The equation of P(e₁ ∪ e₂) describes the condition that the mutually exclusive event stands one of the events occurs, or both occur.
What are Mutually Exclusive events?Mutually Exclusive events are described as in probability the particular addition rule exists practical when two occurrences exist incompatible with one another. It claims that the probability of either event exists equivalent to the probability of each possibility separately.
If e₁ and e₂ stand said to be mutually exclusive events then the probability of an event e₁ happening or the probability of event e₂ occurring exists given as P(e₁) + P(e₂) :
P(e₁ ∪ e₂) = P(e₁) + P(e₂)
Therefore, the equation of P(e₁ ∪ e₂) describes the condition that the mutually exclusive event stands for one of the events that happens, or both happen.
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The square below has an area of x2 + 4x + 4 square meters.
What expression represents the length of one side of the square?
Perfect Squares
Write your answer without any spaces. Ex. x+3
Answer:
The side length of a square is the square root of its area. We know that:
x2 + 4x + 4 = (x + 2)2
Therefore, the side length of the square is x + 2
Louise, Tammy, Delores, and Sheryl score 78 points total in the tennis matches they play. They score a consecutive number of points from smallest to greatest in respect to the order of the names mentioned. How many points does Louise score?
[tex]\huge\boxed{18\ \text{points}}[/tex]
We'll represent Louise's, Tammy's, Delores's, and Sheryl's point values with [tex]x[/tex], [tex]x+1[/tex], [tex]x+2[/tex], and [tex]x+3[/tex] respectively since each one is 1 point more than the last.
Add all of these values up and set it all equal to [tex]78[/tex].
[tex]x+x+1+x+2+x+3=78[/tex]
Now, simplify.
[tex]4x+6=78[/tex]
Subtract [tex]6[/tex] on both sides.
[tex]\begin{aligned}4x+6-6&=78-6\\4x&=72\end{aligned}[/tex]
Divide both sides by [tex]4[/tex].
[tex]\begin{aligned}\frac{4x}{4}&=\frac{72}{4}\\x&=\boxed{18}\end{aligned}[/tex]
Since Louise's score is [tex]x[/tex], the answer is [tex]18[/tex].
Double-checkingTo verify our answer, add the point totals [tex]18[/tex], [tex]19[/tex], [tex]20[/tex], and [tex]21[/tex].
This equals [tex]78[/tex], so we can be sure the answer is correct.
How many different anagrams (including nonsensical words) can be made from the letters in the word statistics, using all the letters?
50,400 different anagrams can be made from the letters in the word statistics.
Given word : STATISTICS
Anagrams are words formed by jumbling the positions of the letters given in the word.
For such problems we do factorial of number of words and divide by the repeated letters factorials.
Total number of letters = 10
They can be permutated among themselves in 10! ways.
Some letters are repeated in word STATISTICS
Since, there are 3 S's and 3 T's and 2 I's
So, Number of anagrams = [tex]\frac{10!}{3!.3!.2!}[/tex]
= [tex]\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3! \times 3 \times 2 \times 1 \times 2 \times 1}[/tex]
= [tex]\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4}{3 \times 2 \times 2}[/tex]
= 10 × 9 × 8 × 7 × 2 × 5
= 50,400
50,400 different anagrams can be made from the letters in the word statistics.
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Need help ASAP! This is due in an hour and this is the last question!!!
the equation with these solutions is:
0 = x^2 - 6x + 6
How to find an equation with the given solutions?
Remember that a quadratic equation with the solutions a and b is written as:
0 = (x - a)*(x - b)
Here we have the solutions:
x = 3 + √3x = 3 - √3Then we can write a quadratic equation of the form:
0 = (x - (3 + √3) )*(x - (3 - √3) )
0 = (x - 3 - √3)*(x - 3 + √3)
Expanding that, we get:
0 = x^2 - 6x + 9 - 3
0 = x^2 - 6x + 6
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Use the laplace transform to solve the given initial-value problem. y'' − 8y' 16y = t, y(0) = 0, y'(0) = 1
If the initial value problem is [tex]y^{11} -8y^{1} -15y=0[/tex] and [tex]y^{1}(0) =1[/tex],y(0)=0 then y(t)=[tex](e^{3t} -e^{5t} )/2[/tex].
