[tex]\begin{aligned}x&=2y+13\\\\x-13&=2y+13-13\\\\x-13&=2y\\\\2y&=x-13\\\\\dfrac{2y}{2}&=\dfrac{x-13}{2}\\\\y&=\dfrac{x-13}{2}\end{aligned}[/tex]

Replace y with g⁻¹(x):

[tex]\boxed{\text{g}^{-1}(x)=\dfrac{x-13}{2}}[/tex]

[tex]\hrulefill[/tex]

As g and g⁻¹ are true inverse functions of each other, the composite function (g⁻¹ o g)(x) will always yield x. Therefore, (g⁻¹ o g)(-4) = -4.

To prove this algebraically, calculate the original function g at the input value x = -4, and then evaluate the inverse function of g at the result.

[tex]\begin{aligned}\left(\text{g}^{-1} \circ \text{g}\right)(-4)&=\text{g}^{-1}\left[\text{g}(-4)\right]\\\\&=\text{g}^{-1}\left[2(-4)+13\right]\\\\&=\text{g}^{-1}\left[5\right]\\\\&=\dfrac{(5)-13}{2}\\\\&=\dfrac{-8}{2}\\\\&=-4\end{aligned}[/tex]

Hence proving that (g⁻¹ o g)(-4) = -4.

[tex]\hrulefill[/tex]

The inverse of a one-to-one function is obtained by reflecting the original function across the line y = x, which swaps the input and output values of the function. Therefore, (x, y) → (y, x).

Given the one-to-one function h is defined as:

[tex]h=\left\{(-3,9), (1,0), (3,-7), (5,2), (9,6)\right\}[/tex]

Then, the inverse of h is defined as:

[tex]h^{-1}=\left\{(9,-3),(0,1),(-7,3),(2,5),(6,9)\right\}[/tex]

Therefore, h⁻¹(9) = -3.

He answers rounded to the correct number of decimals/sig. figs are:a. 15.0 b. 408.1 c. 369 d. 68.65

a. 12.5849+2.4Adding 12.5849 and 2.4 gives: 15. 0 (rounded to one decimal place)  b. 432.5−24.3984Subtracting 24.3984 from 432.5 gives: 408. 1 (rounded to one decimal place)  c. 246×1.5Multiplying 246 and 1.5 gives: 369 (no rounding required)  d. 974.59/14.2Dividing 974.59 by 14.2 gives: 68.65 (rounded to two decimal places)

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The standard deviation of 5, 9, 9, 1, 5, 7, 6 rounded to the nearest tenth is 2.6.

Step 1: Calculate the mean

Mean = (5 + 9 + 9 + 1 + 5 + 7 + 6) / 7 = 42 / 7 = 6

Step 2: Subtract the mean and square the differences

[tex](5 - 6)^2[/tex] = 1

[tex](9 - 6)^2[/tex] = 9

[tex](9 - 6)^2[/tex] = 9

[tex](1 - 6)^2[/tex] = 25

[tex](5 - 6)^2[/tex] = 1

[tex](7 - 6)^2[/tex] = 1

[tex](6 - 6)^2[/tex] = 0

Step 3: Calculate the mean of the squared differences

Mean = (1 + 9 + 9 + 25 + 1 + 1 + 0) / 7 = 46 / 7 = 6.5714

Step 4: Take the square root of the mean

Standard Deviation = sqrt(6.5714) ≈ 2.5651

Rounded to the nearest tenth, the standard deviation is approximately 2.6.

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The real solutions of the polynomial equation x⁴ = 16 are x = ±2.To find the real or imaginary solutions of the polynomial equation x⁴ = 16, we can start by rewriting it as x⁴ - 16 = 0.

We can then factor the equation as a difference of squares: (x²)² - 4² = 0. Now, we have a quadratic equation in the form a² - b² = 0, which can be factored using the difference of squares formula: (x² - 4)(x² + 4) = 0. From this equation, we get two possible cases: Case 1: x² - 4 = 0. Solving for x, we have: x² = 4; x = ±2. Case 2: x² + 4 = 0.  

This equation has no real solutions because the square of a real number is always positive. Therefore, the real solutions of the polynomial equation x⁴ = 16 are x = ±2.

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The given matrix [4 7; 3 5] has an inverse. The inverse matrix is [5 -7; -3 4].

To determine if a matrix has an inverse, we need to check if its determinant is nonzero. Let's denote the given matrix as A: A = [4 7; 3 5]

The determinant of A, denoted as det(A), can be calculated by cross-multiplying and subtracting: det(A) = (4 * 5) - (7 * 3)

      = 20 - 21

      = -1

Since the determinant is nonzero (-1 ≠ 0), the matrix A has an inverse.

To find the inverse matrix, we can use the formula:

[tex]A^(-1)[/tex]= (1/det(A)) * adj(A)

Where adj(A) represents the adjugate of matrix A, obtained by swapping the elements of the main diagonal and changing the sign of the off-diagonal elements. Applying the formula, we have:

[tex]A^(-1)[/tex] = (1/(-1)) * [5 -7; -3 4]

      = [-5 7; 3 -4]

Therefore, the inverse of the given matrix [4 7; 3 5] is [5 -7; -3 4].

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