The intensity L(x) of light x feet beneath the surface of the ocean decreases at a rate proportional to its value at taht location. That is, L(x) satisfies the differential equation dL/dx=-kL, for some k>0 (the constant of proportionality). An experienced diver has determined that the weather condistions on the day of her dive will be such that the light intensity will be cut in half upon diving 19 ft under the surface of the water. She also knows that, once the intensity of the light falls below 1/5 of the surface value, she will haveto make use of the artificial light. How deep can the diver go without having to resort to the use of the artificial light?

The graph of a radical function in form f(x) = a(x + k)^1/n + c can tell you that the domain of the function is all real numbers greater than or equal to -k, and the range of the function depends on the values of "a" and "c".

The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.

Here,
The domain of a radical function in this form is determined by the expression under the radical. For the function to be defined, this expression must be greater than or equal to zero. Therefore, the domain of the function is all real numbers such that x + k is greater than or equal to zero.

The range of the function is determined by the value of "a" and "c". If "a" is positive, the range of the function is all real numbers greater than or equal to "c". If "a" is negative, the range of the function is all real numbers less than or equal to "c".

In summary, the graph of a radical function in form f(x) = a(x + k)^1/n + c can tell you that the domain of the function is all real numbers greater than or equal to -k, and the range of the function depends on the values of "a" and "c".

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A lot of 1000 components contains 300 that are defective. Two components are drawn at random and tested.

a) P(A) is 0.3

b) P(B|A) is 299/999

c) P(A ∩ B) is 0.089

d) P(A' ∩ B) is 0.211

e) P(B) is 0.3

f) P(A|B) is 0.297

g) A and B are not independent, therefore, it is not reasonable to treat A and B as though they were independent

a) P(A) is the probability that the first component drawn is defective. Since there are 300 defective components out of 1000, the probability that the first component drawn is defective is:

P(A) = 300/1000 = 0.3

b) P(B|A) is the conditional probability that the second component drawn is defective given that the first component drawn is defective. Since there are now 299 defective components left out of 999, the probability that the second component drawn is defective given that the first component drawn is defective is:

P(B|A) = 299/999

c) P(A ∩ B) is the probability that both the first and second components drawn are defective. Since there are 300 defective components out of 1000, the probability that the first component drawn is defective is 0.3. If the first component drawn is defective, then there are now 299 defective components left out of 999.

So the probability that the second component drawn is defective given that the first component drawn is defective is 299/999. Therefore, the probability that both components are defective is:

P(A ∩ B) = P(A) * P(B|A) = 0.3 * 299/999 = 0.089

d) P(A' ∩ B) is the probability that the first component drawn is not defective (i.e., it is good) and the second component drawn is defective. Since there are 700 good components out of 1000, the probability that the first component drawn is good is:

P(A') = 700/1000 = 0.7

If the first component drawn is good, then there are 299 defective components left out of 999. So the probability that the second component drawn is defective given that the first component drawn is good is:

P(B|A') = 299/999

Therefore, the probability that the first component drawn is good and the second component drawn is defective is:

P(A' ∩ B) = P(A') * P(B|A') = 0.7 * 299/999 = 0.211

e) P(B) is the probability that the second component drawn is defective. There are 300 defective components out of 1000, so the probability that the second component drawn is defective is:

P(B) = 300/1000 = 0.3

f) P(A|B) is the conditional probability that the first component drawn is defective given that the second component drawn is defective. Using Bayes' theorem, we have:

P(A|B) = P(A ∩ B) / P(B) = (0.3 * 299/999) / 0.3 = 0.089 / 0.3 = 0.297

g) A and B are not independent, because the probability of B depends on whether or not A has occurred. In other words, the probability of drawing a defective component for the second draw depends on whether or not the first draw yielded a defective component.

If A has occurred (i.e., the first component drawn is defective), then the probability of B is higher than if A had not occurred. Therefore, it is not reasonable to treat A and B as though they were independent.

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Complete question is:

A lot of 1000 components contains 300 that are defective. Twocomponents are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective.

a) find P(A)

b) find P(B|A)

c) find P(A ∩ B)

d) find P(A' ∩ B)

e) find P(B)

f) find P(A|B)

g) Are A and B independent? It is reasonable to treat A and B as though they were independent? Explain

The length of the altitude to EM in triangle GEM is 25 units.

Note that if the altitude of the triangle is at most 10, then the maximum area of the intersection of the triangle and the square is 5 * 10=50. This implies that vertex G must be located outside of square AIME.

Now, suppose GE meet AI at X and let GM meet AI at Y.

