7x - 4y = -8
X + 2y = -14

The zeros and their multiplicities of the function f(x)=2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48 are:

x = -4, multiplicity 1

x = (-5 + √(41))/(2), multiplicity 1

x = (-5 - √(41))/(2), multiplicity 1

The zeros of a function f(x) are the values of x that make f(x) equal to 0. The multiplicity of a zero is the number of times that zero appears as a solution. To find the zeros and their multiplicities of the given function f(x)=2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48, we can use synthetic division or factoring.

First, let's use synthetic division to find one of the zeros:

2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48 = 0

Using synthetic division, we can find that x = -4 is a zero of the function:

(-4) | 2  11  -2  -74  -60  48
    | 0  -8  20   88  104 -176
    ---------------------------
      2   3  18   14   44 -128

Now we can divide the original function by (x+4) to find the remaining zeros:

f(x) = (x+4)(2x^(4)-x^(3)+14x^(2)+10x-32)

Using the quadratic formula, we can find the remaining zeros of the function:

x = (-b ± √(b^(2)-4ac))/(2a)

x = (-(10) ± √((10)^(2)-4(2)(-32)))/(2(2))

x = (-10 ± √(164))/(4)

x = (-10 ± √(4*41))/(4)

x = (-10 ± 2√(41))/(4)

x = (-5 ± √(41))/(2)

So the zeros of the function are x = -4, x = (-5 + √(41))/(2), and x = (-5 - √(41))/(2).

The multiplicity of each zero is 1, since each zero appears only once as a solution.

Therefore, the zeros and their multiplicities of the function f(x)=2x^(5)+11x^(4)-2x^(3)-74x^(2)-60x+48 are:

x = -4, multiplicity 1

x = (-5 + √(41))/(2), multiplicity 1

x = (-5 - √(41))/(2), multiplicity 1

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a)age for the sample is 47

b)the variance is 49.67

c)standard deviation is 7.04

d)variation is 14.88%

(a) To determine the average age of the sample, use the formula:  Average age = (Sum of ages) / (Number of observations).

30-39: Add all ages between 30-39 and divide by 8.
40-49: Add all ages between 40-49 and divide by 7.
50-59: Add all ages between 50-59 and divide by 4.
60-69: Add all ages between 60-69 and divide by 5.
70-79: Add all ages between 70-79 and divide by 1.

Therefore, the average age for the sample is 47.

(b) To compute the variance, use the formula: Variance = (Sum of Squared Differences)/ (Number of Observations - 1).

30-39: Sum the squared differences between each age and the mean age, and divide by 7.
40-49: Sum the squared differences between each age and the mean age, and divide by 6.
50-59: Sum the squared differences between each age and the mean age, and divide by 3.
60-69: Sum the squared differences between each age and the mean age, and divide by 4.
70-79: Sum the squared differences between each age and the mean age, and divide by 0.

Therefore, the variance is 49.67.

(c) To compute the standard deviation, use the formula: Standard Deviation = √Variance.

Therefore, the standard deviation is 7.04.

(d) To compute the coefficient of variation, use the formula: Coefficient of Variation = (Standard Deviation/Mean)*100.

Therefore, the coefficient of variation is 14.88%.

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There are 34 pupils in the class who do not wear spectacles.

What is percentage?

Percentage is a way to express a number as a fraction of 100. It is commonly used to show the relationship between two numbers, to compare two quantities, or to express a part of a whole. It is expressed as a fraction, decimal, or ratio.

1. To find the number of pupils who wear spectacles, we can multiply the total number of pupils by the percentage of pupils who wear spectacles:

40 pupils x 15% = 6 pupils

2. To find the number of pupils who do not wear spectacles, we can subtract the number of pupils who wear spectacles from the total number of pupils:

40 pupils - 6 pupils = 34 pupils

Therefore, there are 34 pupils in the class who do not wear spectacles.

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40 m³ is the volume of pyramid .

What is a pyramid defined as?

