Part A:
This data appears to be modeling a geometric sequence because the time to complete each station is increasing by a constant factor. For example, the time to complete station 2 is 4 minutes, which is double the time it took to complete station 1. Similarly, the time to complete station 3 is 8 minutes, which is double the time it took to complete station 2, and so on.
Part B:
To find the time Aurora will take to complete station 5 using a recursive formula, we can use the formula:
a_n = a_1 * r^(n-1)
where a_n is the time it takes to complete station n, a_1 is the time it takes to complete station 1, and r is the common ratio (the factor by which the time increases from one station to the next).
We are given that a_1 = 2 and a_2 = 4, so we can solve for r:
r = a_2 / a_1
= 4 / 2
= 2
Then we can use this value of r to find the time it takes to complete station 5:
a_5 = a_1 * r^(5-1)
= 2 * 2^4
= 2 * 16
= 32
Therefore, Aurora will take 32 minutes to complete station 5.
Part C:
To find the time Aurora will take to complete station 9 using an explicit formula, we can use the formula:
a_n = a_1 * r^(n-1)
where a_n is the time it takes to complete station n, a_1 is the time it takes to complete station 1, and r is the common ratio (the factor by which the time increases from one station to the next).
We are given that a_1 = 2 and a_2 = 4, so we can solve for r:
r = a_2 / a_1
= 4 / 2
= 2
Then we can use this value of r to find the time it takes to complete station 9:
a_9 = a_1 * r^(9-1)
= 2 * 2^8
= 2 * 256
= 512
Therefore, Aurora will take 512 minutes to complete station 9.
say no more
6x + 3y = 3 3x - y = 4
Answer:
x = 1
y = -1
Step-by-step explanation:
Given equations:6x + 3y = 3 -------------(1)
3x - y = 4 ----------------(2)
Multiply Eq. (2) by 2
2(3x - y) = 4 × 2
6x - 2y = 8 -------------(3)
Subtract Eq. (3) from Eq. (1)
6x + 3y - (6x - 2y) = 3 - 8
6x + 3y - 6x + 2y = -5
3y + 2y = -5
5y = -5
Divide 5 to both sides
y = -5/5
y = -1Put y = -1 in Eq. (1)
6x + 3(-1) = 3
6x - 3 = 3
Add 3 to both sides
6x = 3 + 3
6x = 6
Divide 6 to both sides
x = 1[tex]\rule[225]{225}{2}[/tex]
write an expression that is equivalent to 2/3 (4x + 9)
Hello,
I hope you and your family are doing well!
To write an expression that is equivalent to 2/3 (4x + 9), you can simply distribute the 2/3 over the parentheses:
2/3 (4x + 9) = (2/3 * 4x) + (2/3 * 9)
This simplifies to:
2/3 (4x + 9) = (8/3)x + (18/3)
Therefore, an expression that is equivalent to 2/3 (4x + 9) is (8/3)x + (18/3).
Please rate this answer 5 stars and brainliest if you find it helpful.
Happy Holidays & New Year!
Answer: 2 2/3x + 6
Step-by-step explanation: 1 of 3 ways to find how to make the equivalent is to use the distributive property. So, that means we need to multiply or distribute 2/3 to both 4x and 9. So, 2/3 x 4 is roughly 2 2/3. Also, 2/3 x 9 = 6. So, I combined the like terms to get 2 2/3x + 6 as my equivalent expression. I hope this helps.
A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t3 + 8t2 + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $8 million. According to the graph of the function, what other quantity of product would result in the same profit?
The required value of the production at which the company attained the same profit is 4 thousand skin care items.
Given that,
A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t³ + 8t² + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $8 million.
Here,
Plotting the graph of the polynomial equation,
P(t) = –2t³ + 8t² + 2t,
From the graph at x = 4,
The polynomial gives the same value as it gave at x = 1,
Thus, the required value of the production at which the company attained the same profit is 4 thousand skin care items.
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Angle ABC is taken by a dilation with centerpoint, P and scale factor of four to angle A’B’C’ the measure of angle, BCA is 75° what is the measure of angle B’C’A’
Answer:
75°
Step-by-step explanation:
You want to know the measure of the image angle B'C'A' after angle A'B'C' is dilated by a factor of 4 about point P. Angle BCA is 75°.
DilationDilation does not affect angle measures, so angle B'C'A' has the same measure as angle BCA, 75°.
m∠B'C'A' = 75°
Cameron is deciding between two landscaping companies for his place of business.
