in a circle, an angle measuring 9.7 radians intercepts an arc of length 11.8. find the radius of the circle to the nearest 10th.

The scale factor of the two rectangles show a common ratio of 4/5

A scale factor in geometry is a ratio that indicates how much a figure has been extended or shrunk.

When two figures are comparable, the scale factor is the ratio of any matching lengths in the two figures.

A scale factor of higher than 1 indicates expansion, whereas a scale factor of less than 1 indicates decrease. The figure is the same size as the original when the scale factor is 1.

The dimensions of comparable figures can be calculated using scale factors. For instance, we can use the scale factor to determine the length of the corresponding side of the smaller rectangle if we know the scale factor between two identical rectangles and the length of one of its sides of the larger rectangle.

In the given figure;

12/15 = 36/45

Let's find the ratio here;

4/5 =4/5

The scale factor is 4/5

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The Practice Operations with radical expressions is simplified using the basic of the Algebra:

Algebraic expressions incorporating radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both). The root might be an nth root, a square root, or a cube root. Radical expressions can be made simpler by taking them down to their most basic form and, if feasible, getting rid of all of the radicals.

Radical expressions are simplified by taking them down to their most basic form and, if feasible, altogether deleting the radical. An algebraic expression's numerator and denominator are multiplied by the appropriate radical expression if the denominator contains a radical expression.

Practice Operations with radical expressions are:

1) [tex]\sqrt{540}[/tex] = [tex]\sqrt{36 * 15 }[/tex]

= 6√15

2) [tex]\sqrt[3]{432}[/tex] = [tex]\sqrt[3]{216*2}[/tex]

= [tex]6\sqrt[3]{2}[/tex]

3) [tex]\sqrt[3]{128}[/tex] = [tex]\sqrt[3]{64*2}[/tex]

= [tex]4\sqrt[3]{2}[/tex]

4) [tex]-\sqrt[4]{405}[/tex] = [tex]-\sqrt[4]{81*5}[/tex]

= [tex]-3\sqrt[4]{5}[/tex]

5) [tex]\sqrt[3]{-5000}[/tex] = [tex]-\sqrt[3]{1000*5}[/tex]

= [tex]-10\sqrt[3]{5}[/tex]

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which is approximately 3.864 times the length of QS.the circle is approximately 4 times the length of QS, or approximately 4 times 0.966 times the length of QS,

An angle is a measure of the amount of turn between two lines or rays that meet at a common point, known as the vertex of the angle. The angle is typically measured in degrees or radians. In a Euclidean plane, an angle can range from 0 degrees (corresponding to two lines that are parallel to each other) to 180 degrees (corresponding to two lines that form a straight line). An angle greater than 180 degrees is called a reflex angle. Angles are used in many areas of mathematics and physics, such as geometry, trigonometry, and calculus, as well as in real-world applications such as navigation, architecture, and engineering.

by the question.

The ratio of the central angle ZQTS to the whole circle is 1/12, or 0.0833 (rounded to four decimal places). This is because there are 360 degrees in a circle, and 75 is 1/12 of 360.

QS represents 1/4 of the circle's circumference. This is because the central angle ZQTS is 75 degrees, which is 1/3 of a right angle (90 degrees). An inscribed angle that intercepts the same arc as a 1/3 angle will have twice the measure of the 1/3 angle, or 150 degrees. Thus, angle QTS is 150 degrees. Angle QOS is also 150 degrees, since it intercepts the same arc as QTS. Therefore, angle QOT is 60 degrees, since the angles in triangle QOT add up to 180 degrees. Since triangle QOT is an equilateral triangle, QT and QS are equal in length, and angle QTS is 75 degrees, we can use the sine function to find the length of QS. The sine of 75 degrees is approximately 0.966, so QS represents approximately 0.966 times the circumference of the circle. Since QS represents 1/4 of the circumference, the circumference of the circle is approximately 4 times the length of QS, or approximately 4 times 0.966 times the length of QS,

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The answer option to the above question is The 3 ordered pairs are B, (4,10),(4,11),(4,12).