Given the initial value problem be [tex]y^{11} -8y^{1} -15y=0[/tex]and [tex]y^{1}(0) =1[/tex],y(0)=0.
We are required to find the solution of the given initial value problem.
Laplace transform is an integral transformation that converts a function of a real variable to a function of a complex variable.
Take laplace on the DE, we get
[tex]s^{2}-sY(0)-y^{i}(0)-8[sY(s)-y(0)-15Y(s)]=0[/tex]
[tex]s^{2}Y(s)-s(0)-1-8{sY(s)-0)}+15Y(s)=0[/tex]
(Putting the values given in question)
Y(s)=([tex]s^{2} -8s+15)-1=0[/tex]
Y(s)=1/([tex]s^{2} -8s+15[/tex])
Simplifying the above:
=1/([tex]s^{2} -5s-3s+15)[/tex]
=1/[s(s-5)-3(s-5)]
=1/2 [1/(s-3)-1/(s-5)]
Taking inverse of the above we get,
y(t)=[tex](e^{3t} -e^{5t} )/2[/tex]
Hence if the initial value problem is [tex]y^{11} -8y^{1} -15y=0[/tex] and [tex]y^{1}(0) =1[/tex],y(0)=0 then y(t)=[tex](e^{3t} -e^{5t} )/2[/tex].
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Robert wants to fence a rectangular plot of land of at least $500$ square feet while using the least amount of fencing possible. He wants the width of the plot to be $5$ ft longer than the length. What is the width of the plot
The area of a rectangle is the amount of space it would cover on a 2-Dimensional plane. The required value of the width is 25 feet.
A rectangle is a plane shape with equal opposite sides. Its area can be determined by;
Area of a rectangle = length x width
Considering the given question, let the length of the plot be represented by l and its width as w. Given that the width of the plot should be longer than its length by 5, then we have;
w = l + 5
But,
Area of the plot = length x width
500 = l x (l + 5)
= [tex]l^{2}[/tex] + 5l
This implies that,
500 = [tex]l^{2}[/tex] + 5l
[tex]l^{2}[/tex] + 5l - 500 = 0
Applying the quadratic formula, we have;
l = (-b ± [tex]\sqrt{b^{2} - 4ac}[/tex]) / 2a
a = 1, b = 5, c = -500
= (-5 ± [tex]\sqrt{5^{2} - (4*1*-500)}[/tex]/ 2
= (-5 ± 45) / 2
l = (40) / 2 OR l = (-50) / 2
l = 20 OR l = - 25.5
So that,
l = 20
Therefore, the length of the plot is 20 feet.
Thus the width of the plot can be determined as;
w = l + 5
= 20 + 5
w = 25
The width of the plot is 25 feet.
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Hey help mee if you solve it you are intelligent // what number is car park
Answer: The answer is 87. when you look at the picture each number is one number apart from each other like look at
86, 87, 88, 89, 90, 91
85 + 1 = 86
86 + 1 = 87
87 + 1 = 88
89 + 1 = 90
90 + 1 = 91
Step-by-step explanation:
If two cards are drawn from a deck, what is the probability that exactly one of the cards will be a face card?
The probability of getting exactly one face card is 0.72.
According to the questions two cards are drawn from a deck.
Since, we know that
Total number of cards in a deck = 52
Total number of face cards = 3 × 4 = 12
So, the number of ways of selecting 2 cards from a deck = [tex]^{52} C_{2}[/tex]
And, the total number of ways of getting exactly one face cards
= [tex]^{12} C_{1} \times ^{40} C_{1}[/tex] + [tex]^{40} C_{1} \times ^{12} C_{1}[/tex]
= 2[tex]^{40} C_{1} \times ^{12} C_{1}[/tex]
Therefore, the probability of getting exactly one face card
= [tex]\frac{2(^{40} C_{1} \times ^{12} C_{1})}{^{52C_{2} } }[/tex]
[tex]= \frac{2(\frac{40 \times 39!}{1!\times 39!} \frac{12\times 11!}{11!}) }{\frac{52\times 51\times 50!}{2!\times50!} }[/tex]
[tex]= \frac{2(40\times 12)}{26\times 51}[/tex]
[tex]=\frac{2\times 480}{1326}[/tex]
= 0.72
Hence, the probability of getting exactly one face card is 0.72.
