Find the value of (X -a) (X - b) (X - c) (X - d)……(x-z)

The length of the leg of the 45-45-90 triangle is 6.

In geometry, the hypotenuse is the longest side of a right-angled triangle, opposite to the right angle.

The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

In a 45-45-90 triangle, the length of each leg is equal to x, and the length of the hypotenuse is √2 times the length of a leg.

So if the hypotenuse is 6√2, then each leg has length:

x = (6√2)/√2 = 6

Hence, the length of the leg of the 45-45-90 triangle is 6.

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To verify equivalent expressions, you need to evaluate the expressions for different values of x and compare the results. For the given list of x values (0, 1, 2), you can plug them into the two equations one at a time and compare the results.

For x=0:

Equation 1: 0

Equation 2: 0

For x=1:

Equation 1: 1

Equation 2: 1

For x=2:

Equation 1: 4

Equation 2: 8

Since the results of the equations do not match for x=2, the expressions are not equivalent.

To verify equivalent expressions, you can plug in the given values of x into the equations and see if they produce the same result. Here are the steps to do this:

1. Take the first equation and plug in the value of x. For example, if the equation is y = 2x + 1 and x = 0, then y = 2(0) + 1 = 1.

2. Do the same for the second equation with the same value of x. For example, if the second equation is y = x + 1 and x = 0, then y = 0 + 1 = 1.

3. Compare the results of the two equations. If they are the same, then the expressions are equivalent for that value of x.

4. Repeat these steps for the other values of x (1 and 2) and fill out the rest of the table with the results.

5. If the expressions produce the same result for all values of x, then they are equivalent expressions.

I hope this helps! Let me know if you have any further questions.

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The first digit in both numbers is 2, so we can move to the next digit. In 2.218, the digit in the second decimal place is 2, while in 2.21, the digit in the second decimal place is 1. Since 2 is greater than 1, 2.218 is longer than 2.21.

When comparing the length of two decimal numbers, it's important to consider the value of each digit in the number. Let's take the example of 2.218 inches and 2.21 inches.

To begin, we can compare the first digit of each number, which is 2 in both cases. Since the first digit is the same, we need to look at the next digit to determine which number is longer. In 2.218, the second digit is 2, while in 2.21, the second digit is 1. The second digit in a decimal number represents the tenths place, so we can conclude that 2.218 is longer than 2.21.

It's important to note that this method of comparing decimal numbers applies to numbers with the same number of decimal places. If we were comparing 2.218 inches to 2.2 inches, for example, we wouldn't be able to simply look at the second digit. Instead, we would need to compare the numbers digit by digit, starting from the leftmost digit.

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The solution is, Loan origination fee = $696

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Given:

Home value = $58,000

Loan-to-value loan = 80%

Loan origination fee = 1.5 points = 1.5%

Find:

Loan origination fee = ?

Computation:

Total loan amount = Home value × Loan-to-value loan

Total loan amount = $58,000 × 80%

Total loan amount = $46,400

Loan origination fee = Total loan amount × 1.5%

Loan origination fee = $46,400 × 1.5%

Loan origination fee = $696

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Exponential functions and geometric sequences are closely related, as the terms in a geometric sequence can be expressed using an exponential function.

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant called the common ratio. For example, a geometric sequence starting with 2 and with a common ratio of 3 would be: 2, 6, 18, 54, 162, ...

The general formula for a geometric sequence is:

Where:

Exponential functions have the general form:

Where:

If we take the formula for a geometric sequence and rewrite it as an exponential function, we get:

Using the binomial expansion formula, we can simplify this to:

This is an exponential function with base (1 + (r-1)) and exponent (n-1). Therefore, the terms of a geometric sequence can be expressed using an exponential function.

Conversely, if we have an exponential function of the form f(x) = a * b^x, then we can find a geometric sequence by evaluating the function for a range of values of x. For example, if we take f(x) = 2 * 3^x and evaluate it for x = 1, 2, 3, 4, we get the geometric sequence 6, 18, 54, 162.