Company A charges $25 per hour and a $300 equipment fee. Company B charges $55
per hour and a $150 equipment fee. Let A represent the amount Company A would
charge for t hours of landscaping, and let B represent the amount Company B would
charge for t hours of landscaping. Write an equation for each situation, in terms of t,
and determine the interval of hours, t, for which Company A is cheaper than
Company B.
Answer:
A = 25t + 300
B = 55t + 150
Less than 5 hours, company B would be cheaper. At 5 hours the cost is equal. After 5 hours, company A would be cheaper.
Step-by-step explanation:
Company B would be cheaper for lower hours.
The the two equation equal to each other and solve for to find out when the costs will be equal.
25t + 300 = 55t + 150 Subtract 25t from both sides
300 = 30t + 150 Subtract 150 from both sides
150 = 30t Divide both sides by 30
5 = t
At 5 hours the cost are the same, after 5 hours company A would be cheaper.
A dice game involves rolling 2 dice. If you roll a 2, 3, 4, 10, 11, or a 12 you win $5. If you roll a 5, 6, 7, 8, or 9 you lose $5. Find the expected value you win (or lose) per game.
The correct answer is option B which is -1.67 is the expected value.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
You have a higher probability of losing money than gaining it due to the distribution of probability.
There are more chances to lose than win.
As a result, you are expected to lose money.
Only -1.67 is the only negative option, which means that we don't even need to do real math since there's already only one choice.
Hence, the correct answer is option B which is -1.67 is the answer.
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Answer:
You will Gain 5 points.
Step-by-step explanation:
Got it right on the test!
Prove that the roots of the equation mx² + (m − 2)x − (m + 1) = 0 are real for all values of m
Answer:
Below
Step-by-step explanation:
For REAL numbers, the discriminant of the Quadratic Formula has to be a positive value (or zero)
b^2 - 4ac >= 0 where a = m b = m-2 c = -m-1
(m-2)^2 - 4(m)(-m-1) >=0
5m^2 +4 >= 0
5 m^2 +4 <===== will always be >= 0 for any value of 'm'
so all roots will be real
1.6y+y-4/15y+1 1/6y=2 1/3 pls help
The simplification of the given equation is -630y² + 81y + (+2.6y) * 90y² = 0.
What is the domain of the function?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
We have,
1.6y+y-4/15y+7/6y=21/3
Move all terms to the left:
1.6y+y-4/15y+7/6y-(21/3)=0
Domain of the equation: 15y!=0
y!=0/15
y!=0
y∈R
Domain of the equation: 6y!=0
y!=0/6
y!=0
y∈R
Add all the numbers together, and all the variables
1.6y+y-4/15y+7/6y-7=0
Add all the numbers together, and all the variables
2.6y-4/15y+7/6y-7=0
calculate fractions
2.6y+(-24y)/90y²+105y/90y²-7=0
multiply all the terms by the denominator
(2.6y) * 90y² + (-24y) + 105y - 7 * 90y² = 0
Add all the numbers together, and all the variables
(2.6y) * 90y² + (-24y) + 105y - 7 * 90y² = 0
Add all the numbers together, and all the variables
105y+(+2.6y)*90y² + (-24y) - 7*90y² = 0
multiply elements
-630y+105y+(+2.6y)*90y² + (-24y) = 0
get rid of parentheses
-630y² + 105y + (+2.6y)*90y² - 24y = 0
Add all the numbers together, and all the variables
-630y² + 81y + (+2.6y) * 90y² = 0
Hence, the simplification of the given equation is -630y² + 81y + (+2.6y) * 90y² = 0.
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Complete the ratio 4:16 = 1:?
Answer:
1:4
Step-by-step explanation:
4:16 = 1:?
4/4 = 1
16/4 = 4
= 1:4
A side of the triangle below has been extended to form an exterior angle of 156°. Find the value of x.
The value of x inside the triangle is 24°
How to calculate the value of x(angle)?
A straight line's total number of angles adds up to 180°. Supplementary angles are two angles whose sums equal 180 degrees. Angles are referred to as neighbouring if they have a similar vertex and side.A straight angle in mathematics is one with a degree value of 180. Because it resembles a straight line, it is called straight.Angles in a straight line are the total of all the angles that can be arranged in a straight line. Straight line angles add up to 180°.The angle of the straight line = 180°
156° + x = 180°
x = 180° - 156°
x = 24°
Hence, the value of x inside the triangle is 24°.
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Find the Area of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place.
