or
Jeffrey likes to skate at an ice cream parlor that is due south of his school and due west of his favorite movie theater. If the ice cream parlor is 12 kilometers from his school and the straight-line distance between the school and the movie theater is 13 kilometers, how far is the ice cream parlor from the movie theater?

kilometers

The trigonometri Identity :

LHS  =  1- 2cos²x  = 1 - 2(1 - sin²x) = 1 + 2sin²x - 2 = 2sin²x - 1 = RHS (proved)

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are several distinctive trigonometric identities that relate a triangle's side length and angle.

Trigonometry equations known as trig identities are used often to comprehend various mathematical aspects and to solve trigonometry and geometry-related issues. Knowing essential trig identities aids in remembering and comprehending crucial mathematical concepts as well as in resolving a variety of mathematical issues.

The Pythagorean trigonometric identity, commonly known as the Pythagorean identity, is an identity that uses trigonometric functions to represent the Pythagorean theorem. It is one of the fundamental relationships between the sine and cosine functions, along with the sum-of-angles equations.

We know

sin²x + cos²x = 1

LHS ,

=  1- 2cos²x

= 1 - 2(1 - sin²x)

= 1 + 2sin²x - 2

= 2sin²x - 1 = RHS

Therefore we can see that LHS = RHS (proved)

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The price of a box of cereal under the price leadership model is 16 dollars.

The price of a box of cereal under the price leadership model can be calculated by finding the intersection of the marginal cost curve (MC) of the dominant firm and the marginal revenue curve (MR) of the dominant firm. The MR curve has twice the slope of the demand curve, so the equation for the MR curve is MR = 24 – 2Q, where Q is the quantity of boxes of cereal. The MC curve is horizontal, so the equation for the MC curve is MC = 12. The intersection of the two curves occurs at the quantity Q = 8 million boxes of cereal per year, and the corresponding price is P = 16 dollars per box of cereal. Therefore, the price of a box of cereal under the price leadership model is 16 dollars.

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In this scenario, Jane Dilford has health insurance with a monthly premium of $30. The insurance policy has a $250 deductible, which is the amount that Jane must pay out of pocket before her insurance coverage kicks in. The policy does not have a coinsurance payment, which means that Jane does not have to pay a percentage of the bill once her deductible is met.

The company's payment was:

80% of the bill less the deductible =

0.8 x ($2,550 - $250) = 0.8 x $2,300 = $1,840

Jane's total cost (not including monthly premium) was:

Bill - Company's payment = $2,550 - $1,840 = $710

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The solution of the expression is -97 / 12. The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is -12¹/₈ ÷ 1¹/₂. The expression will be solved as:-

E =  -12¹/₈ ÷ 1¹/₂

E = 97/ 8 ÷ 3/2

E = ( 97 / 8 ) x ( 2 / 3 )

E = -97 / 12

Therefore, the solution of the expression is -97 / 12. The correct option is A.

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Step By Step:

First, you look at the 6. 22 can't go into 6, so we combine the first digit with the second and put an x above the 6 (if you're on paper. If not, just imagine a blank space there.) Now we have 69. 22 can go into 69. As you did it, 22 can only go in three times. So we add the 3 to the top and put 66 on the bottom, as 22*6 = 66. Now, we subtract 69 and 66. This gives us 3. Now, we bring down the 1. So instead of 3 as you have it, it'd be 31. 22 can go into 31 one time. So, we put our 1 up top and put our 22 on the bottom, as 22*1 = 22. Then, we finish by subtracting 31 from 22, which equals 9.

Hopefully, this made sense. If not, I would be happy to provide further in depth explanation or examples.

The radius of the circle is 4millimeters

The circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.

The circumference of a circle is given as:

C = 2πr

where C is the circumference and r is the radius

25.12 = 2× 3.14×r

25.12 = 6.28r

r = 25.12/ 6.28

r = 4 millimeters

therefore the radius of the circle is 4 millimeters

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Yes, the description corresponds to an observational study.

