Construct a polynomial function of least degree possible using the given information.
Real roots: −1, 1, 3 and (2,
f(2)) = (2, 7)

The discount that she receives in total is 12 dollars.

Factors are integers (whole numbers) greater than 1 that are multiplied together to produce a given product.

The expression 4x-12 can be factored to (4x - 4) - (4-8).

This means that the discount that Lauren receives on each book is 4 dollars. So, for each book, the price is reduced by 4 dollars.

This means that if the original price of each book is x dollars, then Lauren pays x-4 dollars for each book.

In total, she pays 4(x-4) = 4x-16 dollars for 4 books.

This means that the discount that she receives in total is 12 dollars.

Therefore, we can conclude that Lauren receives a 4 dollar discount on each book she purchases and a total discount of 12 dollars when she purchases four books.

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Errors -in -variables bias represents the option c. arises from error in the measurement of the independent variable.

In a regression model Errors -in -variables bias is not only a problem in small samples.

It can affect large samples as well.

This can lead to biased estimates of the regression coefficients.

This can lead to biased and inconsistent estimates of the regression coefficients and standard errors.

Even if the error in the dependent variable is zero-mean.

Even if the measurement error in the dependent variable is negligible.

The problem is not limited to small samples.

And can be particularly severe when the measurement error in the independent variable is large.

Therefore, the errors -in - variables bias arises from the option c. arises from error in the measurement of the independent variable.

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Answer:

Matrix B is a 3 × 7 matrix.

There are 1300 Roman coins in the museum's collection in total.

How to determine the total number of Roman coins ?

To determine the total number of Roman coins in the museum's collection, we need to use the information given in the histogram. We know that there are 108 coins with a weight between 8 g and 17 g.

We can find the total frequency of all the coins by integrating the frequency density over the entire range of masses. To do this, we need to first find the width of each mass interval, which is given by the difference between the upper and lower mass values of each interval.

From the histogram, we can see that the width of each interval is 5 g.

So, the frequency of the coins between 8 g and 17 g can be calculated as:

Frequency = frequency density × interval width

Frequency = 10 × 5 = 50

This means that there are 50 coins in the museum's collection with a mass between 8 g and 17 g.

To find the total number of coins in the collection, we need to sum up the frequency of all the intervals.

To do this, we can calculate the area of each rectangle formed by the interval width and frequency density, and then sum up all these areas.

The total number of coins in the collection is given by:

Total number of coins = sum of frequencies over all intervals

Total number of coins = 50 + (15 × 15) + (20 × 20) + (25 × 25)

Total number of coins = 50 + 225 + 400 + 625

Total number of coins = 1300

Therefore, there are 1300 Roman coins in the museum's collection in total.

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La tabla representa una función exponencial, ya que la razón entre los términos consecutivos es constante y no varía como en una función lineal.

We can solve [tex]2^{a}[/tex] x[tex]2^{b}[/tex]  = [tex]2^{0}[/tex] by recognizing that [tex]2^{0}[/tex]equals 1 and simplifying the equation to [tex]2^{a+b}[/tex] = 1.

To solve [tex]2^{a}.2^{b}=2^{0}[/tex] for a and b, we must first recognize that 2^0 equals 1, which means that the equation can be rewritten as [tex]2^{a}.2^{b}=1[/tex]. Therefore, we can simplify the equation to [tex]2^{a+b}[/tex] = 1.

Since 2 raised to any negative power is a fraction, we need at least one of the exponents to be negative.

We could also choose other values that make either a or b negative, such as a = -2 and b = 2, or a = -3 and b = 3. The key is to have one negative exponent and one positive exponent so that their sum equals zero.

In summary, we can solve [tex]2^{a}.2^{b}=1[/tex]by recognizing that [tex]2^{0}[/tex] equals 1 and simplifying the equation to [tex]2^{a+b}[/tex] = 1. We must have at least one negative exponent to satisfy the equation, and we can choose various values for a and b as long as their sum equals zero.

