Answer:
The answer is the proof so it is long.
The question doesn't define u(n), but it's not hard to guess.
Group G with operation ∘
For all a and b and c in G:
1) identity: e ∈ G, e∘a = a∘e = a,
2) inverse: a' ∈ G, a∘a' = a'∘a = e,
3) closed: a∘b ∈ G,
4) associative: (a∘b)∘c = a∘(b∘c),
5) (optional) commutative: a∘b = b∘a.
Define group u(n) for n prime is the set of integers 0 < i < n with operation multiplication modulo n.
If n isn't prime, we exclude from the group all integers which share factors with n.
Identity: e = 1. Clearly 1∘a = a∘1 = a. (a is already < n).
Closed: u(n) is closed for n prime. We must show that for all a, b ∈ u(n), the integer product ab is not divisible by n, so that ab ≢ 0 (mod n). Since n is prime, ab ≠ n. Since a < n, b < n, no factors of ab can equal prime n. (If n isn't prime, we already excluded from u(n) all integers sharing factors with n).
Inverse: for all a ∈ u(n), there is a' ∈ u(n) with a∘a' = 1. To find a', we apply Euclid's algorithm and write 1 as a linear combination of n and a. The coefficient of a is a' < n.
Associative and Commutative:
(a∘b)∘c = a∘(b∘c) because (ab)c = a(bc)
a∘b = b∘a because ab = ba.
Answer:
The answer is the proof so it is long.
The question doesn't define u(n), but it's not hard to guess.
Group G with operation ∘
For all a and b and c in G:
1) identity: e ∈ G, e∘a = a∘e = a,
2) inverse: a' ∈ G, a∘a' = a'∘a = e,
3) closed: a∘b ∈ G,
4) associative: (a∘b)∘c = a∘(b∘c),
5) (optional) commutative: a∘b = b∘a.
Define group u(n) for n prime is the set of integers 0 < i < n with operation multiplication modulo n.
If n isn't prime, we exclude from the group all integers which share factors with n.
Identity: e = 1. Clearly 1∘a = a∘1 = a. (a is already < n).
Closed: u(n) is closed for n prime. We must show that for all a, b ∈ u(n), the integer product ab is not divisible by n, so that ab ≢ 0 (mod n). Since n is prime, ab ≠ n. Since a < n, b < n, no factors of ab can equal prime n. (If n isn't prime, we already excluded from u(n) all integers sharing factors with n).
Inverse: for all a ∈ u(n), there is a' ∈ u(n) with a∘a' = 1. To find a', we apply Euclid's algorithm and write 1 as a linear combination of n and a. The coefficient of a is a' < n.
Associative and Commutative:
(a∘b)∘c = a∘(b∘c) because (ab)c = a(bc)
a∘b = b∘a because ab = ba.
The hikers plan to visit a scenic lookout. They will rest after they hike 2 miles. Then they will hike the remaining 1 3/4 miles to the lookout. The trail the hikers will use to return from the lookout is 1/2 mile shorter than the trail they will use to go to the lookout. Each hiker will bring 1/4 gallon of water for each mile to and from the lookout. Determine the total distance, in miles, each hiker will hike? and Determine the total number of gallons of water each hiker will bring ?
Answer:
7 miles1 3/4 gallonsStep-by-step explanation:
The distance to the lookout is the sum of distances before and after the rest stop:
... "to" distance = 2 mi + 1 3/4 mi = 3 3/4 mi
The distance from the lookout is 1/2 mile shorter, so is ...
... "from" distance = 3 3/4 mi - 2/4 mi = 3 1/4 mi
Then the total hike is ...
... total distance = "to" distance + "from" distance
... = 3 3/4 mi + 3 1/4 mi = 6 4/4 mi
... total distance = 7 mi
The water each hiker will bring is ...
... (7 mi) × (1/4 gal/mi) = 7/4 gal = 1 3/4 gal
Each hiker will hike a total of 7 miles, and they will need to bring 1.75 gallons of water for the entire trip.