A three-dimensional shape is a pyramid. A pyramid's flat triangular faces and polygonal base all come together in a summit known as the apex. By fusing the bases together at the peak, a pyramid is created. The lateral face, a triangular feature formed by the connection of each base edge to the apex, is present.

  L= 5

h = 4

s = 6

V = 6 * 4 * 5/3

   = 120/3

   = 40 m³

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To add or subtract the given expressions, we need to combine like terms. Like terms are terms that have the same variable and exponent.

Step 1: Combine like terms for a^(2):
6.9a^(2) + 0 = 6.9a^(2)
Step 2: Combine like terms for b^(2):
-2.3b^(2) + (-2.5b^(2)) = -4.8b^(2)
Step 3: Combine like terms for ab:
2ab + 0 = 2ab
Step 4: Combine like terms for a:
0 + 3.1a = 3.1a
Step 5: Combine like terms for b:
0 + b = b
Step 6: Put all the combined terms together:
6.9a^(2) + (-4.8b^(2)) + 2ab + 3.1a + b
Step 7: Simplify the expression:
6.9a^(2) - 4.8b^(2) + 2ab + 3.1a + b

So the final answer is 6.9a^(2) - 4.8b^(2) + 2ab + 3.1a + b.

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To make equivalent rational expressions, we need to multiply the numerator and denominator of the left-hand side of the equation by the same value.

In this case, we can multiply both the numerator and denominator by (5x^(3))/(5x^(3)) to get the equivalent expression on the right-hand side. (3)/(x^(6)) * (5x^(3))/(5x^(3)) = (15x^(3))/(5x^(9))

Therefore, the value that we need to fill in the blank is (15x^(3)). So the equivalent rational expression is:

(3)/(x^(6))=(15x^(3))/(5x^(9))

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The Complete value for the Table is

x               f(x)                   g(x)

1                8                         1.1

5               20                  1.61051

10              35                  2.5937

20             65                   6.7274

The function f(x) grows with faster rate.

A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

We have f(x) = 3x+ 5 and g(x) = [tex](1.1)^x[/tex]

The Complete value for the Table is

x                   f(x)                                           g(x)

1               3x+ 5 = 3(1) +5= 8                         1.1

5              3x+ 5 = 3(5) +5= 20                      [tex](1.1)^5[/tex]= 1.61051

10             3x+ 5 = 3(10) +5= 35                    [tex](1.1)^{10}[/tex]= 2.5937

20            3x+ 5 = 3(20) +5= 65                    [tex](1.1)^{20}[/tex]= 6.7274

So, the function f(x) grows with faster rate.

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a) Initially, when t = 0, the volume of oil in the tank is given by:

V(0) = 0.5(10 - 0)^3

V(0) = 0.5(1000)

V(0) = 500

So, initially there are 500 litres of oil in the tank.

b) The average rate of change of volume in the first 1 minute is given by:

ΔV/Δt = (V(1) - V(0))/(1 - 0)

ΔV/Δt = (0.5(10 - 1)^3 - 500)/1

ΔV/Δt = (0.5(729) - 500)/1

ΔV/Δt = -285.5

So, the average rate of change of volume in the first 1 minute is -285.5 litres/minute.

c) To estimate the instantaneous rate of change of volume at 5 minutes, we can use the average rate of change over a small interval around 5 minutes. For example, we can use the average rate of change from 4.9 minutes to 5.1 minutes:

ΔV/Δt = (V(5.1) - V(4.9))/(5.1 - 4.9)

ΔV/Δt = (0.5(10 - 5.1)^3 - 0.5(10 - 4.9)^3)/0.2

ΔV/Δt = (-61.4455 - (-62.985))/0.2

ΔV/Δt = 7.6975

So, the estimated instantaneous rate of change of volume at 5 minutes is 7.6975 litres/minute.

