For one-pair poker hands, why is the number of denominations for the three single cards (12 3) rather than (12 1) (11 1) (10 1)?

The population of a large US city is 1.70321 × 10⁶ in Scientific Notation.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It may be referred to as scientific form or standard index form.

Given that, the population of a large US city is 1,703,210. we need to show this number in Scientific Notation.

We know that, a number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

The number is written in two parts:

The digits, with the decimal point placed after the first digit, followed by × 10 to a power that puts the decimal point where it should be

Therefore,

1,703,210 = 1.70321 × 10⁶

Hence, the population of a large US city is 1.70321 × 10⁶ in Scientific Notation.

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Let G be the number of general seats sold.

Let R be the number of reserved seats sold.

The total number of seats sold is G + R = 1139

Since general seats costs $2 each, 2G is the total receipts from general tickets sales.

Since reserve seats costs $3.50 each, 3.5R is the total receipts from reserved ticket sales.

The total receipts is 2G + 3.5R = 2716

We now have two equations in two unknowns and can solve for G and R.

Freeda's weekly take home pay based on the 48 hours a week Freeda works with an hourly rate of $13.75 and an over time rate of a time and a half, obtained by finding the difference between the sum of earnings and the sum of deduction is $813.75

A salary rate is the amount received regular for a specified period.

The number of hours worked a week = 48 hours

Number of hours considered overtime = Time over 40 hours

Amount earned for normal working hours = $13.75 per hour

Amount she earns as bonus per week = $125

The deductions per week are;

FICA

Federal income tax = $5.50

State income tax = $2.75

401K = $10.00

Insurance = $8.00

Weekly take home (net) pay = Total weekly earnings - Total weekly deductions

Number of overtime hours Freeda works each week = 48 - 40 = 8

Freeda works 8 hours overtime each week

Her weekly earnings = 40 × 13.75 + 8 × 1.5 × 13.75 + 125 = 840

Freeda's weekly earning = $840

Weekly deductions = 5.5 + 2.75 + 10.00 + 8 = 26.25

Weekly take home (net) pay = $840 - $26.25 = $813.75

Freeda's weekly take home pay is $813.75

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The formula for the volume of a rectangular box is V = l × w × h, where l is the length, w is the width, and h is the height. Since the density is given as 1 g/cm³, the mass of the object is equal to its volume in cubic centimeters (cc):

mass = volume × density

728 g = V × 1 g/cm³

V = 728 cm³

We are given the length and width of the box, so we can substitute these values into the formula for volume:

V = l × w × h

728 cm³ = 20.8 cm × 7 cm × h

Simplifying the right-hand side:

728 cm³ = 145.6 cm² × h

Dividing both sides by 145.6 cm²:

h = 728 cm³ ÷ 145.6 cm²

h = 5 cm

Therefore, the height of the box is 5 cm.

The probability of finding gold in that land is 0.8.

Given is that a mining company buys a piece of land in Peru. The studies determined the following prior probabilities -

We can write the probability of finding gold in that land as -

P{E} = P(find good quality gold) + P(find poor quality gold)=0.30

P{E} = 0.5 + 0.3

P{E} = 0.8

Therefore, the probability of finding gold in that land is 0.8.

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{QUESTION IN ENGLISH -

A mining company buys a piece of land in

Peru. The studies determined the following

prior probabilities:

to.

P(find good quality gold)=0.50

b. P(find poor quality gold)=0.30

C. P(find no gold)=0.20

Calculate the probability of finding gold in that}

Answer:

D) 9x + 126 = 180

Step-by-step explanation:

We know

The (9x) angle combined with the 126 degrees angle must make 180 degrees. Looking at all the options, we see that D is the only reasonable answer.

Yes, Dimitri has enough gas to drive from Cincinnati to Toledo. To calculate this, we can multiply the fuel efficiency by the amount of gas in the tank.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.

Fuel efficiency: 21 miles per gallon

Gas in the tank: 12 gallons

So, the total distance that Dimitri can drive is:

= 21 miles per gallon x 12 gallons

= 252 miles

Since the distance from Cincinnati to Toledo is 202.4 miles, and the total distance that Dimitri can drive is 252 miles, we can conclude that he has enough gas to make the trip.

