Pls help I’ve been stuck on this for a while

Answer:

I believe the answer is C. (x + 6)2 + (y − 4)2 = 4

Step-by-step explanation:

Hope this helps :)
Please let me know if its incorrect

The required coefficient on x² is 2, so the answer is 2. Option B is correct.

We can start by assuming that the quadratic function has the form:

y = ax² + bx + c

where a, b, and c are unknown coefficients to be determined. We can use the three given points on the graph to set up a system of three equations in three unknowns:

7 = a(1)² + b(1) + c

16 = a(2)² + b(2) + c

29 = a(3)² + b(3) + c

Simplifying each equation, we get:

a + b + c = 7

4a + 2b + c = 16

9a + 3b + c = 29

We can solve this system of equations using any method of our choice, such as elimination or substitution. One possible approach is to subtract equation 1 from equation 2 and equation 2 from equation 3, which gives:

a + b + c = 7

3a + b = 9

5a + b = 13

a = 2; b = 3; c = 2

Therefore, the equation for the quadratic function in standard form is:

y = 2x² + 3x + 2

The coefficient on x² is 2, so the answer is 2.

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Answer:

Kyle needs 112 marks on his sixth test for the mean test grade to be 90.

Step-by-step explanation:

Let the marks Kyle needs for the sixth test be x.

The mean of all tests is given as 90. The formula for mean would be: (sum of marks obtained in each test)/(total number of tests)

which implies,

(90+83+75+84+96+x)/6 = 90,

(428+x)/6 = 90,

428+x = 540,

x = 112

Therefore, Kyle needs 112 marks on his sixth test for the mean test grade to be 90.

The sum of all values divided by the total number of values determines a dataset's mean (also known as the arithmetic mean, which differs from the geometric mean). It is the most widely applied central tendency measure and is frequently called the "average."

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The volume of the smaller solid is 292 in³ under the condition that two similar solids have surface areas of 45 in² and 80 in². The volume of the larger solid is 320 in³.

Given the two solids are similar, so their corresponding sides are proportional. Let us consider them calling  the ratio of the corresponding sides k.  The ratio regarding their surface areas is k² and the ratio of their volumes is k³.

Let us consider  the volume of the smaller solid V. It is given the surface area of the smaller solid is 45 in² and that of the larger solid is 80 in²

k² = 80/45 = 8/9

k = √(8/9)

= 0.94 (approx.)

It is given the volume of the larger solid is 320 in³.

k³ = 320/V

0.94³ = 320/V

V = 320/(0.94³)

= 292 in³ (approx.)

The volume of the smaller solid is 292 in³.

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The probability of not getting red is 87.5%.

Hence, The correct option is C.

We know that;

Probability = Number of favorable outcomes / Number of samples

Given that;

A spinner with repeated colors numbered from 1 to 8 is shown.

Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red .

You only have one of eight (1/8) evenly divided orange sections.

The rest is not red,

P = (1 - 1/8

P =  7/8

P = 0.875

P = 87.5%

Therefore, spinning once will yield 7/8 odds of not landing on red are,

⇒ 0.875 or 87.5%.

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Answer:

-2x > 6, so x < -3

So A is correct.

The expected value represents the losing amount per game equals to $0.55.

Number of dice rolled = 2

To win $5.00 ,

Roll  2,3,4,10,11 or a 12

To lose $5.00 ,

Roll  5,6,7,8 or 9

Probability of winning or losing on a single roll of 2 dice.

There are 36 possible outcomes when rolling 2 dice.

Since each die has 6 possible outcomes.

Out of these 36 possible outcomes.

There are 6 ways to roll a 7 which is a loss.

And 10 ways to roll a 6 or an 8 also a loss.

Total of 16 losing outcomes.

Similarly, there are 5 ways to roll a 2 or a 12 which is a win.

4 ways to roll a 3 or an 11 also a win.

and 3 ways to roll a 4 or a 10 another win.

