Please give a step to step explanation

The probability of selecting a black card first and a red card second from a standard deck of 52 playing cards without replacement is 13/51.

The probability of selecting a black card on the first draw is 26/52, or 1/2, since there are 26 black cards in a standard deck of 52 playing cards.

After the first card is drawn, there are 51 cards remaining, of which 26 are red. Therefore, the probability of selecting a red card on the second draw, given that a black card was selected on the first draw, is 26/51.

To find the probability of both events happening (selecting a black card followed by a red card), we multiply the probabilities of each event:

P(black card first, red card second) = P(black card first) × P(red card second | black card first)

P(black card first, red card second) = (1/2) × (26/51)

P(black card first, red card second) = 13/51

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a. The flagpole is 5 feet away from the building.

b. The height of the flagpole is 8 feet.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

The distance from the building to the flagpole is,

tan35° = 3.5/x.

x = 3.5/0.7.

x = 5 feet.

Now, tan48° = x/5.

x = 5/1.11.

x = 4.5 feet.

Therefore, The height of the flagpole is 4.5 + 3.5 = 8 feet.

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Answer:

199 cm²

Step-by-step explanation:

in the picture

The sequence 3, 18, 108, 648, ..... is a geometric sequence.

The sequence 3.9, 19.5, 97.5, -487.5, ..... is a geometric sequence.

The sequence 1.1, -2.2, 4.4, -8.8, ..... is a geometric sequence.

The sequence 4, 20, 4, 20, ..... is not a geometric sequence.

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

Next, we would determine the common ratio as follows;

Common ratio, r = a₂/a₁ = a₃/a₂

Common ratio, r = 18/3 = 108/18

Common ratio, r = 6 = 6 (geometric sequence).

Common ratio, r = -19.5/3.9 = 97.5/-19.5

Common ratio, r = -5 = -5 (geometric sequence).

Common ratio, r = -2.2/1.1 = 4.4/-2.2

Common ratio, r = -2 = -2 (geometric sequence).

Common ratio, r = 20/4 = 4/20

Common ratio, r = 5 = 0.2 (not a geometric sequence).

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The angle between 0 and 2π  in radians which is Coterminal with angle 55π/8 in radians is 39π/8 radians .

We have to find coterminal angle between 0 and 2π in radians with an angle given in radians,

The angle is "55π/8"  in radians,

On simplifying ,

we get ;

⇒ 55π/8 = (55/8) × π

To find an angle coterminal with this angle between 0 and 2π, we  subtract or add multiples of 2π until we get an angle in range of 0 and 2π.

So , we convert 2π to same units as our angle :

⇒ 2π = 16π/8  ;

Next, we subtract the multiples of 16π/8 until we get an angle between 0 and 2π.

⇒ (55/8)π - 16π/8 = (55-16)π/8 = 39π/8  ;

This angle is between 0 and 2π, so it is coterminal with the angle 55π/8.

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The given question is incomplete , the  complete question is

The angle between 0 and 2π in radians that is coterminal with the angle 55π/8 in radians is  ?

Given that, the coordinates of the endpoints of ij are i(3,5) and j(17,19). point k is on ij and divides it such that ik:jk is 3:4.

The coordinates of the point k are (9,10)

The concept of section formula asserts that if a line segment is divided into two pieces in a certain ratio, the coordinates at the point of division may be obtained using the formula:

(mx2 + nx1)/(m+n), (my2 + ny1)/(m+n) = K

where (x1, y1) and (x2, y2) are the line segment's endpoint coordinates, and m:n is the provided ratio by which the line segment is divided.

The ends of the line segment IJ in this example are I(3,5) and J(17,19), and the ratio by which it is divided is 3:4, implying that IK:JK is 3:4.

As a result, m:n = 3:4, implying that m = 3 and n = 4.