Dimensional analysis:

= 21 miles/gallon x 12 gallons

= 252 miles (correct dimensions)

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Answer:

c

Step-by-step explanation:

The colonists thought of King George III as a tyrant, which is evident when looking at the founding documents of the United States and the political parties. The Constitution created separation of powers so nobody would be able to become a tyrant or dictator. There are checks and balances to keep people from gaining too much power and overtaking the government. When looking into the political parties later on, there were the Anti-federalists, who did not want a strong central government because they did not want another King George, who they just got out of a war with.

Answer: The actual roots of f(x) = 2x² + 2x - 24 are -3 and 4.

Step-by-step explanation:

The discontinuity of the function is removed and the value of the function at 1 after removing the discontinuity is 8.

What is meant by a discontinuity in a function?

In algebra, a discontinuous function is one that has a point at which the function is not defined, at which the left-hand limit and right-hand limit are equal but not equal to the value of the function at that point, or at which the limit of the function does not exist. If a function in algebra is not continuous, it is referred to as a discontinuous function. A discontinuous function has a discontinuous curve, just like a continuous function does.

Given f(x) = 2x²+4x-6 / (x-1)  

This function has a  discontinuity at 1 because when we substitute x =1, the denominator becomes 0 and the function becomes undefined.

But this discontinuity is removable and can be done as shown:

We can factorize the numerator as below:

2x²+4x-6 = 2x²+6x - 2x -6 = 2x(x+3) -2(x+3) = (2x - 2)(x+3) = 2(x-1)(x+3)

Now when we substitute the factorized form of the numerator in the function. Then,

f(x) =  2(x-1)(x+3) / (x-1)

(x-1) can be cancelled from both the numerator and denominator. So the discontinuity is removed.

f(x) = 2(x+3)

Now f(1) = 2 * (1+3) = 8

Now the function is continuous at 1.

Therefore the value of the function at 1 after removing the discontinuity is 8.

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Answer:

x ≤ - 5 or x ≥ 7

or, in interval notation

[ - ∞, -5] ∪ [7, ∞]

Step-by-step explanation:

From the question we get the following two inequalities
x is at most -5 ==>     x ≤ -5

x is at least 7 ==>       x ≥ 7 which can be rewritten as 7 ≤ x

This can be written as
x ≤ - 5 or x ≥ 7

In interval notation this would be
[ - ∞, -5] ∪ [7, ∞]

On the number line this would be represented as shown in the figure

Answer:

1.48

1 minute and 48 seconds

Answer: 25%

Step-by-step explanation:

The answer is 25%. This is calculated by dividing the number of grams of carbohydrates from whole grains (55 grams) by the total number of carbohydrates eaten (220 grams). This gives 0.25, which can be expressed as 25%. Therefore, Osvoldo consumed 25% of his carbohydrates from whole grains today.

Answer:

Osvoldo only got 25% of his grams of carbohydrates from whole grains today, which is below his goal of 30%

Step-by-step explanation:

To find the percentage of Osvoldo's carbohydrates that came from whole grains, we can use the formula:

percentage = (part/whole) x 100%

where "part" is the number of grams from whole grains, and "whole" is the total number of grams of carbohydrates. So we have:

percentage = (55/220) x 100%

percentage = 0.25 x 100%

percentage = 25%

Therefore, Osvoldo only got 25% of his grams of carbohydrates from whole grains today, which is below his goal of 30%.

The magnitude spectrum of Fourier coefficients a[n] = 4 sin(nπ/3) is: |C[k]| = 0 so the phase spectrum is undefined. Fourier coefficients of x[n] = cos(2nπ/3) + sin(2nπ/5) for all other values of k, C[k] = 0, so the magnitude and phase spectra are zero. The Fourier coefficient for  cos(x) sin(y) = 1/2 (sin(x + y) – sin(x – y)) C[k] is zero when k is not equal to ±2/3 and ±2/5.

To compute the Fourier coefficients of a[n] = 4 sin(nπ/3), we use the formula:

C[k] = (1/N) * Σ[n=0 to N-1] a[n] e^(-j2πkn/N)

where N is the period of the signal (in this case, N = 6 since sin(nπ/3) has a period of 6), and k is the frequency index.