First, we need to determine the total distance each hiker will travel:
Initial hike to rest: 2 milesRemaining hike to the lookout: 1 3/4 miles or 1.75 milesTotal distance to the lookout: 2 + 1.75 = 3.75 milesThe return trail is described as 1/2 mile shorter than the trail to the lookout. Therefore:
Return trail distance: 3.75 - 0.5 = 3.25 milesSumming up the distances:
Total hiking distance: 3.75 + 3.25 = 7 milesCalculating Total Water Needed:
Each hiker brings 1/4 gallon of water per mile:
Total miles hiked: 7 milesWater needed per mile: 1/4 gallonTotal water needed: 7 * 1/4 = 1.75 gallonsThus, each hiker will hike a total of 7 miles and will need to bring 1.75 gallons of water for the entire trip.
Choose all of the unit vectors
To choose unit vectors, one must understand that they have a magnitude of one and are directed along the axes in space. For any point P or S, the unit vectors are (i_p, j_p, k_p) or (i_s, j_s, k_s) respectively, each with a magnitude of one.
Explanation:To determine which vectors are unit vectors, you must know that a unit vector has a magnitude (length) of one and indicates direction in space. The given information states that for a point P in space, the unit vectors are (î_p, â_p, k_p). Each of these vectors has a magnitude of one and points in the direction of increasing x, y, and z coordinates, respectively. Similarly, for point S, you have (i_s, j_s, k_s), also with a magnitude of one.
The special types of unit vectors such as î (i-hat), â (j-hat), and k (k-hat) are always of magnitude one and are parallel to the x, y, and z axes, respectively. The vector dê, represents a vector of length d pointing in the positive x-direction, implying dê is also a unit vector if d equals one.
Therefore, in the context provided, all options (a), (b), (c), and (d) are correct if their vectors have a magnitude of one and adhere to the rules to be considered unit vectors.
Help Please
What is the solution of the system?
Use the elimination method.
-4x - 2y = -12
2x + 4y = -12
Enter your answers in the boxes
(x, y) = (6, -6)
Step-by-step explanation:Divide the first equation by 2 to get equal and opposite coefficients for x.
... -2x -y = -6
Add this to the second equation to eliminate x.
... (2x +4y) +(-2x -y) = (-12) +(-6)
... 3y = -18 . . . . . . . . simplify
... y = -6 . . . . . . . . . . divide by 3
Substitute this vaue into any of the equations to find x. We choose to use the reduced first equation above.
... -2x -(-6) = -6
... -2x = -12 . . . . subtract 6
... x = 6 . . . . . . . divide by -2
The solution to the system is (x, y) = (6, -6).
Can someone pls help me find the lowest common denominator of
x³y⁴
Step-by-step explanation:The Lowest Common Denominator of fractions is the Least Common Multiple of their denominators. That is, you want to find the LCM of ...
x³ · yx · y⁴Find the highest power of each of the factors, and multiply those together.
The highest power of x is x³. The highest power of y is y⁴. So, the LCM of these expressions is ...
... x³y⁴
_____
Then the two fractions are ...
... 3y³/(x³y⁴) . . . and . . . 7x²/(x³y⁴)
Which of the following functions is graphed below ?
See the attachment
Step-by-step explanation:The solid dot on the right-hand portion of the curve means the function is defined for x ≥ 2. Choices A and C have that condition.
The function is linear for x ≥ 2, so matches selection C, not A.
Select the correct answer. What is the mode of this data set? {41, 43, 45, 3, 11, 23, 24, 27, 29, 45, 12, 19, 22, 49, 25}
The mode is the number in the set that appears the most.
In the given data set, the number 45 is listed twice while all the other numbers are only listed once.
The mode is 45.
Answer:
45
Step-by-step explanation:
The value which appears most often or has the highest frequency in a data set is said to be the mode.
Here we are given the following data set:
{41, 43, 45, 3, 11, 23, 24, 27, 29, 45, 12, 19, 22, 49, 25}
For this data set, we can see that the number / element 45 has occurred the most often which is twice. So the mode of this data set will be 45.
Which expressions are equivalent to 70 × 5.3
Answer:
35 x 10.6, 140 x 2.65 and 371 x 1
Step-by-step explanation:
Change the fraction to a decimal. a. 6⁄100 b. 43⁄100 c. 3⁄10 d. 4 23⁄1,000
6/100 = 0.06
43/100 = 0.43
3/10 = 0.3
23/1,000 = 0.023
Hope this helps!
Final answer:
To convert fractions to decimals, divide the numerator by the denominator and combine with any whole number for mixed numbers, resulting in 0.06, 0.43, 0.3, and 4.023 respectively for the given fractions.