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Answer: 2

5x - 7 = 3x + 3

2x - 7 = 3

2 is the new value of the coefficent

The answer of the question based on the to represent the area of the figure the answer is given below,

A rectangle is four-sided polygon with opposite sides that are parallel and congruent (equal) in the length.

a) The figure is a rectangle with a length of 2x + 3 and a width of x - 2. The area of the rectangle is:

Area = length x width

Area = (2x + 3)(x - 2)

Using the distributive property of multiplication, we can simplify this expression:

Area = 2x² - 4x + 3x - 6

Area = 2x² - x - 6

Therefore, the expression for the area of the figure is 2x² - x - 6.

The figure is a trapezoid with a height of 3 and two parallel sides of length x + y and x - y. average of lengths of the two sides are:

(x + y + x - y)/2 = 2x/2 = x

So, the area of the trapezoid is:

Area = (1/2) x height x (sum of parallel sides)

Area = (1/2)(x)(3)(x + y + x - y)/2

Area = (3/2) x²

Now, we need to subtract the area of the triangle from the trapezoid. The triangle has a height of 3 and a base of y, so its area is:

(1/2)(y)(3) = (3/2)y

Therefore, the expression for the area of the figure is:

Area = (3/2)x² - (3/2)y.

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The average number of gallons of bottled water consumed in the year 2010 is 35.48 gallons.

The equation W=1.8d+17.48 can be used to find the average number of gallons of bottled water consumed each year by a consumer.

In this equation, W represents the average number of gallons of bottled water consumed, and d represents the number of years since 2000.

To find the average number of gallons of bottled water consumed in a specific year, you can plug in the value of d into the equation and solve for W.

For example, if you want to find the average number of gallons of bottled water consumed in the year 2010, you would plug in the value of d=10 (since 2010 is 10 years after 2000) into the equation:

W=1.8(10)+17.48

W=18+17.48

W=35.48

So, the average number of gallons of bottled water consumed in the year 2010 is 35.48 gallons.

Similarly, you can plug in different values of d into the equation to find the average number of gallons of bottled water consumed in different years.

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A solution to the given compound inequality is m < 6 or m > 2.

In Mathematics, it is very important to note that you do not flip the inequality symbol (sign) when you are solving an inequality by multiplication or division with a positive numerical value (number).

In this context, we can logically deduce that you would flip the inequality symbol (sign) when you isolate the variable in an expression such as it's highlighted in the following steps:

4 - m < - 2

-m < -2 - 4

-m < -6

m < 6

For the second inequality, we have;

12 < -5m + 2

12 - 2 < -5m

10 < -5m

m > -10/5

m > 2.

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The notation f(x) means:
- the value of the function at the number x
- f of x

These two options are the correct ones. The notation f(x) typically refers to a mathematical function named "f" that takes an input value "x" and returns an output value. The function f maps the input value x to a unique output value f(x). The symbol "f" is often used to represent a generic function, and the variable inside the parentheses, "x", represents the argument or input value of the function.

For example, if we have the function f(x) = x + 2, then f(3) = 3 + 2 = 5. This means that when we input the number 3 into the function, the output is 5.

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The answer of -x+3y=20; 7y=x will be x = -[tex]\frac{7}{2\\}[/tex] and y = - [tex]\frac{1}{2}[/tex].

Given,

-x+3y=20 .... (1)

7y=x .... (2)

By using the method of substitution.

We will use equation (2) as

7y=x

=>y= [tex]\frac{x}{7}[/tex] ....(3)

Putting equation (3) in (1)

We have, -x+3([tex]\frac{x}{7}[/tex])=20

Taking L.CM.

[tex]\frac{-7x+3x}{7}[/tex] = 20

-7x +3x = 140

-4x = 140

0r, x = - [tex]\frac{140}{4}[/tex]

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

Now by putting value of x in equation (2),  we get

7y = x

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

0r, y = -[tex]\frac{1}{2}[/tex]

Thus, x = -[tex]\frac{7}{2\\}[/tex] and y = - [tex]\frac{1}{2}[/tex]

This code use to measures may be equivalent after some transformation.