~ Zeph

Answer:

55%

Step-by-step explanation:

To get 55 I just divided 33/60 and multiplied it buy 100

Answer:

a) f(x) = (1/3)√(x-4)

b) f(x) = 4√(x+3)

c) f(x) = 6 - √(x - 2)

After getting the product, and simplifying it the correct statement should be: [tex](3^4) \times (2^3) = 648[/tex]

In mathematics, simplification refers to the process of simplifying an expression or equation without affecting its fundamental meaning or value. Using mathematical tools and rules to simplify an equation makes it simpler to manipulate or solve.

In algebra, simplification might take the form of factoring out common factors, grouping like concepts, or distributing multiplication across addition or subtraction. For instance, merging two like terms will simplify the formula 2x + 4x to 6x. The same strategy can be used to reduce the expression 3(x + 2) - 2(x - 1) to 3x + 4 by spreading out the multiplication and combining related terms.

1. The error is in the simplification of the product of the two terms. The correct way to simplify it is to multiply the coefficients and add the exponents of x.

The correct solution is:

[tex](3x^2)(-2x^4) = (3 \times -2)x^{(2+4)} = -6x^6[/tex]

Therefore, the error is in the sign of the result, which should be negative instead of positive. The correct answer is[tex]-6x^6.[/tex]

2. The error is in the distribution of the exponent on the coefficient 4. The correct way to simplify the product is to add the exponents of a and then multiply by the coefficient 4.

The correct solution is:

[tex]4a^2 \times 3a^5 = (4 \times 3) a^{(2 + 5)} = 12a^7[/tex]

Therefore, the error is in the addition of the coefficients instead of multiplying them, and the incorrect distribution of the exponent on the coefficient 4. The correct answer is [tex]12a^7.[/tex]

3. There is no error in this simplification.

The product of[tex]x^6, x, and $ x^3 $[/tex] is equivalent to [tex]x^{(6+1+3)} = x^{10}[/tex]

However, the answer given in the question, x^9, is incorrect.

4. The given statement is incorrect.

The product of[tex](3^4) and (2^3)[/tex] can be simplified as follows:

[tex](3^4) \times (2^3) = 81 \times 8 = 648[/tex]

Therefore, the correct statement should be:

[tex](3^4) \times (2^3) = 648[/tex]

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In an experimental study, the variable of interest is a changing quantity that would be measured. A number of these different factors, known as the original study factors, are monitored so that information on how the factors impact some other interesting as the predictor variables, or merely the response, can be obtained.

Is the variable under consideration an independent variable?

Interesting outcome variable

This is also referred to as a regression model or an interest component. It is a "input" variable that serves as a factor that what a researcher is able within a contained way to test this same impact of changing the amounts of the predictor variables on the overall result measured. An observation falls under the category of data collection case.

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1/64 fraction is equal to 0.015625 in decimal form.

To change the fraction 1/64 to a decimal, we need to perform division.

1 divided by 64 can be written as:

0.015625

----------

64 | 1.000000

   0

  10

   0

The result of the division is 0.015625. This means that 1/64 is equal to 0.015625 in decimal form.

Note that in this case, we carried the division out to six decimal places, but the question specified that we should carry it out to three decimal places. In that case, we would round the answer to 0.016.

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To convert 1 cubic centimeter (cc) to ounces (oz), apply conversion factor between the two units. The conversion factor is:

1 cc = 0.033814 oz

This means that one cubic centimeter is equivalent to 0.033814 ounces.

Therefore, the mathematical expression to convert 1 cc to oz is:

1 cc * (0.033814 oz/cc) = 0.033814 oz

So, 1 cc is equal to 0.033814 ounces.

A conversion factor is a mathematical expression that expresses the relationship between two units of measurement. It is used to convert measurements between units.

Conversion factors are commonly used to convert measurements between different units of measurement in math, science, and engineering. They are a useful tool for performing calculations and comparing data in various units.

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The prepositional phrase would be B. of the bees.

The prepositional phrase would be C. he took shelter.