Clearly, XY=6 since the area of trapezoid XYME is 80. Also, triangle GXY is similar to triangle GEM.

Let the height of GXY be h.

By the similarity, h/6 = {h + 10}/10,

we get h = 15.

Thus, the height of GEM is

h + 10 = 15 + 10

h = 25 units

So the length of altitude is of triangle GEM is 25 units.

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____The given question is incorrect, the correct question is given below:

Square AIME has sides of length 10 units. Isosceles triangle GEM has

base EM, and the area common to triangle GEM and square AIME is 80

square units. Find the length of the altitude to EM in triangle GEM.

The solution to the system of linear equations can be expressed in vector form as:

x = [x1, x2, x3, x4] = [2-3x3-x4, 3+6x3+x4, x3, x4]

Breaking down the vector components:

A = [-3, 0, 1, 0]

a = [-1, 0, 0, -1]

B = [2, 3, 0, 0]

b = [0, 0, 1, 0]

bb = [0, 0, 0, 1]

C = [0, 0, 1, 0]

cc = [0, 0, 1, 0]

D = [0, 0, 0, 1]

dd = [0, 0, 0, 1]

To obtain this solution in vector form, we first rewrite the equations in standard form:

x1 + 3x3 + x4 = 2

x2 - 6x3 - x4 = 3

Then, we can write the solution as a combination of the homogeneous solution (the particular solution) and the non-homogeneous solution (the vector on the right-hand side). The homogeneous solution is obtained by setting the right-hand side to zero and solving for x3 and x4:

x1 + 3x3 + x4 = 0

x2 - 6x3 - x4 = 0

which gives x3 = -1/3 and x4 = 0. Therefore, the homogeneous solution is [0, 0, -1/3, 0].

The non-homogeneous solution is obtained by setting x3 and x4 to zero and solving for x1 and x2:

x1 = 2

x2 = 3

Therefore, the non-homogeneous solution is [2, 3, 0, 0].

Combining the homogeneous and non-homogeneous solutions, we obtain the final solution in vector form:

x = [0, 0, -1/3, 0] + [2, 3, 0, 0] = [2-3x3-x4, 3+6x3+x4, x3, x4]

with the vectors A, a, B, b, bb, C, cc, D, dd given as above.

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The x-intercepts of the graph of the equation y = x^2 - 3x + 2 are 1 and 2.

The x-intercepts of the graph of the equation y = x^2 - 1 are -1 and 1.

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this exercise, we would use an online graphing calculator to plot the linear function in order to determine the x-intercepts and y-intercepts as shown in the image attached below.

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The expression when simplified is 6x^8y^3

From the question, we have the following parameters that can be used in our computation:

(2x5y2)(3x3y)

Express properly

So, we have

(2x^5y^2)(3x^3y)

Evaluate the products

This gives

6x^(5+3)y^(2+1)

So, we have

6x^8y^3

Hence, the expression is 6x^8y^3

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Answer:

B

Step-by-step explanation:

took the test xx

Yes, 4√5 and 7√5 are like radicals because they have the same radical part, which is √5.

In mathematics, a radical is the inverse of an exponent, which is represented by the symbol ", also known as the root. It can be a square root or a cube root, and the number before the symbol or radical is known as an index number or degree.

Similar radicals have the same index and radicand (the expression under the radical sign). Because the radical sign is not specified, the index is assumed to be 2, and the radicand is 5.

Because 45 and 75 share the same radical part 5, they are considered radicals.

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The correct answer is −8p − 5q. This is because when multiplying two numbers, the two signs are combined.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


Since both −4 and (2p − 5q) are negative, the resulting product is also negative. To calculate the expression, it is simply a matter of multiplying the two numbers together: −4 * (2p − 5q) = −8p − 5q.

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Answer:

28 centimeters (cm) is equal to 280 millimeters (mm).

Step-by-step explanation:

This conversion can be done by multiplying the number of centimeters by 10 since there are 10 millimeters in 1 centimeter. So, 28 cm x 10 mm/cm = 280 mm.

To find the number of terms in a geometric progression, we can use the formula:

n = log[size of last term / size of first term] / log[common ratio]

In this case, the first term is 2, the last term is 256, and the common ratio is 4/2 = 2. Plugging these values into the formula, we get:

n = log[256/2] / log[2] = log[128] / log[2] = 7

Therefore, there are 7 terms in the geometric progression 2, 4, 8, ..., 256.

