Written as a simplified polynomial in standard form, what is the result when
(x − 2)² is subtracted from 4x?

Based on the given data, the distance from center to center of two consecutive holes is approximately 25.83 inches.

To solve this problem, we need to divide the length of the metal strip (excluding the 2 inches on each end) by the number of holes to be drilled, and that will give us the distance from center to center of two consecutive holes.

So the length of the metal strip available for the 12 holes is:

3414 - 2 - 2 = 3410 inches

Dividing this length by the number of holes gives us:

3410 ÷ 12 = 284.166666... inches

To find the distance from center to center of two consecutive holes, we need to divide this value by the number of spaces between the holes, which is 11 (since there are 12 holes, but only 11 spaces between them). So:

284.166666... ÷ 11 = 25.833333...

Rounding this to the nearest hundredth of an inch, we get:

25.83 inches (to the nearest hundredth)

Therefore, the distance from center to center of two consecutive holes is approximately 25.83 inches.

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The quotient is -3x²/2 + 7x/4 + 7/8 and the remainder is 23x/8 - 1. The solution has been obtained by using polynomial long division method.

What is polynomial long division?

A formula for multiplying one polynomial by another of the same degree or lower is known as a long division polynomial. Like with long division of numbers, the components of long division of polynomials include the divisor, quotient, dividend, and remainder.

We are given dividend as -3x⁴+5x³+0x²+2x-1 and divisor as 2x²-x.

Using Polynomial Long Division,

Dividing : -3x⁴+5x³+0x²+2x-1 ("Dividend")

By : 2x²-x ("Divisor")

Dividend                   -3x⁴ + 5x³ + 0x² + 2x - 1

- divisor * -3x²/2       -3x⁴ + 3x³/2

Remainder                       + 7x³/2 + 0x² + 2x - 1

- divisor * 7x/4                  + 7x³/2 - 7x²/4

Remainder                                      7x²/4 + 2x - 1

- divisor * 7/8                                   7x²/4 - 7x/8

Remainder                                                  23x/8 - 1

Quotient : -3x²/2 + 7x/4 + 7/8

Remainder: 23x/8 - 1

Hence, the solution has been obtained.

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The probability of getting two twos is 0.003

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

probability = sample space/total outcome

probability of getting two = 1/6

probability of getting two twos = 1/36

getting two two can only 10times = 1/36 ÷ 10

= 10/36 = 0.003 (nearest thousandth)

therefore the probability of getting two twos in 20 rolls is 0.003( nearest thousandth)

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The GCF of the polynomials are

1. for 15x²+18 , the GCF is 3

2. for -18y⁴+6y³+24y² ,the GCF is 6y²

The GCF stands for the “greatest common factor”. The GCF is defined as the largest number that is a factor of two or more numbers. For example, the GCF of 24 and 36 is 12, because the largest factor that is shared by 24 and 36 is 12. 24 and 36 have other factors in common, but 12 is the largest.

The GCF is the highest factor that can be used to divide through 2 or more terms

1. For 15x²+18, 3 is a factor of 15 and 18 and it's the greatest factor, therefore the GCF is 3

2. For -18y⁴+6y³+24y², between 18,6 and 24, 6 is the greatest factor Ang between y⁴ ,y³, y², y² is the greatest factor. Therefore the GCF of the expression is 6y².

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Answer:

Step-by-step explanation:

In the compound interest formula: A = P(1 + r)^t

A represents the amount of money in the account at the end of the term t, including interest.

P represents the initial principal, or the amount of money invested.

r represents the interest rate, usually expressed as a decimal.

t represents the number of time periods over which the interest is compounded.

In the continuously compounded interest formula: A = Pe^(rt)

A represents the amount of money in the account at the end of the term t, including interest.

P represents the initial principal, or the amount of money invested.

r represents the interest rate, usually expressed as a decimal.

t represents the number of time periods over which the interest is compounded.

So the variables in the formulas and their descriptions are:

A: the amount of money in the account at the end of the term t, including interest

P: the initial principal, or the amount of money invested

r: the interest rate, usually expressed as a decimal

t: the number of time periods over which the interest is compounded.

The volume of the given complex structure would be = 56 m³

The structure is made up of the big and small cubes.