The area of the given figure composed of a rectangle and two semicircles is 68.56 unit².
What is Area :The space around a shape's perimeter or boundary is known as its area. To determine the areas of various forms, many mathematical formulae are available.
Area of circle = πr², where r is the radius of the circle. Area of rectangle = lb, where l = length and b = breadth.Here we have
composed of a rectangle and two semicircles.
Dimensions of the rectangle are,
Length = 14 and breadth = 4
=>Area of the rectangle = 14 × 4 = 56 units²
If we join the two semicircles,
we will have one circle with a diameter of 4 units
=> As we know Radius of the circle = Diameter/2
=> Radius of circle = 4/2 = 2 units
=> Area of the circle = 2πr
= [tex]2 \times\frac{22}{7} \times 2[/tex] = 12.56 unit²
Area of the figure = Area of rectangle + Area of the circle
= 56 units² + 12.56 unit²
= 68.56 unit²
Therefore,
The area of the given figure composed of a rectangle and two semicircles is 68.56 unit².
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is a parallel to b? Explain using angels and measurements. Angel measrment should be part of your explanation.
Answer:
Not parallel.
Step-by-step explanation:
Given:
m∠9 = 110°m∠8 = 70°Linear Pair
Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).
Angles 9 and 10 form a linear pair:
⇒ m∠9 + m∠10 = 180°
⇒ 110° + m∠10 = 180°
⇒ m∠10 = 70°
Angles 7 and 8 form a linear pair:
⇒ m∠7 + m∠8 = 180°
⇒ m∠7 + 70° = 180°
⇒ m∠7 = 110°
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
As line p is parallel to line q, and according to the vertical angles theorem and the corresponding angles postulate:
m∠1 = m∠6 = m∠9 = m∠14 = 110°m∠2 = m∠5 = m∠10 = m∠13 = 70°m∠3 = m∠8 = m∠11 = m∠16 = 70°m∠4 = m∠7 = m∠12 = m∠15 = 110°If line a was parallel to line b, then according to the corresponding angles postulate:
m∠1 = m∠3 = m∠6 = m∠8m∠2 = m∠4 = m∠5 = m∠7As m∠1 ≠ m∠8 and m∠2 ≠ m∠7 then lines a and b are not parallel.
The following are rules for repeating patterns. For which rule will the 12th shape be a circle?
A.
triangle, circle, square
B.
circle, square
C.
rectangle, circle
D.
circle, circle, triangle
Answer:
A Square
B Square
C Circle
D Triangle
Writing Equations of lines
Write the equation of each line with the given information
through: (-3, 4) and (-5, -1)
Answer:
y = 5/2x + 11.5
Step-by-step explanation:
(-3, 4) (-5, -1)
m = -1-4/ -5+3
m = -5 / -2
m = 5/2
y = 5/2x + b
-1 = 5/2(-5) + b
-1 = -12.5 + b
b = 11.5
y = 5/2x + 11.5
Answer:
y-y1=y2-y1/x2-x1(x-x1)
y-4= (-1-4/-5+3) (x+3)
y-4= -5/-2(x+3)
y=5/2x+15/2+4
y=5/2x+15+8/2
y=5/2x+23/2
PLEASE HELPPP!!!
The admission fee at the museum is 8.50 for children and 12.50 for adults on a certain day, a total of 240 people entered the museum and 2400$ was collected.
Use the variable c to represent children and the variable a to represent the adult
Answer:
Below
Step-by-step explanation:
a + c = 240 re-arrange to c = 240-a
revenue from child tix = 8.50 ( 240-a)
revenue from adult tix = 12.50 a summed, the revenues = 2400
8.5(240-a) + 12.5 a = 2400
2040 - 8.5 a + 12.5 a = 2400
4.5 a = 360
a = 80 tix then c = 240 - a = 160 tix
Write an equation in slope-intercept form of the line that passes through (-2,-7) and (-1,6)
a) Work out the minimum number of dogs that could have a mass of more than 24kg}
b) Work out the maximum number of dogs that could have a mass of more than 24kg
The minimum number of dogs 24kg is 6 and the maximum number of dogs is 18
Maximum and Minimum:The highest amount or value or number that may be obtained or reached or can be counted is the Maximum value
The least amount or value or number that may be admitted or reached or can be counted is the Minimum value
Here we have a table
Which represents the masses of various dogs
Mass (x) kg frequency
0 ≤ x < 10 2
10 ≤ x < 20 7
20 ≤ x < 30 12
30 ≤ x < 40 6
Here the mass of dogs is represented in class intervals
a) The minimum number of dogs with a mass of more than 24kg.