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A square field was enlarged by adding 5 feet to the length and width of the original field. if the area of the enlarged field is 576 square feet, what was the side length of the original field?
The side length of the original field is 19 feet.
What is square?
A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one). A square has four axes of symmetry, and its two finite diagonals (as with any rectangle) are equal. Bisection of a square by a diagonal results in two right triangles.Suppose the original square is x feet wide. Since its the length and width are the same,
So, length of side of enlarged field = x+5
Area of new enlarged field = side² = ( x + 5 )²
So, the enlarged shape would be = ( x + 5 ) ( x + 5)
Then , ( x + 5 ) ( x + 5) = 576
( x + 5 )²= 576
x + 5 = √576
x + 5 = 24
x = 24 - 5 ⇒ 19
Hence, The side length of the original field is 19 feet.
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What is a31 of the
arithmetic sequence for
which a5 = 12.4 and
ag = : 22.4?
The value of a₃₁ of the arithmetic sequence exists 77.4.
How to find the value of a₃₁ of the arithmetic sequence?Given: a₅ = 12.4 and a₉ = : 22.4
For the arithmetic sequence a₁, a₂, a₃, ..., the n-th term exists
where d = common difference
a₅ = 12.4,
a₁ + 4d = 12.4 .........(1)
Because a₉ = 22.4,
a₁ + 8d = 22.4 .........(2)
Subtract (1) from (2), we get
a₁ + 8d - (a₁ + 4d) = 22.4 - 12.4
4d = 10
Dividing throughout by 4, we get
d = 2.5
From (1), we get
a₁ = 12.4 - 4 [tex]*[/tex] 2.5 = 2.4
a₃₁ = 2.4 + 30 [tex]*[/tex] 2.5 = 77.4
Therefore, the correct answer is a₃₁ = 77.4
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A map has a scale of 1cm:4km the actual distance between the two cities is 52km. What is the distance between the two cities on the map
Answer:
13cm
Step-by-step explanation:
Given the map scale:
1cm on the map : 4km actual distance
4km actual distance : 1cm on the map
1km actual distance : [tex]\frac{1}{4} =0.25cm[/tex] on the map
Therefore,
52km actual distance = 0.25 * 52 = 13cm
How do I rewrite 1/4 book 1/3 hour as a unit rate?
The unit rate of 1/4 book 1/3 hour in books per hour is 3/4 books per hour.
Unit rateUnit rate is the rate of a quantity in terms of another quantity per unit.
Number of books = 1/4Number of hours = 1/3Unit rate(books per hour) = Number of books / Number of hours
= 1/4 ÷ 1/3
= 1/4 × 3/1
= (1×3) / (4×1)
= 3/4 books per hour
Therefore, the unit rate of 1/4 book 1/3 hour in books per hour is 3/4 books per hour.
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StartFraction 6 Over 7 EndFraction x + one-half = StartFraction 7 Over 8 EndFraction for x?
The value of x in 6/7x + 1/2 = 7/8 is 7/16
How to solve for x?The equation is given as:
6/7x + 1/2 = 7/8
Subtract 1/2 from both sides
6/7x + 1/2 -1/2 = 7/8 -1/2
Evaluate the difference
6/7x = 3/8
Multiply both sides by 7
6x = 21/8
Divides both sides by 6
[tex]x = \frac {7}{16}[/tex]
Hence, the value of x is 7/16
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Consider the exponential function g(x) = 1,296 x .
Find the output values for x-values x = –1.75, –1, –0.25, 0, 0.25, 0.50, 0.75, and 1.
The values associated to the exponential function are listed below:
g(- 1.75) = 3.572 × 10⁻⁶g(- 1) = 7.716 × 10⁻⁴g(- 0.25) = 0.167g(0) = 1g(0.25) = 6g(0.50) = 36g(0.75) = 216g(1) = 1 296How to evaluate an exponential function
Herein we have the exponential function [tex]g(x) = 1\,296^{x}[/tex], which has to be evaluated, that is, replacing the variable x by constants and make use of algebra properties until result is found.
g(- 1.75) = 3.572 × 10⁻⁶
g(- 1) = 7.716 × 10⁻⁴
g(- 0.25) = 0.167
g(0) = 1
g(0.25) = 6
g(0.50) = 36
g(0.75) = 216
g(1) = 1 296
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suppose that a 2 by 10 rectangular grid of seats is filled with people. On the
blow of a whistle, all 20 people get up from their current seat and move to an orthogonally
adjacent seat. How many ways are there for everyone to do this so that at the end of the
move, each seat is taken by exactly one person?