Explanation:
The question asks to change fractions to decimals. Here are the step-by-step conversions:
a. 6⁄100: This fraction means 6 divided by 100, which is 0.06.
b. 43⁄100: Similarly, 43 divided by 100 is 0.43.
c. 3⁄10: Dividing 3 by 10 gives you 0.3.
d. 4 23⁄1,000: For the mixed number, you have the whole number 4 and the fraction 23⁄1,000. The fraction part is 23 divided by 1,000, which is 0.023. So, you combine the whole number and the decimal to get 4.023
Converting fractions to decimals involves dividing the numerator by the denominator and adding any whole number part if it's a mixed number.
Find the unknown side lengths in similar triangles PQR and ABC
A=
B=
Answer:
A=6
B=8
Step-by-step explanation:
The hypotenuse QR is twice the length of BC, so PQ will be twice the length of AB, 2·3 = 6; and PR will be twice the length of AC, 2·4 = 8.
In similar triangles PQR and ABC:
Side PQ (a) is 40/3 units.
Side PR (b) is 50/3 units.
To find the unknown side lengths in similar triangles PQR and ABC, we can use the properties of similar triangles. Two triangles are similar if their corresponding angles are congruent, and their corresponding sides are in proportion.
In this case, we have triangles PQR and ABC:
PQR:
RQ = 10
QP = a
RP = b
ABC:
AB = 3
AC = 4
BC = 5
Since the triangles PQR and ABC are similar, the ratios of corresponding sides must be equal. Specifically, the ratio of the sides in triangle PQR to the sides in triangle ABC should be the same. We can set up proportions to solve for a and b:
RQ / AB = QP / AC = RP / BC
10 / 3 = a / 4 = b / 5
Now, we can solve for a and b separately.
From the first part of the proportion:
10 / 3 = a / 4
Cross-multiply:
10 * 4 = 3 * a
40 = 3a
Now, divide by 3 to solve for a:
a = 40 / 3
From the second part of the proportion:
10 / 3 = b / 5
Cross-multiply:
10 * 5 = 3 * b
50 = 3b
Now, divide by 3 to solve for b:
b = 50 / 3
So, the unknown side lengths are:
a = 40/3
b = 50/3
Therefore, in similar triangles PQR and ABC:
Side PQ (a) is 40/3 units.
Side PR (b) is 50/3 units.
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Which ordered pairs lie on the graph of the exponential function f(x)=−3^(x−1) +2 Select each correct answer.
(−1, 2)
(1, 1)
(0, 0)
(4,−25)
(1, 1), (4, -25)
Step-by-step explanation:You can evaluate the function to see.
f(-1) = -3^(-1-1)+2 = -3^(-2)+2 = -1/9 +2 ≠ 2
f(1) = -3^(1-1) +2 = -1 +2 = 1
f(0) = -3^(0-1) +2 = -1/3 +2 ≠ 0
f(4) = -3^(4 -1) +2 = -27 +2 = -25
_____
Or, you can graph the points and the curve.
Answer:
(1, 1), (4, -25)
Step-by-step explanation:
An apartment complex offers 15 apartments with a view of the river, 8 with two bedrooms, and 6 that have both selections. How many only have a view of the river?
Answer:
9
Step-by-step explanation:
Otf the 15 that have a view of the river, 6 have both selections.
The remaining 9 only have a view of the river.
1. How do you determine whether a function is an inverse of another function?
Add the functions.
Multiply the functions.
Find the composite of the functions.
Apply the vertical line test.
2. Which of the following is the inverse function of f(x) = 3x?
f(x) = x + 3
f(x) = x/3
f(x) = x - 3
f(x) = x3
3. Which of the following statements is true?
A function will always pass the vertical line test.
All the answers are correct.
If the function has an inverse function, then the inverse function will pass the vertical line test.
If a function has an inverse function, then the original function will pass the horizontal line test.
4. What is the inverse function of f(x) = 3(x - 2)3?
5. Which of the following is the inverse function of f(x) = 2x - 3?
f(x) = (2x - 3 + 3)/2
f(x) = x+ 3/2
f(x) = x/2 + 3
f(x) = (x+3)/2
1. If f(x) and g(x) are inverse functions, then f(g(x)) = g(f(x)) = x. Finding the composite of the two functions will tell you if they are inverses.
