Karen needed to put 5 gallons 3 quarts of gas into her boat on Monday and twice as much on Saturday. If she had an 18 gallon jug of gas available, did she have enough gas for both days?

The experimental probability that Roberto will get a hit during his next time at bat is 0.25 or 25%.

The experimental probability of an event is calculated by dividing the number of times the event occurred by the total number of trials.

In this case, the event is "getting a hit" and the number of times it occurred is 11. The total number of trials is 44, which represents the number of times Roberto was at bat.

Experimental probability of getting a hit = Number of times Roberto got a hit / Total number of times at bat

Experimental probability of getting a hit = 11 / 44

Experimental probability of getting a hit = 0.25 or 25%

Therefore, the experimental probability that Roberto will get a hit during his next time at bat is 0.25 or 25%.

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5.4 out of the 12 adult Australian sheep dogs in the sample weigh 65 pounds or more, on average.

We can start by calculating the likelihood that a single adult Australian sheep dog weighs 65 pounds or more using the provided estimate of 45%. If p represents the percentage of adult dogs weighing 65 pounds or more, the following is the result:

p = 0.45

Next, we may calculate the median number of dogs weighing 65 pounds or more using the sample size of 12. If X represents the proportion of dogs in the sample that weigh 65 pounds or more, X will follow a binomial distribution with n = 12 and p = 0.45 as its parameters.

The formula for X's mean or expected value is:

E(X) = np

When we change the values of n and p, we obtain:

E(X) = 12(0.45) = 5.4

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The difference between cardinality and join type is that cardinality describes the relationship between two data tables, while join type is the specific method used to combine the two tables.

Cardinality defines the maximum number of records that can exist in one table for a relationship with another table. Cardinality can be either one-to-one, one-to-many, or many-to-many.

A one-to-many cardinality relationship is when one record in one table can be related to multiple records in another table. For example, a customer can have multiple orders. In this situation, a one-to-one join type is often used because it is the most efficient way to retrieve the related data. This is because one-to-one join type only requires that one record be searched, while a one-to-many join type would require that multiple records be searched in order to find the related records. Additionally, a one-to-one join type ensures that no duplicate records will be returned in the result.

In summary, cardinality describes the relationship between two tables while join type is the specific method used to combine the two tables. A one-to-many cardinality relationship is when one record in one table can be related to multiple records in another table. To efficiently retrieve the related data, a one-to-one join type is often used. This is because it only requires that one record be searched and it ensures that no duplicate records will be returned in the result.

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One way to do this is to subtract 1.8x from both sides of the equation, which gives:

x - 1.8x = 32

Simplifying the left-hand side, we get:

-0.8x = 32

To solve for x, we can divide both sides of the equation by -0.8:

x = 32 / (-0.8)

Simplifying, we get:

x = -40

Answer:

Step-by-step explanation:

3x^16

Answer:

3x^16

Step-by-step explanation:

Therefore, the observed value of the test statistic for testing the null hypothesis H0: p = 0.5 versus the alternative hypothesis H1: [tex]p > 0.5[/tex]is z= 1.8. The correct answer is (e) z=[tex]0.59— 0.5/√0.5(0.5)/100.[/tex]

In this particular question, the observed value of the test statistic for testing the null hypothesis H0: p = 0.5 versus the alternative hypothesis H1: p > 0.5 is to be determined. The question provides a random sample of 100 likely voters in a small city, which produced 59 voters in favor of Candidate A. The formula for calculating the test statistic is as follows:

z= (p- P) / sqrt[P(1-P) / n]

where p is the sample proportion, P is the hypothesized population proportion, and n is the sample size.

Substituting the given values into the formula, we get:

z= [tex](0.59- 0.5) / sqrt[0.5(0.5) / 100][/tex]

z= [tex]0.09 / 0.05[/tex]

z=[tex]1.8[/tex]

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Fatouma lifted 1 kg during the first week and 120 kg during the tenth week. Fatouma lifted 120 kg in 10 weeks, increasing by 2 kg each week.

Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0

Say the mass Fatouma lifted during the first week "x". According to the problem, she increases the weight she lifts by 2 kg every week. So, the mass of second week is "x + 2" kg, during the third week is "x + 4" kg, and so on.

Since there are 10 weeks of training, the mass she lifted during the 10th week is:

x + (10 - 1) × 2 = x + 18

We also know that during the 10th week, she lifted 120 kg. So, we can set up an equation:

x + 18 = 120

Solving for x, we get:

x = 102

Thus, Fatouma lifted 102 kg during the first week of training.

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The true statements for the graph of y=(x+2)²2+4 are:, The vertex of the parabola is at the point (-2, 4)., The graph opens upwards, since the coefficient of the squared term is positive., The y-intercept of the graph is at the point (0, 9)., The x-coordinate of the vertex is -2, which is also the axis of symmetry of the parabola., The graph is a parabola, which is a U-shaped curve.

What is graph?

In mathematics, a graph is a visual representation of a set of points, called vertices or nodes, that are connected by lines or curves, called edges. Graphs are used to model relationships between objects or to represent data in a visual way.

In the context of coordinate geometry, a graph is a visual representation of a function or relation, which shows the relationship between the input values (x-axis) and output values (y-axis). The graph is typically a set of points plotted on a Cartesian plane, where each point represents a unique input-output pair.

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Complete Question:

Select the statements that are true for the graph of y = (x+2)²2 + 4.

a) The vertex of the parabola is (-2, 4).

b) The parabola opens upward.

c) The y-intercept of the parabola is 4.

d) The x-intercepts of the parabola are (-4, 0) and (0, 0).

e) The axis of symmetry of the parabola is a vertical line through x = -2.

The dimensions of the pool are either (21.55, 16.45) or (28.45, 7.55).

The perimeter of the bottom of a rectangular swimming pool is 60 meters, and the area is 221 square meters.

To find the dimensions of the pool, we can use the formula P = 2(l + w) where P is the perimeter and l and w are the length and width of the pool respectively. We can rearrange this formula to solve for either l or w, so we'll solve for l.

2(l + w) = 60
2l + 2w = 60
2l = 60 - 2w
l = (60 - 2w)/2

Now, we can use the formula A = l*w to solve for w.

221 = l*w
221 = (60 - 2w)/2 * w
221 = (60w - 2w^2)/2
442 = 60w - 2w^2
2w^2 - 60w + 442 = 0

Using the quadratic formula, we get w = 16.45 or 7.55.

Now that we know the width, we can use the formula l = (60 - 2w)/2 to find the length. For w = 16.45, l = 21.55, and for w = 7.55, l = 28.45.

Therefore, the dimensions of the pool are either (21.55, 16.45) or (28.45, 7.55).

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Answer:

There are several ways to make 45 cents using different coins:

Nine nickels

Four dimes and one nickel

Three dimes and six nickels

Two dimes and one quarter

One dime, two nickels, and three pennies

One quarter and two dimes

One quarter, one dime, and four nickels

One quarter, three nickels, and five pennies

45 pennies

So there are 9 ways to make 45 cents.

I Hope This Helps!

To make a stable structure, the method of joints can be used to calculate the force BD in the truss shown.

This method uses the equations of equilibrium to determine the forces in the members of a truss. To calculate the force BD, one needs to sum the moments about point A and equate them to zero.

The moment is given by M = FxD, where F is the force, and D is the perpendicular distance from the point of interest to the line of action of the force. Therefore, the force BD can be calculated using the equation:

MAB = 0 = (BD)(2) - (AE)(5)

BD = 5AE/2

To find the forces in members CD and CE using the method of sections, one needs to cut through the truss along a line passing through points C and E.

Then, the force in member CD can be found by using the equation of equilibrium, where the sum of the forces in the x-direction and the sum of the forces in the y-direction must be equal to zero. Similarly, the force in member CE can also be calculated using the same method.

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Answer:

  60.3°

Step-by-step explanation:

You want the measure of angle B in right triangle ABC with leg BC = 8 and leg AC = 14.

The tangent relation is ...

  Tan = Opposite/Adjacent

Applying this to the given triangle, we have ...

  tan(B) = 14/8

The arctangent function gives you the angle from the tangent.

  B = arctan(14/8) ≈ 60.3°

The measure of angle B is about 60.3°.

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Answer: 7x - 7y + 21

Step-by-step explanation:

7( x - y + 3) = 7x - 7y + 21

Answer:

Step-by-step explanation:

holy mocacrise

The propensity scoring method is a statistical technique used to adjust for differences in the characteristics of groups being compared in a study. In this case, we want to adjust for the fact that respondents aged 70 or older are underrepresented in an internet sample.

To do this, we can assign a propensity score to each individual in the sample based on their likelihood of being in the sample, given their age. We can then use this score to weight their responses to account for the underrepresentation of older individuals.

In this case, we know that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. This means that we can assign a propensity score of 3 to each individual aged 70 or older in the sample, and a propensity score of 1 to everyone else.

Using these propensity scores, we can weight the responses of each individual in the sample. Responses from individuals with a propensity score of 3 would be weighted by a factor of 3, while responses from individuals with a propensity score of 1 would be weighted by a factor of 1.

By adjusting for the underrepresentation of older individuals in this way, we can obtain more accurate estimates of the characteristics of the population being studied, and reduce the potential for bias in our analysis.

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A shape's perimeter is calculated by adding the lengths of all of its sides and edges. The V's direction is [tex](-5, -12)[/tex]  .

The complete length of a shape's boundary is referred to as the perimeter in geometry. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

We need to know the lengths of all the sides of Fard ZH in order to calculate its perimeter. We can see from the diagram that  [tex]ZF = ZD + DF = 24 + 28 = 52[/tex]  and [tex]FH = ZG = 30 and ZH = 36.[/tex]

As a result, Fard ZH's perimeter is as follows:

perimeter = [tex]= ZF + FH + ZH + ZG[/tex]

perimeter  [tex]= 52 + 30 + 36 + 30[/tex]

perimeter  [tex]= 148[/tex]

So the perimeter of Fard ZH is [tex]148[/tex]  .

(3) The vector that connects points A and B must be identified in order to determine the direction of V, and it can be written as follows:

[tex]V = (xB - xA, yB - yA)[/tex]

Where xA and yA represent point A's x and y coordinates, and xB and yB represent point B's x and y coordinates.

Plugging in the given values, we get:

[tex]V = (5 - 10, 2 - 14)[/tex]

[tex]V = (-5, -12)[/tex]

Therefore, The V's direction is [tex](-5, -12)[/tex] .

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Answer:

To calculate the total milk yield in one year, we need to multiply the number of dairy cows by the amount of milk each cow produces per year:

Total milk yield = 2650 dairy cows × 2320 gallons of milk per cow per year

Total milk yield = 6,188,000 gallons per year

To write this answer in scientific notation, we need to express the number 6,188,000 as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point to the left until we have a number between 1 and 10, and counting the number of decimal places we moved. In this case, we need to move the decimal point 6 places to the left:

Total milk yield = 6.188 × 10^6 gallons per year

Therefore, the dairy farm yields 6.188 × 10^6 gallons of milk per year.

The probability that a class of 36 has an average midterm mark that is more than 77.83 is 0.0766. This is because the mean of the normally distributed marks is 78 and the standard deviation is 6. Using the standard normal distribution formula, we can calculate the probability that the average mark of 36 students is more than 77.83.

Standard Normal Distribution Formula: P(x > a) = 1 - P(x < a)

P(x > 77.83) = 1 - P(x < 77.83)

P(x > 77.83) = 1 - 0.9234

P(x > 77.83) = 0.0766

New car prices to fall within is $18,300 - $41,900

Interval of prices would we expect at least 95% of new car prices to fall within Suppose that the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. Based on this information, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.How to solve the problem? We know that the average price of new cars is $30,100 and the standard deviation is $5,600. The normal distribution has 95% of the data points within two standard deviations of the mean. Therefore, the interval of prices that we would expect at least 95% of new car prices to fall within is given by:Lower limit: $30,100 - 2 × $5,600 = $18,300Upper limit: $30,100 + 2 × $5,600 = $41,900Thus, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.

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The percentage change in the birth rate of a nation from 1990 to 2000 is -35%.

Percentage change is the relative difference between two values expressed as a percentage of one of the values, where the value of the latter is used as the reference point.

It can be calculated by using the following formula:

Percentage change = ((new value - old value) / old value) x 100

Given the birth rate of a nation in 1990 as 20 and the birth rate in 2000 as 13, the percentage change can be calculated as follows: Percentage change = ((13 - 20) / 20) x 100= (-7 / 20) x 100= -0.35 x 100= -35%

Hence, the percentage change is -35%.

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The rate of change of y = cos x with respect to time is approximately -1.46 cm/sec.

This problem involves finding the rate of change of the dependent variable (y = cos x) with respect to the independent variable (x) at a given rate of change of the independent variable (dx/dt = 4 cm/sec).

Using the chain rule of differentiation, we have:

dy/dt = dy/dx * dx/dt

Taking the derivative of y = cos x with respect to x, we get:

dy/dx = -sin x

Substituting the given value of dx/dt = 4 cm/sec and the value of sin x can be obtained using the identity cos² x + sin² x = 1 and the given value of cos x = cos 0 = 0.95, we get:

dy/dt = dy/dx * dx/dt

= (-sin x) * 4

= (-√(1 - cos² x)) * 4 [Using the identity sin x = √(1 - cos² x)]

= (-√(1 - 0.95²)) * 4

≈ -1.46 cm/sec

Therefore, the rate of change of y = cos x with respect to time is approximately -1.46 cm/sec.

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The given diagram represents a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.

The given diagram represents a right circular cylinder with a height of 10 meters and a radius of 7 meters, which means the base of the cylinder is a circle with a radius of 7 meters. The equation of the circle is (x - 0)² + (y - 0)² = 7², where (0, 0) is the center of the circle.

The cylinder has been sliced by a plane that is parallel to the base and 4 meters from the center of the cylinder. This means the distance between the center of the cylinder and the plane is 4 meters.

Mathematically, the equation of the ellipse can be written as (x - 0)²/4² + (y - 0)²/5² = 1, where the center of the ellipse is (0, 0), and the semi-major axis is 5 meters and the semi-minor axis is 4 meters.

So, the given diagram described as a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², sliced by a plane parallel to the base and 4 meters from the center of the cylinder, resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.

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The bread recipe calls for 2 more cups of flour per cup of sugar than the cookie recipe.

========================================================

Explanation:

I'll use this shorthand

Something like "2 cups of sugar" will shorten to "2s".

The cookies need 3s for every 6f.

Therefore we get this ratio

3s : 6f

And we can divide both sides by 3 to end up with

s : 2f

Meaning "each cup of sugar needs 2 cups of flour".

--------------------

Meanwhile, the bread recipe calls for 2s for every 8f.

2s : 8f

2s/2 : 8f/2 .... divide both sides by 2

s : 4f

When making bread, each cup of sugar needs 4 cups of flour. In other words, the amount of flour is quadruple that of the sugar.

--------------------

Recap

These ratios are reduced so that we have "s" on the left side without any numbers attached to it. In other words, we have 1s.

We can see that the bread needs 2 more cups of flour compared to the cookies (since 4f - 2f = 2f). It's important that we reduce those ratios so that we're talking about the same amount of sugar for each food item.

This is why  choice B   is the final answer.

--------------------

An example:

Each food item will use 1 cup of sugar.

The cookies need twice the amount of flour, so the cookies require 2 cups of flour (because of the ratio s:2f mentioned earlier).

The bread needs quadruple the amount of flour compared to sugar. Meaning the bread needs 4 cups of flour (because of the ratio s:4f).

Then subtract to get

(4 cups flour for bread) - (2 cups flour for cookies) = 2 cups flour

Answer:

Step-by-step explanation:

You want the remainder of a number when divided by 3 if (1) the sum of digits is 5, and (2) the remainder from division by 9 is 5.

The sum of digits of a 2-digit number will be 5 if that number is one of ...

  {14, 23, 32, 41, 50}

In every case, the remainder when divided by 3 is 2. Effectively, it is the remainder of 5 when that is divided by 2.

In addition to the numbers listed above, 2-digit numbers with a sum of digits of 14 will also have a remainder of 5 when divided by 9. This adds five more numbers to the list:

  {59, 68, 77, 86, 95} . . . . have remainders of 5 when divided by 9

The remainders when divided by 3 are all 2 for these numbers as well.

__

Additional comment

The process of (recursively) summing the digits of a positive integer is called "casting out 9s". It effectively finds the modulo 9 value of the number, with the exception that a sum of 9 corresponds to a modulo 9 value of 0.

Since 9 is divisible by 3, the modulo 3 value of a number will be the modulo 3 value of the modulo 9 value. In other words, if the sum of digits is 5, or the remainder from division by 9 is 5, then the mod 3 value is 5 mod 3 = 2.

A burrito costs $2 at Taco Hut. Let's use "b" to represent the cost of a burrito and "t" to represent the cost of a taco.

From the problem, we know that:

4b + 5t = 13 (for Clark)

5b + 3t = 13 (for Bruce)

We want to determine the cost of a burrito, so we can solve for "b" using the second equation:

[tex]5b + 3t = 13\\5b = 13 - 3\\b = (13 - 3t)/5[/tex]

Now we can substitute this expression for "b" into the first equation:

[tex]4b + 5t = 13\\4[(13 - 3t)/5] + 5t = 13\\52/5 - 12t/5 + 5t = 13\\52 - 12t + 25t = 65\\13t = 13\\t = 1[/tex]

So we know that a taco costs $1. Now we can substitute this value into either of the original equations to solve for "b":

[tex]5b + 3t = 13\\5b + 3(1) = 13\\5b = 10\\b = 2[/tex]

Therefore, a burrito costs $2 at Taco Hut.

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Justin's speed on his way to his parents' house was 42 mph. Therefore, his speed on his way back home was 18 mph slower, or 18 mph.

Let's use x mph to represent the pace at which Justin was travelling to his parents' house. Then, as he travelled 24 mph slower owing to the terrible weather, his speed on the way back would be (x - 24) mph.

By dividing the distance he drove by his speed, one may determine how long it took Justin to drive to his parents' house, or:

Time is a function of both speed and distance.

Similar to how long it would take Justin to drive back home:

Time is a function of distance and speed (x - 24)

Justin drove for a total of 12 hours, so we can construct the following equation:

420/x + 420/(x-24) = 12

By multiplying both sides of the equation by x(x-24), we may simplify the equation and find the value of x. After some algebraic fiddling, we arrive at:

[tex]x^2 - 24x - 840 = 0[/tex]

We can find the value of x by using the quadratic formula:

[tex]x = (24 +- \sqrt{(242 + 41840)}) / 2[/tex] or x = -18

We can determine that Justin was travelling at a speed of 42 mph as he made his way to his parents' home because the speed cannot be negative. Thus, he travelled at a speed of 18 mph less on the way back home.

We can confirm the following to see if the solution is accurate:

420/42 + 420/18 = 10 + 23.33 = 33.33

Justin did, in fact, drive for a total of 12 hours, proving that our answer is accurate.

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The extraneous solution which arises when solving for the point of intersection of the line and the square root function is 20.

What is an extraneous solution?

An extraneous solution in mathematics is a solution that develops during the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.

We are given two equations as f(x) = [tex]\frac{-1}{2}[/tex]x + 6 and f(x) = √x - 4.

Now, on equating both the equations, we get

⇒ [tex]\frac{-1}{2}[/tex]x + 6 = √x - 4

On squaring both sides, we get,

⇒ [tex](\frac{-1}{2}x + 6)^{2}[/tex]= x - 4

⇒ [tex]\frac{1}{4}x^{2}[/tex] + 36 - 6x = x - 4

⇒ [tex]\frac{1}{4}x^{2}[/tex] + 40 = 7x

⇒ [tex]\frac{1}{4}x^{2}[/tex] -7x + 40 = 0

⇒ [tex]x^{2}[/tex] -28x + 160 = 0

⇒ x = 20 , 8

For point of intersection, we will substitute x = 20 in both the equations.

So, we get

⇒ f(x) = [tex]\frac{-1}{2}[/tex] (20) + 6

⇒ f(x) = -10 + 6

⇒ f(x) = -4

Similarly,

⇒ f(x) = √20 - 4

⇒ f(x) = √16

⇒ f(x) = 4

Since both the solutions are not same so this is an extraneous solution.

Hence, the extraneous solution which arises is 10.

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The propensity scoring method is a statistical technique used to adjust for differences in the characteristics of groups being compared in a study. In this case, we want to adjust for the fact that respondents aged 70 or older are underrepresented in an internet sample.

To do this, we can assign a propensity score to each individual in the sample based on their likelihood of being in the sample, given their age. We can then use this score to weight their responses to account for the underrepresentation of older individuals.

In this case, we know that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. This means that we can assign a propensity score of 3 to each individual aged 70 or older in the sample, and a propensity score of 1 to everyone else.

Using these propensity scores, we can weight the responses of each individual in the sample. Responses from individuals with a propensity score of 3 would be weighted by a factor of 3, while responses from individuals with a propensity score of 1 would be weighted by a factor of 1.

By adjusting for the underrepresentation of older individuals in this way, we can obtain more accurate estimates of the characteristics of the population being studied, and reduce the potential for bias in our analysis.

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Answer:

19. sqrt{305}

20. 3*sqrt{7}

Step-by-step explanation:

You use the Pythagorean theorem, which can be applied to right triangles. It states that x^2+y^2 = hypotenuse ^2, where x and y are the two sides other than the hypotenuse.

Step-by-step explanation:

hope this will gel help u

We can deduce that X + 4 = 8 by looking at the top row & second column. The X value is therefore 4.

an arrangement of written or printed items on a page that are vertical. a vertical part of a printed page divided into two or more equal columns of numbers.

X + 4 corresponds to a value in the second column and top row.

The third row's value is equal to the first column's value plus two.

(Third row, second column) The value is 12 at the bottom right corner.

First row and the first column, top left, represents value as B.

It reads 8, first row, second column, in the upper right corner.

C is the value located on the bottom left (third row, first column).

We can deduce that X + 4 equals 8 from top row & second column. Hence, we can find X:

X plus 4 = 8

When we take 4 away from both sides, you get:

X = 4

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