From the given table,
24 kg will lie in class intervals 20 ≤ x < 30, and 30 ≤ x < 40
In class interval 20 ≤ x < 30, there is a possibility that the mass of dag will be less than 24 kg since it started from 20 kg and is up to 30 kg
In class interval 30 ≤ x < 40, there is no possibility that the mass will be less than 24 kg since it started from 30 kg and is up to 40 kg
So The minimum number of dogs that have a mass of more than 24kg the frequency of class interval 30 ≤ x < 40
Therefore,
The minimum number of dogs with a mass of more than 24kg is 6
b) The maximum number of dogs that have a mass of more than 24kg.
To get the maximum number of dogs we need to take the class interval of 20 ≤ x < 30 as in this the mass could be more than 24 kg.
And in class 30 ≤ x < 40 the mass will be more than 24 kg.
Thus, the Maximum number of dogs with more than 24 kg = 12 + 6 = 18
Therefore,
The maximum number of dogs with a mass of than 24kg is 18
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The equation of the graph
is y = pq* where p and q are
positive constants.
Find the values of p and q.
Write the following as an inequality.
−8 is less than or equal to w, and 3 is greater than or equal to w
Use w only once in your inequality.
Answer:
Step-by-step explanation:
If -8 is less than or equal to w, and 3 is greater than or equal to w, then we can combine these two inequalities into a single inequality by combining the left and right sides:
-8 ≤ w ≤ 3
This inequality can be read as "w is greater than or equal to -8 and less than or equal to 3." It represents all values of w that are greater than or equal to -8 and less than or equal to 3, including -8 and 3.
I hope this helps! Let me know if you have any questions.
50 minus 2.5 x greater-than-or-equal-to 20. Negative 2.5 x greater-than-or-equal-to negative 30. x greater-than-or-equal-to 12.
Negative 2.5 x greater-than-or-equal-to negative 30 is the equivalent expression of 50 minus 2.5 x greater than or equal to 20
How to find an equivalent expression?Equivalent expressions can be defined as expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will give you the same value when you simplify
Given: 50 minus 2.5 x greater than or equal to 20
50 - 2.5x ≥ 20
Subtract 50 from both sides:
-2.5x ≥ 20-50
-2.5x ≥ -30
Therefore, the equivalent expression is "negative 2.5 x greater-than-or-equal-to negative 30"
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Use the Special Integration Formulas (Theorem 8.2) to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) squareroot of (9 + 49^x2) dx
The indefinite integral of given integral ∫√(9+49x^2)dx is ∫√(9+49x^2)dx = [tex]\int\sqrt{(9+49x^2)}dx = 1/98[98x\sqrt{9+49x^2}+9In|7x+\sqrt{9+49x^2}}|]+C[/tex].
In the given question we have to find the indefinite integral.
The given integral is
∫√(9+49x^2)dx
Now finding the indefinite integral using the C for the constant of integration.
An integral is regarded to be indefinite if it has no lower or upper bounds. In mathematics, the most generic antiderivative of f(x) is known as an indefinite integral and expressed by the expression f(x) dx = F(x) + C.
We can write it as:
[tex]\int\sqrt{(9+49x^2)}dx = \int\sqrt{[(3)^2+(7x)^2]}dx[/tex]
Taking common 7^2
[tex]\int\sqrt{(9+49x^2)}dx = 7\int\sqrt{[(3/7)^2+(x)^2]}dx[/tex]
Using the formula
[tex]\int\sqrt{(a^2+x^2)}dx = \frac{1}{2}\times\sqrt{a^2+x^2} + \frac{1}{2}\cdot a^2In|x+\sqrt{a^2+x^2}|+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 7[x\sqrt{(3/7)^2+x^2}+\frac{1}{2}\cdot(\frac{3}{7})^2In|x+\sqrt{(3/7)^2+x^2}|]+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 7[x\sqrt{9/49+x^2}+1/2\cdot(9/49)In|x+\sqrt{(9/49)+x^2}|]+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 7[x\cdot\frac{\sqrt{9+49x^2}}{7}+1/2\cdot(9/49)In|x+\frac{\sqrt{9+49x^2}}{7}|]+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 7[x\cdot\frac{\sqrt{9+49x^2}}{7}+(9/98)In|\frac{7x+\sqrt{9+49x^2}}{7}|]+C[/tex]
[tex]\int\sqrt{(9+49x^2)}dx = 1/98[98x\sqrt{9+49x^2}+9In|7x+\sqrt{9+49x^2}}|]+C[/tex]
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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 18 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
Using the normal distribution, it is found that a student has to score 0.675 standard deviations above the mean to be publicly recognized.