The volume of the big cube = length × breadth × width = 7 × 3 × 4 = 84 m³

The volume of the small cube cut out = length * breadth * width = 4 × 7 × (4 - 3) = 28 m³

Volume of the complex figure = 84 m³ - 28 m³ = 56 m³

The volume of the complex figure shown in the diagram is 56 m³.

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The probability that none of them will default 0.0066

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

(a) If 1,000 student loans are made, what is the probability of fewer than 50 defaults?

It's a binomial problem but the large n requires using a normal approximation.

mean = np = 1000*0.07 = 70

std = sqrt(npq) = sqrt(70*0.93) = 8.0685

z(50) = (50-70)/[8.0685] = -2.4788

P(# of defaults < 50) = P(z<-2.4788) = 0.0066

(b) More than 100?

z(100) = (100-70)/8.0685 = 3.7182

P(defaults > 100) = P(z>3.7182) = 0.00010035

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Correct question

The default rate on government-guaranteed student loans at a certaing public 4-year institution is 7% (a) If 1,000 student loans are made, what is the probability of fewer than 50 defaults? (b) More than 100? Show your work carefully.

The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

What is a polynomial ?

A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) multiplied by coefficients.

where n is a non-negative integer (the degree of the polynomial), x is the variable, and (the coefficients of the polynomial). The highest power of x in the expression is n, and this term is called the leading term. The coefficient of the leading term, a_n, is called the leading coefficient.

To find the other linear factors of the polynomial function f(x) = x³ - 4x² - 3x + 18, we can use long division by dividing the polynomial function by (x + 2).

Here's how the long division would look like:

x³ - 4x² - 3x + 18

       ÷ x + 2

__________________________

x² - 6x - 20

             ÷ x + 2

__________________________

x - 22

       ÷ x + 2

__________________________

-20

here -20 is the remainder.

The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

So, the other linear factors are x - 22.

Therefore, The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

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The absolute humidity is 500g/m³, specific humidity = 16.67% and mixing ratio = 20%.

Absolute humidity is a measure of the amount of water vapor in a given volume of air, regardless of the total mass of the air. It is expressed as the mass of water vapor per unit volume of air, typically in units of grams per cubic meter (g/m³).

First, we need to find the mass of dry air in the package. Since the total volume of air is 1m³ and the volume of dry air is 2.5m³, the volume of water vapor is 1 -2.5 = -1.5 m³. This means that the water vapor must have condensed and become liquid water, which we can ignore for the purposes of this problem. So the mass of dry air is:

mass of dry air = density of air * volume of dry air

mass of dry air = 1000g/m³ × 2.5m³

mass of dry air = 2500 g

Now we can use this value, along with the given mass of water vapor, to calculate the three measures of humidity:

       absolute humidity = 500g/ 1m³

       absolute humidity =  500g/m³

       specific humidity = 500g/(2500g + 500g)

       specific humidity = 0.1667 (or 16.67% as a percentage)

       mixing ratio = 500g/2500g

       mixing ratio = 0.2 (or 20% as a percentage)

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The perimeter of the triangle is 23x + 17.

Perimeter is simply the sum of all sides of a polygon.

Given the sides of the triangle;

Side one = 10x + 19

Side two = 12x - 2

Side three = x

To find the perimeter, we add the sides

Perimeter = Side one + Side two + side three

Perimeter = 10x + 19 + 12x - 2 + x

Collect and add like terms

Perimeter = 10x + 12x + x - 2 + 19

Perimeter = 23x - 2 + 19

Perimeter = 23x + 17

Therefore, the perimeter is 23x + 17.

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Answer: To calculate the total cost of the units in beginning inventory for each year, we need to multiply the number of units by the per-unit cost:

Year 1: Cost of units in beginning inventory = 0 units * $13 + $5 + $5 = $0

Year 2: Cost of units in beginning inventory = 1,000 units * ($13 + $5 + $5) = 1,000 * $23 = $23,000

To calculate the total cost of the units produced during each year, we need to multiply the number of units by the per-unit cost:

Year 1: Cost of units produced = 10,000 units * ($13 + $5 + $5) = 10,000 * $23 = $230,000

Year 2: Cost of units produced = 9,000 units * ($13 + $5 + $5) = 9,000 * $23 = $207,000

To calculate the total cost of the units sold during each year, we need to multiply the number of units sold by the per-unit cost:

Year 1: Cost of units sold = 9,000 units * ($13 + $5 + $5 + $6) = 9,000 * $29 = $261,000

Year 2: Cost of units sold = 8,000 units * ($13 + $5 + $5 + $6) = 8,000 * $29 = $232,000

To calculate the total variable manufacturing costs for each year, we need to sum the costs of the units in beginning inventory, units produced, and units sold:

Year 1: Total variable manufacturing costs = $0 + $230,000 + $261,000 = $491,000

Year 2: Total variable manufacturing costs = $23,000 + $207,000 + $232,000 = $462,000

To calculate the total fixed manufacturing overhead costs for each year, we need to add the fixed manufacturing overhead per year to the total variable manufacturing costs:

Year 1: Total manufacturing costs = $491,000 + $90,000 = $581,000

Year 2: Total manufacturing costs = $462,000 + $90,000 = $552,000

To calculate the total variable selling and administrative expenses for each year, we need to multiply the number of units sold by the variable selling and administrative expense per unit:

Year 1: Total variable selling and administrative expenses = 9,000 units * $6 = $54,000

Year 2: Total variable selling and administrative expenses = 8,000 units * $6 = $48,000

To calculate the total selling and administrative expenses for each year, we need to add the fixed selling and administrative expenses per year to the total variable selling and administrative expenses:

Year 1: Total selling and administrative expenses = $54,000 + $61,000 = $115,000

Year 2: Total selling and administrative expenses = $48,000 + $61,000 = $109,000

Step-by-step explanation:

Answer:

2 . of(0)=2/1/2 this is answer number 2

The solution is, option 2 neither linear nor exponential.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

The given function is

x    : -5       -3      -1       1      3

f(x) :8192   512   32      2    18

when we plot this function in the excel we get to know that it a regression as shown in the figure attached  

because value of  lies between (0,1)

which shows regression

therefore it is neither linear nor exponential.

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The equation which is in the quadratic form is 6x⁴ + 7x² - 3 = 0. So Option B is correct.

An equation is quadratic in form if it can be written in the form of ax + bx + c = 0, where a, b, and c are constants and x is the variable.

Among the given equations, we can see that the first, third, and fourth equations are not quadratic in form, since they contain x raised to powers other than 2.

The second equation, 6x⁴ + 7x² - 3 = 0, can be written in quadratic form by making a substitution.

If we let y = x², then we can write the equation as 6y² + 7y - 3 = 0,

which is a quadratic equation in y. Substituting back x² for y,

we get:

6x⁴ + 7x² - 3 = 0

So the second equation is quadratic in form.

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Answer:

Step-by-step explanation:

answer b, trust

The distance at which Allison should stand to catch the ball will be 8.32 m.

What is speed?

Speed of an object is defined as the ratio of distance covered by the object to the time taken by the object to cover that distance. In other words its tell how much times an object takes to cover a particular distance.

Now for the given question:

Emily throw the ball at 30° below the horizontal towards Allison at a speed of 12m/s. So here we will calculate the Horizontal and Vertical components of the speed.

[tex]v_{x}[/tex]=12cos30°=10.4 m/s

[tex]v_{y}[/tex]=12sin30°=6 m/s

Vertical distance between Alice and Emily according the question is 8 m.

s= 8 m.

Now by applying Second equation of motion to calculate time take by ball to move from Emily to Allison.

s=[tex]v_{y}[/tex]×t+[tex]\frac{1}{2}[/tex]×a×[tex]t^{2}[/tex]

4= 6×t+[tex]\frac{1}{2}[/tex]×9.8×[tex]t^{2}[/tex]           (a=9.8 m/[tex]s^{2}[/tex] acc. due to gravity a constant)

By solving above quadratic equation we get

t= 0.8 s

To find horizontal distance

d= [tex]v_{x}[/tex]×t

d=10.4×0.8

d= 8.32 m

Hence Allison should stand at a distance of 8.32 m to catch the ball.

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Answer: interest= 670

Step-by-step explanation:

(1+r)^t*principal

The slope of the line with the points (6, 3) and (12, 6) is equal to 1/2.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (6, 12).

Points on y-axis = (3, 6).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (6 - 3)/(12 - 6)

Slope, m = 3/6

Slope, m = 1/2.