ChatGPT Feb 13 Version. Free Research Preview. Our goal is to make AI systems more natural and safe to interact with. Y

The Slope of the lines made from given points will be For A slope=1 and For B slope=∞.

What exactly is a Slope?

A slope of a line is defined as the change in y coordinate divided by the change in x coordinate.

The net change in y-coordinate is denoted by Δy, whereas the net change in x-coordinate is denoted by Δx.

As a result, the change in y-coordinate in relation to the change in x-coordinate is given by,

m = difference in y/difference in x = Δy/Δx=y2-y1/x2-x1

Where "m" shows the slope of a line.

The line's slope may alternatively be represented by

tan θ = Δy/Δx

In general, the slope of a line indicates its steepness and direction. The slope of a straight line between two locations, (x1,y1) and (x2,y2), is simply calculated by finding the difference of the coordinate points.

Now,

Given Coordinates are in form (x1,y1) and (x2,y2)

A. (5, 7) and (-4,-2)

then slope m=-2-7/-4-5

=-9/-9

=1

B. (1,3) and (1, -10)

slope m=-10-3/1-1

=-13/0

=∞

Hence,

           The Slope of the lines made from given points will be For A slope=1 and For B slope=∞.

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Answer:

i don't know

Step-by-step explanation:

Answer: f = 14.6

Step-by-step explanation:

Since you gave the equation 0.3 = 0.5f - 7, here are the following steps to solve:

1. Combine multiplied terms into a single fraction

[tex]0.3=\frac{1f}{2} -7[/tex]

2. Multiply by 1

[tex]0.3 =\frac{f}{2} -7[/tex]

3. Find Common Denominator

[tex]0.3 = \frac{f}{2} + \frac{2(-7)}{2}[/tex]

4. Combine fractions

[tex]0.3 = \frac{f+2(-7)}{2}[/tex]

5. Multiply

[tex]0.3=\frac{f - 14}{2}[/tex]

6. Multiply all terms by the same number to eliminate denominators

[tex]2(0.3)= 2\frac{f-14}{2}[/tex]

7. Simplify

[tex]0.6 = f-14[/tex]

8. Add 14 to both sides

[tex](0.6 + 14) = f (- 14 + 14)[/tex]

9. Simplify

[tex]f= 14.6[/tex]

Let n be an odd integer. By definition, n must be an integer not divisible by 2. Hence, when n2 is divided by 8, the remainder must be 1.

Let n be an odd integer. First, we can express n as 2k+1, where k is an integer. Next, when we square n, we get (2k+1)2. Expanding this gives 4k2+4k+1. Dividing this by 8 gives 4k2+k as the quotient and 1 as the remainder. This proves that the square of an odd integer always have a remainder of 1 when divided by 8.

To summarize, when an odd integer n is squared, the remainder when the result is divided by 8 is always 1. This is because an odd integer is not divisible by 2, and so the quotient will not be a whole number when divided by 8.

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The evaluated values,

(1) 0.38 × 10³ = 380

(2) 0.38 × 100,000 = 38000

(3) 0.38 × 10 = 3.8

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Three expressions are,

0.38 × 10³

0.38 × 100,000

0.38 × 10

Solving,

(1) 0.38 × 10³ = 0.38 x 1000 = 380

(2) 0.38 × 100,000 = 38000

(3) 0.38 × 10 = 3.8

Therefore, the evaluations are given above.

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Answer:

B

Step-by-step explanation:

you got polluted water that's the problem the solution is strict er laws about dumping

A copy machine takes 4.75 minutes to make 171 copies.  

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items. Division is the reciprocal of multiplication.

Time taken by the copy machine to take 36 copies = 1 minute.

Since 36 copies can be printed every minute, you could divide 171 by 36 to determine the time needed to make 171 copies.

[tex]\frac{171}{36}[/tex] = 4.75 minutes.

Time taken to print 171  copies is 4.75 minutes.

Hence, a copy machine takes 4.75 minutes to make 171 copies.

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Tyshawn will be required to put down 25% of the total cost of the vehicle.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Tyshawn wants to spend $19,500 on a car, but the bank will only lend him $14,625 for it. The percentage is then stated as,

P = [($19,500 - $14,625) / $19,500] x 100

P = [($4,875) / $19,500] x 100

P = 0.25 x 100

P = 25%

Tyshawn will be required to put down 25% of the total cost of the vehicle.

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Since (-6, -8) is not a solution to both equations in the system, it is not a solution to the system of equations.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Now in the given question ,

We can check if (-6, -8) is a solution to the system of equations by plugging in these values for x and y in each equation and verifying if both equations are true.

