Define a scheme procedure that takes a set (a list of distinct elements) and generates a list of all subsets of the set. For example, (subsets '(a b c )) returns ((a b c) (b c) (a c) (c) (a b) (b) (a) ()). Then, manually trace your procedure with the provided example. Please study provided examples in the lecture notes to learn how you should manually trace our procedure

Other roots of the given trinomial equation apart from (x -1) will be:

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given a trinomial equation x³ + x²-6x +4 that has a root (x + 1)

Let P(x) = x³ + x²-6x +4

It is given that ( x - 1 ) is one of the factor of p(x)

On dividing p(x) by (x - 1), we get:

P(x) = (x- 1) (x² +2x -1)

For the quotient of the factor we will use the quadratic formula

(x² +2x -1) = 0

From quadratic formula,

x = 1/2a(-b ± √(b² - 4ac))

x = 1/2(-2 ±√(4 +4)

x = -1 ± √2

Thus,

Other roots of the given trinomial equation apart from (x -1) will be:

x = -1 -√2

x = -1 + √2

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Complete question:

if (x - 1) is a factor of x³ + x²-6x +4· find the other two factors​

The probability that a person from the survey who has a tablet also has a laptop is 5.8%.

To calculate this, we can use conditional probability. We know that 62% of respondents have a tablet, and 12% of the respondents who have a laptop also have a tablet. So, the probability that a respondent has a laptop given that they have a tablet can be calculated as follows:

We know that P(laptop and tablet) = 0.12 (since 12% of laptop owners also have a tablet), and P(table) = 0.62 (since 62% of respondents have a tablet). So, plugging these values into the formula gives:

However, this is the probability that a person who has a tablet also has a laptop. The question asks for the probability that a person from the survey who has a tablet also has a laptop, which means we need to consider the overall probability of having a laptop, regardless of whether or not they have a tablet. This can be calculated as follows:

P(laptop) = 0.3

So, the probability that a person from the survey who has a tablet also has a laptop, given that they have a laptop, is:

P(laptop|tablet and laptop) = P(laptop and tablet) / P(laptop) = 0.12 / 0.3 = 0.4 or 5.8%

Therefore, the correct answer is 5.8%.

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Answer:

Step-by-step explanation: first if you do x/32.5 ≤ 117 = 3802.5 and also we know that 1 mile= 32.5, so if you take 32.5 * 117 it also equals 3802.5

so it will take him a minimum of 3802.5 gallons to drive 117 miles

Dakota would need at least 3.6 gallons of gasoline to drive 117 miles to his brother's house.

A statement that compares two numbers or expressions using an inequality symbol, such as (less than), > (greater than), (less than or equal to), or, is known as an inequality in mathematics (greater than or equal to).

Let x be the volume of gasoline required for Dakota to travel 117 miles to his brother's home. The minimum value of x can be calculated using the inequality shown below:

x ≥ 117 / 32.5

Here, we calculate the bare minimum amount of gasoline Dakota would require to travel 117 miles by dividing the whole distance (117 miles) by the miles per gallon (32.5 miles/gallon).

The inequality is reduced to: x ≥ 3.6

Dakota would therefore require 3.6 gallons of fuel to travel 117 miles to his brother's house.

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This person has walked a total of 22 miles. The total displacement vector for this walk is 10.06 miles at an angle of 12.58°. If this person walked straight home, they'd have to walk 10.06 miles.

To find the total displacement vector for this walk, we can use the Pythagorean Theorem to find the magnitude of the displacement vector and the direction of the displacement vector.

First, let's find the magnitude of the displacement vector:

d = √((Δx)² + (Δy)²)

Where Δx is the change in the x-direction and Δy is the change in the y-direction.

Δx = 5 + 4cos(45°) + 0 + 3cos(225°) + 4 = 9.83 miles
Δy = 0 + 4sin(45°) + 6 + 3sin(225°) + 0 = 2.17 miles

d = √((9.83)² + (2.17)²) = √(96.58 + 4.71) = √(101.29) = 10.06 miles

So, the magnitude of the displacement vector is 10.06 miles.

Next, let's find the direction of the displacement vector:

θ = tan⁻¹(Δy/Δx) = tan⁻¹(2.17/9.83) = 12.58°

So, the direction of the displacement vector is 12.58°.

Therefore, the total displacement vector for this walk is 10.06 miles at an angle of 12.58°.

If this person walked straight home, they'd have to walk 10.06 miles.

This person has walked a total of 22 miles. The total displacement vector for this walk is 10.06 miles at an angle of 12.58°. If this person walked straight home, they'd have to walk 10.06 miles.

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The average number of fruit flavored pieces you get in a bowl is 18.

To find the number of fruit flavored pieces you get in a bowl, you can calculate the average of the fruit flavored pieces in the five bowls you poured.

Here's how:

1: Add the number of fruit flavored pieces in each bowl: 3 + 23 + 20 + 23 + 21 = 90

2: Divide the total number of fruit flavored pieces by the number of bowls: 90 / 5 = 18

Therefore, the average number of fruit flavored pieces you get in a bowl is 18.

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If today it was sunny in the morning and raining in the afternoon, and Laura traveled a total of 24 km in 40 minutes, then she is calculated to have rode the electric scooter for  24 minutes in the afternoon.

Let's assume that Laura rode her scooter for x minutes in the morning and for (40 - x) minutes in the afternoon.

In the morning, she traveled a distance of 45 × (x/60) km.

In the afternoon, she traveled a distance of 30 × ((40-x)/60) km.

The total distance traveled is 24 km, so we can set up the equation:

45 × (x/60) + 30 × ((40-x)/60) = 24

Multiplying both sides by 60, we get:

45x + 30(40-x) = 1440

Simplifying and solving for x, we get:

15x + 1200 = 1440

15x = 240

x = 16

Therefore, Laura rode her scooter for (40-16) = 24 minutes in the afternoon.

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The question is :

Laura rides an electric scooter at 45 km/h when it is not raining and at 30 km/h when it is raining. Today it was sunny in the morning and raining in the afternoon, and she traveled a total of 24 km in 40 minutes. How many minutes did she ride in the afternoon?

Slope of PR = Slope of SU = rise / run = -3/2

The slope of a line is the ratio of the rise over the run, which is m = change in y / change in x.

To prove that the slope of line segment PR and the slope of line segment SU are equal, find the slope of each of the line given that are similar triangles:

Slope of PR = rise / run = PQ/QR = -3/2

Slope of SU = rise / run = ST/TU = -6/4 = - 3/2

Therefore, both line segments have the same slope of -3/2.

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The solution to the equation [tex](x+2)^{(1)/(2)}=x-4[/tex] is x = 2.

To solve this equation, we need to square both sides to eliminate the radical. This gives us [tex]x+2 = (x-4)^2[/tex]. Expanding the right side of the equation and simplifying, we get [tex]x^2 - 11x + 20 = 0[/tex]. Factoring this quadratic equation, we get [tex](x-1)(x-20) = 0[/tex], so the solutions are x=1 and x=20.

However, we must check if these solutions are extraneous, meaning they do not satisfy the original equation. Checking x=1, we get [tex](1+2)^{(1)/(2)}=1-4[/tex], which simplifies to [tex]3^{(1)/(2)}=-3[/tex], a contradiction since the square root of a positive number cannot be negative. Therefore, x=1 is an extraneous solution.

Checking x=20, we get [tex](20+2)^{(1)/(2)}=20-4[/tex], which simplifies to [tex]22^{(1)/(2)}=16[/tex], or [tex]22 = 16^2[/tex], which is true. Therefore, x=20 is a valid solution.

In conclusion, the only solution to the equation is x=2, and the solution x=1 is extraneous.

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The product of 2/3 and 3/5 is 2/5    

To represent a fraction on a grid, we need to divide the grid into equal parts based on the denominator of the fraction, and then shade in a number of those parts based on the numerator of the fraction.

Here we have

=> 2/3 × 3/5

To solve 2/3 × 3/5, we multiply the numerators together and the denominators together

=> [ 2/3 × 3/5 ] = 6/15

=> [ 2/3 × 3/5 ] = 2/5        

This multiplication can be represented as given in the picture

Therefore,

The product of 2/3 and 3/5 is 2/5    

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Based on the properties of rectangles, the angles and the side lengths are KN = 11 and NLK = 32

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

JN = 2x + 7, LN = 6x - 1

NKJ = 58 degrees

The diagonals or a rectangle are equal

So, we have

2x + 7 = 6x - 1

Evaluate the like terms

4x = 8

Divide

x = 2

So, we have

KN = 2 * 2 + 7

KN = 11

Adjacent angles in this case add up to 90 degrees

This gives

NLK = 90 - 58

Evaluate

NLK = 32

Hence, the measure of the angle is 32 degrees

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The slope-intercept form of the equation of the line that has a slope of -1/6 and passes through the point (8,0) is y = -1/6x + 4/3.

To find the slope-intercept form of the equation of the line that has the given slope m and passes through the given point, we can use the point-slope form of a linear equation and then rearrange it to the slope-intercept form.

The point-slope form of a linear equation is given by:

y - y₁ = m(x - x₁)

Where m is the slope and (x₁, y₁) is the point that the line passes through.

In this case, m = -1/6 and the point is (8, 0).

Plugging these values into the point-slope form, we get:

y - 0 = -1/6(x - 8)

Simplifying and rearranging to the slope-intercept form, we get:

y = -1/6x + 8/6

y = -1/6x + 4/3

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The supremum of the first subset does not exist, and the supremum of the second subset is 1.

The supremum of a subset of a set is the smallest element in the set that is greater than or equal to all elements in the subset. In other words, it is the least upper bound of the subset.

For the first subset {x^2+11 : x∈R}, the supremum does not exist. This is because the function x^2+11 is always increasing as x increases, so there is no smallest element that is greater than or equal to all elements in the subset.

For the second subset {cosx : x∈R}, the supremum is 1. This is because the cosine function has a range of [-1, 1], meaning that the largest value it can take on is 1. Therefore, the smallest element in the set R that is greater than or equal to all elements in the subset {cosx : x∈R} is 1.

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The values of the variables are y =50 and x = 130

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

The isosceles trapezoid

An isosceles trapezoid is a quadrilateral with two parallel sides of equal length and two non-parallel sides of unequal length.

This means that the base angles are congruent

Using the above as a guide, we have the following for the variable y

y = 50

Solving further, we have the following equation for variable x

x + 50 = 180

Evaluate the equation

x = 130

Hence, the value of x is 130

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Answer:

Aquí hay tres situaciones en las que se hace necesario el uso de números negativos:

Temperaturas: Las temperaturas pueden ser positivas o negativas, dependiendo de si estamos midiendo la temperatura por encima o por debajo del punto de congelación del agua. Por ejemplo, si la temperatura es de -10°C, significa que hace 10 grados bajo cero.

Deudas: Cuando una persona toma un préstamo o usa una tarjeta de crédito, puede acumular una deuda que debe ser pagada en el futuro. Esta deuda se representa con un número negativo, ya que representa el dinero que se debe.

Altitud: Cuando se mide la altitud de un lugar, puede ser por encima o por debajo del nivel del mar. Si la altitud es por debajo del nivel del mar, se representa con un número negativo. Por ejemplo, la altitud del Mar Muerto es de aproximadamente -430 metros.

The midpoint is   [(Yx + Fx)/2, (Yy + Fy)/2]

The distance between 2 points in the map is √[(FVx - CSx)^2 + (FVy - CSy)^2]

To determine the distance between two points on a map, we can use the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]

In this case, we are trying to find the distance between Clear Springs (x1, y1) and Finger Valley (x2, y2). Plug in the coordinates for each point into the formula and solve for d.
d = √[(x2 - x1)^2 + (y2 - y1)^2]

= √[(Finger Valley x - Clear Springs x)^2 + (Finger Valley y - Clear Springs y)^2]
= √[(FVx - CSx)^2 + (FVy - CSy)^2]
Round the answer to one decimal place to get the distance between the two points.

To find the coordinates of the meeting point between you and your friends, we can use the midpoint formula:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]

In this case, we are trying to find the midpoint between your location (x1, y1) and your friends' location (x2, y2). Plug in the coordinates for each point into the formula and solve for the midpoint.
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
= [(Your x + Friends' x)/2, (Your y + Friends' y)/2]
= [(Yx + Fx)/2, (Yy + Fy)/2]
Round the coordinates to one decimal place to get the midpoint, which is the meeting point between you and your friends.'

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let's convert all mixed fractions to improper fractions, let's add all berries and then see how many times 1/2 go into that sum or namely division.

[tex]\stackrel{mixed}{3\frac{1}{4}}\implies \cfrac{3\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{13}{4}} ~\hfill \stackrel{mixed}{4\frac{1}{2}} \implies \cfrac{4\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{9}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ strawberries }{\cfrac{13}{4}}~~ + ~~\stackrel{ blueberries }{\cfrac{9}{2}}\implies \cfrac{(1)13~~ + ~~(2)9}{\underset{\textit{using this LCD}}{4}}\implies \cfrac{13+18}{4}\implies \cfrac{31}{4} \\\\\\ \stackrel{\textit{now let's divide that sum by }\frac{1}{2}}{\cfrac{31}{4}\div \cfrac{1}{2}}\implies \cfrac{31}{4}\cdot \cfrac{2}{1}\implies \cfrac{31}{2}\implies {\Large \begin{array}{llll} 15\frac{1}{2} \end{array}}[/tex]

Answer:

Tamara has $31.01 left

Step-by-step explanation:

Tamara has $70

Dress - $10

Drink - $4.99

Necklace - $20

Snack - $4

Add all of these costs up then subtract them by 70

10 + 4.99 + 20 + 4 = 38.99

70 - 38.99 = 31.01

[tex]70 - (10+4.99+4+20) = 70 - 38.99 = \$ \ 31.01[/tex]

The second column of matrix B can be calculated by solving the equation where A and B are matrices of size (2,3). The second column of B is
[tex][b_21, b_22] = [(1 - a_11b_11 - a_13b_31)/a_12, (-2 - a_11b_12 - a_13b_32)/a_12][/tex]

First, we must transpose both A and B:
[tex]A^t[/tex]= [tex][a_11, a_12, a_13][a_21, a_22, a_23][/tex]

[tex]B^t[/tex] = [tex][b_11, b_21][b_12, b_22][b_13, b_23][/tex]
The second column of B.

[tex]B^tA^t[/tex] = [tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]
[1, -2] = [tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]


Since we have two equations and two unknowns, we can solve for the elements of the second column of B.
Solving for [tex]b_21[/tex]:
[tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]
Solving for [tex]b_22[/tex]:
[tex]-2 = a_11b_12 + a_12b_22 + a_13b_32b_22 = (-2 - a_11b_12 - a_13b_32)/a_12[/tex]

Therefore, the second column of B is:
[tex][b_21, b_22] = [(1 - a_11b_11 - a_13b_31)/a_12, (-2 - a_11b_12 - a_13b_32)/a_12][/tex]

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To find all zeros for the function f(x) = x3 - 12x? - 13x + 24.

To find all zeros for the function f(x) = x3 - 12x? - 13x + 24, we can use the Rational Root Theorem to find the list of possible rational zeros.

The Rational Root Theorem states that if a polynomial f(x) = anxn + an-1xn-1 + ... + a1x + a0 has integer coefficients, then any rational zero of f(x) must be of the form p/q, where p is a factor of the constant term a0 and q is a factor of the leading coefficient an.

In this case, the constant term is 24 and the leading coefficient is 1. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 1 are 1. Therefore, the possible rational zeros are:

±1/1, ±2/1, ±3/1, ±4/1, ±6/1, ±8/1, ±12/1, ±24/1

Simplifying these fractions gives us the list of possible rational zeros:

±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

Now, we can use synthetic division to test each of these possible zeros until we find one that gives us a remainder of 0. Once we find a zero, we can factor it out of the polynomial and continue the process with the remaining polynomial until we have found all the zeros.

For example, if we test the possible zero 2, we get:

2 | 1 -12 -13 24
| 2 -20 -66
-----------------
1 -10 -33 -42

Since the remainder is not 0, 2 is not a zero of the function. We can continue testing the other possible zeros until we find all the zeros of the function.

Once we have found all the zeros, we can write them as a list. For example, if the zeros are 3, -2, and 4, we would write:

The zeros of the function are 3, -2, and 4.

Therefore, to find all zeros for the function f(x) = x3 - 12x? - 13x + 24, we can use the Rational Root Theorem to find the list of possible rational zeros, and then use synthetic division to test each possible zero until we find all the zeros of the function.

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Using the subtraction, the result of (29v)−(−13v+59) is 42v - 59

The distributive property is a fundamental property of arithmetic and algebra that involves the distribution of a factor across a sum or difference of two or more terms. The property states that when you multiply a number or term by a sum or difference in parentheses, you can distribute the multiplication to each term inside the parentheses and then simplify.

To subtract (29v)−(−13v+59), we first need to distribute the negative sign in front of the parentheses, which will change the signs of each term inside. So, we have

= 29v + 13v - 59

Then, we can combine the like terms, which in this case are the two terms with the variable v. We add the coefficients (numbers in front of v) to get

= 42v - 59

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we can reject the null hypothesis

Null Hypothesis (H₀): μ ≥ 50

Alternative Hypothesis (H₁): μ < 50

Assumptions:
- A normal distribution for the population of LCBO stores
- A random sample of 20 stores
- A significance level of 0.05

Critical-value approach:

First, calculate the test statistic using the formula:

Test statistic = (Sample Mean - Population Mean) / (Standard Deviation / √Sample Size)

= (41.3 - 50) / (12.2 / √20)

= -2.6

Then, compare this test statistic to the critical-value.

The critical-value is the value that divides the acceptance and rejection regions of the distribution. The critical-value for a two-tailed test with a significance level of 0.05 is ±1.96.

Since -2.6 is less than -1.96, the test statistic falls into the rejection region and we reject the null hypothesis.

p-value approach:

Calculate the p-value using the formula:

p-value = 1 - CDF(test statistic)

Where CDF is the cumulative distribution function.

= 1 - CDF(-2.6)

= 0.004

Since 0.004 is less than 0.05, we reject the null hypothesis.

In conclusion, based on the critical-value approach and the p-value approach, we can reject the null hypothesis and conclude that the population mean sales increase is less than 50 cases.

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(a) (i) The function f(x) - g(x) is  √(1-x).

    (ii) The function f(x) - g(x) is -x -1   The domain for f-g is all real numbers.
(b) (i) The function  (f-g)(1) = -2

    (ii) The function (f-g)(2) = √(-1). Therefore, (1/2)g(f(2)) is undefined.

(a)

(i) The function f(x) is already given as f(x) = √(1-x). The domain of f is all real numbers for which 1-x is non-negative. Therefore, the domain of f is x ≤ 1.

(ii) The function f-g can be found by subtracting g from f, which gives: f-g = (V1 - x) - (2 + x) = -x - 1. The domain of f-g is the same as the domain of f, which is x ≤ 1.

(b)

(i) To evaluate (f-g)(1), we substitute x = 1 into the expression for f-g, which gives: (f-g)(1) = -(1) - 1 = -2.

(ii) To evaluate (1/2)g(f(2)), we first find f(2) by substituting x = 2 into the expression for f: f(2) = √(1-2) = √(-1). Since the square root of a negative number is not a real number, f(2) is undefined. Therefore, (1/2)g(f(2)) is also undefined.

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If the length of the rectangle is represented by x, then the height and width can be represented by the factors a and b, respectively. Therefore, the expression for the height and width in terms of the length can be written as:

Height = a * x

Width = b * x

These expressions can be used to find the height and width of the rectangle if the length and the factors are known.

For example, if the length is 10 and the factors are 2 and 3, then the height would be 2 * 10 = 20 and the width would be 3 * 10 = 30.

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Answer:

  x=4.3m

Step-by-step explanation:

It is made up by six graphics.

Two triangles=1/2*x*5.6*2=5.6x

Base rectangular: 11.3x

Back rectangular: 11.3*5.6=63.28

Front rectangular:11.3*7.1=80.23

Add together: 5.6x+11.3x+63.28+80.23=216.18

                      16.9x=72.67

                            x=4.3m

Answer: You have to simplify divide by x

Step-by-step explanation:

Answer:

Step-by-step explanation:

4.  16 players enter the tournament.  f(0) = 16(1/2)° = 16

This is the value of y when x=0

5.  After 4 rounds, 1 player is left.  f(4) = 16(1/2)⁴ = 1

6.  Rate of change = Δy/Δx = (4-8) / (2-1) = -4

f(1) = 16(1/2)¹ = 8

f(2) = 16(1/2)² = 4

The average rate of change between rounds 1 and 2 is 4, meaning 4 players are eliminated.

1.3567% is the average percent change in population in California from 2000-2009.

The term "population" is frequently used to describe the total number of people living in a particular location. To estimate the number of the residents within a certain territory, governments conduct censuses.

Population is referred to a group of people who share some established characteristics, such as region, race, culture, nationality, or religion, in sociology or population geography. The social science of demography involves the statistical analysis of populations.

average percent change in population =1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93/9

= 1.3567%

Therefore, 1.3567% is the average percent change in population in California from 2000-2009.

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The name of the formula is a polynomial of degree 25 and is expressed as y = ax25 + bx24 + cx23 + dx22 + ex21 + fx20 + gx19 + hx18 + ix17 + jx16 + kx15 + lx14 + mx13 + nx12 + ox11 + px10 + qx9 + rx8 + sx7 + tx6 + ux5 + vx4 + wx3 + xx2 + yx + z

The formula you have provided is called a polynomial equation. It is a type of algebraic equation that consists of a sum of several terms, each term consisting of a constant coefficient multiplied by a variable raised to a non-negative integer power. In this case, the variable is x and the coefficients are a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, and z. The highest power of the variable in this equation is 25, which means it is a 25th degree polynomial equation.

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Answer:

3

Step-by-step explanation:

7.2<x+4.2

3<x
x>3
the graph would be

The greatest number is 3,600, since it is larger than all the other numbers when expressed in standard notation. Option D is correct.

Scientific notation is a way of expressing very large or very small numbers in a concise and standardized format using powers of ten. In scientific notation, a number is expressed as the product of a coefficient and a power of ten. The coefficient is a number between 1 and 10, and the power of ten indicates how many places the decimal point should be moved.

Standard notation, also known as decimal notation, is a way of expressing numbers using a sequence of digits, where each digit represents a different power of ten. In standard notation, the digits to the left of the decimal point represent the whole part of the number, and the digits to the right of the decimal point represent the fractional part of the number.

To compare these numbers, we need to express them in the same units. We can do this by converting the numbers in scientific notation to standard notation: 2.3 x 10 = 23,

8.6 x 10 = 86

1.2 x 10 = 12

3,600 = 3,600

Hence, D. 3,600 is the correct option.

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