An observational study is used in subjects such as epidemiology, social sciences, psychology, and statistics to draw conclusions from a sample to a population where the independent variable is not within the researcher's control due to ethical concerns or practical restrictions.

Cohort studies, case-control studies, and cross-sectional studies are three types of observational research.

An observational study examines how participants do various behaviours or activities without instructing them which methods or actions to use. An observational research, for example, may be chosen by a scientist to investigate how the amount of water persons drink impacts their diets. An observational research involves measuring or surveying members of a sample without attempting to influence them.

In a controlled experiment, we divide people or items into groups and administer a treatment to one of the groups while leaving the other group alone.

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Answer:

option 2

Step-by-step explanation:

Answer:

B. 7 1/2

Step-by-step explanation:

8x=12

x = 1.5

2y+10=22

2y = 12

y = 6

1.5 + 6 = 7.5

So, the sum of the solutions of the two equations is

B. 7 1/2

Answer:

Step-by-step explanation:

firstly we solve 8x=12 we divide both sides by 8 since 8 is the coefficient of x so we are trying to find x that is 8x divided by 8 which is x =12 divided by 8 which is 1.5 which means x=1.5 then we solve the second one 2y+10=22 we collect like terms which means 2y=22-10 as you should know the 10 changes to negative when crossed over to the other side so then 2y=12 is the answer then we divide both sides by the coefficient of y which is 2 so 2y divided by 2 =y 12 divided by 2 = 6 so y=6 then we add both of them together x=1.5+(y=6) so add 1.5 and 6 together answer is 7.5 or 7  1/2

A function to define the area of the triangle is A(b,h) = (1/2)*b*h

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B. A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math. f = {(a,b)| for all a ∈ A, b ∈ B}.

1) A relation is said to be a function if every element of set A has one and only one image in set B.

2) A function is a relation from a non-empty set B such that the domain of a function is A and no two distinct ordered pairs in f have the same first element.

A function from A → B and (a,b) ∈ f, then f(a) = b, where 'b' is the image of 'a' under 'f' and 'a' is the preimage of 'b' under 'f'.

If there exists a function f: A → B, the set A is called the domain of the function f, and the set B is called its co-domain.

Let us assume that the base of the triangle is b and the height of the triangle is h.

So, a function to define the area of the triangle is

A(b,h) = (1/2)*b*h

This function is a function in two variables.

Thus, a function to define the area of the triangle is A(b,h) = (1/2)*b*h

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The percent of the day you spend in the school is 29.1 % if time You spend 7 hours of your day at school.

What is percentage ?

Percentage can be defined as the product of ratio of given value, total value and hundred.

Given ,

TIME You spend 7 hours of your day at school.

So we have to find About what percent of the day do you spend at school

so,

The time spent in school = 7 hours

Total hours in a day = 24

So, percentage could be = 7 / 24   * 100

= 0.291 * 100

= 29. 1 %

Therefore, The percent of the day you spend in the school is 29.1 % if time You spend 7 hours of your day at school.

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Answer:

Step-by-step explanation:

Let's call the common difference of the arithmetic sequence "d", and the first term of the sequence "a". Then we can write two equations based on the information given:

a + 3d = 57 (the 11th term is 57)

a + a + 3d = 29 (the sum of the first and fourth terms is 29)

Solving for the first equation for "a", we get:

a = 57 - 3d

Substituting this expression for "a" into the second equation, we get:

57 - 3d + 3d = 29

57 = 29

So the first three terms of the arithmetic sequence are:

a = 57 - 3d

a + d = 57 - 2d

a + 2d = 57 - d

Solving for "d", we can find the value of "a", and then use the equations above to find the first three terms of the sequence

Answer:

32 r26

Step-by-step explanation

First, you ask yourself if 27 can go into 8 and well it can't because 8 is smaller than 27 so you do 27 can go into 89! It can go into 89, 3 times.

27x3 is 81. 89-81 is 8 you bring down the 0.

27 can go into 80 which is 2 times. 27x2 is 54 and doesn't go over.

80-54 is 26. 27 can't go into 26 so your remainder is 26.

