The probability for event A is 0.3, the probability for event B is 0.5, and the probability of events A and
the events independent?
because

Answer: The measure of angle J is 40 degrees, 25 minutes, and 16 seconds, which can be expressed in decimal form as 40 + 25/60 + 16/3600 = 40.42111... degrees.

Since ∠J and ∠K are complementary, their measures add up to 90 degrees.

So, the measure of ∠K can be found by subtracting the measure of ∠J from 90 degrees:

∠K = 90 - 40.42111... = 49.57888... degrees

So, the measure of ∠K is approximately 49 degrees, 34 minutes, and 44 seconds.

Step-by-step explanation:

The system of equations to represent the situation are f + l = 20.5 and 6.25f + 9.5l = 149.25, solution is 14 pounds and 6.5 pounds

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We are given that;

Cost of fish=$6.25

Cost of lobster=$9.50

Cost of 20.5 pounds =$149.25

Now, let's use the variables f and l to represent the pounds of fish and lobster sold, respectively. We can set up two equations based on the information given:

f + l = 20.5 (the total weight sold is 20.5 pounds)

6.25f + 9.5l = 149.25 (the total revenue made is $149.25)

Now we can solve the system of equations using any method we prefer. Here's one way to do it using substitution:

f + l = 20.5 (equation 1)

f = 20.5 - l (solve equation 1 for f)

6.25f + 9.5l = 149.25 (equation 2)

6.25(20.5 - l) + 9.5l = 149.25 (substitute f = 20.5 - l into equation 2)

128.13 - 6.25l + 9.5l = 149.25 (distribute the 6.25)

3.25l = 21.12 (combine like terms)

l = 6.5 (divide both sides by 3.25)

Now we can use this value of l to find f:

f + 6.5 = 20.5 (from equation 1)

f = 14 (subtract 6.5 from both sides)

Therefore, by the equations the fish market sold 14 pounds of fish and 6.5 pounds of lobster.

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Answer:

Step-by-step explanation:

The zeros of a polynomial function are the values of x for which the function equals zero. For the given polynomial function p(x) = (2x - 1)(5x + 7)(8x + 9), the zeros can be found by setting each factor equal to zero and solving for x:

2x - 1 = 0, x = 1/2

5x + 7 = 0, x = -7/5

8x + 9 = 0, x = -9/8

Therefore, the zeros of the function are x = 1/2, x = -7/5, and x = -9/8.

In standard form, the polynomial function p(x) can be written as:

p(x) = 80x^3 + 122x^2 - 127x - 63

The relationship between the zeros of p(x) and its coefficients can be seen in Vieta's formulas. Vieta's formulas state that for a polynomial function of degree n with roots r1, r2, ..., rn, the coefficients of the polynomial can be expressed as:

a0 = (-1)^n * p0

a1 = (-1)^(n-1) * p1 / p0

a2 = (-1)^(n-2) * p2 / p0

...

an-1 = (-1) * pn-1 / p0

an = pn / p0

where p0 is the coefficient of the highest degree term (the leading coefficient), and the pi are the elementary symmetric polynomials, which are given by:

p1 = r1 + r2 + ... + rn

p2 = r1r2 + r1r3 + ... + rn-1rn

...

pn-1 = r1r2...rn-1 + r1r2...rn-2 + ... + rn-2rn-1

pn = r1r2...rn

Using Vieta's formulas, we can see that for the polynomial function p(x) given above, the coefficients are related to the zeros as follows:

a0 = -63

a1 = -127

a2 = 122

a3 = 80

And we can also see that:

a0 = (-1)^3 * p0 = -63

a1 = (-1)^(3-1) * p1 / p0 = -127

a2 = (-1)^(3-2) * p2 / p0 = 122

a3 = (-1)^(3-3) * p3 / p0 = 80

Therefore, the coefficients of the polynomial are related to the zeros through Vieta's formulas, which express the coefficients as functions of the zeros, and vice versa.

The polynomial H(x) = x³ - 4x³ + 5x² - 2 divided by (x - 1), will give a quotient of x² - 3x + 2 and a remainder of 0 using the long division, we can write H(x) = (x -1)(x² - 3x + 2).

A polynomial is a mathematical expression which have a sum of powers in one or more variables with coefficients. The highest power of the variable in a polynomial is called its degree.

