Please Help!! 25 points!!

Write the equation of the function in vertex form that has the vertex (1, 2) and the point (-3, 6). If necessary, use reduced fractions and not
decimals.

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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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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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.

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 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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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

The simultaneous equations 2x + 3y = 8 and 4x + 6y = 7 supplied do not have a solution  

A collection of two or more equations, each of which contains two or more variables, each of whose values can simultaneously fulfil one or more of the equations in the collection, with the total number of variables in the collection being equal to or fewer than the total number of equations.

Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. The equations are referred to as simultaneous equations since they are solved simultaneously.

Here are a few examples of simultaneous equations:

2x + 4y = 14

4x − 4y = 4.

Given,

2x + 3y = 8 and 4x + 6y = 7

We get,

2x + 3y = 8 ….. (i)

4x + 6y = 7 ….. (ii)

Then we have Multiply (i) by 4

4x + 6y = 16..... (iii)

Therefore, LHS of (ii) and (iii) are same but RHS is different. As a result, the answer is false.

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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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The correct analysis would be 3 option

Describe statistics using an example.

A statistic is a numerical expression of a sample characteristic. The average amount of points obtained by students in one math class at the conclusion of the term, for instance, is an example of a statistic if we see that class as a sample of the population of all math classes.

The right response is selection 3. To compare the means of two independent groups, use the independent samples t test. to determine whether there is a substantial difference between the means of the two groups. In this instance, we are comparing two different groups of people: those who work the night shift and those who work the day shift. By definition, these two groups of persons would differ, therefore neither a matched sample test nor a one-sample test would be appropriate. Furthermore, we are not interested in person's r, which is a measure of linear correlation between two variables.

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The mean deviation of the scores is 2 when the mean value is 15.

In the statistics, mean deviation indicates the average deviation relative to the mean value of a given statistical data. While calculating mean deviation mean value is subtracted from each data value. After that all these values are added and divided by the total amount of data.

We are given three score 12, 15 and 18

Number of scores, N = 3

mean of the scores = (12+15+18)/ 3

                                =15

Let, mean score is denoted by X

List of scores X1    12

                      X2   15

                      X3    18

Now, we calculate X1 -X= 12- 15 = -3

                             X2-X = 15-15 = 0

                           X3-X = 18- 15 = 3

Absolute value of X1-X = |X1-X| = |-3| = 3

Absolute value of X2-X =|X2-X|= |0| = 0

Absolute value of X3-X = |X3-X| = |3| = 3

Sum of absolute value= ∑|Xi-X| = 6

Hence, mean deviation = ∑|Xi-X|/N = 6/3

mean deviation =2

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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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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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Of the given options the one that is true is if two variables are very strongly associated then the correlation between them will be near 1.0 or -1.0. Hence, option A is correct.

Correlation of 1.0 indicates that the variables are directly related while a correlation of -1.0 indicates that the variables are inversely related.

The degree to which two variables are linearly connected is expressed by the statistical concept of correlation (meaning they change together at a constant rate). It's a typical technique for explaining direct connections without explicitly stating cause and consequence.

However, we utilise correlation to indicate a link between two quantitative variables in statistical terms.

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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:

11.2

Step-by-step explanation:

15x + 32 = 200       Subtract 32 from both sides

15x + 32 - 32 = 200 - 32

15x = 168  Divide both sides by 15

[tex]\frac{15x}{15}[/tex] = [tex]\frac{168}{15}[/tex]

x = 11.2

Answer:

i think the answer is x= 11.2

Step-by-step explanation:

15x= 200-32

15x=168

x=168/15

x=11.2

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 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 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 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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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 domain is {9, 8, -9, 3, 7}, the range is {-8,-9, 5, 8} and the relation is a function

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

{(9,-8), (8,-9), (-9, 5), (3, 8), (7, 8) }

The domain is the set of the x values

So, we have the following representation

x = {9, 8, -9, 3, 7}

Remove repeated entries

x = {9, 8, -9, 3, 7}

So, the domain is {9, 8, -9, 3, 7}

Similarly, we have

Range = {-8,-9, 5, 8}

Also, the relation is a function

This is because the no x value has several y values

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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°

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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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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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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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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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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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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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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