A prepositional phrase is a group of words that includes a preposition (such as "in," "on," "at," "by," "with," etc.) and a noun or pronoun object, along with any associated modifiers.

Prepositional phrases can be used in a variety of ways, including to describe location, time, possession, and other relationships between words in a sentence. In the given statements, the prepositional phrases would be "of the bees" and " he took shelter. "

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200 pounds is approximately equal to 90.7185 kg ( rounded to four decimal places )

To convert 200 pounds to kg, we can use the following formula:

1 pound = 0.453592 kg

The conversion factor is 0.453592

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The mass in kg = conversion factor × The mass in pounds

Substitute the values in the equation

The mass in kg = 0.453592 × 200

Multiply the numbers

= 90.7185 kg  ( rounded to four decimal places )

Therefore, 200 pounds is 90.7185 kg

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The value which is converted from Celsius to Fahrenheit is given by 38 Celsius is equal to 89.6 Fahrenheit.

Units which represents the measurement of the temperature in standard form Celsius and Fahrenheit .

Formula which relates the Celsius and Fahrenheit are given by

(°C × 9/5) + 32 =°F

Now Substitute the value 32 Celsius which needs to convert  into Fahrenheit we get,

(32°C × 9/5) + 32

= ( 288 / 5 ) + 32

= ( 57.6 ) + 32

= 89.6°F

Therefore, the converted value from Celsius to Fahrenheit for the given 32 Celsius is given by 89.6 Fahrenheit.

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The above question is incomplete , the complete question is:

What is the conversion of 32°C to °F ?

The surface area of the right rectangular prism is 652 ft²

The surface area of a right rectangular prism is expressed as;

SA = 2( wl + hl + hw )

From the diagram;

Plug the values into the above formula and solve for the surface area.

SA = 2( wl + hl + hw )

SA = 2( (7×8) + (18×8) + 18×7 )

Simplify

SA = 2( 56 + 144 + 126 )

SA = 2( 326 )

SA = 652 ft²

Therefore, the surface area of the prsim is 652 ft².

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The converted to product four times as much in the CSTR than it was in the PFR that is 400%.

Conversion is a term used to describe the process of transferring a reactant into a product.

In this case, the reactant is being transferred from a 72 l plug flow reactor (PFR) to a 24 l continuous stirred tank reactor (CSTR). The conversion achieved by this process can be determined by calculating the ratio of product to reactant in the CSTR.

Specifically, if the PFR has a conversion of x%, then the conversion achieved in the CSTR will be x/(1-x), where x is the conversion in the PFR.

Therefore, if the PFR has a conversion of 80%, then the CSTR will have a conversion of 80/(1-80) = 400%.

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By applying formula, we were able to convert 51cm to inches, which is 20.08 inches.

First, we need to understand the conversion factor between centimeters and inches. One inch is equal to 2.54 centimeters. This means that we can convert centimeters to inches by dividing the measurement in centimeters by 2.54.

To convert 51cm to inches, we will use the formula:

Measurement in inches = Measurement in centimeters / 2.54

So, to convert 51cm to inches, we will divide 51 by 2.54:

Measurement in inches = 51 / 2.54

Measurement in inches = 20.08 inches (rounded to two decimal places)

Therefore, 51cm is equivalent to 20.08 inches.

In conclusion, knowing measurement conversions is an essential skill to have, especially when dealing with different systems of measurement. To convert centimeters to inches, we divide the measurement in centimeters by 2.54.

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On graphing the given models we got a parabola as shown below

To graph the given equation, find the coordinate points using the given variables. In this problem, we have taken the values of t as 0, 1, and -1 from that find the values of 'h' and form the coordinate points. Now plot the resultant points as a graph.

Here we have

h = - 16t² + 12 represents the height that corn from the ground

Where t represents the time in sec

From given equation,

at t = 0 => h = 12

at t = 1 => h = - 4

at t = -1 => h = -4

Now take h = y and t = x

The coordinates we got are (0, 12) (1, -4) and (-1, -4)

Now use the above points to draw the graph as shown below  

Therefore,

On graphing the given models we got a parabola as shown below

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25 kilometers is approximately equal to 15.5343 miles ( rounded to four decimal places )

The conversion factor from kilometers to miles is 0.621371.