For the first equation y = (1/2)x - 3, if we substitute x = -6 and y = -8, we get:

-8 = (1/2)(-6) - 3

-8 = -3 - 3

-8 = -6

This is not true, so (-6, -8) is not a solution to the first equation.

For the second equation y = (5/2)x + 7, if we substitute x = -6 and y = -8, we get:

-8 = (5/2)(-6) + 7

-8 = -15 + 7

-8 = -8

This equation is true, so (-6, -8) is a solution to the second equation.

Since (-6, -8) is not a solution to both equations in the system, it is not a solution to the system of equations.

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The pie chart is an important type of data representation. It contains different segments and sectors in which each segment and sector of a pie chart forms a specific portion of the total(percentage). The sum of all the data is equal to 360°.

The "pie chart, also known as circle chart divides the circular statistical graphic into sectors or sections to illustrate numerical problems. Each sector represents a proportionate portion of the total.

The Pie-chart works best for determining the composition of something at that time. In most cases, pie charts take the place of other graphs such as bar graphs, line plots, histograms, and so on.

Note: The monthly budget of the family is represented in pie chart​ that is attached as image.

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The area of the castle's floor increases by 5.06% .

How to calculate area of rectangular floor?

By multiplying length and breadth, the rectangle's area will obtain in a square-unit dimension. In the case of a square, the area will become side2. The main difference between square and rectangle is that the length and breadth are equal for square.

Given :

Let the Length and width of the rectangular floor be x and y respectively

then , the area of rectangular floor be x*y

Since,

Ashley increased the length of the castle's floor : 30%

and width of castle's floor : 20%.

New length = x + 30% of x = x + 3x/100 = 103x/100

New width = y + 20% of y =y + 2y/100 = 102y/100

New area of rectangular floor = (103x/100)*(102y/100)

percent increase in area of the castle's floor

= {[(103x/100)*(102y/100) - x*y]*100} / xy

= 506 / 100

= 5.06

Hence, the area of the castle's floor increases by 5.06% .

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The coordinates of the point 'r' that lies along the directed segment from j (10, -5) to k (-2, -3) are equal to the ( 2/3 , -4 ).

We have, coordinates of the point r that lies along the directed line segment from j (10, -5) to k (-2, -3). The ratio of partitions of segment = 2 : 7

Internal section formula, Let consider M(x, y) be the point which divides line segment PQ internally in the ratio m : n. Then, the coordinates of M are calculated by below formula,

M = {[(mx₂ + nx₁ )/(m+n)], [(my₂ + ny₁)/(m+n)]}

j(10, -5) = (x₁,y₁), k(-2,-3) = (x₂,y₂)

Now we can determine the co-ordinate of r by substituting all values, Also, m : n = 2 : 7

r = {[2(10) + 7(-2)/ 2+7 ],[(3(-5) +7(- 3))/2+7 ]}

={[ (20 - 14)/9 ],[(-15 - 21) / 10]}

={6/9 , - 36/9}

= ( 2/3 , -4 )

Hence, required coordinates of r are ( 2/3 , -4 ).

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The point-slope form of a linear equation is:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

Using the given point (2, 0) and slope 1, we can substitute into the equation:

y - 0 = 1(x - 2)

Simplifying, we get:

y = x - 2

So the equation in point-slope form of the line that passes through the point (2, 0) with slope 1 is y = x - 2.

The vectors [8 -2 6] and [12 -3 9] are option (c) linearly independent because neither vector is a multiple of the other.

A vector is an entity that has both magnitude and direction. It is represented by an ordered set of numbers, which correspond to the coordinates of its endpoint in a given coordinate system.

In this problem, we are given two vectors: [8 -2 6] and [12 -3 9]. To determine if they are linearly independent or not, we need to check if one vector can be expressed as a linear combination of the other.

Let us assume that the first vector can be expressed as a linear combination of the second vector. That is, there exist constants a, b, and c such that:

[8 -2 6] = a[12 -3 9] + b

where b is a vector. Simplifying the above equation, we get:

8 = 12a + b1

-2 = -3a + b2

6 = 9a + b3

where b1, b2, and b3 are the respective components of vector b. Now, we can solve for a, b1, b2, and b3 using the system of linear equations. Solving for a, we get a = 2/3. Substituting this value in the remaining equations, we get:

b1 = -4/3, b2 = -2/3, and b3 = 2/3

Therefore, the vector b is [-4/3 -2/3 2/3]. We can verify that the first vector cannot be expressed as a linear combination of the second vector and b. Hence, the given vectors are linearly independent.

