Determine the equation of the circle graphed below.
The equation for the circle graphed in the coordinate axis is:
(x - 5)^2 + (y - 6)^2 = 16
How to determine the equation for the circle?Remember that the equation for a circle whose center is at (a, b) and has a radius R is.
(x - a)^2 + (y - b)^2 = R^2
On the graph, we can see that the center of the circle is at (5, 6), and the radius of the circle is R = 4 units. Then the equation for the circle in the graph is:
(x - 5)^2 + (y - 6)^2 = 4^2
(x - 5)^2 + (y - 6)^2 = 16
That is the equation we wanted to find.
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PLEASE Help me answer these 2 math questions!!!
1. The equation for the function is defined as follows: g(x) = (1/3)^x - 2.
2. The range of the function is given as follows: The set of real numbers less than -5.
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.For item 1, the function has an horizontal asymptote at y = -2, hence it is defined as follows:
y = a(1/3)^x - 2.
When x = 0, y = -1, hence the parameter a is obtained as follows:
-1 = a - 2
a = 1.
Thus the function is:
g(x) = (1/3)^x - 2.
For item 2, we have that the function is:
Reflected over the y-axis, due to the negative sign of a.Has an horizontal asymptote at y = -5.Hence the range of the function is given as follows:
The set of real numbers less than -5.
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a swim team consists of 7 boys and 7 girls. a relay team of 4 swimmers is chosen at random from the team members. what is the probability that 3 boys are selected for the relay team given that the first election was a girl?
The probability that 3 boys are selected for the relay team given that the first election was a girl is approximately 0.122, or 12.2%.
The Bayes theorem can be used,Let B represent the decision to select three boys for the relay team whereas A represents the scenario when a girl was chosen first.
P(B|A) is the conditional probability of B given A.
The Bayes theorem gives us:
P(B|A) is equal to P(A|B)*P(B)/P(A).
Given that the relay team consists of 3 boys, the probability that a girl would be chosen as the first team member is P(A|B). Therefore:
P(A|B) = 7/13 * 6/12 * 5/11 * 7/10 = 0.0871
P(B) represents the likelihood of choosing three males for the relay team in an arbitrary manner.
P(B) = (7C3 * 7C1) / (14C4) = 35/143
P(A) represents the likelihood that a girl will be chosen as the first team member without any restrictions.
P(A) = 7/14 = 1/2
Combining everything, we get the following: P(B|A) = P(A|B) * P(B) / P(A) = 0.0871 * 35/143 / (1/2) = 0.1220.122, or 12.2%.
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You are given that cos(A)=−5/13, with A in Quadrant II, and sin(B)=24/25, with B in Quadrant II. Find cos(A+B). Give your answer as a fraction.
The value for the trigonometric expression cos(A+B) is (5√7 - 288)/325
Explain trigonometry.
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It includes the study of trigonometric functions such as sine, cosine, and tangent, which are used to calculate unknown angles or sides of a triangle. Trigonometry has many practical applications in fields such as engineering, physics, and navigation.
According to the given information
We can use the trigonometric identity cos(A + B) = cos(A)cos(B) - sin(A)sin(B) to find cos(A + B).
Since cos(A) = -5/13 and A is in Quadrant II, we can use the Pythagorean identity sin²A + cos²A = 1 to find sin(A). Solving for sin(A), we get sin²A = 1 - cos²A = 1 - (-5/13)² = 144/169. Since A is in Quadrant II, sin(A) is positive, so sin(A) = √(144/169) = 12/13.
Similarly, since sin(B) = 24/25 and B is in Quadrant II, we can use the Pythagorean identity to find cos(B). Solving for cos(B), we get cos²B = 1 - sin²B = 1 - (24/25)² = 7/625. Since B is in Quadrant II, cos(B) is negative, so cos(B) = -√(7/625) = -√7/25.
Substituting these values into the identity for cos(A + B), we get:
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
= (-5/13)(-√7/25) - (12/13)(24/25)
= (5√7)/(13*25) - (12*24)/(13*25)
= (5√7 - 288)/(13*25)
= (5√7 - 288)/325
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Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y > x2 – 2
y ≥ –x2 + 5
To graph the solution set to the given system of inequalities, we first need to graph the functions f(x) = x^2 - 2 and g(x) = -x^2 + 5.