There are 20! number of ways for everyone to do this so that at the end of the move, each seat is taken by exactly one person.
People are seated in a 2 by 10 rectangle grid. All 20 persons stand up from their seats and relocate to an orthogonally neighboring one upon the blowing of a whistle.
Now, we have to find the number of possible ways in which each seat is taken up by exactly one person after the move.
As the number of people is 20 and 20 seats are to filled exactly once.
So, the number of ways = 20!
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Suppose we want to choose 5 letters, without replacement, from 16 distinct letters.
(a) If the order of the choices is taken into consideration, how many ways can this be done?
(b) If the order of the choices is not taken into consideration, how many ways can this be done?
Answer: Your answers are
A. 1, 287 ways
B. 154,440 ways
Hope this helped :D
Please mark me brainliest
3. Choose the two correct transformations for:
Ay
T
R'
RSTU to R'S'T'U'.
S'
A Rotation 180°clockwise
B Reflection across y = x
OC Reflection across y = -x
OD Rotation 180°counterclockwise
Which of the
following satisfies
this graph?
Answer:
C
Step-by-step explanation:
y is greater or equal to 0
x is also greater or equal to 0
you can see that only one answer choice can be the answer
the line is x-y = 2
the upper side is x-y <= 2
proves that c is the answer
x-y ≤ 2
y ≥ 0
x ≥ 0 satisfies this graph. Thus option C is correct.
What is a graph?A schematic or visual presentation that organizes the depiction of data or quantities is known as a graph. The relationships connecting two or more objects are frequently represented by the spots on a graph. They are employed to arrange data in order to highlight correlations and patterns. This data is presented as a pattern on a graph.
When y is bigger than 0 and x is also.
The equation is 2x-y.
x-y ≤ 2 on the upper side of the graph is represented in this same way.
x-y ≤ 2; y ≥ 0 and x ≥ 0 will be the correct represented points in the graph. Therefore, option C is the correct option.
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Find the circumference of a circle with radius of 4.2in.
Answer: 26.39
Step-by-step explanation:
2xπxr
5x-2y=10
4y+20=10x
Solving systemd
Answer:
The answer is x=2 and y=0.
Step-by-step explanation:
The given Equations are:
5x-2y=10 ----------------- (i)
4y+20=10x ----------------- (ii)
From equation find the value of x, that is:
5x=10+2y (Obtained By adding 2y on both side of Equation (i))
Next divide with 5 on both side to get x:
x=(10+2y)/5 ------------------ (iii)
Put this value of x in equation (ii):
4y+20=10((10+2y)/5)
Simplifying the above equation:
4y+20=2(10+2y)
4y+20=20+4y
From the above equation the solution of y is not possible.
We can make it 0. So,
y=0
Put this value of y in equation (iii), to get value of x:
x=(10+2(0))/5
x=(10+0)/5
x=10/5
x=2
Carmen has taken out a loan for $800 to buy a car. she plans to pay back the loan at a rate of $40 per month. ramona has borrowed $500 to buy a car, which she plans to pay back at a rate of $20 per month. how long will it take ramona to pay back her loan? a. 25 months b. 20 months c. 15 months d. 10 months please select the best answer from the choices provided a b c d
Answer:a
Step-by-step explanation: 20 x 25=500
The volume of a cylindrical can of beans is 45 π cubic centimeters. if the diameter is 6 centimeters, what is the height of the can in centimeters?
Answer:
h = 5 cm
Step-by-step explanation:
Givens
d = 6cm
V = 45cubic cm
Formula
V = pi * r^2 h substitute values into the formula
Solution
d = 2*r
6 = 2*r Divide both sides by 2
6/2 = 2r / 2
3 = r
45 pi cm^3 = pi * (3)^2 * h Divide both sides by pi
45 pi/pi = pi * 9 * h / pi
45 = 9h Divide both sides by 4
45/4 = 9h/9
5 cm
Towns A, B, and C lie on a straight line, as shown below. Jack and Arthur start at Town B and drive for an hour from Town B to Town C, where they stop for an hour to eat lunch. Which of the following graphs could represent their distance from Town A during these two hours?