In this context, the word "equation" refers to the equation of the line that best fits a certain set of data points. A straight line that most accurately depicts the trend or pattern in a collection of data points is called the line of best fit. Predictions or estimations for additional data points that might not be a part of the initial set can be made using the equation of the line of best fit.

According to the given information:

To determine which three ordered pairs are most likely the added data points, we need to consider the slope and y-intercept of the original line of best fit. Since the equation of the line of best fit remains unchanged, the new points must lie on the original line.

The original line of best fit can be determined using a linear regression algorithm. However, we can estimate the slope and y-intercept of the line by simply finding the coordinates of two points on the line.

We can use the first and last points in the original set of data to estimate the slope and y-intercept. Using these points, we find that the equation of the line of best fit is:

y = -0.84x + 10.8

Now we can check which of the given sets of points lie on this line:

A: (4,4), (5,5), (6,6)

For (4,4), y = -0.84(4) + 10.8 = 7.56, which is not equal to 4. So (4,4) is not on the line.

Similarly, (5,5) and (6,6) are not on the line.

Therefore, A is not the correct answer.

B: (4,10),(4,11),(4,12)

For (4,10), y = -0.84(4) + 10.8 = 7.56, which is equal to 10. So (4,10) is on the line.

Similarly, (4,11) and (4,12) are also on the line.

Therefore, B is a possible answer.

C: (8,9),(8,10),(8,11)

For (8,9), y = -0.84(8) + 10.8 = 4.32, which is not equal to 9. So (8,9) is not on the line.

Similarly, (8,10) and (8,11) are not on the line.

Therefore, C is not the correct answer.

D: (10,10),(10,11),(10,12)

For (10,10), y = -0.84(10) + 10.8 = 3.96, which is not equal to 10. So (10,10) is not on the line.

Similarly, (10,11) and (10,12) are not on the line.

Therefore, D is not the correct answer.

Therefore, the answer is B, (4,10),(4,11),(4,12).

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The equation of the line passing through the two given points in slope-intercept form is: y = (-5 / 6)x - 1/6

To find the equation of the line passing through the two given points (–6, 1) and (6, –9) in slope-intercept form, we need to first find the slope of the line.

The slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:

[tex]m = (y_2 - y_1) / (x_2 - x_1)[/tex]

Substituting the values of the given points, we get:

m = (-9 - 1) / (6 - (-6))

m = -10 / 12

m = -5 / 6

Now that we know the slope of the line, we can use the point-slope form of the equation of a line to find its slope-intercept form. The point-slope form of a line passing through a point [tex](x_1, y_1)[/tex] with slope m is given by:

[tex]y - y_1 = m(x - x_1)[/tex]

Substituting the values of the slope and one of the given points (–6, 1), we get:

y - 1 = (-5 / 6)(x - (-6))

y - 1 = (-5 / 6)(x + 6)

Simplifying this equation, we get:

y = (-5 / 6)x - 1/6

Therefore, the equation of the line passing through the two given points in slope-intercept form is: y = (-5 / 6)x - 1/6

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Step-by-step explanation:

Box volume = 2880  cm^3    <=====correct

Cylinder volume = pi * r^2 * h = 3.14 * (6^2) (20) = 2260.8 cm^3

                 (radius, r = 1/2 diameter = 6 cm)

Box can hold this much more:  2880 - 2260.8 = 619.2 cm^3

Binomial expansion of the given algebraic expression is:

729x⁶ − 1458x⁵y + 1215x⁴y² - 540x³y³ + 135x²y⁴ - 18xy⁵ + y⁶

The binomial theorem is one that states the principle for expanding the algebraic expression (x + y)ⁿ and expresses it as a sum of the terms involving individual exponents of variables x and y.

Thus, for example (x + y)³ will be expressed as:

1(x³)(y⁰) + 3(x²)(y¹) + 3(x¹)(y²) + 1(x⁰)(y³)

Similarly, for (3x - y)⁶, using pascals triangle, we have:

1(3x)⁶ + 6(3x)⁵(-y)¹ + 15(3x)⁴(-y)² + 20(3x)³(-y)³ + 15(3x)²(-y)⁴ + 6(3x)¹(-y)⁵ + 1(-y)⁶

= 729x⁶ − 1458x⁵y + 1215x⁴y² - 540x³y³ + 135x²y⁴ - 18xy⁵ + y⁶

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The equation whigh relates x and y points along the incline is: y = 2x - 3

We know that the general form of a slope - intercept form of equation of line is :

y = mx + c

m = slope

and c = y-intercept

We know that slope is nothing but angle of incline.