We shall divide the polynomial x³ - 4x³ + 5x² - 2 by x - 1 as follows;

x³ divided by x equals x²

x - 1 multiplied by x² equals x³ - x²

subtract x³ - x² from x³ - 4x³ + 5x² - 2 will result to -3x² + 5x - 2

-3x² divided by x equals -3x

x - 1 multiplied by -3x equals -3x² + 3x

subtract -3x² + 3x from x³ - 4x³ + 5x² - 2 will result to 2x - 2

2 divided by x equals 2

x - 1 multiplied by 2 equals 2x - 2

subtract 2x - 2 from 2x - 2 will result to a remainder 0

Therefore, the polynomial H(x) = x³ - 4x³ + 5x² - 2 divided by (x - 1), will give a quotient of x² - 3x + 2 and a remainder of 0 using the long division, we can write H(x) = (x -1)(x² - 3x + 2).

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With the sum of digits of a two-digit number is 9. If the digits are reversed, the number is increased by 63. The number is 18. So, the correct option is A.

Let the two-digit number be represented by 10x + y, where x is the tens digit and y is the ones digit. We are told that x + y = 9 and that if the digits are reversed, the number is increased by 63.

If we reverse the digits of the original number, we get 10y + x. The difference between this number and the original number is 63, so we can set up the equation:

10y + x - (10x + y) = 63

Simplifying this equation, we get:

9y - 9x = 63

Dividing both sides by 9, we get:

y - x = 7

Now we have two equations: x + y = 9 and y - x = 7. We can solve this system of equations by adding the two equations:

2y = 16

y = 8

Substituting y = 8 into x + y = 9, we get:

x + 8 = 9

x = 1

Therefore, the original number is 10x + y = 10(1) + 8 = 18. So the answer is (a) 18.

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To calculate the number of containers that Heavey Compressors should be using, we need to determine the number of parts that need to be produced per day and divide it by the number of parts that can fit in each container.

100 parts per 8-hour day / 7 parts per container

= 14.2857 containers (round up to 15)

=15 containers

Therefore,  Heavey Compressors be using 15 containers.

Maximum inventory levels = reorder point + reorder quantity – [minimum consumption × minimum lead time].

= 100+15-[12.5x8]

= 115-100

= 15

Therefore, the maximum system inventory for this part is 15.

The maximum stock position is the largest number of goods a company can store to give its guests with service at the smallest possible cost. It's vital to keep force control in line with demand.

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Complete question:

Heavey Compressors uses a lean production assembly line to make its compressors. In one assembly area, the demand is 100 parts per eight-hour day. It uses a container that holds seven parts. It typically takes about five hours to round-trip a container from one work center to the next and back again. Heavey also desires to hold 20 percent safety stock of this part in the system. a. How many containers should Heavey Compressors be using? Do not round intermediate calculations. Round your answer up to the nearest whole number. containers b. Calculate the maximum system inventory for this part. Use the rounded value of the number of containers from part answer to the nearest whole number. parts c. If the safety stock percentage is reduced to zero, how would this impact the number of containers, all else being equal? calculations. Round your answer up to the nearest whole number. The number of containers will to containers.

We can use the Law of Cosines to solve for angle C:

cos C = (a^2 + b^2 - c^2) / (2ab)

where b is the length of side BC.

We know that B = 40 degrees, so we can find the measure of angle A:

A = 180 - B - C

A = 180 - 40 - C

A = 140 - C

We also know that the sum of the angles in a triangle is 180 degrees, so:

A + B + C = 180

140 - C + 40 + C = 180

180 = 180

This checks out, so we can continue with solving for angle C:

cos C = (a^2 + b^2 - c^2) / (2ab)

cos C = (7^2 + b^2 - 10^2) / (2*7b)

cos C = (49 + b^2 - 100) / (14b)

cos C = (b^2 - 51) / (14b)

We can use the Law of Sines to solve for b:

sin B / b = sin A / a

sin 40 / b = sin (140 - C) / 7

b = sin 40 * 7 / sin (140 - C)

Now we can substitute this value of b into the equation for cos C:

cos C = (b^2 - 51) / (14b)

cos C = [(sin 40 * 7 / sin (140 - C))^2 - 51] / (14 * sin 40 * 7 / sin (140 - C))

Simplifying this equation and solving for cos C, we get:

cos C = 11/14

Therefore, angle C is:

C = cos^-1(11/14)

C ≈ 38.8 degrees

Answer:

A)  Vertex = (-3, 4), y-intercept = (0, -5), x-intercepts = (-5, 0) and (-1, 0), axis of symmetry is x = -3

Step-by-step explanation:

The vertex of a quadratic function is the turning point. As this parabola opens downwards, the vertex is the maximum point of the graph. From inspection of the graph, the maximum point is at (-3, 4). Therefore:

The y-intercept is the point at which the curve crosses the y-axis. From inspection of the graph, the curve crosses the y-axis at y = -5. Therefore:

The x-intercepts are the points at which the curve crosses the x-axis. From inspection of the graph, the curve crosses the x-axis at x = -5 and x = -1. Therefore:

The axis of symmetry is the vertical line that passes through the vertex of the parabola so that the left and right sides of the parabola are symmetrical. So the axis of symmetry is the x-value of the vertex. Therefore:

The domain of the function is [0, 3) and the range of the function is [-4, 5).

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Here the input values in set A is called the domain and the output values in set B is called the range.

Given is a graph of a function.

The input values or domain includes the value of x which forms the curve in the graph.

The output values or range consists of the values of y formed as a result of the input of x.

Look at the x values corresponding to the end points of curve.

The curve extends from x = 0 to x = 3.

But at x = 3, it is an open circle. So x = 3 is not included.

So the input values are from x = 0 to x = 3, where 3 is not included.

Domain in interval notation = [0, 3).

Similarly the values of y extends from y = -4 to y = 5, where 5 is not included, since there is an open circle there.

Range in interval notation = [-4, 5).

Hence the domain and range are [0, 3) and [-4, 5) respectively.

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Answer:

259

Step-by-step explanation:

Answer:259

Step-by-step explanation:

202+57=259

Using Pythagorean theorem, the distance from where she started is 16.4km

The Pythagorean Theorem is a mathematical concept that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, the theorem can be expressed as:

c^2 = a^2 + b^2,

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

c² = 10² + 13²

c² = 269

c = √269

c = 16.4 km

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(a) Average for a student with 99 attendance is 81.1% and (b) The average for a student with 21 attendance is 78.8%.

Professor Cramer determines a final grade based on attendance, two papers, three major tests, and a final exam, the activities carry different weights.

Attendance is worth 3%,

each paper is worth 5%,

each test is worth 13%,

and the final is worth 48%.

(a) The average for a student with 99 on attendance, 75 on the first paper, 61 on the second paper, 94 on test 1, 86 on test 2, 77 on test 3, and 79 on the final exam

= [(99×3%) + (75×5%) + (61×5%) + (94×13%) + (86×13%) + (77×13%) + (79×48%)] ÷ [0.03 + 2(0.05) + 3(0.13) + 0.48]

= [2.97 + 3.75 + 3.05 + 12.22 + 11.18 + 10.01 + 37.92] ÷ 1

= 81.1 %

(b) The average for a student with the above scores on the papers, tests, and final exam, but with a score of only 21 on attendance

= [(21×3%) + (75×5%) + (61×5%) + (94×13%) + (86×13%) + (77×13%) + (79×48%)] ÷ [0.03 + 2(0.05) + 3(0.13) + 0.48]

= [0.63 + 3.75 + 3.05 + 12.22 + 11.18 + 10.01 + 37.92] ÷ 1

= 78.8 %

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Answer:

  $6400.42

Step-by-step explanation:

You want the value after 10 years of $5000.00 invested at 2.5%, compounded annually.

The formula for an amount earning compound interest is ...

  A = P(1 +r/n)^(nt)

where P is the amount invested at annual rate r compounded n times per year for t years.

Here, we have P=$5000, r=0.025, n=1, t=10, and the amount is ...

  A = $5000(1 +0.025)^(1·10) ≈ $6400.42

The final value after 10 years is $6400.42.

In a Quincy College class consisting of 15 students 12 or more have blue eyes.

If half the students at Quincy College have blue eyes, then the most probable event is that a randomly selected student from the college will have blue eyes.

This is because, if half the students have blue eyes, then there is a greater chance that a randomly selected student will have blue eyes than any other eye color.

For example, if we were to consider the event of a randomly selected student having green eyes, this would be less probable because fewer than half the students are likely to have green eyes.

Therefore, the most probable event is that a randomly selected student from Quincy College will have blue eyes.

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The completed table is,

Input    (x)  -1       0    1   2

Output (y)    -6   -2   2    6

Function rule is the rule of writing the relationship between the two variables, one is dependent and another is independent.