The graph of f(x) is a parabola that opens upward and has its vertex at (0, -2). The graph of g(x) is also a parabola, but it opens downward and has its vertex at (0, 5). We can plot these two graphs on the same coordinate plane as follows:
[Insert image of two parabolas on a coordinate plane]
Next, we need to shade the regions of the graph that satisfy the given inequalities. The first inequality y > x^2 - 2 represents the region above the parabola f(x) but below the line y = infinity. The second inequality y ≥ -x^2 + 5 represents the region at or above the parabola g(x). The solution set is the intersection of these two regions.
The shaded region represents all the points (x, y) that satisfy both inequalities, and therefore, the solution set to the system of inequalities.
Find the area of a rectange with a base of 3/7 feet and a height of 9/10 feet
The area of the rectangle is 27/70 square feet.
Area of a rectangleThe area of a rectangle is given by the formula:
Area = base x height
Plugging in the given values, we get:
Area = (3/7) x (9/10)
Simplifying, we get:
Area = (27/70) square feet
Therefore, the area of the rectangle is 27/70 square feet.
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Solve the system algebraically.
y= 3-1/2x
3x+4y=1
What is the value of x?
1. 17/2
1. -11
3. 11
Answer: x = -11
Step-by-step explanation:
Sub in y= 3-1/2x into 3x+4y=1 for y, and solve for x.
[tex]3x+4(3-\frac{1}{2}x) =1\\3x + 12 - 2x =1\\\\\ x = -11[/tex]
Error Analysis The bar graph shows the
results of a school election. A total of 150
students voted. Charlotte says that this
means 40 students voted for Candidate C.
How many students voted for Candidate C
in all? What was Charlotte's likely mistake?
Percent of Votes
40-C
32-
24-
16-
8-
In all how many students voted C
Answer:
To determine the number of students who voted for Candidate C, we need to first find what percent of the total votes they received. Looking at the graph, it appears that Candidate C received approximately 40% of the votes.
To find out how many students this represents, we can set up a proportion:
40% = C/150
Where C is the number of votes received by Candidate C.
To solve for C, we can cross-multiply:
0.4 x 150 = C
C = 60
Therefore, 60 students voted for Candidate C.
Charlotte's mistake was assuming that the percentage of votes for Candidate C directly corresponded to the number of students who voted for them. It's possible that more than one student voted for each candidate, and the percentage of votes represents the proportion of all votes each candidate received.
What fraction is equivalent to 1/4
The numbers are: 2,4,6,8,10,12
A right triangle has side 9 and hypotenuse 15. Use the Pythagorean Theorem to find the length of the third side.
For pythagorean theorem the triangle is a 3, 4 ,5 triangle 15 would be the length 5, and 9 would be the lenght 3. So we would multiply each side to getthe answer your lookin for. Which the third side would be, I think im right, i just did this in my head but im only 11 so dont bully me plsssss
ANSWER 12
Find the surface area
Round to the nearest tenth
V(d)V, left parenthesis, d, right parenthesis models Erica's vertical distance from the top of the valley (in kilometers) after walking
d
dd kilometers along the trail.
What does the statement
V
(
2
)
=
T
V(2)=TV, left parenthesis, 2, right parenthesis, equals, T mean?
The meaning of V(2) is the Erica's vertical distance after walking 2 kilometers along the trail.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The input and output variables for this problem are given as follows:
Input: number of kilometers walked along the trail.Output: vertical distance.V(2) means that the number of km is of 2, hence the meaning of V(2) is the Erica's vertical distance after walking 2 kilometers along the trail.
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Negative 3 6/7 times negative 3 1/3
The expression Negative 3 6/7 times negative 3 1/3 has a value of -12 6/7
Evaluating the mathematical expressionWe have the following statement as the given parameter
Negative 3 6/7 times negative 3 1/3
Next, we rewrite the above statement using numbers and operators
-3 6/7 * 3 1/3
The above statement is a product expression that multiplies the values of -3 6/7 and 3 1/3
Also, there is no need to check if there are like terms in the expression or not
This is because we are multiplying the factors
So, we have
-3 6/7 * 3 1/3 = -27/7 * 10/3
Evaluate
-3 6/7 * 3 1/3 = -9/7 * 10
Rewrite as
-3 6/7 * 3 1/3 = -90/7
Simplify
-3 6/7 * 3 1/3 = -12 6/7
This means that the value of the expression is -12 6/7
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2. Consider this scatter plot.
a)
Draw a line of best fit on the picture of the scatterplot above. (2 pts.)
b) Is there a positive or negative association between a car's price and age? Explain your answer using as
much detail as possible. (3 pts.)