The situation described by the distance from Town A is the first graph.
Given that cities A,B and C are on straight line.
We are required to find the graph appropriate the given situation.
Distance is basically the measurement of how far two things,places are located.It can be measurement from one point to another .
On the first hour,they leave town B to town C moving farther from Town A,hence the distance is increasing on the first hour.
On the second hour they stop for lunch,meaning that the distance remains constant at the point, it was at the end of the first hour.
Hence if towns A,B C lie on a straight line and Jack and Arthur start at town B and drive for an hour from Town B to Town C then the distance shown from Town A during these two hours is first graph.
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Assuming brokerage fees of $6000, calculate the amount of cash needed to retire baldwin's 12. 4s2028 bond early
The amount of cash needed to retire baldwin's bond early based on the brokerage will be $5427896.
How to calculate the cash?It should be noted that from the information given, we are to calculate the amount of cash needed to retire baldwin's bond early based on the brokerage.
This will be:
= 6000 + (5756951 × 94.18/100)
= 6000 + 5421896.45
= 5427896
Therefore, the amount of cash needed to retire baldwin's bond early based on the brokerage will be $5427896.
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Solve each of the following systems of equation.
(b.) 3x + y = 1
6x^2 - y^2 - 2y - 3 = 0
(a) The solution to the given system of equations is x = 1, y = 2, z = -3
(b) The solutions to the system of equations are (3.4142, -9.2426) and (0.5858, -0.7574)
Solving system of equationsFrom the question, we are to solve the given system of equations
The given system of equation is
x + y + z = 0 ----------- (1)
2x + z = -1 ----------- (2)
x - y - z = 2 ----------- (3)
Add equations (1) and (3)
x + y + z = 0 ----------- (1)
x - y - z = 2 ----------- (3)
__________
2x = 2
x = 2/2
x = 1
Substitute the value of x into equation (2) to find z
2x + z = -1
2(1) + z = -1
2 + z = -1
z = -1 -2
z = -3
Substitute the values of x and z into equation (1) to determine the value of y
x + y + z = 0
1 + y + -3 = 0
1 + y - 3 = 0
y = 3 -1
y = 2
Hence, the solution to the given system of equations is x = 1, y = 2, z = -3
b.
The given system of equations is
3x + y = 1 --------- (1)
6x² - y² - 2y -3 = 0 --------- (2)
From equation (1)
3x + y = 1
y = 1 - 3x -------- (3)
Substitute into equation (2)
6x² - y² - 2y -3 = 0
6x² - (1 -3x)² -2(1 -3x) -3 = 0
6x² - (1 -3x)(1 -3x) -2 + 6x -3 = 0
6x² - (1 -3x -3x +9x²) -2 +6x -3 = 0
6x² - (1 -6x + 9x²) +6x -5 = 0
6x² -1 +6x -9x² +6x -5 = 0
-3x² +12x -6 = 0
3x² -12x +6 = 0
x² -4x + 2 = 0
Solve the quadratic equation by the formula method,
x = [-b±√(b²-4ac)]/2a
a = 1, b = -4 and c = 2
Thus,
x = [-(-4)±√((-4)²-4(1)(2))]/2(1)
x = [4±√(16-8)]/2
x = (4±√8)/2
x = (4+√8)/2 OR (4 - √8)/2
x = 3.4142 OR x = 0.5858
Substitute the values of x into equation (3)
y = 1 - 3x
When x = 3.4142
y = 1 - 3(3.4142)
y = -9.2426
When x = 0.5858
y = 1 - 3(0.5858)
y = -0.7574
Hence, the solutions to the system of equations are (3.4142, -9.2426) and (0.5858, -0.7574)
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Given a triangle ABC at points A = (-6, 3) B=(-4,7) C = (-2, 3), and a first transformation of up 2 and right
3, and a second transformation of down 1 and left 6, what would be the location of the final point B"?