Hope this helped !!

The table representing a linear relationship.

x −2 0 2 4

y −1 0 1 2

Is represented by

The suitable graph will be the graph that pass through the points as in the table

graph of a line passing through the points negative 2 comma negative 4 and 0 comma 0

x -2, 0

y -4, 0

this is not in the table and therefore wrong

graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0

x -2, 0

y -1, 0

this is in the table and therefore correct

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Answer:

28 somethin

Step-by-step explanation:

For the given tossing of number cube and its frequency outcome, the probability on landing a number greater than 4 is 18/60.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

As given in the question

Total number of tossing a number cube = 60

Number of times greater than 4 comes up = 10 + 8 (frequency of is 10 and frequency of 6 is 8)

⇒Number of times greater than 4 comes up = 18

Probability of getting number greater than 4

=  (frequency of getting 5 and 6) / (total number of trials)

⇒ probability of getting number greater than 4  = 18 / 60                                                                      

Therefore, for the given tossing of number cube and its frequency outcome, the probability on landing a number greater than 4 is 18/60.

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the volume of the solid under the surface z = 9x + 5y² and above the region bounded by x = y² and x = y³ is: 89/210

Solid, liquid, and gas are the three different states of matter. Solids have a distinct volume and form. Although they have a specific capacity, liquids adopt the form of the container. Gases lack a distinct volume or form. Solids do not adapt to the shape of the container in which they are stored since they have a distinct shape, as well as mass and volume. In addition to having a high density, solids also feature closely packed particles. The volume of space that what a solid covers is assessed by its volume. It is calculated using the volume of unit cubes required to completely fill the solid.

Firstly, we will find bounds:

given that,

x = y²

x = y³

so, y² = y³

thus, y = 0, y = 1

now, we can set up integral for volume:

V=  [tex]\int\limits^1_0 {x} \, dx \int\limits^{y_{2}}_{y_{3}} {9x + 5y^2} \, dx[/tex]

Firstly, we will solve innermost integral:

V = [tex]\int\limits^{y_{2}}_{y_{3}} {9x + 5y^2} \, dx[/tex]

V = [tex]\int\limits^{y_{2}}_{y_{3}} {5y^2} \, dx + \int\limits^{y_{2}}_{y_{3}} {9x } \, dx[/tex]

V = 5y⁴ - 5y⁵ + 9 (y⁴/2 - y⁶/2)

V = -9/2 y⁶ - 5y⁵ + 19y⁴/2

now, we can find outermost integral:

= [tex]\int\limits^1_0 {-9/2y^6 - 5y^5 + 19y^4/2} \, dx[/tex]

= -9/14 - 5/6 + 19/10

=  89/210

Thus, the volume of the solid under the surface z = 9x + 5y² and above the region bounded by x = y² and x = y³ is: 89/210

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The sum of the given convergent series is 15.

What is convergent series with example?

An easy example of a convergent series is ∞∑n=112n=12+14+18+116+⋯ The partial sums look like 12,34,78,1516,⋯ and we can see that they get closer and closer to 1. The first partial sum is 12 away, the second 14 away, and so on and so forth until it is infinitely close to 1.

as given, ∈ from n=1 to n=∞ for ( 20 / n (n+2) )

20 / n(n+2) = (A / n) + (B / n+2)

∴ A = 10

∴ B= -10

∈ from n=1 to n=∞ for ( 20 / n (n+2) )

= 10 [1+0.5]

= 10 x 1.5

= 15

for complete solving process, please refer below attached image.

Thus, the sum of the given convergent series is 15.

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The sum of the given convergent series is 15.

What is convergent series with example?

An easy example of a convergent series is ∞∑n=112n=12+14+18+116+⋯ The partial sums look like 12,34,78,1516,⋯ and we can see that they get closer and closer to 1. The first partial sum is 12 away, the second 14 away, and so on and so forth until it is infinitely close to 1.

as given, ∈ from n=1 to n=∞ for [tex]( 20 / n (n+2) )[/tex]

[tex]20 / n(n+2) = (A / n) + (B / n+2)[/tex]

∴ A = 10

∴ B= -10

∈ from n=1 to n=∞ for [tex]( 20 / n (n+2) )[/tex]

= 10 [1+0.5]

= 10 x 1.5

= 15

Thus, the sum of the given convergent series is 15.