Answer:
Answer: A
Step-by-step explanation: cuz of the
pie chart
College Level Trigonometry question any help will do
Answer:
16.58. my answer needs to be more than 20 characters, soooo... how is your day going?
PLEASE HELP - GIVING MANY POINTS!
After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parabola.
The equation for this parabola is y = -x2 + 19.
In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points.
Linear function: _________________ (You create an equation in y=mx+b form, that means the requirements above).
Create a table of at least four values for YOUR function that includes two points of intersection between the airplane and the rainbow.
x y
Is the linear function you created with your table positive or negative? Explain what it means in context.
What are the solutions or solution to the system of equations created? Explain what it or they represent.
Analyze the two functions. Answer the following reflection questions in complete sentences.
What is the domain and range of the rainbow?
Explain what the domain and range represent in context.
Do all of the values make sense in this situation? Why or why not?
What are the x- and y-intercepts of the rainbow?
Explain what each intercept represents in context.
The x-intercepts of the rainbow are (sqrt(19), 0) and (-sqrt(19), 0), while the y-intercept is (0, 19). In context, the x-intercepts represent the points where the rainbow touches the ground, while the y-intercept represents the highest point of the rainbow.
The linear functionLinear function: y = 3x + 1
x y
3 10
5 16
7 22
9 28
The linear function is positive, which means that the airplane's altitude is increasing as it moves towards the right on the graph. In context, this means that the airplane is ascending as it moves away from the observer towards the rainbow.
The system of equations created by the two functions is:
y = -x^2 + 19
y = 3x + 1
By substituting y in the second equation with the first equation, we get:
-x^2 + 19 = 3x + 1
Solving for x, we get:
x = -2 or x = 5
Substituting these values of x back into either of the equations, we get the corresponding values of y:
(-2, 7) and (5, 16)
These two solutions represent the points of intersection between the rainbow and the airplane's trajectory.
The domain of the rainbow is all real numbers, while the range is y ≤ 19. In context, this means that the rainbow can appear at any point in the observer's field of view, but its highest point is at y = 19.
All of the values in the domain and range make sense in this situation since they are within the physical limits of the observer's perception.
The x-intercepts of the rainbow are (sqrt(19), 0) and (-sqrt(19), 0), while the y-intercept is (0, 19). In context, the x-intercepts represent the points where the rainbow touches the ground, while the y-intercept represents the highest point of the rainbow.
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100 Points! Use synthetic substitution to find f(-3) and f(4) for 3x^4-4x^3+3x^2-5x-3. Photo attached. Please show as much work as possible. Thank you!
f(4) = 537. and f(-3) = 363. To find f(-3), we replace x with -3 in the expression similarly for x=4.
what is expression ?
In mathematics, an expression is a combination of mathematical symbols (such as numbers, variables, and operators) that represents a mathematical object or relationship.
In the given question,
To find f(-3), we replace x with -3 in the expression:
f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3
= 3(81) - 4(-27) + 3(9) + 15 - 3
= 243 + 108 + 15 - 3
= 363
Therefore, f(-3) = 363.
To find f(4), we replace x with 4 in the expression:
f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3
= 3(256) - 4(64) + 3(16) - 20 - 3
= 768 - 256 + 48 - 23
= 537
Therefore, f(4) = 537.
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Could this ordered pair be a solution to this equation?
y = 2x -1
(2, 3)
Step-by-step explanation:
yes .. when you put x=2 y will be 3 .. you get it?
francine can type 3,420 words in 1 hour and 30 minutes at this rate how any words can she type per minute
Francine can type 38 words per minute at this rate.
To find out how many words Francine can type per minute, we need to convert the time she took to type the words into minutes. Since there are 60 minutes in 1 hour, 1 hour and 30 minutes is equivalent to 1 × 60 + 30 = 90 minutes.
Next, we can use the formula:
words per minute = total words / total minutes
where "total words" is the number of words Francine typed (3,420) and "total minutes" is the time she took in minutes (90).
Substituting these values into the formula, we get:
words per minute = 3,420 / 90 = 38
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4.)Write an inequality.
Seven more than the quotient of a
number b and 15 is greater than 6
1 and 1/4 times 1 and 1/3 equals
Write a quadratic function with zeroes – 1 and 6. Write your answer using the variable x and in standard form with a leading coefficient of 1.