When we enter these values into the formula, we get:

K = (3 x 17 + 4 x 3)/(3+4), (3 x 19 + 4 x 5)/(3+4)

When we simplify this expression, we get:

K = ( 51 + 12)/(7), (57 + 20)/(7)

K = (63)/(7),(77)/(7)

K = 9,10

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The measure of the angle x would be 25.2°.

What is a circle theorem?

The circle theorem is a set of mathematical rules and relationships that apply to circles and their components, such as chords, tangents, and angles. These theorems describe how the different parts of a circle relate to each other and are used to solve geometric problems involving circles. Some common circle theorems include the inscribed angle theorem, the chord-chord theorem, and the tangent-secant theorem.

By using the circle theorem, we can write

5x-7 = 119

5x = 119 + 7

5x = 126

x = 126/5

x = 25.2°

Hence, the measure of the angle x would be 25.2°.

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Answer:

350 calories

Step-by-step explanation:

see the attachment.

Calories in one cheeseburgers = 135

And, Calories in one medium fries = 583

We have to given that,

At McDonald's four cheeseburgers and three medium fries have a total of 2290 calories.

And, Six cheeseburgers and two medium fries have 2560 calories.

Let us assume that,

Calories in one cheeseburgers = x

And, Calories in one medium fries = y

Hence, We get;

4x + 3y = 2290  . (i)

6x + 3y = 2560 .. (ii)

From (i);

3y = 2290 - 4x

Substitute above value in (ii);

6x + (2290 - 4x) = 2560

6x - 4x + 2290 = 2560

2x = 2560 - 2290

2x = 270

x = 270 / 2

x = 135

From (ii);

6 x 135 + 3y = 2560

810 + 3y = 2560

3y = 2560 - 810

3y = 1750

y = 1750/3

y = 583

Therefore, Calories in one cheeseburgers = 135

And, Calories in one medium fries = 583

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The time taken by population of bacteria to be doubled whose normal growth is six fold in 10 hours is equal to 3.87 hours.

Let us consider 'n' is the time taken by the bacteria populations.

And P(n) represents the population of the bacteria in time 'n'

Using exponential growth function we know,

P(n) = K e^(a× n)

Where K and 'a' are the constants.

From the given condition we have :

P(10 ) = 6 P(0)

⇒ K e^ (10a) = 6k e^(0 × a )

⇒ e^(10a) = 6

⇒ 10a = log 6

⇒ a = ( log 6 ) / 10

Now required time when population is double :

P(n ) = 2P(0)

⇒  K e^ (n × a) = 2k e^(0 × a )

⇒ e^ [ n ×( log 6 ) / 10 ] = 2

⇒ n ×( log 6 ) / 10 = log 2

⇒ n = ( 10 × log 2 ) / log 6

⇒ n =  ( 10 × 0.3010 ) / 0.7782

⇒ n = 3.8679 hours

⇒ n = 3.87 hours

Therefore, the population of the bacteria will take 3.87 hours to get double.

The above question is incomplete , the complete question is:

A bacteria population increases sixfold in 10 hours. Assuming normal growth, how long did it take for their population to double?

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The height of the triangular prism will be 100mm.

The three-dimensional object has a base of triangular shape and has some height is called a triangular prism.

Given that the height and the base of the triangular shape of the triangular prism are 8 mm and 6.9 mm respectively. The volume of the prism is V = 2760 cubic mm.

The height of the triangular prism will be calculated as:-

Volume = 1/2 x b x h x H

2760 = 1/2 x 8 x 6.9 x H

H = 100 mm

Therefore, the height of the prism is 100mm.

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There are 11/3 pounds of cherries at Johnson's Farm in order to pay the same amount as picking 6 pounds of cherries at Mood's Farm.

In general, the unitary method is a useful tool for solving problems like this where we need to compare the cost of two different scenarios. We can set up equations based on the rates or costs involved, and then use algebra to solve for the unknown variables.