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Answer:

x = - 2 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

10(5x + 12) = 2(5x + 15)  Distribute the 10 and the 2

10(5x) + 10(12)  = 2(5x) + 2(15)

50x + 120 = 10x + 30  Subtract 10x from both sides

50x - 10x +120 = 10x - 10x + 30

40x + 120 = 30    Subtract 120 from both sides

40x + 120 - 120 = 30 - 120

40x = -90  Divide both sides by 40

[tex]\frac{40x}{40}[/tex] = [tex]\frac{-90}{40}[/tex]

x = [tex]\frac{-9}{4}[/tex] or - 2[tex]\frac{1}{4}[/tex]

Helping in the name of Jesus.

Answer:   If x is less than -120, then x-120 will be less than zero, so we have:

|x-120| = -(x-120)

And since x is less than -120, we have:

|x-120| = -(x-120) = -x + 120

Therefore, the simplified expression for |x-120| when x<-120 is -x + 120.

Step-by-step explanation: I would reallyyyyyyyyyyyyyyyyy apreciate brainliest

The Cauchy Integral Formula (Generalized version), we have: ∫C [tex]z^2[/tex] dz = ∫C[tex]z^2[/tex]/(z - 0) dz

To apply the Cauchy-Goursat Theorem, we need to check if the function f(z) is analytic inside the contour C, i.e., it should be differentiable everywhere inside C.

(a) Let f(z) =[tex]ze^(-z)[/tex]. Then, f(z) is entire, i.e., differentiable everywhere in the complex plane. Hence, it is analytic inside the unit circle C. Now, applying the Cauchy-Goursat Theorem, we have:

∮C f(z) dz = 0

(b) Let f(z) = 2. Since 2 is a constant, it is analytic everywhere in the complex plane. Hence, it is analytic inside the unit circle C. Now, applying the Cauchy-Goursat Theorem, we have:

∮C f(z) dz = f(0) × 2πi = 0 (since C does not enclose the origin)

(c) Let f(z) = z tan(2π/2). Since tan(2π/2) is not analytic at z = ±i, f(z) is not analytic inside the unit circle C. Hence, we cannot apply the Cauchy-Goursat Theorem directly to evaluate the integral ∮C f(z) dz.

To evaluate the integral ∮C f(z) dz, we can use the Cauchy Integral Formula (Generalized version) which states that for any analytic function f(z) and any closed contour C, we have:

∮C f(z)/(z - a) dz = 2πi f(a)

where a is any point inside the contour C.

For (a), let's use the Cauchy Integral Formula to evaluate the integral. We have:

f(z) = z[tex]e^{-z[/tex]

∮C f(z) dz = ∮C f(z)/(z - 0) dz (since f(0) = 0)

= 2πi f(0) = 0

For (b), we can use the Cauchy-Goursat Theorem as f(z) = 2 is analytic everywhere inside the circle |z| = 4. Hence, we have:

∮C2 dz = 2πi f(0) = 2πi × 2 = 4πi

For (c), we need to use the Cauchy Integral Formula to evaluate the integral. We have:

f(z) = z tan(π/2)

∮C f(z) dz = ∮C f(z)/(z - i) dz (since i is inside C)

= 2πi f(i) = 2πi × i × tan(π/2) = -2πi

Thus, we have:

∮C f(z) dz ≠ ∮C f(z) dz in general.

Now, let C be the positively oriented boundary of the square whose sides lie along x = ±2 and y = ±2.

(a) Using the Cauchy Integral Formula (Generalized version), we have:

∫C cos(z) dz = ∫C cos(z)/(z - π/2) dz

= 2πi cos(π/2) = 0

(b) Using the Cauchy Integral Formula (Generalized version), we have:

∫C cosh(z) dz = ∫C cosh(z)/(z - 0) dz

= 2πi cosh(0) = 2πi

(c) Using the Cauchy Integral Formula (Generalized version), we have:

∫C [tex]z^2[/tex]dz = ∫C [tex]z^2[/tex]/(z - 0) dz.