Total of 12 winning outcomes.

The probability of winning is 12/36 = 1/3

                                                          =  0.3333 approximately.

The probability of losing is 16/36 = 4/9

                                                        = 0.4444 approximately

The amount of money you can expect to win or lose on a single game,

If you win, you receive $5.00.

If you lose, you lose $5.00.

The expected value you win or lose per game is

Expected value

= (Probability of winning x Amount won) - (Probability of losing x Amount lost)

⇒ Expected value = (1/3 x $5.00) - (4/9 x $5.00)

⇒ Expected value = ($1.67) - ($2.22)

⇒ Expected value = -$0.55

Therefore, on average expected value to lose $0.55 per game.

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Is the relation a function and explain your reasoning: B. The relation is not a function because the output value Walking has different input values, and the same with No walk.

In Mathematics, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).

This ultimately implies that, an input value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the output value on the y-coordinate of a cartesian coordinate.

Based on the table, we can logically deduce that the relation does not represent a function because each of its input value (domain) has more than one dependent value (range) i.e Walked and No Walk.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: 63 minutes

Step-by-step explanation:

Use proportions:

8/84 = 6/x

Cross multiply to get:

8x = 504

Simplify by dividing by 8 on both sides.

x = 63.

Answer:

65 apples

Step-by-step explanation:

We Know

John has 8 boxes of apples.

Each box holds 10 apples.

If 5 of the boxes are full, and 3 of the boxes are half full, how many apples does John have?

Let's solve

5 boxes are full: 5 x 10 = 50 apples

3 boxes are half full = 3(1/2 · 10) = 15 apples

50 + 15 = 65 apples

So, John has 65 apples.

Hence, log(sqrt(3.5.11),9) in its enlarged version is roughly similar to 0.2148. We may answer this question by using the definition of logrithmic.

Mathematical operations that relate to a number's logarithm are known as logarithmic functions. The power that a given basis must be increased in order to obtain a particular number is known as the logarithm of the number.

Although 10 (also known as the common logarithm) is the base that is most frequently used, logarithms can be calculated in relation to any positive base higher than 1. If the base is 10, the logarithm of such an integer x with regard to a base b is written by log(base b)(x), or just log(x).

We can compress the given logarithm via the logarithmic identity log(base a)(bc) = c * log(base a)(b):

Sqrt(3.5.11) = Log((3.5.11)(1/2), 9) = Log((3.5.11)*(1/2), 9) = (1/2) * Log (3.5.11, 9)

We must now calculate that logarithm of 9 in base 3.5.11. This can be changed to a log with a more recognisable column, such as base 10 or base e, using the change-of-base formula. Using the base 10 scale

3.5.11, 9) = 9)/log (3.5.11)

We can calculate this using a calculator:

log(9) = 0.9542 (reduced to 4 decimal places)

log(3.5.11) = log(3) + log(5) + log(11) = 0.4771, 0.6978, and 1.0414, respectively, yielding 2.2174. (rounded to 4 decimal places)

Therefore:

sqrt(3.5.11),9 = (1/2) log(3.5.11,9) = (1/2) log(9)/log(3.5.11)) = (1/2) log(0.9542/2.2174) = 0.2148 log(3.5.11,9) = (1/2) log(3.5.11, 9) = (1/2) 

Hence, log(sqrt(3.5.11),9) in its enlarged version is roughly similar to 0.2148.

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The expanded form of the logarithm is:

log base 9 √(3.5.11) = log base 9 (3) + log base 9 (5) + log base 9 (11)

What is logarithm?

A logarithm is a mathematical function that tells us what exponent is needed to produce a given number, when that number is expressed as a power of a fixed base. In other words, logarithms tell us how many times we need to multiply the base by itself to get the desired number.

We can use the property of logarithms that says:

log base b (a * c) = log base b (a) + log base b (c)

to expand the logarithm.