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

So, to convert kilometers to miles you can multiply the number of kilometers by 0.621371.

The distance in kilometer = 25 kilometers

The distance in miles = conversion factor × The distance in kilometer

Substitute the values in the equation

The distance in miles = 25 × 0.621371

Multiply the numbers

=  15.5343 miles (to three decimal places).

Therefore, 25 km is 15.5343 miles

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Answer:

As x --> ∞, then y --> - ∞

Step-by-step explanation:

As the value of x increases(as the graph goes right), the graph seems to go down, meaning the y-values are getting more an more negative. This means that as x approached infinity, the y values approach negative infinity ( x --> ∞, y --> - ∞ ).

As the value of x decreases(going to the left), the graph seems to go higher and higher. Therefore, as x approaches negative infinity, the y-value approach infinity. ( x --> - ∞, y --> ∞ )

Out of the options given, the one As x --> ∞, then y --> - ∞ is true.

Answer:

Below

Step-by-step explanation:

tan x  = 110 /11

Arctan( tan x) = arctan(110/11)

   x     =   84.3°

The mass of the yogurt is 99 grams.

A ratio is a numerical relationship showing how often one value includes or is included inside another. It is used to compare two numbers.

Given:

A dessert contains yogurt and fruit inside.

The total mass of the dessert = 165 grams.

And the ratio of the mass of fruit to the mass of yogurt is 2 : 3.

Let the mass of the fruit is 2x and the mass of the yogurt is 3x.

So, 2x + 3x = 165

5x = 165

x = 165/5

x = 33

The mass of the yogurt is 33(3) = 99 grams.

Therefore, the required mass is 99 grams.

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The north campus had 600 students and the south campus had 600 students.Using this ratio, we can solve for the total number of students at the north campus, which is 600 students (10 women x 60 = 600 students).

Before the merger, the north campus had 10% of the students as women, which is the same as saying 10 out of every 100 students were women. This means that 100 students would have been 10 women. Using this ratio, we can solve for the total number of students at the north campus, which is 600 students (10 women x 60 = 600 students). The same process can be done for the south campus, which had 50% of its students as women. This means that 50 out of every 100 students were women, which means that the total number of students at the south campus would have been 600 (50 women x 60 = 600 students). Therefore, the north and south campuses had 600 students each before the merger, for a total of 1200 students between the two campuses.

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15) The set is a basis for R² because it is linearly independent and spans R². 16) The set is not a basis for R² because it is linearly dependent. 17) The set is a basis for R³ because it is linearly independent and spans R³. 18) The set is a basis for R³ because it is linearly independent and spans R³.

Exercise 15:

To determine if the set {[5,-2],[10,-3]} is a basis for R², we need to check if the set is linearly independent and spans R².

To check for linear independence, we set the linear combination of the vectors to zero and solve for the coefficients:

c₁[5,-2] + c₂[10,-3] = [0,0]

This leads to the system of linear equations:

5c₁ + 10c₂ = 0

-2c₁ - 3c₂ = 0

Solving for c₁ and c₂ gives us c₁ = 0 and c₂ = 0, which means that the set is linearly independent.

To check for spanning, we need to determine if any vector in R² can be expressed as a linear combination of {[5,-2],[10,-3]}. Let [x,y] be an arbitrary vector in R². We can solve for c₁ and c₂ in the equation c₁[5,-2] + c₂[10,-3] = [x,y] to get c₁ = (3y - 2x)/(-20) and c₂ = (x - 5y)/(-20). Since we were able to express any vector in R² as a linear combination of {[5,-2],[10,-3]}, the set {[5,-2],[10,-3]} is a basis for R².

Exercise 16:

To determine if the set {[-4,6],[2,-3]} is a basis for R², we again need to check for linear independence and spanning.

