okay well for a) the line is perpendicular meaning that it need to go the opposite way of 2/3x+6 so in the new equation would have a negative value times x. also when you are trying to find a perpendicular line i believe you use the inverse of the slope meaning that you would have -3/2 time x. Then you know that the line goes through (-6,4) so you just replace x with -6, add a varible (for example n) and then set the equation equal to 4 since 4 should be the y value that you get when you plug in 4. so it should look like
(-3/2)-6+n=4 you're doing this so that you can figure out the x intercept. Move the n to the right and subtract 4 from both sides, and then solve the numbers on the left. (-3/2)-6 =9 and then 9-4=5 so the y intercept you get is five. then the new eqaution you shoud have is (-3/2)x-5=y
b.) well the x values are both positive meaning that you subtract so there is a distance of 2 units between then and the y values have a negative number and a positive number meaning you add so there is a distance of 5. The slope should be rise over run so the slope is 5/2 and then you can plug in a value of x to find the y intercept. lets use (6,-3) so
(5/2)6+n=-3. isolate the variable and tadaa you get a y intercept of -18. so the equation for the second one is (5/2)x-18=y
The temperature in a city is -1.5 C drag numbers to the empty boxes to complete the sentence and equation correctly ?
The equation for the given scenario is -1.5+1.5 =0.
What is temperature?Temperature is a degree of hotness or coldness the can be measured using a thermometer. It's also a measure of how fast the atoms and molecules of a substance are moving. Temperature is measured in degrees on the Fahrenheit, Celsius, and Kelvin scales.
Given that, the temperature in a city is -1.5° C
Now,
The temperature needs to rise -1.5° C to reach 0° C.
Then, the equation is
-1.5+1.5 =0
0 = 0
Therefore, the equation is -1.5+1.5 =0.
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Find the value of x
in this polygon.
help !!!
Answer:
53°solution,
Sum of exterior angle of polygon=360°
\(3x - 5 + 2x + 10 + 90 = 360 \\ or \: 3x + 2x - 5 + 10 + 90 = 360 \\ or \: 5x + 5 + 90 = 360 \\ or \: 5x + 95 = 360 \\ or \: 5x = 360 - 95 \\ or \: 5x = 265 \\ or \: x = \frac{265}{5} \\ x = 53\)
Hope this helps...
Good luck on your assignment...
In the diagram, the measures of 22, 23 and 26 are 40°. The measure of 21
is 140°. Are lines cand d parallel?
Answer:
c. Yes because ∠2 and ∠6 are congruent.
Step-by-step explanation:
From the picture attached,
m(∠2) = m(∠3) = m(∠6) = 40°
m(∠1) = 140°
Since (∠2 ≅ ∠6) (corresponding angles)
Therefore, by the converse theorem of corresponding angles lines c and d are parallel.
Option c is the answer.
divide 240£ in the ratio 3:5:12
Answer:
Step-by-step explanation:
3x + 5x + 12x = 240
20x = 240
x = 12
Totals: 36 (3*12), 60 (5*12), 144 (12*12)
Draw a circle and label each parts and shade any region
A circle is a two-dimensional geometric shape composed of all points in a plane that are equidistant from a fixed point known as the centre. The radius is the distance between the center and any point on the circle, and the diameter is the distance across the circle passing through the center.
Here is the circle and its each part and region.
(a) The center of the circle is O.
(b) The radius of the circle is OD.
(c) The diameter of the circle is AB.
(d) A sector of the circle is ODA.
(e) A segment of the circle is EF.
(f) A point in the interior of the circle is C.
(g) An arc of the circle is AD.
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Which of the following is a counterexample to the given statement?
The name of every month ends in the letter y.
a. January
b. July
C February
d. December
The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right option is (c) February.
What is a counterexample?
In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.
Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."
Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.
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Find the range of the data set: 7, 12, 15, 4, 23, 15, 25, 9
Answer: Range = 21
Step-by-step explanation: you subtract the highest number by the lowest number in the set to find your range
Solve the L.P.P graphically- Maximize z=y-2x subject to x-y >=2 ,x + y<=4 , x>=0 ,y>=0
Answer: 8y=2h
Step-by-step explanation: you have to subtract the first 2 numbers then add the others and then add letters and boom
consider a polynomial of the form $ax^2 - bx c$ with integer coefficients, such that it has two distinct zeros in the open interval $0 < x < 1.$ find the least positive integer value of $a$ for which such a polynomial exists.
The problem is saying there are two distinct zeros, and both are strictly lie between 0 and 1. The least positive integer value of "a" is 5 for which such a polynomial exists.
Let f(x) = ax² - bx + c , be our polynomial.
where a,b are integers coefficient and c constant. It has two distinct real roots lying between 0 and 1. f(x) can be written as, f(x) = a(x−α)(x−β)
where α and β are the roots of the equation.
we can be observed that f(0)f(1) > 0
As a,b and c are integers f(0)f(1) > 1
f(0) = aαβ , f(1)=a(1−α)(1−β)
=> a²(α)(1−α)(β)(1−β) > 0 -------(1)
Using A.M ≥ G.M, we get
(α+1−α+β+1−β)/4 > (αβ(1−α)(1−β))¹/⁴
Arithmetic Mean and Geometric Mean cannot be equal because the equation has distinct roots.
a²/16 > a²(αβ(1−α)(1−β)).
=> a²/16 > 1
=> a > 4
Therefore, the minimum value of 'a' is 5
The discriminant of the equation,
Δ = b²−4ac ≥ 0
=> b² >20c
consider the minimum value of c = 1,
we get b² >20
=> Minimum Value of b = 5.
Hence, the least positive integer of 'a' is 5.
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Can y’all plz help me plz
Answer:
i think it will be 70 yd
Step-by-step explanation:
(14×5)yd= 70 yd
Answer:
The total area is 179.25yd²
Step-by-step explanation:
You need to break this down into two parts: the rectangle on the left side, and the semicircle on the end.
The radius of the circle is five yards, giving it a diameter of 10 yards. That diameter is also the height of the rectangle, meaning that the rectangle has an area of 14yd × 10yd = 140yd²
The area of a circle is equal to pi times the square of its radius. Given that we only have a semicircle, we need to take that and divide it by two:
a = πr² ÷ 2
a = π × 5² ÷ 2
a = 3.14 × 25 ÷ 2
a = 3.14 × 12.5
a = 39.25
So the circle has an area of 39.25 square yards.
We can then can then add the areas together, giving us a total of 179.25 square yards.
Jackson is preparing many gifts for a family holiday party. Each gift must either be wrapped with wrapping paper or prepared in a gift bag. Jackson can wrap a single gift in 6 minutes and he can do a gift bag in 2 minutes. Jackson prepared a total 25 gifts in 110 minutes. Write a system of equations that could be used to determine the number of gifts Jackson wrapped and the number of gift bags he prepared. Define the variables that you use to write the system.
a) A system of equations that could be used to determine the number of gifts Jackson wrapped and the number of gift bags he prepared is:
6x + 2y = 110x + y = 25.b) The variables used to write the system of equations are the number of single gifts, x, and the number of gift bags, y.
What is a system of equations?A system of equations is two or more equations solved simultaneously.
They are also known as simultaneous equations because the solutions of the variables are obtained at the time.
The time for wrapping a single gift = 6 minutes
The time for wrapping a gift bag = 2 minutes
The total number of gifts prepared = 25
The total time used in preparing the 25 gifts = 110 minutes
Let the number of single gifts = x
Let the number of gift bags = y
Equations:6x + 2y = 110 ... Equation 1
x + y = 25 ... Equation 2
Multiply Equation 2 by 2:
2x + 2y = 50 ... Equation 3
Subtract Equation 3 from Equation 1:
6x + 2y = 110
-
2x + 2y = 50
4x = 60
x = 15
From Equation 2:
x + y = 25
15 + y = 25
y = 10
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What 46821 to the nearest 100
Your teacher may want you to erase the comma when inputting your answer.
============================================================
Explanation:
Circle the digit in the hundreds place value, which is the digit 8. The next digit over is 2. This "2" is not five or larger, so we erase the "21" and replace it with "00".
The number 46,821 rounds to 46,800 which is the final answer.
Effectively, all we're doing is rounding the 821 to 800 and then sticking "46" in front. Notice how 821 is closer to 800 than it is to 900. So that's why we didn't round up to 46,900.
A coral reef is located near to a chemical plant. Scientists measure the number of colonies of coral over a period of 20 years. Each year, the
number of colonies is 5 times the previous year.
Which equation shows the number of colonies, c after t years?
c=5-25²
c=25-3²
c=25-5²
c=25+3t
c=25-20¹
SCALE:
0 - 1 - 2 - n
25-125-625-n
Find out which equation best suits N on the scale.
Answer:
c = 25 * 5^t
Step-by-step explanation:
c = 25 * 5^t
This equation best suits N on the scale as it follows the pattern of the number of colonies being 5 times the previous year.
In the chapter on polynomial interpolation, we investigated the construction of cubic splines to interpolate the data set {(xo,yo), (x1, y1), ..., (xn, yn)}. In this question, we use simpler quadratic splines of the form Qj(x) = αj(x - xj)2 + βj (x - xj) + γj; xj < x < x(j+1 ) j = 0,1,...,n-1. The function Q(x) is formed from the union of the individual splines, and the notation hj = xj+1-x3; is used throughout (b) Calculate the magnitude of the discontinuity in the curvature of Q(x) at x = xj;. Simplify your answer as far as possible
We are asked to calculate the magnitude of the discontinuity in the curvature of the quadratic spline function Q(x) at a specific point x = xj.
To calculate the magnitude of the discontinuity in the curvature of Q(x) at x = xj, we first need to find the expression for the curvature of the quadratic spline. The curvature is given by the second derivative of Q(x) with respect to x. By taking the second derivative of Qj(x) = αj(x - xj)² + βj(x - xj) + γj, we can obtain the expression for the curvature.
Once we have the expression for the curvature, we evaluate it at x = xj to find the value of the curvature at the junction point. The magnitude of the discontinuity in curvature is the absolute difference between the curvature values of the adjacent splines at x = xj.
To simplify the answer, we can substitute the given values of αj, βj, and γj into the expression for the curvature and perform any necessary algebraic simplifications. The final result will be the magnitude of the discontinuity in the curvature at x = xj.
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9. Let W be a subspace of an inner product space V. The orthogonal complement of W is the set w+= {v € V : (v, w) = 0 for all we W}. (a) Prove that W nW+ = {0}. (b) Prove that w+ is a subspace of V.
W+ is closed under scalar multiplication. Since W+ is closed under addition and scalar multiplication, it is a subspace of V. This completes the proof.
(a) Proof that \(W∩W^⊥ = {0}\):
Proof:
Let's suppose for contradiction that there is a non-zero vector, say v, in the intersection of W and its orthogonal complement W+.
Since v is in W+, then it is orthogonal to all the vectors in W. Since v is also in W, then v is orthogonal to itself. Therefore, (v, v) = 0.
Since (v, v) = 0 and v is non-zero, it follows that v is not positive-definite. This is a contradiction since we are working in an inner product space and all vectors are positive-definite. Therefore, the intersection of W and W+ must be {0}. This completes the proof.
(b) Proof that \(W^⊥\) is a subspace of V:
Proof:
Let x and y be vectors in W+. Then (x+y, w) = (x, w) + (y, w)
= 0, since both x and y are in W+.
Therefore, W+ is closed under addition.
Let a be a scalar and x be a vector in W+. Then (ax, w)
= a(x, w)
= 0, since x is in W+.
Therefore, W+ is closed under scalar multiplication.
Since W+ is closed under addition and scalar multiplication, it is a subspace of V. This completes the proof.
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a tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches she has played. at the start of a weekend, her win ratio is exactly $\dfrac{1}{2}$. during the weekend, she plays four matches, winning three and losing one. at the end of the weekend, her win ratio is greater than $\dfrac{503}{1000}$. what's the largest number of matches she could've won before the weekend began?
The largest number of matches she could have won before are 164 matches.
What is a ratio?A ratio shows the relation between two amounts. For example, the ratio of apples to pears in a basket or the ratio of women to men in a town.
How to calculate the number of matches this player had?First represent the matches she had won, using n as a reference. This means:
\(\frac{n}{2n} = \frac{1}{2}\)
Then, based on this let's add the current ratio:
\(\frac{n+3}{2n+4} = \frac{503}{1000}\)
Based on this, let's solve this inequality to find out the number of matches the player won before. Follow these steps:
Cross multiply = 1000n + 3000 > 1006 n + 2012Solve this operation = 1000 - 1006 = 6 and 3000 - 2012 = 988Divide = 988 / 6 = 164.66 which can be rounded as 164Based on the previous process, the number of matches the player could have won before the weekend began was 164 matches.
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Multi Step Problem (Show work!!)
-4 + -5 = 8
Answer:
the answer is -9 not 8
Step-by-step explanation:
solves the equation
8x-2 =3(x-9)
Answer:
-5.2
Step-by-step explanation:
what is the sample standard deviation of the following numbers? 4, 9, 5, 8, 7
Therefore, the sample standard deviation of the given numbers 4, 9, 5, 8, 7 is approximately 2.07.
To find the sample standard deviation of a set of numbers, we can use the following steps:
Calculate the mean (average) of the numbers: (4 + 9 + 5 + 8 + 7) / 5 = 33 / 5 = 6.6
Subtract the mean from each number and square the result:
(4 - 6.6)^2 = (-2.6)^2 = 6.76
(9 - 6.6)^2 = (2.4)^2 = 5.76
(5 - 6.6)^2 = (-1.6)^2 = 2.56
(8 - 6.6)^2 = (1.4)^2 = 1.96
(7 - 6.6)^2 = (0.4)^2 = 0.16
Calculate the sum of the squared differences: 6.76 + 5.76 + 2.56 + 1.96 + 0.16 = 17.2
Divide the sum of squared differences by (n - 1), where n is the number of data points: 17.2 / (5 - 1) = 4.3
Take the square root of the result to get the sample standard deviation: √4.3 ≈ 2.07
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Formalize the following in terms of atomic propositions r, b, and w, first making clear how they correspond to the
English text. (a) Berries are ripe along the path, but rabbits have not been seen in the area.
(b) Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.
(c) If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.
(d) It is not safe to walk along the path, but rabbits have not been seen in the area and the berries along the path are ripe.
e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to
pave been seen in the area.
Walking is not safe on the path whenever rabbits have been seen in the area and berries are ripe along the path.
Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.
Given information and corresponding atomic propositions:
We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:
r: Rabbits have been seen in the area.
b: Berries are ripe along the path.
w: Walking on the path is safe.
Now, let us formalize each of the given statements in terms of these atomic propositions:
a) Berries are ripe along the path, but rabbits have not been seen in the area.
b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.
c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.
d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.
e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.
Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.
The formalizations in terms of atomic propositions are:
a) b ∧ ¬r.b) ¬r ∧ w ∧
b.c) (b → w) ∧ (¬r → w).
d) ¬w ∧ ¬r ∧
b.e) (¬r ∧ ¬b) → w.b ∧
Berries are ripe along the path, but rabbits have not been seen in the area.
This is formalized by using the ∧(logical and) operator.
(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.
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6th grade math i mark as brainliest
9514 1404 393
Answer:
8, 9. Correct
10. 6.1×t
Step-by-step explanation:
8, 9. The answers shown are correct.
__
10. The only product in the given expression is 6.1t, which can be written as ...
6.1×t
when a symbol is used to represent multiplication.
The parts of the product are the multiplicand and the multiplier. Those parts are also called factors.
What scale factor was used in the dilation?
The scale factor used in the dilation of the triangle ABC is 3.
What is the dilation of a triangle?Dilation is a method for generating analogous figures decreasing or increasing their dimensions by some scaling factors.
By dividing distances by the scale factor, each point is stretched outward from the central point D if the scaling factor is more than 1 or inwards if the scale factor is less than 1.
Considering the triangle ABC:
The length of the side AB is 2 units
Compared with triangle DEF, the length of the similar side DE is 6 units
The scaling factor = length of side DE /length of the side AB
The scaling factor = 6 / 2
The scaling factor = 3
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Find a formula for the nth term of the sequence where a_n is calculated directly from n. 5 / 1, 9 / 2, 13 / 6, 17 / 24, 21 / 120, ... a_n = for n ⥠1
The formula for the nth term of the given sequence is: a_n = (4n + 1) / (n!)
Numerators:
-The numerators of the sequence follow the pattern of 4n + 1, where n is the position of the term in the sequence. We can observe that each numerator is obtained by adding 4 to the product of n and 1.
Denominators:
-The denominators of the sequence correspond to the factorials of the corresponding n value. The denominator for each term is given by n!, where n is the position of the term.
Combining the above observations, we can express the nth term of the sequence as:
a_n = (4n + 1) / (n!)
For example:
- The numerator of the first term is 5, which is obtained by adding 4 to the product of 1 and 1, i.e., 4(1) + 1. Similarly, the numerator of the second term is 9, which is obtained by adding 4 to the product of 2 and 1, i.e., 4(2) + 1.
- The denominator of each term is the factorial of the corresponding n value, i.e., n! For example, the denominator of the third term is 6!, which is equal to 720.
- Therefore, the nth term of the sequence can be expressed as (4n + 1) / (n!).
For example, to find the 4th term of the sequence, we plug in n=4 into the formula:
a_4 = (4(4) + 1) / (4!) = 17/24
Similarly, to find the 6th term of the sequence, we plug in n=6 into the formula:
a_6 = (4(6) + 1) / (6!) = 21/120 = 7/40
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Find the distance between the points (4,10) and (0,0) the answer must be a whole number
Answer:
d = \(2\sqrt{29}\)
Step-by-step explanation:
\(d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d= \sqrt{(0-4)^2+(0-10)^2}\\d= \sqrt{(-4)^2+(-10)^2}\\d= \sqrt{16+100}\\d= \sqrt{116}\\d=2 \sqrt{29}\)
What is the sale price of $320 marked down by 20%
320-5
The final selling price of a $320 item with a 20% discount is $256. A product or service is sold at a discounted price for a limited time or during a specific promotional period.
We can multiply the original price by the % decrease as a decimal (i.e., as a fraction out of 1) and then subtract the result from the original price to determine the sale price of an item that has been marked down by a specific percentage.
In this instance, the item has been reduced by 20%, or 0.20 as a decimal. As a result, we may determine the discount amount as:
Discount: $64 ($0.20 x $320)
We must deduct the discount from the original price to determine the sale price:
Discount price: $320 less $64 equals $256.
Hence, the final selling price of a $320 item with a 20% discount is $256.
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PLS HURRYYYYYYYY
Which word describes the 5 in the expression 5n? A. coefficient B. exponent C. product D. sum
Answer:
Step-by-step explanation:
It would be either A or C
Most likely A Hope this helps ya <3
The word describing 5 in the given expression is a coefficient.
What is an expression?An expression, in math, is a sentence with a minimum of two numbers and at least one math operation in it.
Given that an expression 5n, we need determine the word used for number 5,
We know that, the numbers connected to a variable by multiplication is called a coefficient.
Here,
5n = 5 × n,
n = variable, 5 = coefficient.
Hence the word describing 5 in the given expression is a coefficient.
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PLS HELP ME WITH THIS
Using it's concept, the experimental probability of getting an odd number and a number greater than 6 is given by:
1/5.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. An experimental probability is calculated considering the results of previous trials.
In this problem, there are 10 trials, and of those, 2 of them, trial 8 and trial 10, resulted in an odd number and a number greater than 6, hence the probability is:
p = 2/10 = 1/5.
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Help please!!!!! No fake answers
Answer: 13 itk
Step-by-step explanation:
Drag each number to the correct location on the calculation and statement. Each number can be used more than once, but not all numbers will be used.
Complete the calculation and statement about the radian measure of angle θ, as well as the arc that subtends it, both shown on the unit circle above.
Arc length = 1/8 * _____ * r
= ____ * r
= π/4 * ____
= ____ units
The radian measure of an angle is equal to the length of the corresponding arc on the unit circle. Therefore, angle θ has a measure of ___ radians
Options to fill in blanks:
2π
1
π/4
π/2
2π/3
π/6
π
Answer:
Step-by-step explanation:
Arc length of a circle is given by,
Arc length = \(\frac{\theta}{360}(2\pi r)\)
Here, θ = Central angle subtended by the arc
r = Radius of the circle
From the given picture,
θ = 45°
r = 1 unit
Therefore, arc length = \(\frac{45}{360}(2\pi r)\)
= \(\frac{1}{8}(2\pi r)\)
= \(\frac{2\pi }{8}(r)\)
= \(\frac{\pi}{4}(r)\)
Arc length = \(\frac{\pi}{4}(1)\) units
= \(\frac{\pi }{4}\) units
Angle θ has a measure = \(\frac{45}{360}\times \pi\)
= \(\frac{\pi}{8}\) radians
two draws are made at random without replacement from a box containing the following five tickets: golden ticket with a one printed on it. golden ticket with a two printed on it. golden ticket with a three printed on it. golden ticket with a 4 printed on it. golden ticket with a three printed on it. what is the probability that the sum of the tickets is 5? enter you answer as a percentage. the probability is
The probability to draw tickets with a sum of 5 is 30%.
According to the question, there are 5 tickets with 1, 2, and 4 printed on one ticket each, while there are 2 tickets with the number 3 printed on them.
We need to find the probability of drawing 2 tickets with a sum of 5 out.
Probability = no of possibilities for an event/total no. of possibilities
From these 5 tickets, 2 tickets at random can be drawn in
⁵C₂ ways.
= 5 X 4
= 20 ways.
Now the possible combinations to draw a sum of 5 is
(1,4) , (2,3) , (2,3) , (3,2) , (3,2) , (4,1)
= 6 ways
Here there are 2 tickets with 3 printed on them so events concerning 3 will be repeated in the sample space.
Hence, the probability to draw 2 tickets with a sum of 5 is
6/20
= 3/10
= 30%
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