What method do you prefer to use when adding or subtracting fractions and mixed numbers? For example, do you find common denominators first, convert fractions into decimals and then back into fractions, or simplify fractions first and then add or subtract them? Explain why you prefer to use this method. Give at least one example of using this method. As you learn new strategies throughout the unit, you may change which method you prefer to use. If that happens, explain why you changed your preferred method

Answer:

Step-by-step explanation:

80        40

___________

 100        50

The approximate length of the midsegment parallel to xy is 6.63

The midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle and has the same length as each of the two sides.

To find the midpoint of a line segment, we average the x-coordinates and the y-coordinates of its endpoints.

Since the question stated that the midsegment is parallel to xy, we need to find midpoint of xw and yw.

First, let's find the midpoint of side xw:

Midpoint of xw : ((-14+10)/2, (20+4)/2) = (-2, 12)

Midpoint of yw : ((-14-2)/2, (20-4)/2) = (-8, 8 )

The length of a line segment between two points (x1, y1) and (x2, y2) in a two-dimensional coordinate system can be calculated using the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Length line of midpoint xw and midpoint yw :

√((-2-(-8))^2 + (12-(8))^2) = √(6^2 + 4^2) = √(36 + 8) = √44

So, the length of the midsegment is parallel to XY, which is approximately equal to √44 = 6.63

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The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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Using the binomial distribution, the probability of at least 5 people in a population of 200 getting a virus with a probability of 0.02 is 0.1237. The probability of between 70 and 105 people in a population of 300 having a gene with a probability of 0.25 is 0.9189. The probability of rolling a 2 or 3 at least 6 and at most 10 times in 19 rolls of a fair die is 0.0065.

This scenario follows a binomial distribution with n=200 and p=0.02, where n is the number of trials and p is the probability of success. We want to find the probability of at least 5 people getting the virus, which can be written as P(X≥5). Using the binomial probability formula, we get:

P(X≥5) = 1 - P(X<5) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=3) - P(X=4)

Using a binomial probability table or calculator, we can find the probabilities for each value of X:

P(X=0) = 0.9802, P(X=1) = 0.0392, P(X=2) = 0.0012, P(X=3) = 0.00003, P(X=4) = 0.0000006

Therefore,

P(X≥5) = 1 - (0.9802 + 0.0392 + 0.0012 + 0.00003 + 0.0000006) ≈ 0.038

So the probability that at least 5 people in a population of 200 get the virus is approximately 0.038.

This scenario follows a binomial distribution with n=300 and p=0.25. We want to find the probability that between 70 and 105 people have the gene, which can be written as:

P(70≤X≤105) = P(X≤105) - P(X<70)

Using a binomial probability table or calculator, we can find the probabilities for each value of X:

P(X<70) = 0.015, P(X≤105) = 0.999999999999997

Therefore,

P(70≤X≤105) = 0.999999999999997 - 0.015 ≈ 0.985

So the probability that between 70 and 105 people in a population of 300 have the gene is approximately 0.985.

This scenario follows a binomial distribution with n=19 and p=1/3, where p is the probability of getting either 2 or 3. We want to find the probability that the result is either 2 or 3 at least 6 and at most 10 times, which can be written as:

P(6≤X≤10) = P(X≤10) - P(X<6)

Using a binomial probability table or calculator, we can find the probabilities for each value of X:

P(X<6) = 0.778, P(X≤10) = 0.9999

Therefore,

P(6≤X≤10) = 0.9999 - 0.778 ≈ 0.221

So the probability that the result is either 2 or 3 at least 6 and at most 10 times in 19 rolls of a fair die is approximately 0.221.