From figure we can observe that the line passes through points (3, 3) and (6, 9)

Using the formula of slope,

m = (9 - 3) / (6 - 3)

m =  6/3

m = 2

So the equation of line would be

y = 2x + c

As line passes though point (3, 3),

3 = 2(3) + c

3 = 6 + c

c = - 3

So, the equation that relates x and y for points along the incline is:

y = 2x - 3

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The complete question is:

All three points displayed are on the line. you'll need to write an equation that relates x and y for points along the incline. what is this equation?

The probability of Jose being the president and Ellen being the vice president in a committee of eight people choosing leaders at random is 1/56.

The probability of Jose being chosen as the president and Ellen being chosen as the vice president is:

P(Jose as president and Ellen as vice president) = P(Jose as president) * P(Ellen as vice president | Jose as president)

Since the assignments are made at random and there are no restrictions on who can be chosen for each position, the probability of Jose being chosen as president is 1/8, and the probability of Ellen being chosen as vice president, given that Jose is president, is 1/7 (since there are 7 remaining people who can be chosen for the position of secretary).

Therefore,

P(Jose as president and Ellen as vice president) = (1/8) * (1/7) = 1/56

So the probability that Jose is president and Ellen is vice president is 1/56.

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_____The given question is incomplete, the complete question is given below:

A committee of eight people must choose a president, a vice president, and a secretary.

Two of the committee members are Ellen and Jose. Assume the assignments are made at random. What is the probability that Jose is president and Ellen is vice president?

The measure of the angle of elevation is 58°( nearest degree)

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

The height of the pole will represent the opposite to the angle of elevation and the length of the shade will be the adjascent to the angle of elevation.

Represent the angle of elevation by x

Tan x = opp/adj

Tan x = 8/5

Tan x = 1.6

x = tan^-1(1.6)

x = 58° ( nearest degree)

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Answer:

[tex]y = - 5x - 4[/tex]

Step-by-step explanation:

[tex] - 9 = - 5(1) + b[/tex]

[tex] - 9 = - 5 + b[/tex]

[tex]b = - 4[/tex]

[tex]y = - 5x - 4[/tex]

The final answer is "2.2" < x  < 6.4 which is the pοssible length οf x.

The triangle inequality theοrem is a cοrnerstοne οf geοmetry and states that any triangle's sum οf its first twο sides is always greater than its third side. Fοr a triangle with sides a, b, and c, a + b > c, b + c > a, and a + c > b.

Accοrding tο the Triangle Inequality Theοrem, the length οf the third side must be greater than the sum οf the lengths οf the triangle's twο sides.

Therefοre, the pοssible length οf a triangle is equal tο the prοduct οf the sum οf the twο sides and the difference οf the twο sides.

Therefοre,

4.3 - 2.1 <  x < 4.3 + 2.1

2.2 < x < 6.4

Since "2.2" x 6.4 is a pοssible length fοr f x, that is the final answer.

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Complete Question:

What is the range of possible sizes for side xxx? < x <

Answer:

(x,y) = (-5,-8)

Answer:

Step-by-step explanation:3x+7=x-3. 3x-x=-3-7. 2x=-10. X=-5. but y=x-3. So. Y=-5-3=-8

Thus, the angle of depression from the plane to the building is found as:

Ф = 27.90°.

The angle of depression is indeed the angle formed by a line drawn from the observer's line of sight down to an object below it.

It is frequently used in navigating, surveying, and trigonometry to describe its position of an object in relation to an observer's point of view. Degrees are used to express the depression's angle.

Give data:

Let the height  h = 420 ft.

Let the distance x = 896 ft.

angle of depression is found using the trigonometric formula:

tan Ф = height/distance

tan Ф = h/x

tan Ф = 420/896

tan Ф = 0.46875

Ф = tan⁻¹(0.46875)

Ф = 27.90°.