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The ball is in the air for approximately 0.8 seconds before Ellie catches it.

The acceleration a body experiences as a result of gravity is known as the acceleration due to gravity. Its acceleration is around 9.81 metres per second squared close to the Earth's surface. In kinematics, many equations that describe how things move when affected by gravity include the acceleration caused by gravity as a constant.

Using kinematic equation to solve for the time (t):

Δy = vit + 0.5a*t²

Rearranging we have:

t = √((Δy - 0.5at²) / vi)

Substituting the values:

t = √((1 - 0.59.81t²) / 6)

t = 0.798 seconds

Hence, the ball is in the air for approximately 0.8 seconds before Ellie catches it.

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The profit for a selling price of $10 is approximately $64,692. To find the quadratic regression equation for this set of data, we can use the method of least squares to fit a quadratic function to the given data points.

The equation of a quadratic function is y =[tex]ax^2[/tex] + bx + c, where a, b, and c are constants. We will use column A for the widget selling price (x) and column B for the total profit earned at that price (y). Using calculator with regression capabilities, we can obtain the following quadratic regression equation for the given data:

y = -180.69[tex]x^2[/tex] + 4623.75x + 1423.64

To find the profit for a selling price of 10 dollars, we can simply substitute x = 10 into the equation and evaluate:

y =[tex]-180.69[/tex][tex](10)^2[/tex] + 4623.75(10) + 1423.64

y = -18069 + 46237.5 + 1423.64

y = 64692.14

Therefore, the profit for a selling price of 10 dollars is approximately $64,692.

The complete question is:

Company X tried selling widgets at various prices to see how much profit they would make. The following table shows the widget selling price, x, and the total profit earned at that price, y. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the profit, to the nearest dollar, for a selling price of 10 dollars.

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The cross product a ⨯b: A = 4, 5, 0 , b = 1, 0, 3

cross product {15, -12, -5}

dot products with 'a' and 'b': 0 and 0

For vectors a = {4, 5, 0} and b = {1, 0, 3}, you want the cross product and verification that the cross product is orthogonal to both 'a' and 'b'.

Cross product:

The cross product of 4i+5j+0k and 1i+0j+3k is the determinant :

  [tex]\left[\begin{array}{ccc}i&j&k\\4&5&0\\1&0&3\end{array}\right][/tex]

 = 15i - 12j -5k

As a list of coefficients, the cross product is c = {15, -12, -5}.

Orthogonal

Vectors are orthogonal if their dot product is 0.

a· c = {4, 5, 0}·{15, -12, -5} = (4·15) -(5·12) +(0·(-5)) = 60 -60 = 0

b· c = {1, 0, 3}·{15, -12, -5} = (1·15) +(0·(-12)) +(3·(-5)) = 15 -15 = 0

The dot products are both zero, so the cross product is orthogonal to both of the vectors that created it.

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If a matrix A is 5 x 3 and the product AB is 5x7, the size of B is 3x7.

The product of two matrices A and B, denoted as AB, is possible only if the number of columns of A is equal to the number of rows of B. In this case, A is 5x3, which means it has 3 columns.

And since the product AB is 5x7, it means the resulting matrix has 7 columns. Therefore, the number of columns of B must be equal to 7. And since A has 3 columns, the number of rows of B must be equal to 3 for the product to be possible.

Thus, the size of B is 3x7.

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The proof involves showing that the bisecting line QS and the parallel sides QR and PS create pairs of congruent angles, which then proves that opposite sides are parallel. Therefore, PQRS is a parallelogram.

Proof:

Since QS bisects PR at T, we know that PT = RT and QT = TS.

Also, QR is parallel to PS. Therefore, angle QTS is congruent to angle RPT (alternate interior angles).

Using the same reasoning, we can show that angle PST is congruent to angle QRP (alternate interior angles).