We are given that, the output is 4 less than the input.

The table given in the problem is;

Input    (x)  -1   0  1  2

Output (y)

Thus we need to write such a function, which gives the value of (y) is 4 less than the value of (x), when we put this into the function.

y = 4x - 2

Complete the table using the above function rule;

At (x) equal to -1,

y = 4(-1)-2

y = -6

At (x) equal to 0,

y = 4(0)-2

y = -2

At (x) equal to 1,

y = 4(1)-2

y = 2

At (x) equal to 2,

y = 4(2)-2

y = 6

Hence, the function rule for the statement, "the output is 2 less than 4 times x the input is y = 4x - 2 and the completed table is,

Input    (x)  -1       0    1   2

Output (y)    -6   -2   2    6

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The number of parent chaperones required on the trip (p) variable is the dependent variable.

According to the question,

s = the number of band students on the trip

p = the number of parent chaperones required on the trip

As the question already said the number of students on the trip determines how many parent chaperones are required to go along, therefore s , the variable of number of student is a independent variable as it does not depends on another variable.

And 'p' ,  the number of parent chaperones required on the trip depend on number of students. Therefore 'p' is dependent variable.

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The correct answer is A, as the mean cost of all 12 trips can be calculated by adding up the total cost of all the trips and dividing by the total number of trips.

The proposed solution is wrong as the mean cost of all 12 trips cannot be calculated by taking the average of the means of the two employees. Taking the average of the means of the two employees assumes that they took the same number of trips and that their trip costs are equally weighted in the total cost calculation, which is not necessarily true.

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False. The equation [tex]x = x2u + x3v[/tex] describes a line through the origin, not a plane.

The equation [tex]x = x2u + x3v[/tex] describes a line through the origin, not a plane. This equation can be written as [tex]x = x2u + x3v[/tex], which is the same as [tex]ux2 + vx3 - x = 0[/tex]. This equation is in the form of [tex]ax + by + cz = d[/tex], with a = u, b = v, c = -1, and d = 0. Since the coefficients of [tex]x2, x3[/tex], and x are all non-zero, we can conclude that this equation describes a line, not a plane. To confirm, we can calculate the direction vector for the line. The direction vector is (u, v, -1), which is a single vector and not two or more vectors that would be necessary to describe a plane.

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The lateral surface area of a prism is the sum of the areas of all its rectangular faces.

Surface area is a two-dimensional measure that refers to the total area of a surface, such as the area of a two-dimensional shape, a three-dimensional solid, or a combination of both. It is the sum of the areas of all the faces of a solid object. It is also referred to as the area of the boundary of a three-dimensional object. It can be used to calculate the volume of an object, and is also used in other calculations like area of the base of a triangle, area of a circle, and more.

It is calculated by multiplying the perimeter of the base by the height of the prism. For example, if the base of a prism is a square with side length s and the height is h, then the lateral surface area of the prism can be calculated as 4sh. If the base of the prism is a rectangle with length l and width w, then the lateral surface area of the prism can be calculated as 2lw + 2wh.

The lateral surface area of a prism can also be calculated by adding the areas of the triangular faces. If the base of the prism is a triangle with side lengths a, b, and c, then the lateral surface area of the prism can be calculated as a + b + c.

It is important to note that the lateral surface area of a prism is different from its surface area. The surface area of a prism is the sum of the areas of its lateral faces and its two bases.

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Complete question:

How to find the lateral surface area of the prism?

Answer:

Step-by-step explanation:

it is 77.6

Answer: C

asdfasdasdasdfasdf

The appropriate method for the biologist to use for inference to the population is A) A one-sample t-interval for a population mean.

In this situation, the biologist wants to estimate the average weight of a population of dolphins living in a certain region of the ocean. The biologist will collect a random sample of dolphins and use the sample weights to create the estimate.

here, we have,

Therefore, the appropriate method for inference to the population is to use a one-sample t-interval for a population mean.

This method is used when we want to estimate the population mean using a sample mean and the standard deviation of the sample.

The t-interval takes into account the uncertainty of the estimate due to the random sampling process, which makes it an appropriate method for this situation.

Hence, The appropriate method for the biologist to use for inference to the population is A) A one-sample t-interval for a population mean.