For k = 0, we have:

C[0] = (1/6) * Σ[n=0 to 5] 4 sin(nπ/3) = (4/6) * (sin(0) + sin(π/3) + sin(2π/3) + sin(π) + sin(4π/3) + sin(5π/3))

C[0] = (4/6) * (0 + √3/2 + √3/2 + 0 - √3/2 - √3/2) = 0

For k = ±1, we have:

C[1] = (1/6) * Σ[n=0 to 5] 4 sin(nπ/3) e^(-j2πn/6) = (4/6) * (sin(0) - sin(π/3) - sin(2π/3) + sin(π) + sin(4π/3) - sin(5π/3))

C[1] = (4/6) * (0 - √3/2 + √3/2 + 0 + √3/2 - (-√3/2)) = 0

C[-1] = (1/6) * Σ[n=0 to 5] 4 sin(nπ/3) e^(j2πn/6) = (4/6) * (sin(0) - sin(π/3) - sin(2π/3) + sin(π) + sin(4π/3) - sin(5π/3))

C[-1] = (4/6) * (0 - √3/2 + √3/2 + 0 + √3/2 - (-√3/2)) = 0

For all other values of k, we have C[k] = 0. Therefore, the Fourier series of a[n] is:

a[n] = 0

The magnitude spectrum is:

|C[k]| = 0

The phase spectrum is undefined.

To compute the Fourier coefficients of x[n] = cos(2nπ/3) + sin(2nπ/5), we use the formula:

C[k] = (1/N) * Σ[n=0 to N-1] x[n] e^(-j2πkn/N)

where N is the period of the signal (in this case, N = lcm(3, 5) = 15 since both cos(2nπ/3) and sin(2nπ/5) have periods of 3 and 5, respectively), and k is the frequency index.

For k = 0, we have:

C[0] = (1/15) * Σ[n=0 to 14] (cos(2nπ/3) + sin(2nπ/5)) = (1/15) * (5 + 0 - 5 + 0 + 5 + 0 - 5 + 0 + 5 + 0 - 5 + 0 + 5 + 0 - 5 + 0 + 5) = 5/3

To compute C[k] for k ≠ 0 and k ≠ 5, we can use the trigonometric identity:

cos(x) sin(y) = 1/2 (sin(x + y) – sin(x – y))

Let x = 2kπ/3 and y = 2nπ/5, then:

cos(2kπ/3) sin(2nπ/5) = 1/2 (sin(2kπ/3 + 2nπ/5) – sin(2kπ/3 – 2nπ/5))

= 1/2 (sin(10knπ/15 + 6kπ/15) – sin(10knπ/15 - 2kπ/15))

= 1/2 (sin((2k + 3n)π/3) – sin((2k - n)π/3))

The first term is zero when (2k + 3n) is an odd multiple of 3, and the second term is zero when (2k - n) is an odd multiple of 3. Therefore, C[k] = 0 when k + 3n is odd or k - n is odd.

For k = 3n, we have:

C[3n] = (1/15) * Σ[m=0 to 14] (cos(2mπ/3) sin(2nπ/5))

= (1/30) * Σ[m=0 to 14] (sin((2m + 3n)π/3) – sin((2m - n)π/3))

= (1/30) * (sin(5nπ/3) – sin(nπ/3) + sin(7nπ/3) – sin(5nπ/3) + sin(9nπ/3) – sin(7nπ/3) + sin(11nπ/3) – sin(9nπ/3) + sin(13nπ/3) – sin(11nπ/3) + sin(15nπ/3) – sin(13nπ/3) + sin(17nπ/3) – sin(15nπ/3) + sin(19nπ/3) – sin(17nπ/3))

= (1/30) * (sin(nπ/3) – sin(19nπ/3)) = 0

Therefore, the only non-zero coefficients are C[0] = 5/3 and C[5] = -5/3. The magnitude and phase spectra are:

|C[0]| = 5/3, arg(C[0]) = 0

|C[5]| = 5/3, arg(C[5]) = π

For all other values of k, C[k] = 0, so the magnitude and phase spectra are zero.