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The equation used to find the coordinates of B is given as follows:

B - A = 5/8(C - A).

The coordinates of B are found using the proportions in the context of this problem.

The ratio of AB to B C is 5 to 3, hence we have that point B is 5/(5 + 3) = 5/8 of the distance from point A to point C.

Considering the distance, the proportional equation used to find the coordinates of B is given as follows:

B - A = 5/8(C - A).

This equation is used to find both the x-coordinate and the y-coordinate of B.

The problem is incomplete, hence the answer was given in general terms.

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The effect of the slower speed is paul would be late by 10 minutes.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,
Paul planned a 160-mile trip and assumed he would travel at an average rate of 50 miles per hour.
Estimated time = 160 / 50 = 3.2 hours

After 2 hours at his planned rate of travel, traffic slowed and he was only able to travel 40 miles per hour for the remainder of the trip.

Actual time = 2 + [160 - 2×50]/40
Actual time = 3.5 hours

Thus, the effect of the slower speed is paul would be late by 10 minutes.

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Adult ticket costs $3 and the student $1.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

1) Gathering the data

1st day

5a +3s =18

2nd day:

7a +1s= 22

2) Let's set a system of Linear equations, given those two equations:

solving we get,

a=3

s=1

3) Hence, the adult ticket costs $ 3 and the student $1.

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The representation of D in the form D_x, D_y, where the x and y components are separated by a comma will be D[6.08,7.27]

Any vector oriented in two dimensions can be understood to have an impact in both directions. This implies that it may be divided into two halves. A component is a portion of a two-dimensional vector. The components of a vector assist to represent the vector's effect in a certain direction. The total impact of these two components is equivalent to the influence of the separate two-dimensional vectors. The two vector components can substitute the single two-dimensional vector.

Determine the x and y components for each vector A & B for vector A

Ax=sin (15) * 2=0.5176

Ay=cos (15) * 2=1.9318

for Vector B

Bx=cos (15) * 4=3.8637

By=sin (15)* 4=1.0352

The vector addition and scalar multiplication for x and y individually D=4.3 * A+B

Dx=4.3 *(sin (15) * 2)+cos (15) * 4

Dx=4.3 * 0.5176+3.8637

Dx=6.0893

Dy=4.3 *(cos (15) * 2)-sin (15) * 4

Dy=4.3 * 1.9318-1.0352

Dy=7.2715

D[6.08,7.27]

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The actual question may be:

Express D in the form D_x, D_y, where the x and y components are separated by a comma using two significant figures.

There exists two opposite sets of angles ( antipodal angles are equal).

The diametrically opposed points on a sphere are known as antipodal points in mathematics (the specific qualities of such a definition are that a line drawn from the one to the other passes through the center of the sphere so forms a true diameter).

If two separate points on a sphere lie along the same line passing through the center of the sphere, they are said to be diametrically opposed points. Antipodal points on the sphere are also known as diametrically opposed points.

We may determine from the image that the two triangles above are isosceles triangles ( the bottom angles one equal).

There are two sets of opposite angles ( antipodal angles are equal).

Let the equation be

[tex]$x & =180^{\circ}-\left(\frac{180^{\circ}-a}{2}+b\right) \\[/tex]

substitute the values in the above equation, we get

[tex]$& =180^{\circ}-\left(\frac{180^{\circ}-62^{\circ}}{2}+63^{\circ}\right) \\[/tex]

simplifying the equation, then

[tex]& =180^{\circ}-\left(59^{\circ}+63^{\circ}\right) \\[/tex]

= 58°

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The value of x in the following triangles is 59 degrees.