2. To find the inverse of a function, swap x and y, then solve for y.
... x = 3y
... x/3 = y . . . . . matches f(x) = x/3
3. A function will pass the vertical line test. If its inverse is also a function, that, too, will pass the vertical line test. Since the inverse of a function is that function reflected across y=x, any inverse function that passes the vertical line test corresponds to an original function that passes the horizontal line test. (A vertical line reflected across y=x is a horizontal line.)
4. See 2.
... x = 3(y -2)³
... (x/3) = (y -2)³ . . . . divide by 3
... ∛(x/3) = y -2 . . . . .take the cube root
... 2+∛(x/3) = y . . . . .add 2
... f(x) = 2+∛(x/3) . . . . is the inverse
5. See 2.
... x = 2y -3
... x+3 = 2y . . . . . add 3
... (x+3)/2 = y . . . .divide by 2
... f(x) = (x+3)/2 . . . . is the inverse
A composite function is the combination of multiple functions.
The correct answers are:
Find the composite of the functions. The inverse of f(x) = 3x is [tex]f'(x) = \frac x3[/tex].All answers are trueThe inverse of [tex]f(x) = 3(x - 2)^3[/tex] is: [tex]f^{-1}(x) =2 + \sqrt[3]{\frac x3}[/tex]The inverse of [tex]f(x) =2x - 3[/tex] is [tex]f^{-1}(x) = \frac{x + 3}{2}[/tex]1. Test for inverse function
To test if two functions are inverse of one another, we simply find their composites.
Assume the functions are g(x) and h(x).
We simply test for [tex]g(h^{-1}(x))[/tex] and [tex]h(g^{-1}(x))[/tex]
If they are equal, then both functions are inverse functions
2. Inverse of f(x) = 3x
Rewrite as:
[tex]y = 3x[/tex]
Swap y and x
[tex]x = 3y[/tex]
Make y the subject
[tex]y = \frac x3[/tex]
Hence, the inverse function is: [tex]f'(x) = \frac x3[/tex]
3. True statements
A function has unique ordered pairs; so, it will pass the vertical line test.
Because it has unique ordered pairs, the inverse function will pass the vertical line tests, and the horizontal line tests.
Hence;
(b) All answers are correct
4. Inverse of [tex]f(x) = 3(x - 2)^3[/tex]
Rewrite as:
[tex]y = 3(x - 2)^3[/tex]
Swap x and y
[tex]x = 3(y - 2)^3[/tex]
Solve for y: Divide both sides by 3
[tex](y -2)^3 = \frac x3[/tex]
Take cube roots of both sides
[tex]y -2 = \sqrt[3]{\frac x3}[/tex]
Add 2 to both sides
[tex]y =2 + \sqrt[3]{\frac x3}[/tex]
Hence, the inverse function is: [tex]f^{-1}(x) =2 + \sqrt[3]{\frac x3}[/tex]
5. The inverse of [tex]f(x) =2x - 3[/tex]
Rewrite as:
[tex]y =2x - 3[/tex]
Swap x and y
[tex]x =2y - 3[/tex]
Solve for y: Add 3 to both sides
[tex]2y = x + 3[/tex]
Divide both sides by 2
[tex]y = \frac{x + 3}{2}[/tex]
Hence, the inverse function is: [tex]f^{-1}(x) = \frac{x + 3}{2}[/tex]
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What is one method to find the measure of angle B?
Answer:
A is the right one
Step-by-step explanation:
it is right on edge
We find angle B by using the pythagorean theorem to find BC then solve the equation tanB=8/BC
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
BCD is a right angle triangle
We have to find the angle B from the triangle
BD is the hypotenuse which is √89
DC is the opposite side of angle B
We can find angle B by using sine function.
Or we can find the length of BC by using pythagorean theorem
then find the tanB function
tanB=8/BC
Hence, we find angle B by using the pythagorean theorem to find BC then solve the equation tanB=8/BC
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Find the discriminant and determine how many solutions the equation has and if they are imaginary or real. Please show all work.
y = 4x^2 - 5x + 1
Answer:
as discriminant = 9, it has two real solutions.
Step-by-step explanation:
for eqn ax^2 + bx + c, discriminant = b^2 - 4ac
y = 4x^2 - 5x + 1
discriminant = (-5)^2 - 4(4)(1)
= 25 - 16
= 9
as discriminant > 0, it has two real solutions.