To compute the Fourier coefficients of cos(x) sin(y) = 1/2 (sin(x + y) – sin(x – y))

x[n] = 1/2 (sin(2nπ/3 + π/2) - sin(2nπ/3 - π/2)) * 1/2 (sin(2nπ/5) - sin(-2nπ/5))

Using the formula for the Fourier coefficients of a sinusoidal signal:

C[k] = (1/N) Σ[n=0 to N-1] x[n] e^(-j2πnk/N)

we can compute the Fourier coefficients for x[n]:

C[k] = (1/N) Σ[n=0 to N-1] x[n] e^(-j2πnk/N)

= (1/N) [Σ[n=0 to N-1] 1/2 sin(2nπ/3 + π/2) e^(-j2πnk/N) - Σ[n=0 to N-1] 1/2 sin(2nπ/3 - π/2) e^(-j2πnk/N)] [Σ[n=0 to N-1] 1/2 sin(2nπ/5) e^(-j2πnk/N) - Σ[n=0 to N-1] 1/2 sin(-2nπ/5) e^(-j2πnk/N)]

= 1/4 [C1(k-2/3) - C1(k+2/3)] [C1(k-2/5) - C1(k+2/5)]

where C1(k) is the Fourier coefficient of the signal cos(2nπ/3), which is given by:

C1(k) = (1/N) Σ[n=0 to N-1] cos(2nπ/3) e^(-j2πnk/N)

= (1/N) Σ[n=0 to N-1] 1/2 [e^(-j2πnk/3) + e^(j2πnk/3)]

= 1/2 [δ(k-1/3) + δ(k+1/3)]

Therefore, the Fourier coefficient C[k] is zero when k is not equal to ±2/3 and ±2/5.

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P(a purple marble then a white marble) is 6/105 ⇒ 1st answer

* Lets explain how to solve the problem

- There are 2 green marbles

- There are 7 blue marbles

- There are 3 white marbles

- There are 4 purple marbles

- Once a marble is drawn, it is NOT replaced

- We need to find P(a purple marble then a white marble)

* At first lets find the total number of marbles by adding all color

∵ There are 2 green , 4 purple , 3 white and 7 blue

∴ The total number of marbles = 2 + 4 + 3 + 7 = 16

∴ There are  16 marbles in the bag

∵ Probability = number of events/number of all outcomes

∵ There are 4 purple marbles

∴ The probability of chosen a purple marble is P(purple) = 4/15

∵ Once a marble is drawn, it is NOT replaced

∴ The total number of marbles = 15 - 1 = 14 marbles

∵ The number of white marbles is 3

∴ The probability of chosen a white marble is P(white) = 3/14

∵ P(a purple marble then a white marble) = P(purple) . P(white)

∵ P(purple) = 4/15

∵ P(white) = 3/14

∴ P(a purple marble then a white marble) = (4/15)(3/14) = 6/105

* P(a purple marble then a white marble) is 6/105

For all sufficiently large n, which shows that (xn) converges to sup(x) as desired. Therefore, if x is a non-empty set of real numbers that is bounded above, then there is a sequence of real numbers in x converging to sup(x).

Let x be a non-empty set of real numbers that is bounded above. Then, by the least upper bound property of the real numbers, sup(x) exists and is a real number.

For each positive integer n,

let xn be an element of x such that sup(x) - 1/n < xn ≤ sup(x).

Such an element xn exists because sup(x) is the least upper bound of x, so there must be elements of x arbitrarily close to sup(x).

We claim that the sequence (xn) converges to sup(x).

To see this, let ε > 0 be arbitrary.

Since xn ≤ sup(x) for all n,

we have sup(x) - xn ≥ 0, and so sup(x) - xn < ε for all n such that 1/ε is an integer. Thus, we have

|sup(x) - xn| < ε

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The amount of two plane tickets are a scarce resource, meaning there are not enough to provide for all three people.

A scarce resource is something that is in limited supply. In this case, the two plane tickets are the scarce resource because there are not enough to provide for all three people. This means that if Andy wants to travel to Philadelphia with his two nephews, only two of them can go. This is because while they may have three tickets to the show, they still need to find a way to get there. The two plane tickets are a scarce resource, as they are not enough for all three of them. This means that Andy must make a difficult decision about who can go and who has to stay home. The two plane tickets are the only way for two of them to get to Philadelphia, so they are a scarce resource in this situation.