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The correct question is:

A marine biologist wants to estimate the average weight of a population of dolphins living in a certain region of the ocean. The biologist will collect a random sample of dolphins and use the sample weights to create the estimate Which of the following is an appropriate method for the biologist to use for inference to the population?

A A one-sample t-interval for a population mean

B A one-sample t-interval for a sample mean

C A one-sample 2-interval for a population proportion

D A matched-pairs t-interval for a mean difference

E A two-sample t-interval for a difference between means

(Part 1)  The expression [tex]18\sqrt{8}[/tex] can be written in the form [tex]a\sqrt{b}[/tex] as [tex]36\sqrt{2}[/tex], where a and b are integers and b is as small as possible.

(Part 2)  The expression [tex]8\sqrt{18}[/tex] can be written in the form [tex]a\sqrt{b}[/tex] as [tex]16\sqrt{3}[/tex].

(Part 3)  The expression [tex]18\sqrt{8}[/tex] - [tex]8\sqrt{18}[/tex] + [tex]\sqrt{n}[/tex] is equal to ([tex]36\sqrt{2}[/tex] - [tex]16\sqrt{3}[/tex]) + [tex]\sqrt{n}[/tex].

(Part 1) Expressing [tex]18\sqrt{8}[/tex] in the form [tex]a\sqrt{b}[/tex], where a and b are integers and b is as small as possible:

We can factor [tex]\sqrt{8}[/tex] as [tex]\sqrt{2}[/tex]* [tex]\sqrt{4}[/tex]

So, [tex]18\sqrt{8}[/tex]= 18 * [tex]\sqrt{2}[/tex] *[tex]\sqrt{4}[/tex] = 18 *[tex]\sqrt{2}[/tex] * 2 = [tex]36\sqrt{2}[/tex]

So the expression [tex]18\sqrt{8}[/tex] can be written in the form [tex]a\sqrt{b}[/tex] as [tex]36\sqrt{2}[/tex], where a = 36 and b = 2.

(Part 2) Expressing [tex]8\sqrt{18}[/tex] in the form [tex]a\sqrt{b}[/tex], where a and b are integers and b is as small as possible:

We can factor [tex]\sqrt{18}[/tex] as [tex]\sqrt{3}[/tex] * [tex]\sqrt{6}[/tex]

So, [tex]8\sqrt{18}[/tex] = 8 * [tex]\sqrt{3}[/tex] * [tex]\sqrt{6}[/tex]

[tex]8\sqrt{18}[/tex]= 8 * [tex]\sqrt{3}[/tex] * [tex]\sqrt{2}[/tex] * [tex]\sqrt{3}[/tex]

[tex]8\sqrt{18}[/tex]= 8 *[tex]\sqrt{6}[/tex]* [tex]\sqrt{2}[/tex]

[tex]8\sqrt{18}[/tex]= 8 * [tex]\sqrt{2}[/tex] * [tex]\sqrt{6}[/tex]

[tex]8\sqrt{18}[/tex]= 8 * 2 * [tex]\sqrt{3}[/tex]

[tex]8\sqrt{18}[/tex]= [tex]16\sqrt{3}[/tex]

So the expression [tex]8\sqrt{18}[/tex] can be written in the form [tex]a\sqrt{b}[/tex] as [tex]16\sqrt{3}[/tex], where a = 16 and b = 3.

(Part 3) [tex]18\sqrt{8}[/tex] - [tex]8\sqrt{18}[/tex] + [tex]\sqrt{n}[/tex]:

We can substitute the simplified forms of [tex]18\sqrt{8}[/tex] and [tex]8\sqrt{18}[/tex] from parts 1 and 2 into this expression:

[tex]18\sqrt{8}[/tex] - [tex]8\sqrt{18}[/tex] + [tex]\sqrt{n}[/tex] = [tex]36\sqrt{2}[/tex] - [tex]16\sqrt{3}[/tex] + [tex]\sqrt{n}[/tex] = ([tex]36\sqrt{2}[/tex] - [tex]16\sqrt{3}[/tex]) + [tex]\sqrt{n}[/tex].

So, the expression [tex]18\sqrt{8}[/tex] - [tex]8\sqrt{18}[/tex] + [tex]\sqrt{n}[/tex] is equal to ([tex]36\sqrt{2}[/tex] - [tex]16\sqrt{3}[/tex]) + [tex]\sqrt{n}[/tex] where n is an unknown constant.

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The integral for the volume of the solid is ∫2π(eᵇ)(dy)

In calculus, finding the volume of a solid is an important concept. One method to do this is by using integration.