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The solution is,

(a) Output = 37

(b) Input = 9

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

Given

y=5x -3

Solving (a): Output, when input = 8

This means that, we solve for y when x = 8

So, we have:

y=5x -3

 =5*8 -3

 =40 - 3

 = 37

Solving (b): Input, when output = 42

This means that, we solve for x when y = 42

So, we have:

y=5x -3

5x = 42+3

    = 45

Collect like terms

Divide both sides by 5

x = 9

Hence, The solution is,

(a) Output = 37

(b) Input = 9

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The discounted price of the ticket is $198.

The total cost of the ticket with the discount and service fee is $214.33.

A percentage is a ratio or number that may be expressed as a fraction of 100. Moreover, it is denoted by the sign "%."

Given:

The cost of a ticket on an airline is $220.

And Jameson receives a discount of 10%.

To find the discounted price:

The discounted price = 220 - 220 x 10 / 100

The discounted price = $198.

And the service charge is 8.25%.

So, the amount of service charge,

= 198 x 8.25/100

= 16.33

The total cost of a ticket = $198 + $16.33 = $214.33

Therefore, the cost is $214.33.

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Answer:

  1 1/6 cups

Step-by-step explanation:

You want to know the amount of bleach to use with 3 1/2 gallons of water to obtain the same strength as 1 2/3 cups of bleach in 5 gallons of water.

The quantities are proportional, so the amount of bleach (b) will need to be ...

  b/(3 1/2 gal) = (1 2/3 cups)/(5 gal)

Multiplying by 3 1/2 gal, we get ...

  b = (3 1/2)(1 2/3)/5 cups = 1 1/6 cups

Mrs. Hanson should use 1 1/6 cups of bleach in 3 1/2 gallons of water.

Answer:

A. A lively accompaniment

Step-by-step explanation:

B. Dissonant - would most likely result in a eerie mood

C. A slow tempo - could result in melancholy or calm emotions

D. A minor key - could also result in melancholy emotions

The amount after 13 years with a compound interest of 6.9 % is given by the equation A = $ 5,149.69

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount after compound interest be represented as A

Now , the equation will be

The principal amount P = $ 2,100

The rate of interest r = 6.9 %

The number of years b = 13 years

when compounded continuously ,

The compound interest amount A = Pe^rt

Substituting the values in the equation , we get

A = 2,100.00 ( 2.71828 ) ^ ( 0.069 ) ( 13 )

A = 2,100 ( 2.71828 )^( 0.897 )

On further simplification , we get

A = $ 5,149.69

Hence , the amount after 13 years is $ 5,149.69

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On solving the provided question we can say that The average rate of change between x₁ and x₂ and a function f(x), is 10.

The subject of mathematics includes quantities and their variatiοns, equations and related structures, shapes and their locations, and places where they can be fοund. The term "functiοn" refers to the relationship between a set of inputs, each of which has an assοciated output.

A connectiοn between inputs and οutputs in which each input leads tο a single, distinct result is known as a function. Each functiοn is given a domain and a codοmain, or scope. Usually, f is used to denοte functions (x). input is an x. There are fοur main types of functiοns accessible. based οn the following factors: on functiοns, one-to-one functiοns, many-to-one functions, inside functiοns, and on functions.

The average rate of change between x=x and a function f(x)

F(x₂) - F(x₁)/(x₂) - x₁

so,

f(x) = x²

average rate = f(6) - f(4) / 6-4 = 36-16 / 2 = 20/2 = 10

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The measure of <1 is 36 degree.

Complementary angles are those whose combined angle is exactly 90 degrees.

For example, 30 degrees and 60 degrees are complementary angles.

As, the complementary angle have sum of angles are 90 degree.

So, 2x+ 3x= 90

5x = 90

x= 18

Then, the measure of <CBD is 3x = 3(18)= 54 degree.

As, <1 is Complementary angle of <CBD.

So, the measure of <1 = 90- 54 = 36 degree

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If a rectangular room is 2 meters longer than it is wide, and its perimeter is 24 meters then the  dimensions of the room: 7 meter x 5 meter

Perimeter is a mathematical term, it indicates total outer boundary of a figure, we define it only for two dimensional figures.

Perimeter = Sum of length of the all the sides

Let x be the width of the room in meters.