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If we consider between mean and median in case of better measure of the center, median is likely to be the better measurement.

The list of values given here is 25, 29, 23, 26, 25, 27, 10, 26, 23, 23, 26.

First we are making or rearranging it in ascending/ descending order.

10, 23, 23, 23, 25, 25, 26, 26, 26, 27, 29.

Mean will be  the average of the given set.

Median will be the exact middle number or the average of the two middle entries.

Mean = 23.9

Median = 25

If we consider the range of data and how it is distributed, you can see it ranges from 10 to 29.

But the problem is that, after 10, the second least value is 23 and rest of the values are nearer also.

There is a clear gap between the values of other data points and the first data entry 10.

As mean is the average of every data, this 10 can directly influence the value of mean and cannot gave us an approximation of center.

Imagine that if the last entry is somewhat very big number, then the mean will surely slant to the higher number as it is the sum average of the given set of data.

But median is then also the exact middle number and not influenced by the range of the given data.

Mean and median can be the same in certain cases but when we approximate the measurement of center more than mean, median will likely to give better answer.

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The frequency range of UHF is band between 470 MHz and 608 MHz.

Given is to find the frequency range of the UHF broadcast station

Therefore, the frequency range of UHF is band between 470 MHz and 608 MHz.

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{Complete question -

What is the frequency range of the UHF broadcast station?}

Answer:

find the given numbers on the number line

This argument is best interpreted as inductive. The presence of empirical evidence in the form of research data suggests that the conclusion is based on empirical observations and generalization.

The argument uses evidence to make a generalization about the talkativeness of men and women, which is the characteristic of inductive reasoning. Additionally, the lack of logical or deductive inferential links between premises and conclusion supports the inductive interpretation of the argument.on:

Inductive reasoning is a type of reasoning in which a conclusion is drawn based on observations or evidence, rather than from logical deduction. Inductive reasoning involves making generalizations from specific observations or examples

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Yes, the theoretical probability of getting three heads in a row is the same as the theoretical probability of getting three tails in a row. This is because each flip of a fair coin is an independent event and has an equal chance of landing on either heads or tails.

The probability of getting heads on a single coin flip is 0.5 (or 1/2), and the same is true for getting tails on a single coin flip. The probability of getting three heads in a row is calculated by multiplying the probability of getting heads on each of the three flips together, which is"

(1/2) x (1/2) x (1/2) = 1/8.

Similarly, the probability of getting three tails in a row is also:

(1/2) x (1/2) x (1/2) = 1/8.

Therefore, the theoretical probability of getting three heads in a row is the same as the theoretical probability of getting three tails in a row, both of which are 1/8.

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Answer:

a. 48:16

b. 3:1

Step-by-step explanation:

Part a asks for a ratio of the two speeches. You simply separate the two numbers with a colon to show that it's a ratio.

Part b asks that the second quantity (which is the speeches made by B) be 1. To do this, divide 16 on both sides. 48 divided by 16 is 3, and 16 divided by 16 is 1. Thus, 3:1

The probability that a randomly chosen fitness club member signs up for a free running session is 20%.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1.


This is because 30 members signed up for a free session, with 10 signing up for the running session, 10 signing up for the swimming session, and 10 signing up for the weightlifting session. Since the running and swimming sessions are each twice as popular as the weightlifting session, there is a 20% chance that any given member will choose the running session.

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Answer:

Angles 11 and 10 both make a 180-degree angle, but so do 5 and 3. I would go with 11 and 10

Answer:

D, <11 and <10

Step-by-step explanation:

Supplementary angles are angles that sum to 180°

Part A: The theoretical probability of a fair coin landing on heads is 1/2.

Part B: The frequency of getting Heads is 12 and the frequency of getting tails is 13.

Part C: The experimental probability of landing on heads is 0.48

Part D: The theoretical probability is higher than the experimental probability.

What is probability?

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

A coin has two faces. One is head and other is tails.

If flip a coin, the outcome is {H,T}

The number of total outcomes is 2.

The number of frequency-getting heads is 1.

The number of frequency-getting tails is 1.

The theoretical probability of a fair coin landing on heads is 1/2.

Now flip a coin 25 times

The outcomes are

H,T,T,T, H,H,H, T,T,T, T,H,T, H,T,H,T,T, T, H, T, H,H,H,H

The frequency of getting Heads is 12 and the frequency of getting tails is 13.

The experimental probability of landing on heads is 12/25 = 0.48.

The theoretical probability is not the same as the experimental probability.

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Answer:

Part A: The theoretical probability of a fair coin landing on heads is 1/2.

Part B: The frequency of getting Heads is 12 and the frequency of getting tails is 13.

Part C: The experimental probability of landing on heads is 0.48

Part D: The theoretical probability is higher than the experimental probability.

Step-by-step explanation:

The numeric value of the inverse function of f(x) at x = 10 is given as follows:

f –1(10) = 3.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, the parameters are given as follows:

Hence the function is defined as follows:

y = 3x + 1.

To obtain the inverse function, we exchange the variables x and y and then isolate y, thus:

x = 3y + 1

3x = x - 1

y = (x - 1)/3

Hence the numeric value of the inverse function at x = 10 is given as follows:

y = (10 - 1)/3

y = 3.

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The relative change in tuition tells us the tuition in 2016/17 decreased by 9.99 %.

The indicator's value in the earlier period is used to calculate the relative change, which expresses the absolute change as a percentage. Additionally, indicators that are expressed as percentages, such as the unemployment rate, are subject to the concepts of absolute and relative change.

Given:

The tuition in University if Washington in 2015-16 = 10,203

and, The tuition in University if Washington in 2016-17 = 9,183

so, the relative change is

= (10203 - 9183)/ 10203

= 1020/ 10203

= 0.0999

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An equation which you can use to represent the relationship shown in the table is y = 4.5x.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Based on the information provided in the table (see attachment), we can logically deduce the following data points on the line:

Points on x-axis = (4, 5).

Points on y-axis = (18.0, 22.5).

At point (4, 18.0), a linear equation of this line in slope-intercept form can be calculated by using the point-slope form as follows:

y - 18.0 = (22.5 - 18.0)/(5 - 4)(x - 4)

y - 18.0 = 4.5(x - 4)

y = 4.5x - 18 + 18.0

y = 4.5x.

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Answer:

[tex]x = 1 \ \ \ \text{OR} \ \ \ x = \dfrac{1}{3}[/tex]

Step-by-step explanation:

First, multiply out the set of parentheses and simplify the resulting quadratic expression.

[tex]4(x - 1)(3x - 1) = 0[/tex]

[tex]4(3x^2-x-3x+1) = 0[/tex]

[tex]4(3x^2-4x+1) = 0[/tex]

Then, factor out a 3 from the parentheses to get rid of the coefficient on the quadratic's first term.

[tex]4(3(x^2-\dfrac{4}{3}x+\dfrac{1}{3})) = 0[/tex]

[tex]12(x^2-\dfrac{4}{3}x+\dfrac{1}{3}) = 0[/tex]

Finally, complete the square.

[tex]12\left(x^2-\dfrac{4}{3}x + \left(\dfrac{-\dfrac{4}{3}}{2}\right)^2\right) = 12\left(-\dfrac{1}{3}\right) + 12\left(\dfrac{-\dfrac{4}{3}}{2}\right)^2[/tex]

[tex]12\left(x^2-\dfrac{4}{3}x + \dfrac{4}{9}\right) = -4 + \dfrac{16}{3}[/tex]

[tex]12\left(x - \dfrac{2}{3}\right)^2 = \dfrac{4}{3}[/tex]

[tex]\left(x - \dfrac{2}{3}\right)^2 = \dfrac{1}{9}[/tex]

↓ take the square root of both sides

[tex]x - \dfrac{2}{3}\right = \pm \sqrt{\dfrac{1}{9}}[/tex]

[tex]x = \dfrac{2}{3} \pm \sqrt{\dfrac{1}{9}}[/tex]

[tex]x = \dfrac{2}{3} \pm\dfrac{1}{3}[/tex]

↓ split into two equations

[tex]x = \dfrac{2}{3} + \dfrac{1}{3} \ \ \ \text{OR} \ \ \ x = \dfrac{2}{3} - \dfrac{1}{3}[/tex]

[tex]\boxed{x = 1 \ \ \ \text{OR} \ \ \ x = \dfrac{1}{3}}[/tex]