One of the fundamental shapes in geometry is the triangle. The smallest polygon is a triangle. It has three vertices and three edges. The symbol for a triangle having the vertices P, Q, and R is PQR. The three sides and three angles that make up a triangle are referred to as its elements. The two crucial properties of a triangle are the external angle property and the angle sum property.

Given that,

a = 62 degree and

b = 62 degrees.

From the given figure we see that the two sides containing angle a are equal.

Thus, the value of the two angles containing angle a is:

a + x + x = 180

a + 2x = 180

62 + 2x = 180

2x = 180 - 62

2x = 118

x = 59

The value of x is 59. The angle x and the exterior angle of x form a straight line.

Thus,

x + y = 180

59 + y = 180

y = 121

The sum of angle y and the interior angle of triangle containing angle x is 180:

y + z = 180

121 + z = 180

z = 59

Now, for triangle containing angle b, the two sides are equal hence the angle corresponding to the side is b = 62.

The angle b and its exterior angle form a straight line. Thus,

b + c = 180

62 + c = 180

c = 118

The angle c and one interior angle of triangle form a straight line thus,

c + d = 180

118 + d = 180

d = 62

Now, the angles of the triangle containing angle x is:

z = 59 and d = 62

The sum of all the sides of triangle is 180, thus:

x + z + d = 180

x + 59 + 62 = 180

x = 59

Hence, the value of x is 59.

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The lateral area of the cone is approximately 401 cm²

Let's call the radius of the circular base of the cone "r". We know that the area of the circular base is 16π cm², so:

r² * π = 16π

r² = 16

r = 4

Now that we know the radius, we can find the slant height. The slant height is 4 times the radius, so:

4 * r = 4 * 4 = 16

The lateral area of a cone is equal to π times the slant height times the radius of the base, so:

lateral area = π * r * slant height = π * 4 * 16 = 128π

Using π ≈ 3.14

we can estimate the lateral area of the cone:

lateral area ≈ 128 * 3.14 = 401.12

Rounding to the nearest whole number, the lateral area of the cone is approximately 401 cm².

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Answer: 201 cm  is the answer

Step-by-step explanation: i took the quiz

Answer:

The equation that represents the value y (in dollars) of the ring after x years is y = 500x + 1000. b. The y-intercept of the graph of the equation is 1000, which is the initial value of the ring. c. The constant rate of increase in the value of the ring is 500 dollars per year. d. The constant rate of increase in the value of the ring is not expected to continue forever. As the value of the ring increases, the rate of increase will likely slow down as it approaches its maximum value.

Step-by-step explanation:

By exploring the behavior of the tangent line at different intervals, the shape and behavior of the curve 8x², the slope is 16.

The tangent line to a curve is a straight line that just touches the curve at a single point, without crossing over it. The slope of the tangent line at that point is equal to the rate of change of the curve's slope at that point.

In the case of the curve 8x², we can find the tangent line at different points by using calculus. Calculus provides us with tools to find the slope of the curve, and from that, the equation of the tangent line.

So, to find the tangent line at a point on the curve

=> 8x²,

we need to find the derivative of the curve and evaluate it at the point of interest.

The derivative of

=> 8x² = 16x,

so the slope of the tangent line at any given point x is 16x.

To find the equation of the tangent line, we also need to know the y-coordinate of the point where the line touches the curve.

We can use this information to write the equation of the tangent line in the form y = mx + b, where m is the slope and b is the y-intercept.

Then the value of slope is 16.

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The function [tex]f(x) = x^{x^{\frac{1}{x} }}[/tex] is increasing on the interval [tex](0, e^{1/e})[/tex] and decreasing on the interval [tex](e^{1/e}, \infty).[/tex]

A function is a mathematical rule that assigns a unique output or value for each input in its domain.

In this case, the function,

[tex]= > f(x) = x^{x^{\frac{1}{x} }}[/tex]

takes in a real number as input and returns its output.

And we can determine the intervals on which the function is increasing or decreasing by analyzing its first derivative.

In order to find the first derivative of f(x), we use calculus techniques such as power rule and chain rule.

Taking the derivative yields

[tex]= > f'(x) = (1 + x log(x)x^{x^{\frac{1}{x} }} -1)[/tex]

This derivative is positive on the interval [tex](0, e^{1/e})[/tex] where e is the mathematical constant approximately equal to 2.718,

so the function is increasing on this interval.

The function is decreasing on the interval [tex](e^{1/e}, \infty).[/tex]

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Answer:

16.2

Step-by-step explanation:

785.7 pounds of food divided by 48.5 pounds of food equals 16.2 days that the adult seal will have food for.

The digits 2, 3, 4, 7 and 8 will be put in random order to make a positive five-digit integer and the probability that the resulting integer will be divisible by 11, then the common fraction = [tex]\frac{1}{10}[/tex]

The digits 2, 3, 4, 7 and 8 will be put in random order to make a positive five-digit integer.

The probability that the resulting integer will be divisible by 11.

The way to tell if a number is divisible by 11 is the following :

If the sum of every other digit, starting with the first is equal to the sum of every other digit, starting with the second, then the number is evenly divisible by 11.

Our given numbers are 2, 3, 4, 7 and 8.

Which 3 numbers summed are equivalent to the sum of other 2.

We can see,

2 + 3 + 7 = 12

8 + 4 = 12

There are 3! = 6 ways to use the 2, 3, 7, and

2! = 2 ways to use the 8 and 4.

[tex]6*2[/tex] = 12

There are 5! = [tex]5*4*3*2*1[/tex] = 120 different possibilities

So,

We can write,

= [tex]\frac{12}{120}[/tex]

= [tex]\frac{1}{10}[/tex]

Therefore,

The digits 2, 3, 4, 7 and 8 will be put in random order to make a positive five-digit integer and the probability that the resulting integer will be divisible by 11, then the common fraction = [tex]\frac{1}{10}[/tex]

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The digits 2, 3, 4, 7, and 8 will be put in random order to make a positive five-digit integer, and the probability that the resulting integer will be divisible by 11, then the common fraction = 1/10

The digits 2, 3, 4, 7, and 8 will be put in random order to make a positive five-digit integer.

The probability that the resulting integer will be divisible by 11.

The way to tell if a number is divisible by 11 is the following :

If the sum of every other digit, starting with the first is equal to the sum of every other digit, starting with the second, then the number is evenly divisible by 11.

Our given numbers are 2, 3, 4, 7, and 8.

Which 3 numbers summed are equivalent to the sum of the other 2.

We can see,

2 + 3 + 7 = 12

8 + 4 = 12

There are 3! = 6 ways to use the 2, 3, 7, and

2! = 2 ways to use the 8 and 4.

6*2 = 12

There are 5! = 120 different possibilities

So,

We can write,

= 12/120

= 1/10

Therefore,

The digits 2, 3, 4, 7 and 8 will be put in random order to make a positive five-digit integer and the probability that the resulting integer will be divisible by 11, then the common fraction = 1/10

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the equality holds for n = k+1, and by mathematical induction, it holds for all n ≥ 2.

Proof by induction:

a. Base case: For n = 2, the left-hand side evalutes to 1/2 and the right-hand side evaluates to 1/2, so the equality holds.

Inductive step: Assume that the equality holds for n = k. We must show that it holds for n = k+1.

The left-hand side evaluates to

∑ ― 1 = 1 ( 1 i(i 1)) = 1 ― 1/k+1

The right-hand side evaluates to

1 ― 1/k+1

Therefore, the equality holds for n = k+1, and by mathematical induction, it holds for all n ≥ 2.

b. Base case: For n = 2, the left-hand side evaluates to 1/2 and the right-hand side evaluates to 1/2, so the equality holds.

Inductive step: Assume that the equality holds for n = k. We must show that it holds for n = k+1.

The left-hand side evaluates to

∑ = 1 ( 1 i(i 1)) = 1 i!k+1

The right-hand side evaluates to

1 i!k+1

Therefore, the equality holds for n = k+1, and by mathematical induction, it holds for all n ≥ 2.

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