Setting the linear combination of the vectors to zero and solving for the coefficients gives:

c₁[-4,6] + c₂[2,-3] = [0,0]

which leads to the system of linear equations:

-4c₁ + 2c₂ = 0

6c₁ - 3c₂ = 0

Solving for c₁ and c₂ gives us c₁ = c₂ = 0, which means that the set is linearly independent.

To check for spanning, we again need to determine if any vector in R² can be expressed as a linear combination of {[-4,6],[2,-3]}. Let [x,y] be an arbitrary vector in R². Solving for c₁ and c₂ in the equation c₁[-4,6] + c₂[2,-3] = [x,y] gives us c₁ = (-3y + 2x)/(-20) and c₂ = (6y - 4x)/(-20). However, we notice that the determinant of the matrix formed by the two vectors is zero, which means that the vectors are linearly dependent and cannot form a basis for R².

Exercise 17:

To determine if the set {[0,1,-2],[5,-7,4],[6,3,5]} is a basis for R³, we need to check for linear independence and spanning.

Setting the linear combination of the vectors to zero and solving for the coefficients gives:

c₁[0,1,-2] + c₂[5,-7,4] + c₃[6,3,5] = [0,0,0]

which leads to the system of linear equations:

5c₂ + 6c₃ = 0

c₁ - 7c₂ + 3c₃ = 0

-2c₁ + 4c₂ + 5c₃ = 0

Solving for c₁, c₂, and c₃ gives us c₁ = c₂ = c₃ = 0, which means that the set is linearly independent.

To check for spanning, we need to determine if any vector in R³ can be expressed as a linear combination of {[0,1,-2],[5,-7,4],[6,3,5]}. Let [x,y,z] be an arbitrary vector in R³. We can solve for c₁, c₂, and c₃ in the equation c₁[0,1,-2] + c₂[5,-7,4] + c₃[6,3,5] = [x,y,z] to get c₁ = (-5y - 6z)/(-47), c₂ = (-2x - 3z)/(-47), and c₃ = (x + y)/47. Since we were able to express any vector in R³ as a linear combination of {[0,1,-2],[5,-7,4],[6,3,5]}, the set {[0,1,-2],[5,-7,4],[6,3,5]} is a basis for R³.

Exercise 18:

To determine if the set {[1,1,-2],[-5,-1,2],[7,0,-5]} is a basis for R³, we need to check for linear independence and spanning.

Setting the linear combination of the vectors to zero and solving for the coefficients gives:

c₁[1,1,-2] + c₂[-5,-1,2] + c₃[7,0,-5] = [0,0,0]

which leads to the system of linear equations:

c₁ - 5c₂ + 7c₃ = 0

c₁ - c₂ = 0

-2c₁ + 2c₂ - 5c₃ = 0

Solving for c₁, c₂, and c₃ gives us c₁ = c₂ = c₃ = 0, which means that the set is linearly independent.

To check for spanning, we need to determine if any vector in R³ can be expressed as a linear combination of {[1,1,-2],[-5,-1,2],[7,0,-5]}. Let [x,y,z] be an arbitrary vector in R³. We can solve for c₁, c₂, and c₃ in the equation c₁[1,1,-2] + c₂[-5,-1,2] + c₃[7,0,-5] = [x,y,z] to get c₁ = (y - 7z - 1)/(-10), c₂ = (-x + z + 1)/10, and c₃ = (2x - 2y + 5z)/10. Since we were able to express any vector in R³ as a linear combination of {[1,1,-2],[-5,-1,2],[7,0,-5]}, the set {[1,1,-2],[-5,-1,2],[7,0,-5]} is a basis for R³.

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Complete question:

Determine which sets in exercises 15–18 are bases for R² or R³. justify each answer!

15. {[5,-2],[10,-3]}

16. {[-4,6],[2,-3]}

17. {[0,1,-2],[5,-7,4],[6,3,5]}

18. {[1,1,-2],[-5,-1,2],[7,0,-5]}

The value of 85g increased by 120% is equal to 187g.