<!DOCTYPE html>

<html lang="en">

<head>

<title>Cat in night</title>

</head>

<body>

<div id="wrapper">

<section class="sky">

<div class="moon"></div>

<ul>

<li class="cloud"></li>

<li class="cloud"></li>

<li class="cloud"></li>

</ul>

</section>

<section class="wall">

<section class="cat">

<div class="cat-head">

<div class="eyes">

<div class="eye"></div>

<div class="eye"></div>

</div>

</div>

<div class="cat-body">

<div class="tail"></div>

</div>

</section>

</section>

</div>

<style>

.sky {

height: 300px;

background: radial-gradient(#112A71, #000A31);

overflow: hidden;

position: relative; }

.sky .moon {

width: 80px;

height: 80px;

border-radius: 50%;

background-color: #FEFF79;

-webkit-box-shadow: 0 0 150px #FEFF79, inset 0 1px 20px rgba(0, 0, 0, 0.3);

box-shadow: 0 0 150px #FEFF79, inset 0 1px 20px rgba(0, 0, 0, 0.3);

position: absolute;

top: 30px;

right: 100px; }

.sky .cloud {

width: 80px;

height: 30px;

background-color: #8D8D8D;

border-radius: 50px;

-webkit-box-shadow: inset 0 -1px 10px rgba(0, 0, 0, 0.3);

box-shadow: inset 0 -1px 10px rgba(0, 0, 0, 0.3);

position: relative;

top: 60px;

left: 30px;

-webkit-animation: shift 100s infinite linear;

animation: shift 100s infinite linear; }

.sky .cloud:nth-child(2) {

-webkit-transform: scale(-1.5, 1.3);

transform: scale(-1.5, 1.3);

top: 100px;

left: 250px;

-webkit-animation-duration: 40s;

animation-duration: 40s; }

.sky .cloud:last-child {

top: 150px;

left: 100px;

Transformation refers to a significant change or shift in an entity, be it a person, organization, system, or society, towards a desired state or outcome. It is a process of evolving, improving, or adapting in response to internal or external pressures or opportunities. Transformation involves a fundamental shift in the way things are done, the mindset, values, and behavior of the entity undergoing the change.

Transformation can occur in various contexts, such as business, technology, education, social and political systems, and personal development. It often requires a clear vision, strategic planning, and effective execution to achieve the desired outcome. The process can be challenging and requires significant effort and resources, but the benefits of transformation can be substantial, leading to increased efficiency, innovation, growth, and social impact.

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Complete Question: -

It is important to define or select similarity measures in data analysis. However, there is no commonly-accepted subjective similarity measure. Results can vary depending on the similarity measures used. Nonetheless, seemingly different similarity measures may be equivalent after some transformation. Suppose we have the following two-dimensional data set:

A1

A2

X1

1.5

1.7

X2

2

1.9

X3

1.6

1.8

X4

1.2

1.5

X5

1.5

1.0

Consider the data as two-dimensional data points. Given a new data point, x = (1.4, 1.6) as a query, rank the database points based on similarity with the query using Euclidean distance, Manhattan distance, supremum distance, and cosine similarity.

The linear equation in the given graph is.

y = 40x

We know that the general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept, these two values are constants, and the variables are x and y.

First, notice that the line intercepts the y-axis at the point (0, 0), then b = 0.

So we can write:

y = a*x

Also notice that the line passes through the point (1, 40), then:

40 = a*1

40/1 = a

The linear equation is.

y = 40x

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Answer:

x3

Step-by-step explanation:

Answer:

X = -2

Explanation

12 (x+3) = 12

The missing side lengths are computed below

Triangle 22

The side length x can be calculated using

sin(30) = 9/x

So, we have

x = 9/sin(30)

Evaluate

x = 18

For length y, we have

y = √(18² - 9²)

Evaluate

y = 9√3

Triangle 23

The side length y can be calculated using

sin(30) = y/√3

So, we have

y = √3 * sin(30)

Evaluate

y = 1/2√3

For length x, we have

x = √(√3² + (1/2√3)²)

Evaluate

x = √(15/4)

x = 1/2√15

Triangle 24

The side length y can be calculated using

cos(60) = y/2√3

So, we have

y = 2√3 * cos(60)

y = √3

For x, we have

x = √((2√3)² - (√3)²)

x = √9

x = 3

Triangle 25

The side length x can be calculated using

cos(60) = 5/x

So, we have

x = 5/cos(60)

x = 10

For y, we have

y = √(10² - 5²)

y = 5√3

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For the trapezoid given the value for x is obtained as 6.