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The 10-ounce box is the better buy as it has a lower cost per ounce.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

To determine which box of cereal is a better buy, you can calculate the cost per ounce for each option.

For the 10-ounce box, the cost per ounce is:

= 1.86/10

Apply the division operation,

= $0.186 per ounce.

For the 14-ounce box, the cost per ounce is:

= 2.85/14

= $0.203 per ounce.

Therefore, the 10-ounce box is the better buy as it has a lower cost per ounce.

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a. The probability of Mikayla drawing black pencil from the bag if each pencil is removed from the bag after it is drawn, is 2/7.

b. The probability of Mikayla drawing blue pencil from the bag if each pencil is removed from the bag after it is drawn, is 15/28.

c. The probability of Mikayla drawing cyan pencil from the bag if each pencil is removed from the bag after it is drawn, 5/28.

Mikayla has a bag of pencils with 8 black, 15 blue, and 5 cyan pencils.

Total Number of Black Pencil = 8

Total Number of Blue Pencil = 15

Total Number of Cyan Pencil = 5

Total Number of pencil = Total Number of Black Pencil + Total Number of Blue Pencil + Total Number of Cyan Pencil

Total Number of pencil = 8 + 15 + 5

Total Number of pencil = 28

a. We have to determine the probability of Mikayla drawing black pencil from the bag if each pencil is removed from the bag after it is drawn.

The Probability = Total Number of black pencil/Total Number of pencil

The Probability = 8/28

The Probability = 2/7

b. We have to determine the probability of Mikayla drawing blue pencil from the bag if each pencil is removed from the bag after it is drawn.

The Probability = Total Number of blue pencil/Total Number of pencil

The Probability = 15/28

c. We have to determine the probability of Mikayla drawing cyan pencil from the bag if each pencil is removed from the bag after it is drawn.

The Probability = Total Number of cyan pencil/Total Number of pencil

The Probability = 5/28

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The complete question is:

Mikayla has a bag of pencils with 8 black, 15 blue, and 5 cyan pencils. find the following probabilities of Mikayla drawing the given pencils from the bag if each pencil is removed from the bag after it is drawn.

a. Only black pencil left

b. Only Blue pencil left

c. Only cyan pencil left

The statements about the Delian League that is true is A. Sparta never joined the league and resented Athens’s power and treatment of allies.

Following the Persian War, the Delian League was established in 478 BCE as a military coalition to protect the Ionian Greeks from any potential threats. Athens served as its principal leader and used its sizable and potent navy to defend all of its members who were unable to defend themselves.

Since Athens dominated the Delian League and Athens and Sparta had historically been adversaries, Sparta decided against joining. Although Athens and Sparta put their disagreements aside to overcome their common foe during the Persian Conflicts, they resumed their rivalry when the wars were over.

Therefore, option A is correct.

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The probability she pulls out a purple piece of candy would be 0.22.

Given is Sam's fathers collection.

The probability that tle would be green is -

P{E} = 4/20
P{E} = 1/5

Therefore, the probability she pulls out a purple piece of candy would be 0.22.

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a. The quarter has the smallest spread of data is Q3

b. The quarter has the largest spread of data is Q1

c. The interquartile range (IQR) is 1.5

d. There are more data in the interval 10–13

e. The interval has the fewest data in it is 10 - 12.

In statistics, a box plot is a graphical representation of a set of data that shows its distribution, median, and quartiles. It can be used to quickly and easily identify the range, spread, and skewness of a data set. Now let's take a look at the box plot you provided and answer your questions.

a. The quarter with the smallest spread of data is the second quarter, which ranges from approximately 4 to 6. The spread of this quarter can be calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1), which is approximately 0.5.

b. The quarter with the largest spread of data is the fourth quarter, which ranges from approximately 10 to 13. The spread of this quarter can also be calculated as the difference between Q3 and Q1, which is approximately 2.5.

c. The interquartile range (IQR) is a measure of the spread of the middle 50% of the data and is calculated as the difference between Q3 and Q1. In this case, the IQR is approximately 1.5 (6 - 4.5).

d. To determine whether there are more data in the interval 5-10 or 10-13, we can look at the box plot and see that the box and whiskers cover a larger range for the interval 10-13. Therefore, there are likely more data points in this interval.

e. To determine which interval has the fewest data, we can look at the box plot and see which interval has the smallest box and shortest whiskers. In this case, that would be the interval 10-12, which has a relatively small box and short whiskers compared to the other intervals. Therefore, we can conclude that this interval has the fewest data points.

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