Lin has 27 marbles. He divides them into 3 equal groups and gives 1 group to Jill. Jill then gives 2 of hers away. How many marbles does Jill have now?

Therefore, Equations 1 and 2 are: Equation 1: g = 360h

Equation 2: w = 2,000 + 360h.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal in solving an equation is to find the value of the variable that makes the equation true. Equations are used extensively in mathematics and science to model real-world phenomena and solve problems.

by the question.

We know that the hose puts water into the pool at a rate of 360 gallons per hour. Therefore, after h hours, the hose has put g gallons of water into the pool. We can express this relationship using the following equation:

Equation 1: g = 360h

We also know that the pool already had 2,000 gallons of water in it before Johnathan started filling it with the hose. Therefore, the total number of gallons of water in the pool after h hours is given by:

w = 2,000 + g

We can substitute the expression for g from Equation 1 into this equation to obtain an equation that relates g and w:

Equation 2: w = 2,000 + 360h

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We may take the number of people who ordered a salad out of the total to find the number of individuals who did not order one:

12 - 4 = 8 people did not order a salad.

The expression to use to estimate the number of persons that ordered the salad would be

(1/3) x 12 = 4 people ordered a salad

Every mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Everything with a variable value is anything whose value changes over time. Typically, alphabetical letters like a, b, c, m, n, p, x, y, and z are used to denote expression variables. A combination of several variables and integers can be used to create a variety of expressions.

from the question:

We can utilize the information that 1/6 of customers ordered a shrimp po'boy and 1/2 ordered a cheeseburger to estimate how many individuals ordered the salad. Hence, the proportion of customers that choose a salad is:

1 - (1/6 + 1/2) = 1 - 2/3 = 1/3

Hence, to count how many people ordered the salad, the statement would be:

4 individuals (1/3) x 12 ordered salads.

We may take the number of people who ordered a salad out of the total to find the number of individuals who did not order one:

Those who did not order a salad were 12 - 4 = 8.

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The triangular system has, by means of fractions, a total shaded area of 27 / 2 square centimeters.

In this problem we have the area of an entire triangle, from which we need to determine the total shaded area, this can be done by subtracting triangles from the entire triangle, by means of fractions, whose complete operation is shown below:

A = 32 - (1 / 4) · 32 - (3 / 4) · (1 / 4) · 32 - (3 / 4)² · (1 / 4) · 32

A = [1 - 1 / 4 - (3 / 4) · (1 / 4) - (3 / 4)² · (1 / 4)] · 32

A = 27 / 2 cm²

Please notice that shaded areas are positive and blank areas are negative.

By means of fractions, the total shaded area of the triangular system is equal to 27 / 2 square centimeters.

The statement is incomplete. After a quick investigation we conclude that the complete statement is the following:

The area of a complete triangle (without blank spaces) is 32 square centimeters, please compute the total shaded area, that is, the area of the composite figure seen in the figure.

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Answer:

56 muffins

Step-by-step explanation:

Since it takes  1/8 cup to make one muffin, 1 cup can make 8 times as many muffins or 8 muffins with 1 cup of raisins

With 7 cups he can make 7 x 8 = 56 muffins

"From days 3 to 5, the high temperature changed by an average of almost 4 degrees per day," is the appropriate answer.

We can determine the average rate of change from day 3 to day 5 by splitting the difference in high temperature between those two days by the distance between them (which is 2), or 2.

The highest temps on Day 3 was 85°F.

The highest temperature on Day 5 was 77°F.

Extreme temperature variation: 77°F to 85°F equals -8°F

Between day three and day five, there are two days.

(Change in maximum temperature) / (number of days) yields an average rate of change of -8°F / 2°F per day.

This leads to the conclusion that the right response is "The high temperature changed by an average of 4 degrees per day from day 3 to day 5".

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According the question given above the present value of the cash flows is $12,114.36.

Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.

Tο calculate the present value (PV) οf the cash flοws (CFs), we need tο discοunt each cash flοw tο its present value using the given rate οf 12%. The fοrmula tο calculate the present value οf a cash flοw is:

[tex]PV = CF / (1 + r)^n[/tex]

where:

PV = present value οf the cash flοw

CF = cash flοw amοunt

r = discοunt rate

n = number οf periοds (in this case, the number οf years)

Using this fοrmula, we can calculate the present value οf each cash flοw as fοllοws:

[tex]PV(CF0) = 0 / (1 + 0.12)^0 = 0[/tex]

[tex]PV(CF1) = 1500 / (1 + 0.12)^1 = 1339.29[/tex]

[tex]PV(CF2) = 1500 / (1 + 0.12)^2 = 1191.08[/tex]

[tex]PV(CF3) = 3000 / (1 + 0.12)^3 = 2382.16[/tex]

[tex]PV(CF4) = 4500 / (1 + 0.12)^4 = 3221.56[/tex]

[tex]PV(CF5) = 5000 / (1 + 0.12)^5 = 3080.27[/tex]

Tο find the present value οf all the cash flοws, we simply add up the present values οf each cash flοw:

PV = PV(CF0) + PV(CF1) + PV(CF2) + PV(CF3) + PV(CF4) + PV(CF5)

= 0 + 1339.29 +1191.08 + 2382.16 + 3221.56 + 3080.27

= 12114.36

Therefοre, the present value οf the cash flοws is $12,114.36.

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Answer: Let's denote the first term of the geometric sequence as "a", and the common ratio as "r". Then, we can use the given information to set up a system of equations:

a * r^3 = 18 (the fourth term is 18, so ar^3 is the fourth term)

a * r^6 = 16/3 (the seventh term is 16/3, so ar^6 is the seventh term)

To solve for "a" and "r", we can divide the second equation by the first equation:

(a * r^6) / (a * r^3) = (16/3) / 18

Simplifying this expression, we get:

r^3 = (16/3) / 18 = 16/54 = 8/27

Taking the cube root of both sides, we get:

r = 2/3

Substituting this value of "r" into the first equation, we can solve for "a":

a * (2/3)^3 = 18

a = 18 / (2/3)^3

a = 27

Therefore, the first term of the geometric sequence is 27, and the nth term is given by:

a * r^(n-1) = 27 * (2/3)^(n-1)

Step-by-step explanation:

Answer:

e

Step-by-step explanation:

5(4x +3)=-4(5-2x)

5×4x +5×3=-4 ×5 -4 × -2x

20x +15=-20+8x

Answer:

x ≈ 46.1

Step-by-step explanation:

using the sine ratio in the right triangle

sin19° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{15}{x}[/tex] ( multiply both sides by x )

x × sin19° = 15 ( divide both sides by sin19° )

x = [tex]\frac{15}{sin19}[/tex] ≈ 46.1 ( to the nearest tenth )

The rule broken in the first argument is of undistributed middle.

The rule broken in the second argument is of exclusive middle.

What is Converse?

In logic and mathematics,  converse of statement is formed by switching  hypothesis and conclusion of original statement. For example,  converse of the statement "If it rains, the streets get wet" is "If the streets get wet, it is raining."

The first argument violates the rule of the undistributed middle. The argument appears to be the fallacy of the converse of the inverse. This is a form of invalid reasoning where the contrapositive of a true statement is used as evidence for the original statement. The argument could be stated in syllogistic form as:

Premise 1: All P are Q.

Premise 2: No Q are S.

Conclusion: Some P are not S.

This argument is invalid because it violates the rule of the undistributed middle. The middle term Q is not distributed in either premise, which means that we cannot logically conclude anything about the relationship between P and S.

The second argument violates the rule of the exclusive middle. The argument appears to be the fallacy of the illicit conversion. This is a form of invalid reasoning where the subject and predicate terms of a statement are switched without changing the truth value of the statement. The argument could be stated in syllogistic form as:

Premise 1: All A are B.

Premise 2: All B are C.

Conclusion: All C are A.

This argument is invalid because it violates the rule of the exclusive middle. The argument assumes that there are only three categories of things: A, B, and C. However, this assumption is not justified, and there may be other categories that are not included in the argument.

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Answer:

80 percent

Step-by-step explanation:

Step-by-step explanation:

a parallel line has the same slope. they just have different y-intersects (the y- value when x = 0).

the slope is the factor of x : -53

the y-intercept is given with the provided point (0, 2).

so, line j is

y = -53x + 2

Answer:

Step-by-step explanation:

If 1-2i is a zero of the polynomial, then its conjugate 1+2i is also a zero. This is because complex zeros of a polynomial with real coefficients always occur in conjugate pairs.

Let's use synthetic division to factor out the polynomial with the given zeros:

1-2i | 4 0 17 14 65

| 4 -8i -9+2i -12

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

4 4 -8i -9+2i 53

So we have factored the polynomial as:

f(x) = (x - 1 + 2i)(x - 1 - 2i)(4x^2 + 4x - 53)

Now we need to find the zeros of the quadratic factor:

4x^2 + 4x - 53 = 0

Using the quadratic formula, we get:

x = (-4 ± sqrt(16 + 4453)) / 8

x = (-4 ± sqrt(848)) / 8

x = (-4 ± 4sqrt(53)) / 8

x = (-1 ± sqrt(53)) / 2

So the remaining zeros are (-1 + sqrt(53))/2 and (-1 - sqrt(53))/2.

Their realized income must be $567,000 per year to make the monthly payments on the mortgage.

The average interest rate on a 30-year fixed mortgage as of today, March 9, 2023, is 7.13%, up 7 basis points from one week ago. The average 30-year fixed refinancing interest rate is currently 7.12%, which is a decrease of 2 basis points over the previous week.

We must apply the following calculation to compute the amount of money needed each month to pay the mortgage:

Payment each month is (P * r) / (1 - (1 + r)(-n))

where:

P is the principal sum (the amount of the house minus the down payment)

r is the ongoing interest rate (annual interest rate divided by 12)

n is the overall number of payments (number of years multiplied by 12)

The major sum, as far as we are aware, is:

P = $187,500 - (20% * $187,500) = $150,000

The monthly interest rate is as follows because we also know that the interest rate is 4.65%:

r = 0.0465 / 12 = 0.003875

Finding the total number of payments is our last step. The number of months it will take to pay off the mortgage may be calculated using the knowledge that they will be paying $1,575 per month:

$1,575 = ($150,000 * 0.003875) / (1 - (1 + 0.003875)^(-n))

This equation is simplified, and the result is:

1 - (1 + 0.003875)^(-n) = ($150,000 * 0.003875) / $1,575

(1 + 0.003875)^(-n) = 1 - (($150,000 * 0.003875) / $1,575)

(-n) * log(1 + 0.003875) = log(1 - (($150,000 * 0.003875) / $1,575))

n = log(1 - (($150,000 * 0.003875) / $1,575)) / log(1 + 0.003875)

Calculating n, we discover that it roughly corresponds to 360 months (or 30 years).

Their realised income must therefore be:

Realized income is $1,575 multiplied by 12 months in a year for 30 years, or $567,000 annually.

Their realised income must be $567,000 annually in order to cover the mortgage payments.

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The probability that the sample mean weight change is greater than 10 pounds is p(M > 10) = 0.9088.

To find the probability that the sample mean will be greater than M = 10 pounds, we need to standardize the sample mean using the formula for z-score:

z = (M - µ) / (σ / √n)

Substituting the given values, we get:

z = (10 - 15) / (6 / √4)

z = -1.33

Using a standard normal distribution table or calculator, we can find the probability that z is greater than -1.33, which is approximately 0.9088.

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The true inequality from the list of options is (c) -x - 6 > -3.5

To determine which inequality is true when x is -5, we need to substitute -5 for x in each inequality and simplify.

a) -x – 6 < -3.5

Substituting x = -5, we get:

-(-5) - 6 < -3.5

5 - 6 < -3.5

-1 < -3.5

This is false, so option a) is not true.

b) -x – 6 > 3.5

Substituting x = -5, we get:

-(-5) - 6 > 3.5

5 - 6 > 3.5

-1 > 3.5

This is false, so option b) is not true.

c) -x - 6 > -3.5

Substituting x = -5, we get:

-(-5) - 6 > -3.5

5 - 6 > -3.5

-1 > -3.5

This is true, so option c) is true.

Hence, the correct option is (c) -x - 6 > -3.5

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Complete question

Which inequality is true when the value of x is -5?

a) -x – 6 < -3.5

b) -x – 6 > 3.5

c) -x - 6 > -3.5

d) x - 6 > -3.5

There are total 56 combination of your locker contains 3 non-repeating digits from the numbers 0-9.

Combinations are mathematical operations that count all possible arrangements of a set of components when the order in which they are selected is irrelevant. Components for combos can be selected in any hierarchy.

Moreover, there are two other kinds of combinations (the specific sequence is not relevant at this time): It's acceptable to repeat phrases like "coins in your pocket" (5,5,5,10,10) In the same way, lottery numbers (2,14,15,27,30,33)

Combinations are mathematical operations that count all possible arrangements of a set of components when the order in which they are selected is irrelevant. Components for combos can be selected in any hierarchy.

Permutations and combinations are compatible.

As the first digit is fixed i.e. 9,

So, there are 2 non-repeating digits left,

Using permutations,

we are left with 8 × 7 = 56 ways.

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Answer:

slope = [tex]\frac{11}{15}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-x_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (9, 4 ) and (x₂, y₂ ) = (- 6, - 7 )

m = [tex]\frac{-7-4}{-6-9}[/tex] = [tex]\frac{-11}{-15}[/tex] = [tex]\frac{11}{15}[/tex]

Answer:

The answer is B)2

Step-by-step explanation:

As you can see, the length and height of the bigger rectangle is twice the length and height of the smaller rectangle.

A graph that represent the given function include the following: graph C.

In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

By critically observing the graph of the piecewise-defined function g shown in the image attached below, we can logically deduce the following functions;

When the domain is x < -2, we have:

f(x) = 5 (< should be used because the endpoint is an open circle).

When the domain is -2 ≤ x < 0, we have:

f(x) = 3 (< should be used because the endpoint is an open circle and ≤ for the closed circle).

When the domain is 0 ≤ x < 2, we have:

f(x) = 0 (< should be used because the endpoint is an open circle and ≤ for the closed circle).

When the domain is x ≥ 2, we have:

f(x) = -3 (≥ should be used because the endpoint is a closed circle).

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Answer:

-f(x+3) and -2f(x)+4

Step-by-step explanation:

it is all the ones with a negative in front of the function, so that is -f(x+3) and -2f(x)+4.

Answer:

Step-by-step explanation:

You want to know the names of a 4-sided figure with opposite sides congruent and adjacent sides perpendicular.

A 4-sided figure is a quadrilateral.

When opposite sides are the same length, the quadrilateral is a parallelogram.

When corners of a parallelogram are right angles, it is a rectangle.

__

Additional comment

A rhombus also has congruent adjacent sides, as does a square. We are not told that is the case here. A trapezoid is not a parallelogram.

The types of functions are as follows:

1) Quadratic function

2) None of the above

3) Exponential function.

What is a function?

A relation between a set of inputs and a set of allowable outputs is called a function. It has the property that every input is associated with exactly one output. A function from one set X to another allocates precisely one element of the other set Y to each element of X. Both the set X and the set Y are referred to as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.

The ways to determine the different functions are  as follows:

a) If for a constant change in x-values, the y-values also change constantly, the function is linear.

b) If as the x values change constantly, the y- values also change, but the difference in differences of y-values remains constant, then the function is quadratic.

c) If the ratio between two consecutive y- values is the same, when x-values change constantly, then the function is exponential.

Let us look into each function.

1) x-values are increasing constantly by one.

The difference in y-values are:

13-7 = 6

21-13 = 8

31-21 = 10

43-31 = 12

Now the difference of difference in y-values.

8-6 = 2

10-8 = 2

12-10 = 2

This is constant. So the function is a quadratic function.

2) The difference in y-values are:

-6+21 = 15

-21+30 = 9

-33+30=  -3

-30 + 33 = 3

This function can be categorised as none of the above.

3) The ratio of the consecutive y-values are:

-12/-3 = 4

-48/-12 = 4

-192/-48 = 4

-768/-192 = 4

Since the ratio is constant, the function is an exponential function.

Therefore the types of functions are as follows:

1) Quadratic function

2) None of the above

3) Exponential function.

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Answer:

To find the inverse of the function p(x) = 4x - 8, we need to switch the x and y variables and solve for y.

Step 1: Replace p(x) with y.

y = 4x - 8

Step 2: Switch x and y variables.

x = 4y - 8

Step 3: Solve for y.

Add 8 to both sides:

x + 8 = 4y

Divide both sides by 4:

y = (x + 8)/4

Therefore, the inverse of the function p(x) = 4x - 8 is q(x) = (x + 8)/4.

Step-by-step explanation:

Answer:see answer

Step-by-step explanation:see answer

Answer:

y=96                                          

     




..........................................................................

Therefore, the probability that the average weight of the sample of 39 Goliath Grouper is within 14 pounds of the average weight of all Goliath Grouper caught on the Treasure Coast is approximately 0.2342 or 23.42%.

In mathematics and statistics, the mean is a measure of central tendency of a set of numerical data. It is also known as the arithmetic mean or average, and is calculated by summing up all the values in the dataset and then dividing by the number of values. The mean provides a useful summary of the data as it gives an idea of the typical or average value in the dataset. It is commonly used in various fields, including finance, science, and social sciences, to analyze and interpret data. However, the mean can be sensitive to extreme values or outliers in the dataset, so it is important to consider other measures of central tendency, such as the median and mode, in addition to the mean.

Here,

We can approach this problem using the central limit theorem, which states that the distribution of sample means will be approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Let's first calculate the standard error of the mean:

standard error of the mean = standard deviation / sqrt(sample size)

= 74 / √(39)

≈ 11.83

Next, we need to find the z-score corresponding to a sample mean within 14 pounds of the population mean:

z = (sample mean - population mean) / standard error of the mean

= (418 - 14 - 418) / 11.83

= -1.19

Using a standard normal distribution table or calculator, we can find that the probability of a z-score less than -1.19 is about 0.1171. Since we're interested in the probability that the sample mean is within 14 pounds of the population mean, we can multiply this probability by 2 to account for the area under the curve in both tails:

P(sample mean within 14 pounds of population mean) ≈ 2 * 0.1171 ≈ 0.2342

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The answer is each of the 4 friends would get 13 snowballs.

52 divided by 4 = 13

Answer: 52 divided by 4 is 13 each of them would get 13 snowballlllsssssss!!!!

Step-by-step explanation:

Part A:

We are given that the height of a tree in a scale drawing is 3.75 inches. The scale of the drawing is 1 inch: 50 feet.

To find the height of the actual tree, we can use the ratio of the drawing scale to the real-life scale. For every 1 inch on the drawing, there are 50 feet in real life.

Therefore, we can set up a proportion:

[tex]$\frac{1 \ \text{inch}}{50 \ \text{feet}} = \frac{3.75 \ \text{inches}}{x \ \text{feet}}$where $x$ is the height of the actual tree in feet.We can solve for $x$ by cross-multiplying:$1 \ \text{inch} \cdot x = 3.75 \ \text{inches} \cdot 50 \ \text{feet}$$x = \frac{3.75 \ \text{inches} \cdot 50 \ \text{feet}}{1 \ \text{inch}} = 187.5 \ \text{feet}$Therefore, the height of the tree is $\boxed{D \ 187.5 \ \text{ft}}$.[/tex]

[tex]Part B:We are now given a new scale drawing where the height of the same tree is 6 inches. We need to find the new scale.Since the tree's height in the new drawing is different, we can use a new proportion to find the new scale.Let the new scale be $1$ inch to $x$ feet. We can set up a proportion:[/tex]

[tex]$\frac{1 \ \text{inch}}{x \ \text{feet}} = \frac{6 \ \text{inches}}{187.5 \ \text{feet}}$where $187.5$ feet is the height of the tree in real life.We can solve for $x$ by cross-multiplying:$1 \ \text{inch} \cdot 187.5 \ \text{feet} = 6 \ \text{inches} \cdot x \ \text{feet}$$x = \frac{1 \ \text{inch} \cdot 187.5 \ \text{feet}}{6 \ \text{inches}} = 31.25 \ \text{ft}$Therefore, the new scale is $\boxed{1 \ \text{inch} : 31.25 \ \text{ft}}$.[/tex]

Answer:

Step-by-step explanation:

Part A:

We can use a proportion to solve for the height of the tree:

1 inch on the drawing represents 50 feet in real life.

So, 3.75 inches on the drawing would represent:

3.75 inches * (50 feet/1 inch) = 187.5 feet

Therefore, the height of the tree is 187.5 feet.

The answer is D) 187.5 ft.

Part B:

The ratio of the height of the tree on the new scale drawing to its actual height must be the same as the ratio of the height of the tree on the original scale drawing to its actual height.

Let the new scale be 1 in. : x feet.

Then, we have the proportion:

1 in. / 50 ft. = 6 in. / (x) ft.

Solving for x, we get:

x = (6 in. * 50 ft.) / 1 in.

x = 300 ft.

Therefore, the new scale is 1 in. : 300 ft.

The answer is 1 in. : 300 ft.

After answering the presented question, we can conclude that As a equation result, the system of equations solution is [tex]x = 64/3 \\and \\y = 62/3.[/tex]

In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). The argument "2[tex]x + 3 = 9,"[/tex] for example, states that the sentence "2x Plus 3" equals the value "9." The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. In the equation [tex]"x^2 + 2x - 3 = 0,"[/tex] the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.

[tex](a) x + y = 34[/tex]

[tex]2x - y = 30[/tex]

The matrix of coefficients is | 1 1 | | 2 -1 |

This matrix's determinant is 130 - 342 = -62.

We can obtain the values of x and y using Cramer's Rule as follows:

[tex]x = det(A1)/det(A) = (-64)/(-3), = 64/3.[/tex]

[tex]y = det(A2)/det(A) = (-62)/(-3), = 62/3.[/tex]

As a result, the system of equations solution is [tex]x = 64/3 and y = 62/3.[/tex]

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The n-th term οf the sequence is given by the fοrmula a_n = 2n + 12.

An arithmetic prοgressiοn is a sequence οf numbers where each term is οbtained by adding a fixed value (called the cοmmοn difference) tο the previοus term. It is a type οf sequence that fοllοws a specific pattern, where the difference between cοnsecutive terms is cοnstant. Arithmetic prοgressiοns are cοmmοnly used in mathematics and variοus fields such as finance, physics, and cοmputer science.

The given sequence has a cοmmοn difference οf 2 between cοnsecutive terms. Therefοre, we can find the n-th term by adding (n-1) times the cοmmοn difference tο the first term οf the sequence.

The first term οf the sequence is 14, and the cοmmοn difference is 2.

Sο, the explicit fοrmula fοr the n-th term οf the sequence is:

a_n = 14 + 2(n-1)

Simplifying, we get:

a_n = 2n + 12

Therefοre, the n-th term οf the sequence is given by the fοrmula a_n = 2n + 12.

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