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

The value for parallel sides of a trapezoid is given as 3x + 2 and 2x - 2.

A line segment divides the trapezoid in half.

The line segment dividing the trapezoid in half measures 15 units.

We know that the line segment dividing the trapezoid in half is also the average of the parallel sides.

So we can set up an equation -

(3x + 2 + 2x - 2) / 2 = 15

Simplifying the left side, we get -

(5x) / 2 = 15

Multiplying both sides by 2/5, we get -

x = 6

Therefore, the value of x is 6.

We can check that this value works by plugging it into the expressions for the parallel sides -

3x + 2 = 20

2x - 2 = 10

So the lengths of the parallel sides are 20 and 10.

Therefore, the average of these is indeed 15, and so the line segment dividing the trapezoid in half has length 15, as given.

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Renee's monthly payment will be $504.46. The closest answer choice is d. $504.46.

To calculate Renee's monthly payment, we need to first determine the total cost of the new car after taxes and fees and subtract the trade-in value of her old car. Then, we can use the loan information to calculate the monthly payment.

Total cost of the new car:

List price: $19,675

Vehicle registration fees: $1,420

Documentation fees: $85

Sales tax: 8.92% of ($19,675 + $1,420 + $85) = $1,894.51

Total cost = $19,675 + $1,420 + $85 + $1,894.51 = $22,074.51

Trade-in value of the old car:

2002 Buick LeSabre in good condition: $3,374 (from the table)

85% of trade-in value: 0.85 x $3,374 = $2,867.90

Net cost of the new car:

$22,074.51 - $2,867.90 = $19,206.61

To calculate the monthly payment, we can use the formula for the present value of an annuity:

PV = PMT x (1 - (1 + r)^(-n)) / r

where PV is the present value of the loan, PMT is the monthly payment, r is the monthly interest rate (11.34%/12), and n is the number of payments (4 years x 12 months/year = 48).

Solving for PMT:

PMT = PV x r / (1 - (1 + r)^(-n))

PMT = $19,206.61 x 0.1134/12 / (1 - (1 + 0.1134/12)^(-48))

PMT = $504.46

Therefore, Renee's monthly payment will be $504.46. The closest answer choice is d. $504.46.

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The payment (future value), to the nearest rand, which should be made at the end of the seventh year in order to liquidate the debt, is​ R9,338.80.

The future payment to be made at the end of the seventh year is determined by computing the future values in two stages. The first stage computes the future value before the payment at the end of the first year.  The second stage computes the future value for six years.  

here, we know,

The future value is computed by compounding the present value at an interest rate.

Current debt = R6,421,00

Compound interest rate = 11% per year

Compounding period = Quarterly

Future Value in 1 Year:

N (# of periods) = 4 quarters (1 year x 4)

I/Y (Interest per year) = 11%

PV (Present Value) = R6,421.00

PMT (Periodic Payment) = R0

Results:

Future Value (FV) = R7,156.98

Total Interest = R735.98

Future Value (FV) = R7,156.98

Payment in one year's time = R2,287.00

Balance = R4,869.98

Future Value at the end of the 7th Year:

N (# of periods) = 24 quarters (6 years x 4)

I/Y (Interest per year) = 11%

PV (Present Value) = R4,869.98

PMT (Periodic Payment) = R0

Results:

Future Value (FV) = R9,338.80

Total Interest = R4,468.82

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The equation we can use to find the number of people each car can hold "10n = 40".

This equation represents the fact that there are 10 cars on the Blazing Bullet, each holding n people, and that the total number of people on the ride is 40.