Answer:
Discriminant = 9 and the equation has two real solutions
Step-by-step explanation:
For a quadratic equation in the form of y = ax^2 + bx + c, its discriminant is equal to b^2 - 4ac.
If discriminant < 0, then the equation has two imaginary solutions. If it is 0, then the equation has 1 real solution and if it is > 0, 2 real solutions.
In this case, y = 4x^2 - 5x + 1.
So its discriminant = -5^2 - 4*4*1
= 9 so it has two real solutions.
50 POINTS FOR CORRECT ANSWER @PlatoNation
REPORTED IF INCORRECT
Answer:
About 2614 years.
Step-by-step explanation:
We are given k, and the information that N/N0 = 0.77, so the C-14 function becomes:
[tex]N=N_0\cdot e^{-kt} \\0.77N_0 = N_0\cdot e^{-kt}\\0.77 = e^{-0.0001 t}[/tex]
and we can solve for t:
[tex]0.77 = e^{-0.0001 t}\\\ln0.77 = \ln e^{-0.0001 t}\\\ln 0.77 = -0.0001 t\implies\\t = -\frac{\ln0.77}{0.0001}=2613.65\approx 2614\,\,\,\mbox{years}[/tex]
The estimated age of the bird skeleton is 2614 years.
help please !!!
What is the recursive rule for an=−3n+1 ?
an=
a1=
To find a1, put 1 in the given equation and evaluate.
... a1 = -3·1 +1
... a1 = -2
Each time n increases by 1, an is 3 less than the previous value. So, you can write the recursion relation as ...
... a[n] = a[n-1] - 3
the scale on a map is 1 cm for every 400 km .If the Maine and Japan are 22 cm apart on the map, what is the distance between Maine and Japan?
Answer:
8,800
Step-by-step explanation:
400 km
1 cm
=
d
22 cm
A jetski rental company charges a $50 deposit, plus $25 per hour to rent a jetski. This can be represented by the formula T = 25h + 50, where T is the total cost, and h is the number of hours rented. If the deposited is changed to $40 and the hourly rate is changed to $35, how much more money will the company make on a hour of rental?
Answer:
None, the answer will be the same
Step-by-step explanation:
find each side length,round to the nearest tenth if necessary 11.
We can use a modified form of the Pythagorean Theorem to find the length of x, also known as side b.
Pythagorean Theorem:
a^2 + b^2 = c^2
We can fill in the values of a^2 and c^2, and then solve for b.
14^2 + b^2 = 25^2
196 + b^2 = 625
Subtract 196 from both sides.
b^2 = 429
√ both sides.
b = 20.7
The value of x, or b, is equal to 20.7.keep on getting 10x+12
[tex]\dfrac{13x+10}{2x^2-5x-25}[/tex]
Step-by-step explanation:Multiply the first fraction by (x-5)/(x-5) and the second by (2x+5)/(2x+5). Now, you have both fractions with the common denominator (2x+5)(x-5).
[tex]\dfrac{3}{2x+5}+\dfrac{5}{x-5}=\dfrac{3(x-5)}{(2x+5)(x-5)}+\dfrac{5(2x+5)}{(2x+5)(x-5)}\\\\=\dfrac{3(x-5)+5(2x+5)}{(2x+5)(x-5)}=\dfrac{3x-15+10x+25}{2x^2-5x-25}\\\\=\dfrac{13x+10}{2x^2-5x-25}[/tex]
The table shows formulas for the recommended heart rates during exercise for a person who is "a" years old. Write and solve a compound inequality to determine the heart rate range for a 16 year old person.
Answer:
102 ≤ heart rate ≤ 183.6
Step-by-step explanation:
... lower limit ≤ heart rate ≤ upper limit
Put 16 where "a" is and do the arithmetic.
... lower limit = 0.5(220 -16) = 102
... upper limit = 0.9(220 -16) = 183.6
Then the inequality is ...
... 102 ≤ heart rate ≤ 183.6
_____
Comment on the problem
There is nothing to "solve" here. One only needs to evaluate the limits.
In this Compound Inequality question, The recommended heart rate range for a 16 year old person, according to the provided formulas, is between 102 and 183.6 beats per minute.
Given that the age 'a' is represented by 16 years, we can simply substitute this value into the two given formulas to find the recommended heart rate range.