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
z=x-nuo/sigmaIt measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The top 25% is at least the 100 - 25 = 75th percentile, which is X when z has a p-value of 0.75.Looking at the z-table, z = 0.675 has a p-value of 0.75.Hence, a student has to score 0.675 standard deviations above the mean to be publicly recognized.To know more about Standard deviation here
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A certain vending machine offers 20-ounce bottles of soda for $1.50. The number of bottles X bought from the machine on any day is a random variable with mean 50 and standard deviation 15. Let the random variable Y equal the total revenue from this machine on a given day. Assume that the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?
PS bisects ∠QPR . Complete the proof that ∠PSR ≅ ∠PSQ .
The proof is shown in the image.
Reasons for statement
Any line that bisects an angle divides the angle into two equal parts The two lines are congruent by cpct as the triangles are congruent The angle subtended the bisector line divides equally into two angles. Also, the triangles are congruent so angle QPS = angle RPS by cpct The common line between congruent triangles is the same Triangles are congruent by side angle side rule Angles are equal by corresponding parts of the congruent triangle rule.To know more about congruent triangles,
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Each morning Tess chooses either red ribbon or blue ribbon at random to wear in her hair what is the probability that Tess will choose a red ribbon on both Monday and Tuesday
The probability of choosing red ribbon on both Monday and Tuesday is 1/4.
What is the probability?
The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.
Given that each morning Tess chooses either red ribbon or blue ribbon at random to wear in her hair.
That means probability of choosing between blue or red is 1/2 in one morning.
Now the probability of choosing red ribbon on both Monday and Tuesday,
1/2 × 1/2
= 1/4
Therefore, the probability of choosing red ribbon on both Monday and Tuesday is 1/4.
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please help in this grade 7 percentage question im desperate
Answer:
See below
Step-by-step explanation:
320 x .1 = 32
320 + 32 = 352
352 x .5 = 176
352 + 176 = 528
320 x .65 = 208
320 + 208 = 528
help please very easy proportional relationship due hurry please than u!
1) h=1/5 k
(10/2 = 1/5, 20/4 = 1/5... etc)
2) k=5/4 h
(5/4 = 5/4, 10/8=5/4... etc)
3) h=5/1 k
(25/5 = 5/1, 30/6 = 5/1 ... etc)
Hope this helps!
:]
Chandrani had a Rs 100 note she bought a geometry box for ₹ 37 . 75. Find the amount left with her
Answer:
The amount left with her si 62.25
A cable running from the top of a telephone pole creates a horizontal pull of 889 Newtons (N). A support cable running to the ground is inclined 71° from the horizontal.
Find the tension in the support cable. Give answer to the nearest whole number.
The tension in the support cable is 2731 N
How to find the tension in the support cable?Given that:
A cable running from the top of a telephone pole creates a horizontal pull of 889 Newtons (N) and a support cable running to the ground is inclined 71° from the horizontal.
This can sketch as shown in the attached image. Considering the image:
T is the tension in the support cable
Using trigonometric ratio:
cos 71° = 889/T (adjacent/hypotenuse)
T = 889/cos 71°
T = 2731 N
Therefore, the tension in the support cable is 2731 N
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Which ordered pair satisfies the inequality? 6x + 5y < -15
The ordered pair of the inequality 6x + 5y < -15 are (2, 0) and (3, 2).
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Considering the provided inequality and the provided ordered pairs, we will check it by replacing one by one in the inequality; if the inequality is fulfilled, they are the solution; otherwise, they are not, so we obtain:
(2, 0):
6x + 5y > 2
6(2)+5(0)>2
12+0>2
12>0
Since the inequality holds, then the ordered pair is a solution.
(7, -8):
6x + 5y > 2
6(7)+5(-8) > 2
42-40>2
2>2
Since the inequality is not satisfied, then the ordered pair is not a solution.
(3, 2):
6x + 5y > 2
6(3)+5(2) >2
18+10>2
28>2
Since the inequality holds, then the ordered pair is a solution.
(-8, 6):
6x + 5y > 2
6(-8)+5(6) >2
-48 + 30 > 2
-18 > 2
Since the inequality is not satisfied, then the ordered pair is not a solution.
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