Now, we have two pairs of congruent angles in the quadrilateral PQRS, which means that the opposite sides are parallel.

Therefore, PQRS is a parallelogram.

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Answer:

h=

[tex] \frac{15}{4} [/tex]

Step-by-step explanation:

Divide both sides by 8:

[tex]2 - 7 + 4h = \frac{80}{8} [/tex]

Divide 80 by 8 to get 10:

[tex]2 - 7 + 4h = 10[/tex]

subtract 7 from 2 to get -5:

[tex] - 5 + 4h = 10[/tex]

add 5 to both sides:

[tex]4h = 10 + 5[/tex]

Add 10 and 5 to get 15:

[tex]4h = 15[/tex]

divide both sides by 4.:

[tex]h = \frac{15}{4} [/tex]

Hopefully this helps! :)

The most expensive health insurance plan for someone who fills 7 prescriptions each month is Option B, which has a total monthly cost of $240.

To identify the most expensive health insurance plan, we need to calculate the total cost for each option per month. The total cost can be found by adding the monthly insurance premium to the product of the co-pay per prescription and the number of prescriptions per month.

From the calculations, Option B is the most expensive plan as it cost $240 per month.

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Answer:

Step-by-step explanation:

Line A passes through (5,1) and (0,-2). So

     gradient line A =[tex]=\frac{-2-1}{0-5} =\frac{3}{5}[/tex]

Since the lines are parallel they have equal gradients, so  [tex]m=\frac{3}{5}[/tex].

The line passes through point P and so has y-intercept = 3 (so c=3).

So the equation of the new line is:

                       [tex]y=\frac{3}{5} x+3[/tex]

The distance between the Eiffel tower and the location where the observer is standing is 2869.2929 meters.

Therefore, you are 2869.2929 meters away from the Eiffel tower.

The Eiffel Tower is 300m tall. If a person is standing at a certain location in Paris, the tower subtends an angle of 6 degrees. To calculate the distance from the Eiffel tower, trigonometry is used. Here's how you can calculate the distance between the Eiffel tower and the location you are standing in Paris;

Let AB be the height of the Eiffel Tower, which is 300 m.
Let AC be the distance between the observer and the base of the Eiffel Tower.
Let the angle of elevation at A be θ = 6 degrees.
Now, from the diagram, it is clear that;
Tan θ = AB/AC
Therefore, AC = AB/Tan θ
Substituting values, we get:
AC = 300/Tan 6 degrees
AC = 300/0.104528
AC = 2869.2929 meters.

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In equation h=3.25w+19, the number 3.25 represents the rate of change in the height of the sunflower per week (w), and the constant term of 19 represents the initial height of the sunflower when it was first planted.

The equation h=3.25w+19 is in slope-intercept form, which means that it can be written as y=mx+b, where y represents the dependent variable (in this case, the height of the sunflower), x represents the independent variable (the number of weeks since the sunflower was planted), m represents the slope of the line, and b represents the y-intercept (the value of y when x=0).

In this equation, the slope is 3.25, which means that for each additional week that passes since the sunflower was planted, its height increases by an average of 3.25 inches. So, the number 3.25 represents the rate of change of the height of the sunflower with respect to time.

This means that for every additional week that passes since the sunflower was planted, the height of the sunflower increases by 3.25 inches on average.

The equation also includes a constant term of 19, which represents the initial height of the sunflower when it was first planted, before any weeks had passed.

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Each data point's ones digit is displayed in the second column, while its tens digit is displayed in the first column. Each "1|1" in the key denotes the value "11" in the data collection.