In mathematics, a value or ratio that can be expressed as a fraction of 100 is known as a percentage. When determining a percentage of a number, we should first divide it by 100 before multiplying the result by 100. As a result, the proportion refers to a component per 100. The word "percent" denotes a percentage. The letter "%" stands for it.

Now in the given question ,

To increase 85g by 120%, we need to find 120% of 85g and add it to 85g.

To find 120% of 85g, we can first convert 120% to a decimal by dividing by 100:

120% = 120/100 = 1.2

Then we can multiply 1.2 by 85g:

1.2 x 85g = 102g

So, increasing 85g by 120% gives us:

85g + 102g = 187g

Therefore, 85g increased by 120% is equal to 187g.

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The variable x has no true value in the similar shapes

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

The figure

Using the figure, we have the following ratio

3x : 4x - 1 = 4x - 1 : x² - x - 2

Factorize

3x : 4x - 1 = 4x - 1 : x² + x - 2x - 2

So, we have

3x : 4x - 1 = 4x - 1 : x(x + 1) - 2(x + 1)

This gives

3x : 4x - 1 = 4x - 1 : (x - 2)(x + 1)

Express as fraction

3x/(4x - 1) = (4x - 1)/(x - 2)(x + 1)

So, we have

3x(x - 2)(x + 1) = (4x - 1)(4x - 1)

Using a graphing tool, we have

x = undefined

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The steps to calculate the retirement bank rate are

1) Calculate your current retirement savings

2) Estimate your future retirement savings

3) Calculate your retirement savings rate

4) Adjust your savings rate as needed

Calculating your retirement savings rate can be a helpful way to ensure you're saving enough money to support your retirement. Here are the steps to calculate your bank rate retirement online:

Calculate your current retirement savings: You'll need to calculate the total amount of money you've saved for retirement so far,

Estimate your future retirement savings: You can use an online retirement calculator to estimate the amount of money you'll have saved by the time you retire based on your current savings rate,

Calculate your retirement savings rate: To calculate your retirement savings rate, divide your total retirement savings by your retirement savings goal.

Adjust your savings rate as needed: If your retirement savings rate is lower than you'd like, consider increasing your savings rate by contributing more money to your retirement accounts or exploring other investment options.

It's important to keep in mind that retirement planning is a complex process, and there are many factors that can impact your retirement savings rate, such as inflation, unexpected expenses, and changes in the stock market.

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The given sequence is an arithmetic sequence.

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a fixed constant called the common difference to the previous term. A geometric sequence is a sequence of numbers in which each term after the first is obtained by multiplying the previous term by a fixed constant called the common ratio.

In the given sequence

103.8 - 111 = -7.2

96.6 - 103.8 = -7.2

Similarly we can observe that each term is obtained by subtracting 7.2 from the previous term. Therefore, the common difference is -7.2, and the sequence is an arithmetic sequence.

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Dot plot 2, on the other hand, is skewed and does not have a symmetrical distribution, which may not be a good representation of the sample means.

What is normal distribution ?

Normal distribution is a statistical concept that describes a symmetrical, bell-shaped curve that is characterized by its mean and standard deviation. It is a continuous probability distribution that represents the probability of a random variable taking on a certain value.

As per the Central Limit Theorem, the sample means of a sufficiently large sample size taken from any population tend to follow a normal distribution, regardless of the shape of the population distribution. Therefore, the dot plot that is likely to represent the means of the samples of size 10 from this population is dot plot 1 because it has a more symmetrical distribution, which is more similar to a normal distribution.

Hence, Dot plot 2, on the other hand, is skewed and does not have a symmetrical distribution, which may not be a good representation of the sample means.

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Answer:

Jennifer will choose office 3, as it has a area of 98ft

Step-by-step explanation:

1. Has a area of 96ft  ( 12 x 8 = 96 )

2. Has a area of 90ft ( 9 x 10 = 90 )

3. Has a area of 98ft ( 14 x 7 = 98 )

4. Has a area of 90ft ( 15 x 6 = 90 )