Answer:
If the zeroes of a quadratic function are -1 and 6, then its factored form is:
(x + 1)(x - 6) = 0
Expanding the left side:
x^2 - 5x - 6 = 0
So the quadratic function in standard form is:
f(x) = x^2 - 5x - 6
Answer:
f(x) = x^2 - 5x - 6
Step-by-step explanation:
To create a quadratic function with zeroes -1 and 6, we can start by using the zero product property to write out the factors of the equation:
(x + 1)(x - 6) = 0
Expanding the factors, we get:
x^2 - 5x - 6 = 0
This quadratic equation is in standard form with a leading coefficient of 1. Therefore, the quadratic function with zeroes -1 and 6 is:
f(x) = x^2 - 5x - 6
This function can also be graphed on the coordinate plane as a parabola with a vertex at (2.5, -10.25) and its axis of symmetry at x = 2.5. The graph would intersect the x-axis at -1 and 6, confirming that these are the zeroes of the function.
Find the equation of a line that passes through the points (4, 1) and (12, -3).
The equation of the line that passes through the points (4, 1) and (12, -3) is y = (-1/2)x + 3.
Explain the term equation
An equation is a mathematical statement that expresses the equality of two expressions or values. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to represent relationships between quantities and to solve problems in various fields, including mathematics, physics, and engineering.
According to the given information
We can use the point-slope form of the equation of a line to find the equation of the line that passes through the two given points.
The point-slope form of the equation of a line is:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line.
To find the slope of the line that passes through (4, 1) and (12, -3), we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (4, 1) and (x2, y2) = (12, -3)
m = (-3 - 1) / (12 - 4) = -4 / 8 = -1/2
Now that we have the slope of the line, we can use one of the two given points and the slope to find the equation of the line. Let's use the point (4, 1):
y - y1 = m(x - x1)
y - 1 = (-1/2)(x - 4)
Distributing the -1/2, we get:
y - 1 = (-1/2)x + 2
Adding 1 to both sides, we get:
y = (-1/2)x + 3
Therefore, the equation of the line that passes through the points (4, 1) and (12, -3) is y = (-1/2)x + 3.
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Please help if you can calculate it!
A survey was conducted one month ago to review the calories of lunch boxes provided by the supplier "Better
Lunch". In a sample with 300 lunch boxes, there were 273 lunch boxes with calories below 650 and the other
27 lunch boxes with calories above 650. Besides, the mean calories was 550 and standard deviation was 40.
(a) Find the point estimate of the population proportion of lunch boxes provided by "Better Lunch" had
calories above 650.
(b) Calculate the sampling error at 98% confidence level for the estimate of the population proportion of
lunch boxes provided by "Better Lunch" had calories above 650.
(c) Construct a 98% confidence interval estimate of the population proportion of lunch boxes provided by
"Better Lunch" had calories above 650.
(d) "Better Lunch" follows government's suggestions to change the menu in order to reduce the lunch boxes'
calories. Suppose after the menu update, each lunch box's calories can be reduced by 4%. Find the
sample mean and sample standard deviation of calories of the above sample after the change. Hence,
construct a 90% confidence interval estimate of the population mean calories in a lunch box after the
change.
The 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.
How to construct a 90% confidence interval estimate of the population mean calories in a lunch box after the change.(a) The point estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 0.09, which is equal to 27/300.
(b) The sampling error at 98% confidence level for the estimate of the population proportion can be calculated using the following formula:
Sampling error = z*(standard deviation/square root of sample size)
Where z is the critical value at 98% confidence level, which can be found using a standard normal distribution table or calculator. For a 98% confidence level, the z value is 2.33.
Substituting the values, we get:
Sampling error = 2.33*(sqrt(0.09*0.91/300)) = 0.049 or 4.9%
Therefore, the sampling error at 98% confidence level for the estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 4.9%.
(c) The 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 can be calculated using the following formula:
Confidence interval = point estimate ± (z*standard error)
Where point estimate is 0.09, z is the critical value at 98% confidence level which is 2.33, and standard error is the standard deviation divided by the square root of sample size.
Substituting the values, we get:
Confidence interval = 0.09 ± (2.33*sqrt(0.09*0.91/300)) = 0.09 ± 0.114 or (0.026, 0.154)
Therefore, the 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is between 0.026 and 0.154.