Therefore, we have:

log base 9 √(3.5.11) = log base 9 √(3 * 5 * 11)

= log base 9 (3) + log base 9 (5) + log base 9 (11)

So, the expanded form of the logarithm is:

log base 9 √(3.5.11) = log base 9 (3) + log base 9 (5) + log base 9 (11)

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Yes (-3,-2) is true.

No (1,6) is false

No (0,4)  is false

To determine if an ordered pair is a point of intersection between the line and the parabola, we need to check if the coordinates satisfy both equations.

(-3, -2)

y = 2x + 4 => -2

= 2(-3) + 4 => -2 = -2 (True)

y = x² + 4x + 1 => -2

= (-3)² + 4(-3) + 1 => -2 = -2 (True)

Answer: Yes

(1, 6)

y = 2x + 4 => 6

= 2(1) + 4 => 6 = 6 (True)

y = x² + 4x + 1 => 6

= (1)² + 4(1) + 1 => 6 ≠ 6 (False)

Answer: No

(0, 4)

y = 2x + 4 => 4

= 2(0) + 4 => 4 = 4 (True)

y = x² + 4x + 1 => 4

= (0)² + 4(0) + 1 => 4 ≠ 1 (False)

Answer: No

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a) Etsuko's maximum speed is 4.19 m/s.

b) Bachico is traveling 1.61 times faster than Etsuko.

c) The maximum distance from the pole to the outer ring of horses is 3.56 meters.

d) The time between consecutive "yays" is 7.5 seconds.

Let's call the maximum speed of the carousel V. Then, the circumference of the circular path traveled by the outermost ring of horses is:

C = 2πr, where r is the distance between the pole and the outermost ring of horses.

The time it takes for the carousel to complete one revolution is:

T = C/V

We can use the information given in the problem to set up an equation for the total time it takes for the siblings to pass their mother 17 times:

T = T₁ + 16T₂ = 6 minutes = 360 seconds

So, the time it takes for Etsuko's horse to complete one revolution is:

T₁ = C₁/V

The distance that Etsuko's horse travels between consecutive passes of the mother is equal to the difference in the distances traveled by the innermost and middle rings of horses during one revolution, which is:

Δd = 2.41 - 1.5 = 0.91

So, the time it takes for the carousel to complete one revolution between subsequent passes of the mother is:

Solving for V, we get:

V = 4.19 m/s

Therefore, Etsuko's maximum speed is 4.19 m/s.

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Answer:

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

Use the formula for compound interest :

Where:

In this problem, we have:

Now, let's plug these values into the formula:

After 6 years, Lex will have approximately $1780.77 in his savings account.

Answer: A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6 can be expressed in the following form:

f(x) = 7x^5 + ... + ... + ... + ... + 6

Step-by-step explanation: Since the polynomial has a degree of 5, it will have 6 terms in total, including the constant term. However, the other coefficients are unknown, so we need more information to determine them. For example, we could be given additional roots or points on the curve.

Without any further information, the polynomial can only be expressed in this general form.

A. If the bank had compounded the interest quarterly for the three years, the interest rate would be divided by 4 (since there are 4 quarters in a year) and the number of compounding periods would be multiplied by 4. This is because the interest would be calculated and added to the account balance every quarter, rather than just once a year.

B. To represent the account balance if interest is compounded quarterly, we need to use the formula for compound interest with quarterly compounding:

A = P(1 + r/n)^(nt)

where A is the account balance, P is the principal (initial deposit), r is the annual interest rate (8.5%), n is the number of times the interest is compounded per year (4 for quarterly compounding), and t is the number of years (3).

Substituting the given values into the formula, we get:

A = 1500(1 + 0.085/4)^(4×3)

A = 1500(1.02125)^12

A ≈ $1,969.36

Therefore, the new expression for the account balance, in dollars, if interest is compounded quarterly is:

$1,969.36 = 1500(1 + 0.085/4)^(4×3)

A coin is biased so that the probability a head comes up when it is flipped is 0.6. Therefore, we can expect to get 6 heads when a biased coin with a probability of 0.6 for heads is flipped 10 times.