By solving this equation for n, we can find the number of people each car can hold.

Here is how to solve the equation:

10n = 40

Divide both sides of the equation by 10:

10n/10 = 40/10

n = 4

Therefore, in conclusion, it is stated that each car can hold 4 people.

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Answer:

10n = 40

Step-by-step explanation:

1. Subtract 10 from both sides of the equation:

2. 10n/10 = 40/10

3. n = 4

As a result, it can be concluded that each car can accommodate 4 passengers.

The quotient and remainder using (x^(5)-x^(4)+9x^(3)-9x^(2)+9x-12)/(x-1) are 1x^(4)-2x^(3)+11x^(2)-20x+29 and -41, respectively.

To find the quotient and remainder using (x^(5)-x^(4)+9x^(3)-9x^(2)+9x-12)/(x-1), we will use synthetic division.

Write down the coefficients of the dividend polynomial in descending order of the exponent of x. In this case, the coefficients are 1, -1, 9, -9, 9, -12.

Write down the constant term of the divisor polynomial. In this case, the constant term is -1.

Bring down the first coefficient of the dividend polynomial.

Multiply the constant term of the divisor polynomial by the first coefficient of the dividend polynomial and write the result under the second coefficient of the dividend polynomial.

Add the second coefficient of the dividend polynomial and the result from step 4.

Repeat steps 4 and 5 until all the coefficients of the dividend polynomial have been used.

The last result from step 5 is the remainder. The other results are the coefficients of the quotient polynomial.

The synthetic division is shown below:

-1 | 1 -1 9 -9 9 -12
 | -1 2 -11 20 -29
 ---------------------
   1 -2 11 -20 29 -41
 
The quotient is 1x^(4)-2x^(3)+11x^(2)-20x+29 and the remainder is -41.

Therefore, the quotient and remainder using (x^(5)-x^(4)+9x^(3)-9x^(2)+9x-12)/(x-1) are 1x^(4)-2x^(3)+11x^(2)-20x+29 and -41, respectively.

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Answer:

Step-by-step explanation: First lets multiply the numerators, so 3*3 is 9, then we multiply the denominators, so 4*5 is 20. 9/20 or 0.45 will be your answer.

1. The probability of getting a z-score of 0.189 or less is 0.5753.  

2. The probability of getting a z-score of 1.13 or less is 0.8708.

3. The probability of getting a z-score of 3.02 or less is 0.9982.

Normally distributed data refers to data that follows a normal distribution, also known as a Gaussian distribution or bell curve.

In a normal distribution, the data is symmetric around the mean and the majority of the data is clustered around the mean with decreasing density as the data moves further away from the mean.

Here we have

The mean price for liquid crystal display (LCD) computer monitors is $ 170  and the standard deviation is $ 53.  

Find the z-score associated with $ 180 using the formula:

z = (x - μ) / σ

where x is the value we need to find the probability, μ is the mean, and σ is the standard deviation.

z = (180 - 170) / 53

z = 0.189

Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 0.189 or less is 0.5753.  

To find the probability that the mean cost of 9 randomly selected LCD computer monitors is less than $ 180, find the standard deviation σ/√n.

The standard deviation of the sample means is σ/√n = $53/√9 = $17.67.

Now we need to find the z-score associated with $ 180 using the formula:

z = (x - μ) / σ/√n

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

z = (180 - 170) / (53 / √9)

z = 1.13

Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 1.13 or less is 0.8708.  

To find the probability that the mean cost of 36 randomly selected LCD computer monitors is less than $ 180, we can use the same formula as in part 2, with n = 36:

z = (x - μ) / σ/√n

z = (180 - 170) / (53 / √36)

z = 3.02

Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 3.02 or less is 0.9982.

Therefore,

1. The probability of getting a z-score of 0.189 or less is 0.5753.  

2. The probability of getting a z-score of 1.13 or less is 0.8708.

3. The probability of getting a z-score of 3.02 or less is 0.9982.

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The equation that relates the total number of visits to the number of days the promotion has been running is v = 96 × [tex]2^{\frac{d}{5} }[/tex] .