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a) P(A and B) = 0

b) P(A or B) = 0.9

c) P(not A) = 0.75

d) P(not B) = 0.35

e) P(not (A or B)) = 0.1

f) P(A and (not B)) = 0.25

Two mutually exclusive events mean that both cannot occur simultaneously. Let A be the event that A happens and B be the event that B happens. Then, the probability of A and B together happening (P(A and B)) is 0 as the two events cannot happen simultaneously.a) P(A and B)=0b) P(A or B)P(A or B) = P(A) + P(B) - P(A and B)P(A or B) = P(A) + P(B) - 0= 0.25 + 0.65= 0.9c) P(not A)P(not A) = 1 - P(A)P(not A) = 1 - 0.25= 0.75d) P(not B)P(not B) = 1 - P(B)P(not B) = 1 - 0.65= 0.35e) P(not (A or B))P(not (A or B)) = 1 - P(A or B)P(not (A or B)) = 1 - 0.9= 0.1f) P(A and (not B))P(A and (not B)) = P(A) - P(A and B)P(A and (not B)) = P(A) - P(A) x P(B)= 0.25 - 0= 0.25.

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Approximately 22.65 milligrams will remain after 53 hours.

To determine the number of milligrams that will remain after 53 hours, we can use the formula for exponential decay:

N(t) = N₀ * e^(-kt),

where:

N(t) represents the remaining amount at time t,

N₀ is the initial amount,

k is the decay constant,

and e is the base of the natural logarithm.

Given that after 8 hours, 50 mg of the substance remains, we can set up an equation:

50 = 100 * e^(-8k).

To find the decay constant k, we can rearrange the equation:

e^(-8k) = 50 / 100,

e^(-8k) = 0.5.

Taking the natural logarithm (ln) of both sides:

-8k = ln(0.5).

Now, let's solve for k:

k = ln(0.5) / -8 ≈ -0.08664.

With the decay constant determined, we can find the remaining amount after 53 hours:

N(53) = 100 * e^(-0.08664 * 53).

Calculating this value:

N(53) ≈ 100 * e^(-4.59192) ≈ 22.65.

Therefore, approximately 22.65 milligrams will remain after 53 hours.

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Answer:

D. She is correct; the histogram is skewed to the right because there is less data on the right side.

Step-by-step explanation:

I just did it on edge

Option D is correct. She is correct; the histogram is skewed to the right because there is fewer data on the right side.

A skewed distribution is one in which one of the two sides is biased (either left or right). It's like a mountain tilting to one side (left or right).

Like the picture, a left skewed graph has an extended tail on the left side of the main peak. A right skewed graph features an extended tail on the right side of the main peak.

She is correct; the histogram is skewed to the right because there is fewer data on the right side.

Hence, option D is correct.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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Answer:

c = -5

d = -10

Step-by-step explanation:

A biologist is tracking a bird when it was at A.

Coordinates of point A are (2, 4).

This bird moves from point A to point B.

Coordinates of the point B are (-3, -6).

Vector form of vector represented by \(\overrightarrow{AB}=<x_2-x_1, y_2-y_1>\)

By substituting the coordinates of points A and B,

\(\overrightarrow{AB}=<(-3-2),(-6-4)>\)

      = < -5, -10 >

\(\overrightarrow{AB}=\binom{-5}{-10}\)

By comparing it with the vector form of [cd]

c = -5

d = -10

Step-by-step explanation:

the area of a triangle

baseline × height / 2

in our case

baseline × height / 2 = 60 in²

height = 6×baseline - 16

baseline × (6×baseline - 16) / 2 = 60

baseline × (3×baseline - 8) = 60

3×baseline² - 8×baseline = 60

baseline = x

3x² - 8x - 60 = 0

general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 3

b = -8

c = -60

x = (8 ± sqrt(64 - 4×3×-60))/(2×3) =

= (8 ± sqrt(64 + 720))/6 = (8 ± sqrt(784))/6 =

= (8 ± 28)/6

x1 = (8 + 28)/6 = 36/6 = 6

x2 = (8 - 28)/6 = -20/6 = -10/3

x2 as a negative number is not a valid solution for a length in a geometric shape.

so, x = 6 in is our solution for the baseline.

height = 6x - 16 = 6×6 - 16 = 36 - 16 = 20 in

base = 6 in

Answer:

x<-14

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form: x<-14

Answer:

A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet and the volume of each large box is 12 cubic feet. There were twice as many small boxes shipped as large boxes shipped and the total volume of all boxes was 168 cubic feet. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.

\underline{\text{Define Variables:}}

Define Variables:

​  

May choose any letters.

\text{Let }s=

Let s=

\,\,\text{the number of small boxes shipped}

the number of small boxes shipped

\text{Let }l=

Let l=

\,\,\text{the number of large boxes shipped}

the number of large boxes shipped

Each small box has a volume of 6 cubic feet, so the volume of ss small boxes would be 6s6s cubic feet. Each large box has a volume of 12 cubic feet, so the volume of ll large boxes would be 12l12l cubic feet. Therefore, the total volume 6s+12l6s+12l equals 168:168:

6s+12l=168

6s+12l=168

Since there were twice as many small boxes shipped as large boxes, there were more small boxes, so if we multiply 2 by the number of large boxes, we will get the number of small boxes, meaning ss equals 2l.2l.

let s = number of small boxes shipped

let l= number of large boxes shipped

6s+121 = 168

s=21

The number of small boxes shipped are 14 and the number of large boxes shipped are 7.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, the volume of each small box is 6 cubic feet and the volume of each large box is 12 cubic feet.

Let the number of small boxes be x and the number of large boxes be y.

There were twice as many small boxes shipped as large boxes

So, x=2y ------(I)

The total volume of all boxes was 168 cubic feet.

6x+12y=168 ------(II)

Substitute equation (I) in equation (II), we get

6(2y)+12y=168

12y+12y=168

24y=168

y=7

Substitute y=7 in equation (I), we get

x=14

Therefore, the number of small boxes shipped are 14 and the number of large boxes shipped are 7.

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A. N, B ≥ 0 (non-negativity constraint)

B. The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.

C.  You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

D. You can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

(a)

The linear programming model to find the best investment strategy for this client can be formulated as follows:

Maximize: 0.09N + 0.08B

Subject to:

N + B ≤ 85 (maximum investment of $85,000)

N ≤ 55 (maximum investment of $55,000 in the internet fund)

6N + 4B ≤ 410 (maximum risk rating of 410 for a moderate investor)

N, B ≥ 0 (non-negativity constraint)

(b)

To solve the problem using Excel Solver, you can set up the following spreadsheet model:

Cell A1: N (amount invested in the internet fund)

Cell B1: B (amount invested in the Blue Chip fund)

Cell C1: =0.09A1 + 0.08B1 (annual return for the portfolio)

Constraints:

Cell A2: ≤ 85

Cell B2: ≤ 85

Cell C2: ≤ 55

Cell D2: ≤ 410

The objective is to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints.

Using Excel Solver, set the objective to maximize the value in cell C1 by changing the values in cells A1 and B1, subject to the constraints in cells A2, B2, C2, and D2.

The recommended investment portfolio (in dollars) for this client can be found by reading the values in cells A1 and B1.

(b)

For the aggressive investor with a maximum portfolio risk rating of 450, the linear programming model remains the same, except for the constraint on the maximum risk rating.

The new constraint would be: 6N + 4B ≤ 450

Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

(d)

For the conservative investor with a maximum portfolio risk rating of 320, the linear programming model remains the same, except for the constraint on the maximum risk rating.

The new constraint would be: 6N + 4B ≤ 320

Using the same spreadsheet model as before, with the updated constraint, you can solve for the recommended investment portfolio (in dollars) by reading the values in cells A1 and B1.

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The rule for X is to multiply it by 2.

By following the given instructions, we can deduce the rule for X by observing the outputs for different input values. Let's start with some examples:

1.If we input 1 and receive 2 as the output, it suggests that the rule is X multiplied by 2.

2.If we input 2 and receive 4 as the output, it further supports the rule of X multiplied by 2.

3.Similarly, for inputting 3 and getting 6 as the output, it continues to reinforce the rule of X multiplied by 2.

By analyzing these outputs, it becomes apparent that the rule for X is to multiply it by 2. This conclusion is based on the consistent pattern observed in the outputs, where they are double the input values.

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The price of the car is $130,000, Simple interest for 4 years is $26000, Simple interest for 2 years is 2 years, The interest saved by paying the loan off sooner is $13000.

Simple interest is a method of calculating interest that does not take into consideration numerous periods of interest charges or payments. Accrued interest is unaffected by the interest rate; it simply applies to the loan or investment's principle.

Let us suppose the price of the dream car is $130,000.

The simple interest is given by the formula:

SI = PRT

where, P is the principal amount = $130,000.

R is the rate = 5% = 0.05

T is the time.

The price of the vehicle is $130,000.

Given that, T = 4 years.

Substitute the value in formula of SI.

SI = 130000 (0.05) (4)

SI = 26000

Given that T = 2 years.

Substitute the value:

SI = 130000 (0.05)(2)

SI = 13000

The interest saved by paying the loan off sooner is:

I = 26000 - 13000

I = 13000

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part a.

the percentage of eggs between 42 and 45mm is 48.48%

part b.

The median width is approximately (42+45)/2 = 43.5mm.

The median length is approximately (56+59)/2 = 57.5mm.

part c.

The width of grade A chicken eggs has a range of about 24mm.

part d.

I think its impossible to determine because we don't have the value for the standard deviation.

The second option should be correct.

A histogram is described as an approximate representation of the distribution of numerical data.

part a.

From the histogram, we see that the frequency for the bin that ranges from 42 to 45mm is 4 and we have  a total of 33 eggwe use this values and calculate the percentage of eggs between 42 and 45mm is 48.48%.

part b.

we have an  estimation  that the median of the width is 48mm and the median of the length is around 60mm.

part c.

Also from the histogram, we notice  that the smallest value is around 36mm and the largest value is around 66mm, hence the width of grade A chicken eggs has a range of about 24mm.

In a histogram, the range is the width that the bars cover along the x-axis and these are approximate values because histograms display bin values rather than raw data values.

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Employees in the transportation and shipping industry today are required to know advanced math for several reasons. Here are some of the most important ones:

1. Efficiency: In the transportation and shipping industry, time is money. To maximize efficiency, workers need to be able to calculate distances, speeds, and travel times accurately.

This requires a solid understanding of advanced math concepts such as algebra, calculus, and trigonometry.

2. Safety: Transporting goods and people comes with risks. To ensure safety, employees need to understand the physics of motion, forces, and momentum.

This requires knowledge of advanced math concepts such as vectors, kinematics, and dynamics.

3. Technology: The transportation and shipping industry is becoming increasingly automated and technology-driven. Employees need to be able to understand and use complex algorithms, statistical models, and data analysis tools.

This requires advanced math skills such as statistics, probability theory, and linear algebra.

4. Regulations: The transportation and shipping industry is subject to a wide range of regulations, including safety standards, environmental laws, and trade policies.

Compliance with these regulations often requires complex calculations and data analysis. Advanced math skills are essential for navigating this regulatory landscape.

In summary, advanced math skills are essential for employees in the transportation and shipping industry to ensure efficiency, safety, technology adoption, and compliance with regulations.

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Answer:

here it is

Step-by-step explanation:

if u have any question tell me

The fraction of the check and tip did John pay is 5/24.

What are rational numbers?

It is possible to express rational numbers in the form pq, where p and q are integers and q0. The distinction between fractions and rational numbers is that the numerator or denominator of a fraction cannot be negative. As a result, the numerator and denominator of a fraction are whole numbers (denominator 0), as opposed to integers in the case of rational numbers.

Here, we have

Given: A group of three friends ate dinner at a restaurant. When they settled the check and tip, Peter paid 4/5 as much as John paid, and John paid 1/3 as much as Ralph paid.

we have to find a fraction of the check and tip did John pay.

p, j, r, the fractions that each paid.

p + j + r = 1....(1)

p = (4/5)j and j = (1/3)r

From equation(1), we get

(4/5)j + j + 3j = 1

j(4/5 + 1 + 3) = 1

(24/5)j = 1

j = 5/24

We have

r = 3j

r = 3(5/24)

r = 5/8

Hence, the fraction of the check and tip did John pay is 5/24.

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0.017 m/min is the height of increasing water.

What is the volume of a cylinder?

A cylinder's volume refers to the amount of interior room it has to hold a given quantity of material.

Formula to calculate the volume of a cylinder

volume = π r² h

where r is the radius of the cylinder and h is the height.

Here, we have

radius = 6m

dV/dt = 3

We have to find:  dh/dt

volume = π r² h

Differentiating both sides with respect to t, we get

dV/dt = π[2r(dr/dt)h + r²(dh/dt)]

r remains constant (r = 6), dr/dt = 0

So, dV/dt = πr²(dh/dt)

Substituting the values, we get

2 = π(6)²(dh/dt)

dh/dt = 2/(36π)

= 0.017m/min

Hence, 0.017 m/min is the height of increasing water.

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Answer:

Step-by-step explanation: if the width is x then the length is 2x+3

The perimeter is 2x+2(2x+3)=42

then 6x+6=42

6x=36

x=6

Then the length is 2*6+3=15

In general, an appropriate null hypothesis is one that states there is no significant difference or relationship between two variables.

Therefore, out of the options given, the appropriate null hypothesis would be "selection was not a significant factor."
An appropriate null hypothesis is "Selection has no effect on the observed outcome. "it means that any differences observed in the data are due to chance, and not due to a specific selection process or factor. The null hypothesis serves as a starting point in statistical analysis, and researchers aim to either accept or reject it based on the evidence collected.

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The triangle similar to triangle ABC will be the triangle with the corresponding angles as same as 50°, 75°, 55°.

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a triangle ABC in which angle [A] is 50° and angle [C] is 75°

The third angle of the triangle would be -

A + B + C = 180

50 + 75 + C = 180

C = 180 - 125

C = 55°

The triangle similar to triangle ABC will be the triangle with the corresponding angles as same as 50°, 75°, 55°.

Therefore, the triangle similar to triangle ABC will be the triangle with the corresponding angles as same as 50°, 75°, 55°.

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Answer:

y = 25 + 3.5x, where x is a half hour

y = 25 + 3.5 (4 * 2) = $53

Step-by-step explanation:

Answer:

La respuesta correcta es la opción C: 91 cm³.

Step-by-step explanation:

La fórmula del volumen de un cubo es la siguiente:

\( V = a^{3} \)

En dónde:

a: es cada lado del cubo = 4,5 cm

Entonces, el volumen del cubo es:

\( V = a^{3} = (4,5 cm)^{3} = 91.1 cm^{3} \approx 91 cm^{3} \)

Por lo tanto, la respuesta correcta es la opción C: 91 cm³.  

Espero que te sea de utilidad!

Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."

2: The total cost of the merchandise is $3,332.00.

5: The company's gross margin and operating expenses, are $211,000 and $191,720.

Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.

Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.

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The time required to ring up the customer with 11 items is; 20 seconds

A linear equation is defined as an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

We are given the linear equation:

t = p + 9

Where;

p is the variable that represents the number of items being purchased

t reprensts the time required to ring up the customer.

Thus:

When p = 11 items, we have:

t = 11 + 9

t = 20 seconds

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Answer:

y = 8 + x

350x + 70y = 1,400----->5x + y = 20

5x + 8 + x = 20

6x + 8 = 20

6x = 12

x = 2, y = 10

2 sliders, 10 onion rings

The value of x is 8.5 for the given equation \(\frac{x-6.5}{2.0}=1\).

To solve the following equation we need to move all the x terms to one side and move all the constant terms to the other side. For this equation, the constant term is 6.5 and the x term is x.

\(\[\frac{x-6.5}{2.0}=1\]\)

First, we will multiply both sides by 2.0.\(\[2.0 \times \frac{x-6.5}{2.0}=2.0 \times 1\]\)

Simplify it,\(\[x-6.5=2.0\]\)

Add 6.5 to both sides,\(\[x=2.0+6.5\]\)

Thus, x= 8.5

An equation is an expression that has a relation between two or more variables. In this equation \(\(\frac{x-6.5}{2.0}=1\) ,\)we have one variable which is x. To solve this equation, we need to isolate the variable x. Here, we have to move all the x terms to one side and move all the constant terms to the other side.We started with the given equation:\(\[\frac{x-6.5}{2.0}=1\]\)

Then, we multiplied both sides of the equation by 2.0, and Lastly, we added 6.5 to both sides to isolate x. Thus, we got the value of x, which is x=8.5.

The value of x is 8.5 for the given equation \(\frac{x-6.5}{2.0}=1\). To solve this equation, we followed the steps as discussed above. We have one variable in this equation, and to isolate it, we moved all the x terms to one side and moved all the constant terms to the other side.

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