Thus, the angle of depression from the plane to the building is found as:

Ф = 27.90°.

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a) The residuals are 0, 1, -5, -6, -7, 1, and -12 for x = 1, 2, 3, 4, 5, 6, and 10, respectively.

b) the equation y = 2x + 3 may not be a good fit for the given data.

What is the linear equation?

A linear equation is an equation that describes a straight line in a two-dimensional space. It is a mathematical expression that relates two variables, usually x and y, such that one variable is a function of the other. The general form of a linear equation is:

y = mx + b

a. To calculate the residuals, we need to find the predicted values of y using the given equation and then subtract them from the actual values of y.

For x = 1, y = 2(1) + 3 = 5, residual = 5 - 5 = 0

For x = 2, y = 2(2) + 3 = 7, residual = 8 - 7 = 1

For x = 3, y = 2(3) + 3 = 9, residual = 4 - 9 = -5

For x = 4, y = 2(4) + 3 = 11, residual = 5 - 11 = -6

For x = 5, y = 2(5) + 3 = 13, residual = 6 - 13 = -7

For x = 6, y = 2(6) + 3 = 15, residual = 16 - 15 = 1

For x = 10, y = 2(10) + 3 = 23, residual = 11 - 23 = -12

So, the residuals are 0, 1, -5, -6, -7, 1, and -12 for x = 1, 2, 3, 4, 5, 6, and 10, respectively.

We can plot these points (x, residual) on a scatter plot.

b. The points on the scatter plot show a random pattern, which suggests that the model may not be a good fit.

The negative residuals for x = 3, 4, and 5 indicate that the actual values of y are lower than the predicted values, while the large negative residual for x = 10 indicates a much larger error.

Additionally, the residual for x = 6 is positive, which means the actual value of y is higher than the predicted value.

Therefore, the model may not be a good fit for the given data.

The points (1, 0), (2, 1), (3, -5), (4, -6), (5, -7), (6, 1), and (10, -12) show a random pattern on the scatter plot, which suggests that the model may not be a good fit.

Thus, the equation y = 2x + 3 may not be a good fit for the given data.

Hence, a) the residuals are 0, 1, -5, -6, -7, 1, and -12 for x = 1, 2, 3, 4, 5, 6, and 10, respectively.

b) the equation y = 2x + 3 may not be a good fit for the given data.

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Answer:

The expression you use to find the amount of miles would be 5xT=X miles.

or 5t

Answer:

Step-by-step explanation:

Its 4.24 to the nearest hundredth because I input the square root of 18 in my caclulator.

The new weight of wrestler 1 is w_{(n+2)/2} = w_{(n+3)/2} - 1

The new weight of wrestler 2 is w_{(n+4)/2} = w_{(n+3)/2} + 2.

Let's suppose the weights of the wrestlers before the two new wrestlers joined the team are arranged in increasing order as follows:

w_1 ≤ w_2 ≤ w_3 ≤ ... ≤ w_n

where;

Since the mean weight remains unchanged, we have:

(w_1 + w_2 + w_3 + ... + w_n) / n = (w_1 + w_2 + w_3 + ... + w_n + x + y) / (n+2)

where x and y are the weights of the two new wrestlers.

Simplifying the above equation, we get:

2(w_1 + w_2 + w_3 + ... + w_n) = nw_1 + nw_2 + nw_3 + ... + nw_n + 2x + 2y

which can be further simplified as:

2(w_1 + w_2 + w_3 + ... + w_n) - 2nw_n = (n-2)w_1 + (n-2)w_2 + (n-2)w_3 + ... + (n-2)w_{n-1} + 2x + 2y

Since the median weight increases by 3 pounds, the new median weight is the weight of the (n+3)/2-th wrestler.

where;

We can express this in terms of the weights of the original wrestlers and the weights of the new wrestlers as follows:

If n+2 is even, then the new median weight is the average of the (n+2)/2-th and (n+4)/2-th weights.

If n+2 is odd, then the new median weight is the (n+3)/2-th weight.

In either case, we have:

w_{(n+2)/2} + w_{(n+4)/2} = 2(w_{(n+3)/2} - 3)

Substituting the weights of the original wrestlers and the new wrestlers using the equation we derived earlier, we get:

[(n-1)w_{(n+2)/2} + (n-1)w_{(n+4)/2} + 2x + 2y] + [(n-1)w_{(n+2)/2} + (n-1)w_{(n+4)/2}] = 2[(n+2)w_{(n+3)/2} - 6]

Simplifying and rearranging the terms, we get:

4w_{(n+3)/2} - 2w_{(n+2)/2} - 2w_{(n+4)/2} = x + y - 3

Substituting x + y = 2w_{(n+3)/2} - 3, we get:

w_{(n+4)/2} - w_{(n+2)/2} = 3 - w_{(n+3)/2}

Since the weights are arranged in increasing order, we have:

w_{(n+2)/2} ≤ w_{(n+3)/2} ≤ w_{(n+4)/2}

Therefore, the only possible solution is:

w_{(n+2)/2} = w_{(n+3)/2} - 1

w_{(n+4)/2} = w_{(n+3)/2} + 2

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The sum that shows how many concert tickets were sold using the given parameters is: ²/₅x + 60

Algebraic expressions are defined as the simple idea of expressing numbers with the aid of letters or alphabets without even specifying their actual values.

Let the total number of tickets available for sale be denoted as x.

We are told that 100 tickets were sold last week. Thus:

Amount of tickets left unsold = (x - 100)

We are now told that 2/5 of the remaining tickets were sold this week. Thus:

Number of tickets sold this week = ²/₅(x - 100)

Thus:

Total Number of Tickets sold = 100 + ²/₅(x - 100)

= 100 + ²/₅x - 40

= ²/₅x + 60

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The answer of the given question based on Quadrilateral ABCD is inscribed in the circle on finding the measure of the angle ∠B is  70°.

A quadrilateral is a geometric shape that consists of four straight sides, connected end-to-end to form a closed figure. Examples of the quadrilaterals are rectangles, squares, parallelograms, trapezoids, and rhombuses. In a quadrilateral, the interior angles add up to 360° degrees. Quadrilaterals can have opposite sides parallel (as in parallelograms) or opposite sides equal in length (as in kites). They are widely used in geometry and mathematics in general.

In a circle, the opposite angles of a quadrilateral inscribed in the circle are supplementary. Therefore, we have:

m∠B + m∠D = 180°

We are given that B = (4x - 20)°, so we can substitute this into the equation above and solve for x:

m∠B + m∠D = 180°

(4x - 20)° + 115° = 180° (Note that m∠D is given as 115° in the diagram)

4x - 20 + 115 = 180

4x + 95 = 180

4x = 85

x = 21.25

Now that we know x, we can find the measure of angle ∠B:

m∠B = 4x - 20°

m∠B = 4(21.25) - 20°

m∠B = 70°

Therefore, the measure of angle ∠B is 70°.

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Answer:

20cm

Step-by-step explanation:

90cm ÷ 1/2 the length 90 = 20cm

Answer and explanation:

Background info:

y = mx + b, where,

 If we look at the y-values in the table, we see that 4 ounces is added each time (16 + 4 = 20 + 4 = 24...).  Similarly, if we look at the x-values in the table, we see that 0.5 hours is added each time (0 + 0.5 = 0.5 + 0.5 = 1 ...).

Therefore, since the change in y is 4 (oz) and the change in x is 0.5 (hr), we divide 4 by 0.5 to find the slope:

4 / 0.5 = 8 = m

As we can see on the table, when x is 0, y = 16.  Thus, 16 is our y-intercept.

Thus, the general equation for the table is y = 8x + 16

Interpreting the slope and y-intercept:  When we consider our units, slope in context of this problem is change in ounces / change in hours.  We can think of 8 as the fraction 8 over 1.  

Answer: 40 degrees

Step-by-step explanation:

There are 9 sides in a nonagon and 360 degrees make the shape up.

360 degrees divided by  9 EQUAL SIDES of a nonagon = 40 degrees

The quadratic equation 2x^2 - x + 10 = 0 can be solved using the quadratic formula, which is:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

Here, a = 2, b = -1, and c = 10. Substituting these values, we get:

x = [-(-1) ± sqrt((-1)^2 - 4(2)(10))] / 2(2)

x = [1 ± sqrt(1 - 80)] / 4

x = [1 ± sqrt(-79)] / 4

Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, the answer is "No solution".

An equation that can be used to find the lightest and heaviest acceptable weights, x, for the filled canister include the following: B. |x − 42| = 0.9.

In Mathematics, an absolute value function is a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0) of a cartesian coordinate (graph).

Mathematically, an absolute value function can be represented by the following mathematical equation:

|x| = x, x ≥ 0.

|x| = x, x < 0.

Based on the information provided about the desired weight of the canister and the popcorn, an equation that models the situation is given by;

|x − 42| = 0.9.

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The critical value t for constructing a 99% confidence interval for a  with 11 degrees of freedom is approximately 3.106.

A t-distribution table is a table of values that shows the critical values for the t-distribution, which is a probability distribution used in statistics.

The table is typically organized by degrees of freedom and the level of significance (α) for a two-tailed test.

To find the critical value t* for a 99% confidence interval for a mean with 11 degrees of freedom, we can use a t-distribution table or a calculator.

Using a t-distribution table, we can find the critical value that corresponds to a 99% confidence level and 11 degrees of freedom.

The table shows that the critical value is approximately 3.106.

Alternatively, we can use a calculator that has a t-distribution function.

For example, using the function (0.005, 11) in Microsoft Excel will give us the same result of approximately 3.106.

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Answer:

82.8 in.

Step-by-step explanation:

Answer:

experimental probability approaches theoretical probability when the sample size is large.

Step-by-step explanation:

This illustrates that experimental probability approaches theoretical probability when the sample size is large. As the number of tosses increases, the experimental probability of both coins being heads for both Deena and Jackson approaches the theoretical probability of 1/4 (since the probability of getting heads on a single coin toss is 1/2, and the probability of getting heads on two coin tosses is (1/2) * (1/2) = 1/4). This is because the law of large numbers states that as the sample size increases, the experimental probability approaches the theoretical probability. Therefore, the more tosses that are performed, the closer the experimental probability will be to the theoretical probability.

Keelin's hourly rate increased by 7.89%. To calculate the percentage increase in Keelin's hourly rate, we need to determine the difference between the new and old rates and express that difference as a percentage of the old rate.

First, we find the difference between the two rates:

$10.25 - $9.50 = $0.75

This means that Keelin's hourly rate increased by $0.75 per hour.

Next, we need to express this increase as a percentage of the old rate:

($0.75 / $9.50) x 100% = 7.89%

Therefore, Keelin's hourly rate increased by 7.89%.

A percent increase is a measure of the increase in a quantity compared to the original value. In this case, the original value is Keelin's hourly rate of $9.50, and the new value is $10.25. The percentage increase is calculated by finding the difference between the new and old values and expressing that difference as a percentage of the original value.

A percentage increase is useful in analyzing changes over time or comparing changes in different variables. In this case, knowing the percentage increase in Keelin's hourly rate can help her understand how much her pay has increased and plan for future financial goals. It can also be helpful for an employer to calculate percentage increases in employee salaries when determining raises or promotions.

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To convert 1/5 to a decimal number by long division, we divide 1 by 5 and keep adding 0s to the dividend until we have enough decimal places and 1/5 as a decimal number is 0.2.

0.2 | 1.0000

   |-------

   | 0

   |----

     1

So, 1/5 as a decimal number is 0.2.

Part O:

If we keep repeating the division process in part N, we will get the same result of 0.2 because 1/5 has a finite decimal representation.

Part P:

From the three long-division calculations we have completed, we can conclude that the quotient, or result, from the long-division process can either end or continue indefinitely.

In part N, we found that 1/5 has a finite decimal representation, so the long division process ended.

However, for other fractions, such as 1/3, the long division process will continue indefinitely because the quotient has a repeating pattern of digits.

Read more about long division here:

https://brainly.com/question/25289437

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