To find the volume of the solid obtained by rotating the region bounded by y=ln(x), y=0, and x=5 about the y-axis, we can use the method of cylindrical shells. This involves dividing the region into infinitely thin vertical strips and rotating each strip around the y-axis to create cylindrical shells.

To set up the integral, we can use the formula for the volume of a cylindrical shell, which is 2πrhΔx, where r is the distance from the y-axis to the edge of the strip, h is the height of the strip, and Δx is the thickness of the strip.

Since we are rotating around the y-axis, we need to express the curves in terms of y instead of x. Using the inverse of the natural logarithm function, we can rewrite

=> y=ln(x) as x=eᵇ.

Thus, the region is bounded by x=5, y=0, and

=> x=eᵇ.

Next, we need to find the distance from the y-axis to the edge of the strip, which is simply the x-value at a given y. This is given by r=e^y.

The height of the strip is simply Δy, the thickness of the strip. To find this, we can take the difference between two consecutive y-values. Thus, Δy=dy.

Putting it all together, the integral for the volume of the solid is:

=> ∫2π(eᵇ)(dy)

This integral represents the sum of the volumes of all the cylindrical shells that make up the solid. However, we still need to evaluate the integral to get the actual volume of the solid.

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It is determined that she has a sebaceous cyst. This encounter should be reported with code(s)  L72.9. So option B is correct.

The ICD-10-CM code for sebaceous cysts is unspecified. The other options are not specific to a sebaceous cyst or are not relevant to the given scenario.

L72.1 is for the epidermal cyst, L30.9 is for unspecified dermatitis, and L72.3 is for the inflamed sebaceous cyst.

ICD-10-CM codes are used for medical diagnosis coding and are important for medical record-keeping, insurance reimbursement, and data analysis.

Each code corresponds to a specific medical condition, and it is essential to choose the correct code that accurately represents the patient's diagnosis.

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Answer:

y= 2x+12

Step-by-step explanation:

y=mx+c

y= 2x+12

(0,y) (-4,4)

2=y-4/4

8=y-4

12=y

Therefore, 4 people have been to Europe but not Asia.

A Venn diagram is a visual representation of sets and their relationships. It is used to show the similarities and differences between different sets of data. A Venn diagram consists of overlapping circles or other shapes, each representing a set. The size of each circle is proportional to the number of elements in the set it represents. The overlapping parts of the circles represent the elements that are shared by two or more sets. The non-overlapping parts represent the elements that are unique to each set. By analyzing the intersections and differences between sets in a Venn diagram, we can gain insights into the relationships between them. Venn diagrams are often used in mathematics, logic, statistics, and other fields to represent complex relationships between sets of data. They are also used in education to teach critical thinking and problem-solving skills.

Here,

Let E be the set of people who have been to Europe, A be the set of people who have been to Asia, and N be the set of people who have been to neither.

From the problem, we know that:

|E| = 5 (5 people have been to Europe)

|A| = 3 (3 people have been to Asia)

|E ∩ A| = 1 (1 person has been to both Europe and Asia)

To find the number of people who have been to Europe but not Asia, we need to find |E \ A|. We can use the formula:

|E \ A| = |E| - |E ∩ A|

Substituting the values we know:

|E \ A| = 5 - 1 = 4

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The probabilities are given as follows:

It is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

Uniformly distributed between 11 minutes and 14 minutes, hence the bounds are given as follows:

a = 11, b = 14.

As the uniform distribution is a continuous distribution, the probability of an exact value, such as X = 11, is of zero.

The probability of a value between 11 and 13 is given as follows:

p = (13 - 11)/(14 - 11) = 2/3.

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Answer:

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The air inside the beach ball with a radius of 20 inches is 33493.33 cubic inches.

The capacity of a sphere is its volume. It is the area that the sphere occupies. Cubic measurements of a sphere's volume include m3, cm3, in3, etc. The sphere has a round, three-dimensional shape. Its shape is determined by three axes: the x, y, and z axes. Sports like basketball and football are all examples of spheres with volume.

The volume of the cube is given as:

V = (4/3) πr³

Substituting the value of r = 20 inches we have:

V = (4/3)π(20)³

V = (4/3)(3.14)(20)³

V = 33493.33 cubic inches.

Hence, the air inside the beach ball with a radius of 20 inches is 33493.33 cubic inches.

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