To find the expected number of heads when a biased coin is flipped 10 times, we can use the formula:

Expected number of heads = Probability of getting a head × Number of times the coin is flipped

In this case, the probability of getting a head is 0.6 and the coin is flipped 10 times. So the expected number of heads is:
Expected number of heads = probability of getting a head x number of times flipped

Expected number of heads = 0.6 x 10

Expected number of heads = 6

Therefore, the expected number of heads when the coin is flipped 10 times is 6.

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The mean is 89, the median is 89, the mode is 89, and the range is 22.

The mean is 72.6, the median is 76, there is no mode, and the range is 25.

The mean is 60.5, the median is 57.5, there is no mode, and the range is 55.

The mean, median, mode, and range of the given data are calculated as follows:

Mean = sum of values/ number of values

The median is the middle score when the scores are arranged in order from lowest to highest

Mode is the number that occurs most

The range is the difference between the largest and smallest values

1. Mean = (98 + 89 + 76 + 93 + 89) / 5

Mean = 89

76, 89, 89, 93, 98

The median is 89.

The mode is also 89.

Range = 98 - 76

Range = 22

2. Mean = (59 + 63 + 84 + 76 + 81) / 5

Mean = 72.6

Median: 59, 63, 76, 81, 84

The median is 76.

There is no mode for this set of score

Range = 84 - 59

Range = 25

3. Mean = (36 + 48 + 67 + 91) / 4

Mean = 60.5

Median: 36, 48, 67, 91

Median = (48 + 67) / 2

Median = 57.5

The data has no mode

Range = 91 - 36

Range = 55

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Answer:

Step-by-step explanation:

the sum of the internal angles of a regular or irregular pentagon is 540°, we remove the known angles and we will have the answer

540 - 110 - 110 - 120 - 120 =

80°

To solve the equation 2y − 2.3 = 4.1  for y, we can use algebraic manipulation.

In order to remove the constant term on the left-hand side of the equation, we first add 2.3 to both sides of the equation:

                                 2y - 2.3 = 4.1

                     +2.3                          +2.3

                                   2y = 6.4

Now, we divide both sides by 2 to isolate y:

                                 2y = 6.4

                            ÷2               ÷2

                                  y = 3.2

So, the solution to this equation is  y = 3.2

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We need to isolate the variable on one side of the equation in order to solve an equation like this. By carrying out the same method on both sides of the equation, we can do this. In this example, we divided both sides by 2 to isolate y after adding 2.3 to both sides to remove the constant term on the left-hand side.

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- A term in an algebraic equation that has no variables and is steady is known as a constant term in mathematics. A constant is a fixed, unchanging value. A constant in algebra can be a number on its own or sometimes a letter like a, b, or c to show a fixed integer.

- To separate y from all other terms in an equation, the equation must be rewritten so that y is on one side and all other terms are on the other side. It allows us to calculate the value of y and solve for it.

- Mathematical operations including addition, subtraction, multiplication, and division are used to rearrange algebraic expressions or equations to try to simplify or solve them. This process is known as algebraic manipulation. By doing the opposite operations (undoing) to any equation, algebraic manipulation tries to isolate a variable or simplify an expression in order to solve for a certain variable.

Since the p-value is less than the significance level of 0.10, we reject the null hypothesis. Since the confidence interval does not contain 0, it supports the alternative hypothesis that commercial trucks have a higher proportion of violations than passenger cars.

a. Hypothesis Test:

Null Hypothesis: The proportion of passenger cars with only rear license plates is equal to or greater than the proportion of commercial trucks with only rear license plates.

Alternative Hypothesis: The proportion of commercial trucks with only rear license plates is greater than the proportion of passenger cars with only rear license plates.