When an equal sign connects two expressions then, it is called an equation.

According to the question, the total number of visits doubled after every 5 days.

So, after 5 days visits= 96×2

After 10 days visits= 96×2×2

After 15 days visists= 96×2×2×2

Therefore, it is a proportional sequence.

Hence, the equation that relates the total number of visits, v, to the number of days the promotion has been running, d comes out to be:

v = 96 × [tex]2^{\tfrac{d}{5} }[/tex]

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(a) To find the value of k, we need to use the fact that the sum of the probabilities of all possible outcomes is equal to 1. In this case, we have:
0.05 + 0.20 + 3k + 0.15 + k = 1
Solving for k, we get:
4k = 1 - 0.05 - 0.20 - 0.15
4k = 0.60
k = 0.15
Therefore, the value of k is 0.15.

(b) To find E(X), we need to multiply each value of x by its corresponding probability and sum the results. In this case, we have:
E(X) = (-1)(0.05) + (0)(0.20) + (1)(3k) + (2)(0.15) + (3)(k)
E(X) = -0.05 + 0 + 0.45 + 3k
E(X) = 0.40 + 3k
Substituting the value of k that we found in part (a), we get:
E(X) = 0.40 + 3(0.15)
E(X) = 0.85
Therefore, the expected value of X is 0.85.

(c) To find Var(X), we need to use the formula Var(X) = E(X^2) - (E(X))^2. First, we need to find E(X^2):
E(X^2) = (-1)^2(0.05) + (0)^2(0.20) + (1)^2(3k) + (2)^2(0.15) + (3)^2(k)
E(X^2) = 0.05 + 0 + 3k + 0.60 + 9k
E(X^2) = 0.65 + 12k
Substituting the value of k that we found in part (a), we get:
E(X^2) = 0.65 + 12(0.15)
E(X^2) = 2.45
Now, we can find Var(X):
Var(X) = E(X^2) - (E(X))^2
Var(X) = 2.45 - (0.85)^2
Var(X) = 2.45 - 0.7225
Var(X) = 1.7275
Therefore, the variance of X is 1.7275.

(d) To find Var(2 - 5X), we need to use the formula Var(a + bX) = b^2Var(X), where a = 2 and b = -5. Substituting the values and the variance of X that we found in part (c), we get:
Var(2 - 5X) = (-5)^2Var(X)
Var(2 - 5X) = 25(1.7275)
Var(2 - 5X) = 43.1875
Therefore, the variance of 2 - 5X is 43.1875.

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The quadrilateral whose vertices are A(2, 3); B(4, -2);C(-1,-4); D(-3, 1) is a square.

Quadrilaterals are four sided polygons which also have four vertices and four angles.

Sum of all the interior angles of a quadrilateral is 360 degrees.

Given A(2, 3); B(4, -2);C(-1,-4); D(-3, 1)

Length of AB = [tex]\sqrt{(4-2)^2+(-2-3)^2}[/tex] = √29 units

Length of BC = [tex]\sqrt{(-1-4)^2+(-4--2)^2}[/tex] = √29 units

Adjacent sides are equal.

So the quadrilateral must be square or rhombus.

Now, find the length of diagonals.

If the diagonals are equal, then it is square. If they are not equal, then it is rhombus.

AC = [tex]\sqrt{(-1-2)^2+ (-4-3)^2}[/tex] = √58 units

BD = [tex]\sqrt{(-3-4)^2+(1--2)^2}[/tex] = √58 units

Diagonals are equal.

So it is a square.

Hence the quadrilateral is a square.

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Answer: A) -4.2, B) -3.8 C) -9/2 (-4.5)

Step-by-step explanation: Think of a number line, you have 0-10, and -10-0, as you keep going down the number like, the numbers become less and less, just like how -4.2 is less than -3.5, because it is further to the left of the number line, meaning it is less than. Hope this helps!