(d) After the menu update, the sample mean of the calories of the above sample can be calculated as follows:
New sample mean = 0.96 * 550 = 528
The sample standard deviation after the change is still 40, assuming the variability of calories is not affected by the menu update.
To construct a 90% confidence interval estimate of the population mean calories in a lunch box after the change, we can use the following formula:
Confidence interval = sample mean ± (t*standard error)
Where t is the critical value at 90% confidence level with degrees of freedom (df) = sample size - 1. Using a t-distribution table or calculator with df = 299, we find that t = 1.645.
The standard error can be calculated as follows:
Standard error = standard deviation/sqrt(sample size) = 40/sqrt(300) = 2.31
Substituting the values, we get:
Confidence interval = 528 ± (1.645*2.31) = 528 ± 3.8 or (524.2, 531.8)
Therefore, the 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.
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What is the volume and surface area of a rectangular prism that is 11 ft long, 8 ft wide, and 4 ft tall?
Answer:
Here
Step-by-step explanation:
The volume of a rectangular prism is found by multiplying the length, width, and height.
Volume = Length x Width x Height
Volume = 11 ft x 8 ft x 4 ft
Volume = 352 cubic feet
The surface area of a rectangular prism is found by adding up the areas of all six faces.
Surface area = 2lw + 2lh + 2wh
Surface area = (2 x 11 ft x 8 ft) + (2 x 11 ft x 4 ft) + (2 x 8 ft x 4 ft)
Surface area = 176 + 88 + 64
Surface area = 328 square feet
Therefore, the volume of the rectangular prism is 352 cubic feet and the surface area is 328 square feet.
HELLLPPP ME PLSSS ITS URGENT
The ratio of the volume of both spheres is: 1/(24√3)
What is the volume of the sphere?The formula for the volume of a sphere is expressed as:
V = ⁴/₃πr³
where:
r is radius
V is volume
We are told that the radii of the two spheres have a ratio of 1:2√3. Thus:
Volume of sphere A/Volume of sphere B = (1:2√3)³
= 1/(24√3)
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if tan68° = 1/m, express the following in terms of m:
1. tan22°
The price of an item has been reduced by 45%. The original price was $55. what is the price now?
Answer:
45% = 0.45
(you do this by bringing the decimal over 2 places)
multiply $55 and 0.45 to get $24.75
final answer = $24.75
Carly ordered shoes online from her favorite store. The shipping costs for her
purchase is $5.50. Her total cost for the entire purchase is $60.75. Which
equation below could be used to calculate s, the cost of her shoes without
shipping included?
The equation to calculate the cost of her shoes without shipping included is: x = 55.25
The equation to calculate s, the cost of her shoesLet x be the cost of Carly's shoes.
The problem states that the total cost of her purchase (including shoes and shipping) is $60.75, so we can set up the equation:
x + 5.50 = 60.75
To find the cost of her shoes without shipping, we need to isolate x. We can do this by subtracting 5.50 from both sides:
x + 5.50 - 5.50 = 60.75 - 5.50
Simplifying:
x = 55.25
Therefore, the equation to calculate the cost of her shoes without shipping included is: x = 55.25
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A bag contains 18 small red, 19 small black, 13 large black, and 15 large red T-shirts, and nothing else. What is the least number of T-shirts Alpa must take out of the bag (without looking at them) to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color?
Alpa must take out at least 19 T-shirts from the bag to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color.
What is the Pigeonhole Principle?
The Pigeonhole Principle is a fundamental concept in combinatorics, which is a branch of mathematics that deals with counting and analyzing the properties of sets of objects. The principle states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.
We can solve this problem using the Pigeonhole Principle, which states that if n+1 objects are distributed among n boxes, then there is at least one box that contains two or more objects.
In this case, we want to be sure that we have at least two T-shirts that differ only by size or only by color.
So we need to find the minimum number of T-shirts that we must take out of the bag to guarantee this.
Let's consider the worst-case scenario, where we take out all the T-shirts that are of one size or one color.
If we take out all 18 small red T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color (since we could still get a small black T-shirt).
Similarly, if we take out all 19 small black T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.
If we take out all 13 large black T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.
If we take out all 15 large red T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.
So we need to take out at least 19 T-shirts to be sure that we have at least two T-shirts that differ only by size or only by color. (We add one to the largest number of T-shirts of one color or size.)
Therefore, Alpa must take out at least 19 T-shirts from the bag to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color.
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