To begin, let's use a unitary method to find the total cost of picking cherries at Johnson's Farm. We know the entry fee is $26, so we can start with that. Then, for each pound of cherries picked, the cost is $6. So, if we let x be the number of pounds of cherries picked, the total cost at Johnson's Farm would be:

Total Cost = $26 + $6x

Now, let's use a unitary method to find the total cost of picking cherries at Mood's Farm. We know that there is no entry fee, so we can start with just the per-pound cost of $8. If we let y be the number of pounds of cherries picked, the total cost at Mood's Farm would be:

Total Cost = $8y

To find how many pounds of cherries you would need to pick at each farm in order to pay the same amount, we need to set these two total costs equal to each other and solve for x:

$26 + $6x = $8y

$6x = $8y - $26

x = (8/6)y - 13/3

x = (4/3)y - 13/3

So, if you picked 6 pounds of cherries at Mood's Farm (y = 6), the equivalent cost at Johnson's Farm would be:

x = (4/3)(6) - 13/3

x = 8 - 13/3

x = 11/3

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Doane's rule is used for choosing the number of histogram bins, not for determining the minimum sample size needed for a multiple regression analysis.

However, a commonly cited rule of thumb is that the sample size should be at least 10 times the number of predictors, so for a multiple regression dataset with 3 predictors, a minimum of 30 observations may be recommended.

Doane's rule is a guideline for choosing the number of histogram bins based on the sample size and skewness of the data. It suggests that the number of bins should be approximately equal to 1 + log2(N) + log2(1 + |g1|/SE(g1)), where N is the sample size and g1 is the sample skewness.

It is important to note that Doane's rule is used for determining the number of bins for a histogram, not for determining the minimum sample size needed for a multiple regression analysis.

That being said, in general, the minimum sample size needed for a multiple regression analysis depends on a variety of factors, including the number of predictors, the strength of the relationships between the predictors and the outcome variable, the desired statistical power, and the level of significance. There is no set minimum sample size that applies to all situations. However, a commonly cited rule of thumb is that the sample size should be at least 10 times the number of predictors, so for a multiple regression dataset with 3 predictors, a minimum of 30 observations may be recommended.

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Option B. Area under the curve. In a density curve, the proportion of data is represented by the area under the curve.

The area under the curve represents the proportion of data points that fall within a certain range of values, and the height of the curve at any given point represents the relative frequency or density of data points at that value. The total area under the curve is equal to 1, indicating that the sum of the proportions of data points in all possible intervals is equal to 100%.

It's important to note that the total area under the curve is equal to 1, indicating that the sum of the proportions of data points in all possible intervals is equal to 100%. This means that the density curve provides a complete picture of the distribution of the data, and the shape of the curve can be used to make inferences about the distribution, such as whether it is symmetrical, skewed, bimodal, etc.

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The measure <h = 45 degree, <g= 135 degree, <h = 55 degree and

<k = 125 degree.

When two lines converge, vertical angles are created. Because the angles are opposite one another, vertical angles are also known as vertically opposite angles. They are constantly on par.

Given:

As, from the Figure

<h + 135 = 180 (Linear Pair)

<h = 180 - 135

<h = 45

and, <g = 135 (Vertical Opposite Angle)

Now, <m + 125 = 180 (Linear Pair)

<m = 180 - 125

<h = 55

and, <k = 125 (Vertical Opposite Angle)

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We have drawn the graph for the given inequality.

What is inequality?

Inequality is a mathematical statement that compares two values or expressions and shows their relative size. It is represented by the symbols >, <, ≥, or ≤, which respectively mean "greater than", "less than", "greater than or equal to", and "less than or equal to". Inequalities can also include variables and can be used to describe a range of possible values for that variable.

For the given inequality y ≤ 3/5x-5

we can draw the graph as shown below:

Hence, we have drawn the graph for the given inequality.

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The amount of time that Nora practices flips is; t = 1 ¹/₄

How to Solve Algebra problems?

The BODMAS rule would be used to simplify the expression, BODMAS is an abbreviation for bracket, of, division, multiplication, addition and subtraction. It dictates the order in which a mathematical expression should be solved.

We are told that;

Nora spends time practicing flips on the trampolines. Let this be t.

Then, she spends 1/2 of an hour eating birthday cake with her friends.

Thus, total amount of time spent on flips and eating with her friends is;

t + ¹/₂ = 1 ³/₄

t = 1 ³/₄ - ¹/₂

t = 1 ¹/₄

Thus , the amount of time that Nora practices flips is; t = 1 ¹/₄

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Given question is incomplete , Complete Question is;

After arguing for two weeks, Nora convinced her parents to have her birthday party at FlyZone trampoline park. As soon as she gets there, Nora spends time practicing flips on the trampolines. Then, she spends 1/2 of an hour eating birthday cake with her friends. In all, Nora spends 1 3/4 hours at FlyZone. Which equation can you use to find the amount of time Nora practices flips?

Solve this equation for (t) to find the amount of time Nora practices flips

The solution of the expression for the value of k is [tex]\dfrac{8}{3^{15}}[/tex].

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

The given expression is,

[tex]\dfrac{3^8}{2}\times \dfrac{3^8}{4}\times k = 3[/tex]

The given expression will be solved as below,

[tex]\dfrac{3^8}{2}\times \dfrac{3^8}{4}\times k = 3[/tex]

Apply the properties of exponents which say that the number with the same base its exponents will be added.

[tex]\dfrac{3^{16}}{8}\times k = 3[/tex]

Now cross-multiply the number 3 by the ratio of 8 and the 3¹⁶ and solve for the value of k,

[tex]k = \dfrac{8}{3^{15}}[/tex]

Therefore, the value of k will be calculated as the ratio  [tex]\dfrac{8}{3^{15}}[/tex].

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The volume of a right circular cylinder with a diameter of 10 meters and a height of 16 meters is 400π m³.

Volume is the amount of space occupied by an object in three dimensions. It is a measure of how much space is contained within a solid shape, such as a cube, sphere, or cylinder. The unit of volume can vary based on the system of measurement being used, but common units include cubic meters, cubic centimeters, liters, and gallons. Volume is calculated by multiplying the area of the base of the object by its height or depth, depending on the shape of the object.

The volume of a right circular cylinder is given by the formula V = πr²h, where V is the volume of the cylinder, r is the radius of the circular base, and h is the height of the cylinder.

In words, the volume of a right circular cylinder is equal to the area of the circular base (πr²) multiplied by the height (h). This formula holds true regardless of the dimensions of the cylinder, as long as it has a circular base and straight sides that are perpendicular to the base.

The volume of a right circular cylinder is given by the formula V = πr²h, where r is the radius of the circular base and h is the height of the cylinder.

Since the diameter of the circular base is 10 meters, the radius is half of that, or 5 meters. The height of the cylinder is 16 meters.

Substituting these values into the formula, we get:

V = π(5)²(16) = 400π

Therefore, the volume of the cylinder is 400π cubic meters.

So the answer is 400π m³.

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Step-by-step explanation:

9-3 =6

So we have 6 dollars for 3 bracelets

Which means each bracelet costs 2 dollar each

So 9x-3x=6x

A) The average energy lost to ions in the second of two collisions separated by a time t is (eEt)2 2m is (1/3) (eEt)2 / m

B) The average energy loss to the ions per collision is (eEt)2/m is (ne2 / m) E2

In the Drude model, collisions between electrons and ions can cause energy loss, and this loss can be calculated using the average energy lost per collision. Specifically, if an electron experiences two collisions separated by a time t, the average energy lost to the ions in the second collision can be calculated.

We can use the formula for the energy gained by an electron in a uniform electric field: ΔE = eEt, where e is the charge of an electron, E is the electric field strength, and t is the time during which the electron experiences the field.

To do this, we can use the fact that the mean free path of an electron in a metal, before it experiences a collision, is given by λ = vτ, where v is the mean speed of the electron and τ is the average time between collisions.

The average energy lost in the second collision, over all directions of motion, is then given by:

(1/4π) ∫∫ ΔE2 (cosθ) dΩ

where θ is the angle between the direction of motion before the first collision and the direction of motion after the second collision, and dΩ is an element of solid angle. The factor (cosθ) accounts for the projection of the energy loss along the direction of motion.

After some calculations, we obtain the result:

(1/3) (eEt)2 / m

where m is the mass of an electron. This is the average energy lost to the ions in the second collision, over all possible directions of motion.

To answer part (b) of the question, we need to use the result of Problem 1(b), which states that the average time between collisions is given by τ = m/(ne2), where n is the number density of electrons in the metal. Using this formula, we can express the average energy loss per collision as:

(eEt)2 / mτ = (eEt)2 / (m^2 / ne2) = ne2 (eEt)2 / m

This is the average energy lost to the ions per collision, and we can use it to calculate the average loss per unit volume of the metal, which is given by:

(ne2 / m) E2

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The slope between the points is same, hence the points lie on the same line. The point (2, 3) does not lie on the graph of y = 3x - 4.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The given points are, (1,3) (4,2) (-2,4):

Calculate the slope of the line formed by the points.

The slope of the line is given by:

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

For (1,3) (4,2):

m = (2 - 3) / (4 - 1) = -1/3

For (4,2) (-2,4):

m = (4 - 2) / (-2 - 4) = 2/ -6 = -1/3

The slope between the points is same, hence the points lie on the same line.

The equation of the graph is:

y = 3x - 4

The given point is (2, 3):

Substituting the point in the equation:

3 = 3(2) - 4

3 = 6 - 4

3 = 2

False.

Hence, the point (2, 3) does not lie on the graph of y = 3x - 4.

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Answer:

1/4 as fraction

0.25 as decimal

= 0.25

Step-by-step explanation:

Factors of 24 starting at 1 are:
1 x 24 = 24

2 x 12 = 24

3 x  8  = 24

4 x 6 =  24

Then the pattern repeats in decreasing orders of products of numbers . 6 x 4, 8,x 3 etc which are duplicates of the ones shown above

Factors of 24 are:

1, 2, 3, 4, 6, 8, 12, 24

There are 8 factors

Out of the 8 factors, only two  - 12 and 24 are two digit numbers

P(factor is a 2 digit number = # two-digit numbers/Total # factors

= 2/8

= 1/4

= 0.25

Answer:

1/4 as a fraction

0.25 as decimal

0.25

follow me if my answer was helpful to you

The answer to the given fill in the blanks is "Residual". in a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the Residual come from a normal distribution.

In linear regression, we make several assumptions about the relationship between the predictor variable and the response variable. One of these assumptions is that the residuals (the differences between the predicted values and the actual values) follow a normal distribution with a mean of zero and constant variance. To check this assumption, we can create a normal quantile plot of the residuals. A normal quantile plot is a graphical method that compares the distribution of the residuals to a normal distribution. If the residuals are normally distributed, the plot should follow a straight line. If the plot deviates from a straight line, it suggests that the residuals are not normally distributed. A non-normal distribution of residuals can have several implications, such as indicating the presence of outliers or influencing the accuracy of the model’s prediction. Therefore, checking for normality of residuals is a crucial step in evaluating the model's assumptions and determining whether the model is appropriate for the data.

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The empirical rule tells us that for a normal distribution with mean μ and standard deviation σ, approximately 99.7% of the observations fall between 98 and 122.

Since the distribution is bell-shaped, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentage of observations that fall within certain ranges.

According to the empirical rule, for a normal distribution with mean μ and standard deviation σ:

About 68% of the observations fall within one standard deviation of the mean, i.e., between μ - σ and μ + σ.