Then the length of the room is 2 meters longer, which means it is x+2 meters.

In this case, we know that the perimeter is 24 meters.

So we can set up an equation:

Perimeter = 2Length + 2Width

Substituting the values we know:

24 = 2(x+2) + 2x

Simplifying the equation:

24 = 2x + 4 + 2x

24 = 4x + 4

20 = 4x

x = 5

So the width of the room is 5 meters, and the length is x+2 = 7 meters.

Therefore, the dimensions of the room are 7 meters by 5 meters.

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Answer:domain is (2, ∞), range is (-∞,∞)

Step-by-step explanation:

domain is (2, ∞) as it aproaches 2 but never reaches and range is (-∞,∞)

Answer: If the lady sells each brouse for 1500 KSH and makes a profit of 150 KSH for each brouse, then the cost price of the brouse is 1500 KSH - 150 KSH = 1350 KSH.

So, the lady pays 1350 KSH for each brouse.

Step-by-step explanation:

The correct solution to the problem is m = 92 and the error made was subtracting 7 from both sides of the equation instead of dividing both sides by 7

Incorrect Work/Solution:

m = the number of messages Nigel sent

644 = 7m

subtract 7 from both sides

644 - 7= 7m - 7

637 = m

Nigel sent an average of 637 messages

each day last week.

Correct solution:

644 = 7m

divide both sides by 7

m = 644/7

m = 92

Therefore, Nigel sent an average of 92 messages

each day last week.

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a) The probability that on a random minute, at least 3 people show up is 0.080.

b) The probability that he will have to wait at least 3 minutes for the next person to show up is 1 - (5/2e) .

c) The probability that he will have to wait at least 3 more minutes for the next person to show up is 2/e.

A probability distribution called the Poisson distribution is used to indicate how frequently an event is likely to happen over a given timeframe.

Given:

a)  Let X be the number of people who show up during a random minute.

Then X follows a Poisson distribution with parameter λ = 1.

The probability of at least 3 people showing up in a random minute is:

P(X ≥ 3) = 1 - P(X < 3)

= 1 - (P(X = 0) + P(X = 1) + P(X = 2))

We can use the Poisson probability mass function to find P(X = k) for k = 0, 1, 2:

P(X = k) = ([tex]e^{-\lambda[/tex]) x ([tex]\lambda^k[/tex]) / k!

Plugging in λ = 1, we get:

P(X = 0) = [tex]e^{-1[/tex] / 0! = 1/e

P(X = 1) = [tex]e^{-1[/tex] x 1 / 1! = 1/e

P(X = 2) = [tex]e^{-1[/tex] x 1 / 2! = 1/2e

So, the probability of at least 3 people showing up in a random minute is:

= 1 - (P(X = 0) + P(X = 1) + P(X = 2))

= 1 - (1/e + 1/e + 1/2e)

= 1 - (2/e + 1/2e)

= 1 - (5/2e)

= 0.080

b) The probability of having to wait at least 3 minutes for the next person to show up

= 1 - P(X <= 2)

= 1 - (5/2e)

c) Now,

P(X ≤ 1)

= P(X = 0) + P(X = 1)

= (1/e) + (1/e)

= 2/e

So, the probability of having to wait at least 3 more minutes for the next person to show up

= 1 - (2/e)

= 1 - P(X <= 1).

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The equation of the plane containing the line x = 2 + t, y = 4 − t, z = 3 − 3t and is parallel to the plane 5x + 2y + z = 3 is 5x + 2y + z = 21

What is a plane?

Any flat, three-dimensional, infinitely long surface is considered to be a plane. It can alternatively be thought of as the two-dimensional equivalent of a point with zero dimensions, a line with one dimension, and a space with three dimensions.

Given that, a plane is containing the line x = 2 + t, y = 4 − t, z = 3 − 3t and is parallel to the plane 5x + 2y + z = 3

Any  plan e parallel to the plane 5x + 2y + z = 3 , should be in the form of 5x + 2y + z = k

Now, this plane should contain the line mentioned above

On substituting the terms,

5(2 + t) + 2(4 - t) + (3 - 3t) = k

10 + 5t + 8 - 2t + 3 -3t = k

21 = k

Therefore, The equation of the required plane is 5x + 2y + z = 21

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