The term "statistical data" refers to numerical data that is gathered from a sample or population in order to characterise or draw conclusions about a larger group. Observational studies, surveys, experiments, and other techniques can all be used to gather statistical data, as can data from already-existing records and databases. Many approaches and methodologies, including data visualisation, inferential statistics, and descriptive statistics, can be used to examine statistical data. Measures of central tendency (mean, median, mode), indicators of dispersion (standard deviation, range, interquartile range), and graphical representations are some examples of the key characteristics of a dataset that are summarised and described using descriptive statistics (histograms, box plots, scatter plots). A bigger population can be inferred from a sample of data using inferential statistics, on the other hand.

given

The stem-and-leaf plot that depicts the data set accurately is as follows:

Season Points for the 2021 Riverside Red Dragon Football

0 0 3

1 1 7 7 7 7

2 0 0 0 2 4 8 8

3 1 3

Key 1|1 = 11

This stem-and-leaf plot depicts the frequency distribution of the data set in an accurate manner.

Each data point's ones digit is displayed in the second column, while its tens digit is displayed in the first column. Each "1|1" in the key denotes the value "11" in the data collection.

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To make  a departure timetable:

The simplest: download a predefined template from Microsoft Excel.

To create a template: select A1:E2 > Merge and Center > click WEEKLY SCHEDULE > select Center Alignment.

Add borders and titles. Type the time in A3. In A4 and A5, enter time > fill cell > add days > save template.

1. Start Excel and open a new blank workbook.

2. Select the range A1:E2 and on the Home tab, select Merge and Center in the Alignment group.

3.

Type "WEEKLY SCHEDULE" in A1:E2, change the font size to 18, and select Center Alignment in the Alignment group.

4. Select cells F1:H2, on the Home tab, in the Font group, select the Border drop-down menu, and then select All Borders.

5. Enter “Daily Start Time” into F1, “Time Interval” into G1, and “Start Date” into H1.

Select the Select All icon (between 1 and A on the worksheet), then double-click the line dividing two columns to resize all cells to fit the contents.

6. Select cell A3 and enter "TIME".

7. Select cell A4 and enter the time you want the program to start.

To follow this example, enter "7:00".

8. In cell A5, enter the next interval to be listed in the plan. To follow this example, enter "7:30". Select A4:A5 and drag the fill handle down to fill the time increment for the rest of the day.

9. In cell B3, enter the day of the week you want the schedule to start. To follow this example, enter "SUNDAY".

10. Drag the fill handle to the right to automatically fill the calendar with the remaining days of the week.

11. Select row 3. Make the font bold and change the font size to 14.

12. Change the hour font size in column A to 12.

13. Choose the Select All icon or press Ctrl+A and choose Center from the Alignment group on the Home tab.

14. Select cells A1:H2. In the Font group on the Home tab, select the Fill Color drop-down list and choose a fill color for the selected cells.

15. Select the body of the program. Select the Border drop-down menu in the Font group and select All Borders.

16. Save the program that  we have made as time table.

Complete Question:

How can we help the park manager to draw a departure timetable in excel?

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Answer:

3

Step-by-step explanation:

0.15c - 0.072 = 0.078c = (0.15 - 0.072)c = 0.078 times the coefficient c.

To factor 0.15c - 0.072, the first step is to find the greatest common factor (GCF) of the terms. In this case, the GCF is 0.072. This means that 0.072 can be divided out of both terms.

The next step is to divide out 0.072 from both terms. This gives 0.15c/0.072 = 0.208 and -0.072/0.072 = -1.

After this, we can combine the terms by multiplying the coefficients: 0.208 x -1 = -0.208.

Therefore, 0.15c - 0.072 can be factored as -0.208c. This means that 0.15c - 0.072 is equal to -0.208 times the coefficient c.

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Answer:

5/6π(4.25 in)^2

Step-by-step explanation:

Step 1: Calculate the full area of the disk using the formula for the area of a circle: A = π × r2

A = π × (4.25 inches)2

A = 56.41π inches2

Step 2: Calculate 5/6 of the full area.

A = (5/6) × 56.41π inches2

A = 47.01π inches2

Therefore, the area of 5/6 of the disk is 47.01π inches2.

The Distance after 18 minutes travelled is calculated as: 19.8 miles

In the distance, speed and time relationship, we know that:

Speed = Distance/Time

From the table, we see the distance the car travels in y miles after x minutes. Thus:

We can use slope formula to find the average speed which is:

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

Thus:

Constant speed = (22 - 11)/(20 - 10)

Constant Speed = 11/10 = 1.1 miles per minute

Thus, distance after 18 minutes is:

Distance = 1.1 * 18 = 19.8 miles

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The system of equations given consisted of two equations, both of which represented the cost of the pizzas ordered by the two customers, Karen and Malik. each regular pizza costs $41 and each deluxe pizza costs $22.

System of equations:

6r + 7d = 226

6r + 9d = 270

Solving:

6r + 7d = 226

6r + 9d = 270

-6r -6r

7d -9d = -44

d = -44/2

d = -22

6r + (-22) = 226

6r = 248

r = 248/6

r = 41

Each regular pizza costs $41, and each deluxe pizza costs $22.

The system of equations given consisted of two equations, both of which represented the cost of the pizzas ordered by the two customers, Karen and Malik. To solve this system of equations, we first subtracted 6r from both equations, leaving us with 7d and -9d on one side. We then divided both sides by -2, leaving us with d = -22. We then added 22 to the other equation, leaving us with 6r = 248. Finally, we divided both sides by 6, leaving us with r = 41. Thus, each regular pizza costs $41 and each deluxe pizza costs $22.

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the linear equations that have an infinite number of solutions are (x – 3/7) = 2/3 (3/2x – 9/14), 3x – 18 = 3(–6 + 4.1).

To determine which linear equations have an infinite number of solutions, we need to check if the equations are equivalent. Two linear equations are equivalent if they have the same slope and y-intercept, or if they represent the same line.

Let's check each of the given equations:

(x – 3/7) = 2/3 (3/2x – 9/14)

Multiplying both sides by 14, we get:

14x - 6 = 28/3x - 6

Multiplying both sides by 3, we get:

42x - 18 = 28x - 18

Subtracting 28x and adding 18 to both sides, we get:

14x = 0

Dividing both sides by 14, we get:

x = 0

Substituting x = 0 into the original equation, we get:

(-3/7) = (-9/14)

The left-hand side is equal to the right-hand side, which means the equation is true for all values of x. Therefore, this equation has an infinite number of solutions.

8(x + 2) = 5x – 14

Expanding the left-hand side, we get:

8x + 16 = 5x - 14

Subtracting 5x and subtracting 16 from both sides, we get:

3x = -30

Dividing both sides by 3, we get:

x = -10

Substituting x = -10 into the original equation, we get:

8(-8) = 5(-10) - 14

-64 = -64

The left-hand side is equal to the right-hand side, which means the equation is true for x = -10. Therefore, this equation has exactly one solution.

3x – 18 = 3(–6 + 4.1x)

Expanding the right-hand side, we get:

3x - 18 = -18 + 12.3x

Subtracting 3x and adding 18 to both sides, we get:

0 = 0.3x

Dividing both sides by 0.3, we get:

x = 0

Substituting x = 0 into the original equation, we get:

-18 = -18

The left-hand side is equal to the right-hand side, which means the equation is true for all values of x. Therefore, this equation has an infinite number of solutions.

1/2(6x + 10) = 7(3/7x – 2)

Expanding both sides, we get:

3x + 5 = 3x - 14

This equation simplifies to 5 = -14, which is not true for any value of x. Therefore, this equation has no solutions.

2x – 3.5 = 2.1(5x + 8)

Expanding the right-hand side, we get:

2x - 3.5 = 10.5x + 16.8

Subtracting 2x and adding 3.5 to both sides, we get:

0 = 8.5x + 20.3

This equation simplifies to 0 = 0, which is true for all values of x. Therefore, this equation has an infinite number of solutions.

Therefore, the linear equations that have an infinite number of solutions are (x – 3/7) = 2/3 (3/2x – 9/14), 3x – 18 = 3(–6 + 4.1).

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This gives a result of t = 10, meaning that it will take 10 days for the amount of money in the box to be reduced to 25 cents.

If there are R125 in a box and half of the total is removed each day, it will take 10 days to reduce the total to 25 cents. This is because the total amount is being halved each day, and the amount remaining at the end of each day is the amount left at the start of the day, divided by two. This can be expressed mathematically using the formula[tex]R125/(2^t)[/tex] = 25, where t is the number of days.If we solve the equation for t, we get t = log2(R125/25). This gives a result of t = 10, meaning that it will take 10 days for the amount of money in the box to be reduced to 25 cents.To calculate this process over the 10 days, we can use the formula [tex]R125/(2^t)[/tex] for each day, where t is the day number. Starting at day 0, the amount remaining would be R125. At the end of day 1, the amount remaining would be R125/2 = R62.50. At the end of day 2, the amount remaining would be R62.50/2 = R31.25. This process continues until at the end of day 10, the amount remaining would be R0.25.

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Option C includes a 5 unit upshift, a mirror along the y-axis, and a 1.5 scale factor dilation. Therefore sequence of transformation in C will produce the same result. .

The ideal selection is B. Reflection along the y-axis, a 5 unit upshift, and a 1.5 scale factor for elongation

Option A says: 15-turn clockwise spin and  2 unit translation to the right

Rotation and translation are rigid transformations that create congruent as well as similar figures while preserving the measurements of matching sides and angles. Therefore, this series of transformations is incorrect because it will not result in a similar or congruent picture.

Option B involves 90-degree anticlockwise spin and reflection along the x-axis.

Reflection and rotation are rigid transformations that create congruent as well as similar figures while preserving the measurements of corresponding sides and angles. Consequently, this series of changes won't result in a similar Thus, it is untrue.

Option C includes a 5 unit upshift, a mirror along the y-axis, and a 1.5 scale factor dilation.

Translation and reflection are rigid transformations that create congruent as well as similar figures while preserving the measurements of matching sides and angles. The picture will no longer be congruent after dilation with a scale factor of 1.5, but it will still be similar because the measure of the angles remains constant. This series of transformations will therefore result in a similar but incongruent image, and is therefore accurate.

Option D calls for a scale factor of 2 followed by a scale factor of 0.5.

With a scale factor of 2, dilation results in the side widths of The picture will eventually grow to be twice as long as the preimage.

The side lengths of the picture with double side lengths will then be halved by dilation once more with a scale factor of 0.5.

The figure will eventually return to its initial condition, which is identical to and consistent with itself. Therefore, this series of transformations is incorrect because it won't result in a similar or congruent picture.

The best choice is C.

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Complete question:

Which sequence of transformations will produce the same result?

Option A says: 15-turn clockwise spin and 2-unit translation to the right

Option B: involves a 90-degree anticlockwise spin and reflection along the x-axis.

Option C: includes a 5-unit upshift, a mirror along the y-axis, and a 1.5 scale factor dilation.

Option D: calls for a scale factor of 2 followed by a scale factor of 0.5.

the age of jill and tony is 10 and 8 respectively

Twice Jill's Age Added To Three Times Tony's Age Is 44

2m + 3n = 44

Jill's Age Equals Tony's Age Plus 2 Years

m = n + 2

by solving the both equation we get

2(n + 2) + 3n = 44

5n + 4 = 44

5n = 44 - 4

n = 40/5

n = 8

again

m = 8 + 2

m = 10

so the age of jill and tony is 10 and 8 respectively

There are numerous methods to define a mathematical equation. A model is just a mathematical statement that says two theoretical results are equal. For instance, in the equation 3x + 5 = 14, the terms 3x + 5 and 14 are two different formulations that are separated by the symbol "equal." The simplest and most fundamental algebraic equations in mathematics contain one or more parameters.

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