About 95% of the observations fall within two standard deviations of the mean, i.e., between μ - 2σ and μ + 2σ.

About 99.7% of the observations fall within three standard deviations of the mean, i.e., between μ - 3σ and μ + 3σ.

In this case, the mean is 110 and the standard deviation is 4. Therefore:

About 68% of the observations fall between 110 - 4 = 106 and 110 + 4 = 114.

About 95% of the observations fall between 110 - 2(4) = 102 and 110 + 2(4) = 118.

About 99.7% of the observations fall between 110 - 3(4) = 98 and 110 + 3(4) = 122.

So approximately 99.7% of the observations fall between 98 and 122.

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The value of x in the coordinates (-12,1) and (x,7), having a slope of 1/8 is 36.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given that;

Point 1 (-12,1)

Point 2 (x,7)

Slope m = 1/8

Plug the values into the slope formula and solve for x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

1/8 = ( 7 - 1 )/( x - (-12) )

1/8 = ( 6 )/( x + 12)

Cross multiply

( x + 12) = 6 × 8

x + 12 = 48

x + 12 - 12 = 48 - 12

x = 36

Therefore, the value of x is 36.

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Significant figures with representation of x are a) 14.8 m = 14.x m. b) $10.25 = 10.2x. c) 0.05 L = 0.0x L. d) 1.000 g/mL = 1.00x g/mL. e)  6200cm = 6200x cm. f)  403 kg = 40x kg.

a) 14.8m has 3 significant figures. Representation with x in place of estimated digit: 14.x m. b) $10.25 has 4 significant figures. Representation with x in place of estimated digit: 10.2x. c) 0.05 L has 1 significant figure. Representation with x in place of estimated digit: 0.0x L. d) 1.000 g/mL has 4 significant figures. Representation with x in place of estimated digit: 1.00x g/mL. e) 6200cm has 2 significant figures. Representation with x in place of estimated digit: 6200x cm. f) 403 kg has 3 significant figures. Representation with x in place of estimated digit: 40x kg. Significant figures are the digits in a measurement that are reliable and accurate. They provide an indication of the precision of a measurement, and allow us to communicate the level of certainty we have in a particular value. When determining the number of significant figures in a measurement, we typically follow a set of rules. Non-zero digits are always significant, zeros between non-zero digits are significant, and trailing zeros to the right of the decimal point are significant. Zeros at the beginning of a number or to the left of a non-zero digit are not significant. The use of significant figures is important in science and engineering to ensure accurate and reliable measurements. When performing calculations with measurements, the result should be reported with the same number of significant figures as the least precise measurement used in the calculation. In addition, when rounding a number, the last digit should be rounded to the nearest value consistent with the number of significant figures being used. Understanding significant figures is an important part of scientific and mathematical communication, and can help to ensure accuracy and consistency in the reporting of data and calculations.

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The correct option regarding when Chicago first exceeded Phoenix in the percentage of calls answers within 10 seconds is given as follows:

C. Between September and October.

The output of the graph represents the percentage of calls answered within 10 seconds.

Chicago and Phoenix are represented as follows:

At the beginning of September, the red line was above the green line, but at the beginning of October, the green line was above the red line, hence the correct option is given by option C.

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We are assuming that the random selection is without replacement, which means that once a slip is drawn, it is not put back into the hat.

There are 5 possible pairs of numbers that add up to 12 when drawing two slips of paper numbered 1 through 14 without replacement. These pairs are:

1 and 11

2 and 10

3 and 9

4 and 8

5 and 7

Next, we need to find the number of ways to draw each pair. Since the order in which the slips are drawn does not matter, each pair can be drawn in 2 different ways. So, for each of the 5 pairs, there are 2 ways to draw the pair.

Each pair of numbers can be drawn in 2 different order (the order in which the slips are drawn does not matter in this case), so the total number of ways to draw two slips so that the sum of the numbers is 12 is [tex]5 * 2 = 10[/tex].

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