Let p1 be the proportion of passenger cars with only rear license plates, and p2 be the proportion of commercial trucks with only rear license plates.

The test statistic for comparing two proportions is the z-test.

z = ((p1 - p2) - 0) / √(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

where p_hat = (x1 + x2) / (n1 + n2) is the pooled sample proportion, and x1 and x2 are the number of successes (only rear license plates) in the two samples, and n1 and n2 are the sample sizes.

Plugging in the values, we get:

p1 = 227/2094 = 0.1084

p2 = 46/330 = 0.1394

p_hat = (227 + 46) / (2094 + 330) = 0.1116

n1 = 2094

n2 = 330

z = ((0.1084 - 0.1394) - 0) / √(0.1116 * (1 - 0.1116) * (1/2094 + 1/330))

= -1.68

The p-value for this one-tailed test is P(Z < -1.68) = 0.0475.

Conclusion: The data provides sufficient evidence to support the claim that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

b. Confidence Interval:

We can also construct a confidence interval to estimate the difference in proportions with a specified level of confidence.

A 90% confidence interval for the difference in proportions can be calculated as:

(p1 - p2) ± z√(p1(1-p1)/n1 + p2*(1-p2)/n2)

Plugging in the values, we get:

(p1 - p2) ± 1.645√(0.1084(1-0.1084)/2094 + 0.1394*(1-0.1394)/330)

= (-0.0499, 0.0094)

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Answer:
Range: Men: 10, Women: 11
MAD: Men: 2.833333 (17/6), Women: 3

Step-by-step explanation:

The range of the men's scores is 75-65 (highest-lowest), which is 10.

The range of the woman's scores is 80-69, which is 11.

The MAD is the mean of the absolute difference between the terms and the mean, which is very painful to do, but in the sake of the problem, I will be doing.

Men's MAD:
The mean is [tex]\frac{65+68+70+72+73+75}{6}[/tex], which is 70.5.

Sigh.

Now, we find the difference of each term to the mean.

[tex]70.5-65= 5.5[/tex]

[tex]70.5-68=2.5[/tex]

[tex]70.5 - 70 = 0.5[/tex]

[tex]72-70.5=1.5[/tex]

[tex]73-70.5=2.5[/tex]

[tex]75-70.5=4.5[/tex]

wow. Now, we find the mean of these numbers.

[tex]\frac{5.5 + 2.5 + 0.5 + 1.5 + 2.5 + 4.5}{6}[/tex]= 17/6=2.8333333333 This is the MAD.

For the Women's, I'll speed over it.

The mean is 74.

The MAD is 3.

The probability that sum of the two dice on a roll is 5 given that the blue die for that roll landed on 6 is 0.25 or 25%.

If we know that the blue die landed on 6, then we only need to consider the possible outcomes of the roll of the red die that would result in a sum of 5.

If red die shows 1, 2, 3 or 4, then the sum of the dice will be 6. There are a total of 6 possible outcomes for the roll of the red die (since it is a standard 6-sided die), but we can eliminate the outcomes 5 and 6 since they would result in a sum greater than 5.

So, out of the 4 possible outcomes for the roll of the red die that would result in a sum of 5, only one of them will occur if the blue die landed on 6. Therefore, the probability of getting a sum of 5 given that the blue die landed on 6 is:

1/4 = 0.25 or 25%

Hence the probability of the sum being 5 is 0.25 or 25%.

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The correct answer is D. No, events E and G are not necessarily disjoint. The mutual exclusivity of events F and G does not guarantee the mutual exclusivity of events E and G.

The example provided in option D shows that events E and F are disjoint, events F and G are disjoint, but events E and G are not disjoint. This is because they share the element 2.

For example, E = {0,1,2}, F = {3,4,5}, and G = {2,6,7} .

Therefore, the mutual exclusivity of events F and G does not guarantee the mutual exclusivity of events E and G.

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The probability that the length of time between charges will be between 40 and 70 hours is 0.656.

To solve this problem, we need to standardize the values of 40 and 70 using the given mean and standard deviation, and then use the standard normal distribution table to find the probability.

Standardizing 40: z = (x - mu) / sigma z = (40- 50)/15 z = -2/3

Standardizing 70: z = (x-mu) / sigma z = (70- 50)/15 z 4/3

Now we look up the probabilities associated

with the standardized values -2/3 and 4/3 in the

standard normal distribution table.

Using the table, we find that the probability of z being less than -2/3 is 0.2525 and the probability of z being less than 4/3 is 0.9082.

So the probability of the length of time being between 40 and 70 hours can be found by subtracting the probability of z being less than -2/3 from the probability of z being less than 4/3:

P(40 < x <70) = P(-2/3 <z < 4/3) = P(z < 4/3) - P(z< -2/3)

P(40 < x < 70) = 0.9082-0.2525 P(40 < x <70) = 0.6557

Therefore, the probability that the length of time between charges will be between 40 and 70 hours is approximately 0.656, which is closest to option B.

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Answer: C. k is equal to one fourth

Step-by-step explanation:

formula for parabola in vertex form

y= a(x-h)²+k     (h, k) is vertex here it is (0,0)

f(x)=ax²   another point we can plug in is (1,2)

2=a1

a= 2

so f(x)= 2x²

g(x)= f(kx)     plug in kx into f(x)

g(x) = 2(kx)²

g(x) =  2(k²)(x²)    plug in a point and find k (4,2)

2 = 2 k²4²

k²=1/16

k=1/4

C

The solution is : the velocity of the person on the walk way with respect to the observers on the ground is D 1.7 m/s.

Here, we have,

In order to find the velocity of the person on the walk way with respect to the person on the ground we have to apply relative velocity concept.

Consider the observer on the ground as B and the person walking on the pathway as A.

The relative velocity is the velocity that the body A would appear to an observer on the body B and vice versa.

Mathematically speaking the relative velocity is the vector difference between the velocities of two bodies.

Relative velocity = Velocity of Body A- Velocity of Body B.

Velocity of the person walking on the walkway (A)= 1.5 m/s.(given)

Velocity of the observer on the ground (B)= -0.2 m/s(given).

Relative velocity of object A with respect to B = 1.5 - (-0.2)= 1.7 m/s.

Thus the velocity of the person on the walk way with respect to the observers on the ground is 1.7 m/s.

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complete question:

A person is strolling along a moving walkway at a constant velocity of +1.00 m/s with respect tot he walkway, which moves at a constant velocity of +0.50 m/s with respect to the ground. An observer on the ground is walking at a constant velocity of -0.2 m/s. what is the velocity of the person on the walk way with respect to the observers on the ground?

A - 0.7 m/s

B + 1.3 m/s

C - 0.3 m/s

D + 1.7 ms

The data distribution is skewed and the mean of the emails is less than the median number of emails.

The median is 22 and the mean is 20.2.

The mean can be found by adding up the number of emails and dividing it by the number of days :
= ( 15 + 16 + 18 + 19 + 22 + 22 + 22 + 22 + 23 + 23 ) / 10

= 20. 2

The median is the number in the middle. As there are 10 numbers, the median would be:

= (Position 5 + Position 6) / 2

= ( 22 + 22 )  / 2

= 22

The mean is less than the median.

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The equation is given as n = c + 2

The plant grows c inches in the first week.

The plant grows n inches in the second week.

mаthеmаticаlly, the equаtion requires that wea rea to to show thе relаtionship between thе growth in thе first wееk (c) and thе growth in thе seсond wееk (n).

thе growth in thе seсond wееk (n) is said to be  2 inсhes more than thе growth in thе first wееk (c) from the given question.

The equation would be

n = c + 2

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