The lower limit of the heart rate is given by the formula 0.5 x (220 - a) and the upper limit is given by the formula 0.9 x (220 - a).
For the lower limit, substituting a = 16, we get 0.5 x (220 - 16) = 102 beats per minute. Similarly, for the upper limit, we get 0.9 x (220 - 16) = 183.6 beats per minute.
Therefore the range of the heart rate for a 16 year old person is 102 to 183.6 beats per minute.
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Reuben attached a wire between two poles on a hill as shown which is the closest to x the distance between the two poles
Answer:
75 ft
Step-by-step explanation:
Here we are given a right angled triangle with a known angle of 20°, length of the hypotenuse to be 80 and we are to find the length of the base x.
For that, we can use the formula for cosine for which we need an angle and the lengths of base and hypotenuse.
[tex]cos \alpha =\frac{base}{hypotenuse}[/tex]
So putting in the given values to get:
[tex]cos 20=\frac{x}{80} \\\\x= cos 20*80\\\\x=75.17[/tex]
Therefore, the value of x is the closest to 75 ft.
my sides are all the same length. my area is 9 square meters. what is the length of one of my sides?
Answer:
3
Step-by-step explanation:
if the length and width is 3, 3 times 3 is 9
2x − y = 3
4x = 6 + 2y
a. infinitely many solutions
b. x = 2, y = 1
c. y = 2x - 3
d. x = 4, y = 5
Answer:
a. Infinitely many solutions
Step-by-step explanation:
The given equations are 2x - y = 3
4x = 6 + 2y
We can use substitution method to solve these system of equations.
2x - y = 3
y = 2x - 3
Now plug in y = 2x - 3 in the second equation, we get
4x = 6 + 2(2x - 3)
4x = 6 + 4x - 6
4x = 4x
Here we get infinitely many solution.
Both the equations are the same.
Thank you.
In △ABC, AB=8, BC=10, and AC=12. Let M, N, and K be the midpoints of the sides of △ABC. Find length of each side of △MNK.
Answer:
The side lengths are 4, 5, and 6.
Step-by-step explanation:
Each midsegment is half the length of the parallel side, so the side lengths of ΔMNK are 4, 5, and 6.
It isn't clear which point is the midpoint of what segment. If it is true that ...
M is the midpoint of ABN is the midpoint of BCK is the midpoint of ACthen ...
MN = AC/2 = 6NK = AB/2 = 4KM = BC/2 = 5Answer:
4, 5, 6
Step-by-step explanation:
The diameter of a hydrogen atom 0.000000000106 meter. write this diameter in scientific notation
The Diameter of Hydrogen Atom in Scientific Notation is :
✿ 1.06 × 10⁻¹⁰ Meters
Answer:
1.06 x 10-10 mStep-by-step explanation: I just solve it.
I need help with this please
Each of these sequences goes into the classification box above it.
Step-by-step explanation:If the difference of terms is a constant, it is arithmetic.
... (3 -(-1)) = 4 = (7 -3), so the first sequence is arithmetic
If the ratio of terms is a constant, it is geometric.
... 12/36 = 1/3 = 4/12, so the second sequence is geometric
The third sequence has neither constant differences nor constant ratios, so is neither arithmetic nor geometric.
please help me asap!
Answer:
d 31 degrees
Step-by-step explanation:
We can use the formula
<C = 1/2 (arc AE - arc BD)
Let substitute in what we know
ARC AE = 120
ARC BD = 58
<C = 1/2 (120 - 58)
<c = 1/2(62)
<c = 31
the average temperature in Alaska in January is -9°F in February it is -16°F which month has the coldest temperature
Answer:
February
Step-by-step explanation:
February is colder by 7°F
-9 - 7 = -16
~
Answer:February
Step-by-step explanation:
If you see the number line below -16 is more far than -9
-------------------------------------------------------------------------------------------------
' ' '
-16 -9 0
Which inequality represents the graph shown below?
Answer:
2<x<∞
Step-by-step explanation:
The arrow has a filled in circle at around the 2.5 mark which allows us to deduce that the number 2 is not included in the inequality but almost all the numbers after 2 i.e. (2.1,2.2,2.3,2.4,2.4... etc ) are included. This gives us our lower bound.
The arrow goes to positive infinity. Which gives us our upper or left bound.
Answer:
r>(greater than or equal to)2.5
Step-by-step explanation: