If you roll a number cube 108 times, how many times
would you expect to roll the number one using the
data above?

The answers to both the subparts using probability are shown:

(A) The probability that every sign is unique is 378/845.

(B) The probability that each sign is unique and that the first number is the biggest one among the others is 189/1690.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

The probability is calculated by dividing the total number of outcomes by the total number of potential events.

Odds and probability are two different concepts.

Calculating odds involves dividing the probability of an event by the probability that it won't happen.

(A) Since there are three positions for letters and four places for numbers.

Consequently, the final result will be 10⁴×26³.

Since each letter and number should be distinct, the necessary probability is:

= 10 * 9 * 8 * 7 * 26 * 25 * 24 / 10⁴ * 26³

= 378/845

(B) In this instance, the likelihood that the first number will be the greatest among the four numbers is 1/4 because it should be.

In order to obtain the result, multiply the result in (a) by 1/4 as follows:

= 378/845 * 1/4

= 189/1690

Therefore, the answers to both the subparts using probability are shown:

(A) The probability that every sign is unique is 378/845.

(B) The probability that each sign is unique and that the first number is the biggest one among the others is 189/1690.

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A closed under addition can be proved if the sum of any two members of the set also belongs to the set.

We can take any two even integers and add them together. The result is an even integer. A set is closed under scalar multiplication if the product of any member and a scalar is also in the set. In other words, if x is in S and a is any scalar then ax will be in the set if the set is closed under scalar multiplication. For example, the set of 2 x 2 diagonal matrices is closed under scalar multiplication.

For example,

A = {( x, y) , y = 0 }

B= { (x, y) , x+ y = 1 }

Typical elements of A are (1,0), (2,0). The element (1,1) is an element not in A. Typical elements of B are (1,0), (1/2,1/2). The element (1,1) is an element not in B. Now A and B carry an addition that is  (x, y)+(x', y')=(x + y, x' + y')). Saying that A is closed under addition just means that whenever you take two elements in A, the sum of those elements is again in A. Let's check if this is the case: two elements in A have the form (x, 0) and (x', 0). The sum of those elements is (x + x', 0), and this is again in A. Thus A is closed under addition.

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The plums that remain with George after sharing 22 with Jude will be equal to 50.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.

Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the data mentioned in the question,

We first need to determine how many plums Jude received. Decide to round everything to the sixteenth.

George is having 3/8 = 6/16

Terry is having 1/4 = 4/16

Samuel is having 3/16

So, remaining will go to Jude = (16 - (6 + 4 + 3))/16 = 3/16

Consequently, if Jude received 3/16 of the plums, and she received 36 plums, 1/16 of the total plums is,

= 36/3 = 12 plums (As a side note, there were 192 plums in total).

George has got 6/16 plums = 6 × 12 = 72

Then, he gave 22 plums to Jude, so he has left with,

72–22 = 50 left.

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We can construct a 30-degree angle by bisecting a 60-degree constructed angle.

By following the given steps we can create a 30-degree angle,

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Answer:

B

Step-by-step explanation:

the order of a matrix are given as

m × n ( m is the number of rows and n the number of columns

matrix A is of order 2 × 3

matrix B is of order 3 × 2

for the matrices to be conformable for multiplication then

the number of columns in A is equal to the number of rows in B

This is the case here , then the order of the resulting product is

AB :  2 × 3 × 3 × 2 the outer values , that is 2 × 2

Answer:

  x = 14

Step-by-step explanation:

You want the value of x in ∆OPQ, where ∠O = (2x − 5)°, ∠P = (3x − 8)°, and ∠Q = (10x – 17)º.

The angle sum theorem tells you the sum of angles in a triangle is 180°. This means ...

  ∠O +∠P +∠Q = 180°

  (2x -5)° +(3x -8)° +(10x -17)° = 180° . . . . . use the given expressions

  15x -30 = 180 . . . . . . divide by °, collect terms

  x -2 = 12 . . . . . . . . . divide by 15

  x = 14 . . . . . . . . . . add 2

The value of x is 14.

__

Additional comment

The measures of the angles are ...

  O = 23°, P = 34°, Q = 123°

Formula for solving mean deviation is [tex]\frac{[\sum |X-\mu|]}{N}[/tex].

Mean Deviation Definition:

The mean deviation is defined as a statistical measure that is used to calculate the average deviation from the mean value of the given data set. The mean deviation of the data values can be easily calculated using the below procedure.

Step 1: Find the mean value for the given data values

Step 2: Now, subtract the mean value from each of the data values given (Note: Ignore the minus symbol)

Step 3: Now, find the mean of those values obtained in step 2.

Mean Deviation Formula

The formula to calculate the mean deviation for the given data set is given below.

Mean Deviation = [tex]\frac{[\sum |X-\mu|]}{N}[/tex]

Here,

Σ represents the addition of values

X represents each value in the data set

µ represents the mean of the data set

N represents the number of data values

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Answer: 5

Step-by-step explanation: If n is the exponent and the base is 10, 6.72342 is to be multiplied by 10 power 5 to give the answer as 672342.

6.72342 * 10^5 = 6.72342 * 100000

                          = 672342

We can claim that when two-digit numbers (14, 25, 36, 47, 58, and 69) are added to 27, the results are reversed.

A number is referred to be a 2-digit number when it has two digits.

The range of 2-digit numbers, which have two digits, is 10 to 99.

They can't start with zero since it will be interpreted as a single-digit number.

The digit in the tens slot might be any value between 1 and 9.

The numbers 45, 78, and 12 all have two digits, for example.

So, we know:

14 + 27 = 41

25 + 27 = 52

36 + 27 = 63

47 + 27 = 74

58 + 27 = 85

69 + 27 = 96

Therefore, we can claim that when two-digit numbers (14, 25, 36, 47, 58, and 69) are added to 27, the results are reversed.

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The vertices of the image of quadrilateral ABCD, after a dilation with a scale factor of 3, are given as follows:

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure, thus a dilation is classified as a non-rigid transformation.

The vertices of the quadrilateral ABCD in this problem are given as follows:

A(-4, 1), B(-2, 3), C(0, -2) and D(-5, -2).

The scale factor of the dilation is given as follows:

k = 3.

Then the coordinates of the image, given by the answer at the beginning of the answer, were obtained multiplying the coordinates of each of the vertices by 3.

The problem asks for the coordinates of the image of quadrilateral ABCD after the dilation with the given scale factor.

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The value of c square when the given equation y = 4x - 10 is written in standard form is equal to 100.

As given in the question,

Given equation is equal to :

y = 4x - 10

Standard form of the equation in the slope intercept form is written as:

y = mx + c

Here value of m represent slope is equal to 4

And value of c represents the y-intercept form is equal to -10.

Value of c square is given by :

c = -10

Squaring both the sides we get,

⇒c² = ( -10 )²

⇒c² = 100

Therefore, the value of c square in the given equation is equal to 100.

The given question is incomplete , the complete question is :

When the equation y = 4x - 10 is written in the standard form the value of C Square will be?

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The 4 parts of a function are Function name, Parameters ,Body, Return statement.

1. Function name: This is the name of the function, which is used to identify the function and call it when needed. It should be descriptive, so that it is easy to understand what the function does.

2. Parameters: Parameters are values that are passed into the function when it is called. They are used to provide the function with the necessary data it needs to perform its task.

3. Body: This is the code that will be executed when the function is called. It contains the instructions that the function needs to perform its task.

4. Return statement: This is the statement that is used to return the result of the function. It can be used to return a value or object. It can also be used to return a status code, such as success or failure.

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the distance between the chord is 23 cm

It is given that AB = 30cm and CD = 16cm

Join the lines OA and OC

We know that AO = 17cm and CO = 17cm

Construct OM ⊥ CD and OL ⊥ AB

The perpendicular from the centre of a circle to a chord bisects the chord

We know that

AL = ½ × AB

By substituting the values

AL = ½ × 30

So we get

AL = 15cm

We know that

CM = ½ × CD

By substituting the values

CM = ½ × 16

So we get

CM = 8cm

Consider △ ALO

Using the Pythagoras theorem it can be written as

AO^2 = OL^2 + AL^2

By substituting the values

17^2 = OL^2 + 15^2

So we get

OL^2 = 17^2 - 15^2

On further calculation

OL^2 = 289 – 225

By subtraction

OL^2 = 64

By taking the square root

OL = √64

OL = 8cm

Consider △ CMO

Using the Pythagoras theorem it can be written as

CO^2 = CM^2 + OM^2

By substituting the values

17^2 = 82 + OM^2

So we get

OM^2 = 17^2 - 8^2

On further calculation

OM^2 = 289 – 64

By subtraction

OM^2 = 225

By taking the square root

OM = √225

OM = 15cm

So the distance between the chords = OM + OL

By substituting the values

Distance between the chords = 8 + 15 = 23cm

Therefore, the distance between the chords is 23 cm.

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Theorems related to equilateral traingle :

Theorem 1: The sum of measures of all 3 interior angles of a triangle is [tex]180^0[/tex].

Theorem 2: The angles opposite to equal sides are also equal in measure.

Theorem 3: The sum of the related internal angles is the measure of the exterior angle of a triangle.

Theorem 4:If a line splits any two triangle sides in the same proportion, it is parallel to the third side of the triangle.

Theorem 5: Each angle of an equilateral traingle have equal measure of [tex]60^0[/tex].

Theorem 6: Any two triangle sides can add up to a length that is longer than the third side.

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The  expression used to represent the binomial theorem example is equal to ( 5 + 0.1 )⁴ .

As given in the question,

Example used to represents the binomial theorem is written as:

( 5 + 0.1 )⁴

Compare it with standard form and apply binomial theorem to simplify the considered example:

( a + b )ⁿ = ⁿC₀aⁿb⁰ +  ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +..............+  ⁿCₙa⁰bⁿ

Here in the considered example :

value of a = 5

value pf b = 0.1

value pf n = 4

Substitute the value in the formula to get the value using binomial theorem:

( 5 + 0.1 )⁴

=  ⁴C₀5⁴(0.1)⁰ +  ⁴C₁5⁴⁻¹(0.1)¹ + ⁴C₂5⁴⁻²(0.1)² +  ⁴C₃5⁴⁻³(0.1)³ +  ⁴C₄5⁴⁻⁴(0.1)⁴

= 5⁴ + 4(5)³(0.1) + 6(5)²(0.1)² + 4(5)(0.1)³ + (0.1)⁴

= 625 + 50 + 1.5 + 0.02 + 0.0001

=676.5201

Therefore, the example of the binomial theorem is given by ( 5 + 0.1 )⁴.

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Answer:

Step-by-step explanation:

your right

The 3 ways to write a linear equation is Slope-Intercept Form, Point-Slope Form, Standard Form.

1. Slope-Intercept Form: This form of linear equation is written as y = mx + b, where m is the slope of the line, x is the independent variable, and b is the y-intercept. This form of the equation can be used to graph the line by finding the x-intercept and y-intercept.

2. Point-Slope Form: This form of linear equation is written as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. This form of the equation can be used to graph the line by finding a second point on the line and connecting the two points.

3. Standard Form: This form of linear equation is written as ax + by = c, where a and b are not both 0, and c is a constant. This form of the equation can be used to graph the line by finding two points that satisfy the equation.

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The value of the function at x = -9 will be 13/5. Then the correct option is A.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

f(x) = (3/5)x + 8

The degree of the function is one. Then the function is a linear function.

The value of the function at x = -9 will be given as,

f(-9) = (3/5)(-9) + 8

f(-9) = - 27 / 5 + 8

f(-9) = (- 27 + 40) / 5

f(-9) = 13 / 5

The value of the function at x = -9 will be 13/5. Then the correct option is A.

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The complete function is f(x) = (3/5)x + 8.

Tim puts two pickles in each of the five lunch bags, leaving him with three pickles.

If Tim puts the same number of pickles in each of the lunch bags and as many as possible, only a maximum of two can be put in each of the bags:

Dividing 13 pickles by 5 lunch bags, the answer is 2 pickles with a reminder of 3 pickles

13 ÷ 5 = 13/5

Therefore, Tim puts two pickles in each of the five lunch bags and is left with three pickles.

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Formula for pyramids:

Volume V = /3 B*h

Surface area  S = B + 1/2 p*s

A pyramid's height is measured perpendicularly from its apex to its base, while its slant height is measured angularly from of the apex to the midway of one of its triangular faces.

Here are the calculations for any pyramid's volume and surface area.

Volume V = /3 B*h

Surface area S = B + 1/2 p*s

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Answer:

hello im ur friend and im going to give u the answer next year

The numeric value of the expression c = 5a + 6b is given as follows:

c = 759.5.

The expression in this problem is defined as follows:

c = 5a + 6b.

To obtain the numeric value of the expression, the values of a and b have to be known, and they are discovered solving the system of equations presented as follows:

In standard format, the system is given as follows:

Multiplying the first equation by 6 and the second by -5, we have that:

Adding the two equations, we have that the variable b is given as follows:

-2b = -119

b = 119/2

b = 59.5.

Then the variable a is obtained as follows:

5a + 8 = 7(59.5) - 6

a = (7(59.5) - 6 - 8)/5

a = 80.5.

Thus the numeric value of the expression is given as follows:

c = 5(80.5) + 6(59.5)

c = 759.5.

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Try the slop formula. x1 - x2 over y1 - y2. Also, try to cross multiply what you already have.

[tex]\displaystyle\\Answer:\ y=-\frac{3}{2}x+1[/tex]

Step-by-step explanation:

The condition of perpendicularity of the two lines given by the equations:

                             [tex]\displaystyle\\\left \{ {{y_1=m_1x+b_1} \atop {y_2=m_1x+b_2}} \right.[/tex]

   is the relation: m₁ x m₂=-1

[tex]\displaystyle\\Hence,\ m_2=-\frac{1}{m_1}[/tex]

[tex]\displaystyle\\Given: y=\frac{2}{3}x+\frac{2}{3}\ == > \ m_1=\frac{2}{3} \\\\Thus,\ m_2=-\frac{1}{\frac{2}{3} } \\\\m_2=-\frac{3}{2}[/tex]

The equation of the Point-Slope Form is expressed as:

           y-y₁=m(x-x₁)    

(-2,4)  that is   x₁=-2      y₁=4

[tex]\displaystyle\\Therefore,\\\ y-4=-\frac{3}{2} (x-(-2))\\\\y-4+4=-\frac{3}{2} (x+2)+4\\\\y=-\frac{3}{2}(x)-\frac{3}{2}(2) +4\\\\y=-\frac{3}{2}x -3+4\\\\y=-\frac{3}{2}x+1[/tex]

The median for the given set of scores is 13.

The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.

Given,

A set of scores 19, 5, 12, 13, 14.

Arranging the set of numbers in ascending order,

=> 5,12,13,14,19

For a total of an odd number of outcomes, the median is defined as the middlemost value after sorting the data in ascending (OR) descending order.

For a total of an even number of outcomes, the median is calculated as the average of the two middlemost values after sorting the data in ascending (OR) descending order.

The total number of terms in the given data is 5, Hence the middlemost value is (5+1)/2 rd value is considered as the median,

Median= 3rd term = 13

Therefore, the median for the given set of scores is 13

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The median of the given data is 4.5.

The middle value in a sorted, ascending, or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.

For finding the median, the data should be arranged in ascending or descending order first.

Arranging the data in ascending order, we get 1, 2, 3, 3, 4, 5, 5, 7, 7, 9.

There is an even number of observations.

Hence the median is the mean value of  (n/2)th and [(n/2)+1]th term.

Here, the 10/2th term = 5th term which is 4

[(n/2)+1]th term= 6th term which is 5

thus, 4+5/2 = 4.5

Hence, the median of the given data is 4.5.

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What is polynomial function?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

Since we know that complex solutions ALWAYS come in pairs, the minimal polynomial must include the root of 4-i as an acceptable root..

This leads to a polynomial of ...

p(x) = (x - 5)(x - (4+i))(x - (4-i))

Now we can simplify...

(x - (4+i))(x - (4-i)) --> x2 + [(4+i)+(4-i)]x + (4+i)(4-i) --> x2 + 8x + [ 16 -4i + 4i -i2 ] = x2 + 8x +17

Take this quadratic and multiply by (x-5) to get the final, minimal polynomial...

p(x) = (x-5)(x2 + 8x +17) = x3 + 8x2 + 17x -5x2 + 40x - 85 = x3 + 3x2 + 57x - 85

So p(x) = x3 + 3x2 + 57x - 85

p(x) has only real coefficients, the leading coefficient of 1, and is the smallest to allow for the two solutions requested

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Your question is incomplete but it could be this,

You can work no more than 60 hours each week at your two jobs. Dog walking pays $7 per hour and your sales job at Computers & More, Inc. pays $12 per hour. You need to earn at least $450 each week to pay your bills. Your friend solves the system of inequalities x + y < 60 and 7x + 12y > 450 and tells you that a possible solution is (-3, 50). Is this a possible solution, why or why not?

No, (-3, 50) is not a possible solution to the system of inequalities x + y < 60 and 7x + 12y > 450. The first inequality, x + y < 60, represents the constraint that the total number of hours you work at both jobs must be less than 60. The second inequality, 7x + 12y > 450, represents the constraint that the total amount of money you earn must be at least $450.

The solution (-3, 50) does not satisfy either of these constraints. The value of y, 50, represents the number of hours you work at the sales job, and is greater than the maximum value allowed by the first inequality. Additionally, the value of x, -3, represents the number of hours you work dog walking, which is negative. This is not possible, as you cannot work negative hours. Therefore, (-3, 50) is not a valid solution to the system of inequalities.

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The root of the quadratic equation x² + 5x = -6 are -2 and -3.

Given that,

The quadratic equation x² + 5x = -6 with the variable x.

We have to find what are the root of the quadratic equation.

We know that,

Take the quadratic equation x² + 5x = -6

x² + 5x = -6

x² + 5x +6=0

Now find the factors for 6

6=2×3

So,

2+3=5

We get

x² + 2x + 3x+6=0

Taking the common terms

x (x+2) + 3(x+2)=0

(x+2) (x+3)=0

Now

x+2=0

x=-2

And

x+3=0

x=-3

Therefore, The root of the quadratic equation x²+5x = -6 are -2 and -3.

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The width of the interval will be is 5 or ( 49.5 , 54.5 ) .

Given :

The minimum value is called the lower class limit and the maximum value is called the upper class limit. For class interval 50-54, the lower class limit is 50 and the upper class limit is 54.

Class boundaries are the numbers used to separate classes. It is the real limits of a class. For non-overlapping classes, the lower class boundary of each class is calculated by subtracting 0.5 from the lower class limit. The upper class boundary of each class is calculated by adding 0.5 to the upper class limit.

Example: For class interval 50-54, the lower class boundary is 49.5 and the upper class class boundary is 54.5

Considering the question given, to get the real limits of the interval 50-54, 0.5 is subtracted from the lower class limit to give 49.5. Also, 0.5 is added to the upper class limit to give 54.5.

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The ratio in which line segment joining (-1, 3) and (4, -7) is is 3: 2 and at a point (2,-3).

A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.

a piece of a geometric figure that has been removed by one or more points, lines, or planes is known as segment.

The formula that we used is:

[tex]P(x,y)=\frac{mx2+nx1}{m+n},\frac{my2+ny1}{m+n}[/tex]

x = m(x₂) + n(x₁)/(m + n)

⇒ 2 = m(-1) + n(3)/(m + n)

⇒ 2(m + n) = 3n - m

⇒ 2m + 2n = 3n - m

⇒ m/n = 3/2

Therefore, The ratio in which line segment joining (-1, 3) and (4, -7) is is 3: 2 and at a point (2,-3).

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