Select one:
O a. (-7,8)
O b. (7,-4)
Oc. (-7,4)
O d. (-1,8)
Given a triangle ABC at points A = (-6, 3) B=(-4,7) C = (-2, 3), and a first transformation of up 2 and right 3, and a second transformation of down 1 and left 6, the final point B" is located at (-7, 8), which is option (a).
What is transformation?In mathematics, a transformation refers to a change or mapping of one set of values to another set. In geometry, a transformation involves changing the position, size, or orientation of a geometric object.
To find the location of the final point B", we need to apply the two transformations given to the initial point B (-4, 7).
First transformation: up 2 and right 3
This means we add 2 to the y-coordinate (to move the point up) and add 3 to the x-coordinate (to move the point right).
So, the new location of B after the first transformation is: (-4 + 3, 7 + 2) = (-1, 9)
Second transformation: down 1 and left 6
This means we subtract 1 from the y-coordinate (to move the point down) and subtract 6 from the x-coordinate (to move the point left).
So, the new location of B" after the second transformation is: (-1 - 6, 9 - 1) = (-7, 8)
Therefore, the final point B" is located at (-7, 8), the correct option is a.
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Given these facts, determine how many cans of paint you would need to buy to paint 2 walls.
1st wall: 20 ft. x 8ft.
2nd wall: 40ft. x 8ft.
1 can will cover 200 square feet of wall.
Answer:
3 cans
Step-by-step explanation:
A = lw
a = 20 x 8 = 160[tex]ft^{2}[/tex]
a = 40 x 8 = 320 [tex]ft^{2}[/tex]
Together this is 480 [tex]ft^{2}[/tex]
I would need 3 cans.
What is the annual interest paid on an account that has a $1000 balance if the rate is [tex]7\frac{1}{2}[/tex]%?
The annual interest paid on the account is $75
How to determine the annual interest
The formula for determining annual interest is given as;
Interest = PRT/100
where;
P is the principal amount = $1000R is the rate = 7. 5%T is the time = 1 year, since it's an annual paymentSubstitute the values
Annual Interest = 1000 × 7. 5 × 1/ 100
Annual interest = 7500/ 100
Annual interest = $75
Thus, the annual interest paid on the account is $75
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Point C is at (-9, -2) and point M is at (-1, 4). Point M
is the midpoint of the line segment whose endpoints
are C and D.
What are the coordinates of endpoint D?
Answer:
The coordinates of D is (7, 10)
Explanation:
Let the coordinates of endpoint D be (x, y)
Mid-point formula:
[tex]\sf (x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]
Applying formula:
[tex]\sf (-1, \:4) = (\dfrac{-9+ x}{2},\: \dfrac{-2+y}{2} )[/tex]
Comparing found:
[tex]\sf -1 =\dfrac{-9+ x}{2} \quad and \quad \: 4 = \dfrac{-2+y}{2}[/tex]
[tex]\sf 2(-1)+9 =x \quad and \quad \: 2(4)+2 =y[/tex]
[tex]\sf x = 7 \quad and \quad \: y = 10[/tex]
So, coordinates of D is (7, 10)
The answer is (7, 10).
Remember the midpoint formula : [tex]\boxed {M = (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})}[/tex]
Finding the x coordinate of D
x = (x₁ + x₂) ÷ 2-1 = (-9 + x₂) ÷ 2-2 = -9 + x₂x₂ = 7Finding the y coordinate at D
y = (y₁ + y₂) ÷ 24 = (-2 + y₂) ÷ 28 = -2 + y₂y₂ = 10If the store has only 12 red balloons and only 8 blue balloons but at least 29 of each other color of balloon, how many combinations of balloons can be chosen?
The number of combinations of balloons that can be chosen is 1716.
Selections and combinations are synonyms. Combinations represent the choosing of items from a predetermined group of items. We're not trying to arrange anything here. We're going to pick them.
Utilizing the combinations formula, it is simple to determine how many distinct groups of r objects each may be created from the provided n unique objects.
Number of red balloons = 12
Number of blue balloons = 8
First, we figure out how to choose from 13 red and 9 blue balloons.
There are 7 balloons left out of the 29 total (i.e. 29 - 13 - 9)
So, n = 7+7-1
n = 13
r = 7
Number of combinations of balloons = [tex]_{13} C_{7}[/tex]
= 13!/(13-7)!7!
= 13!/6!7!
= 1716
Learn more about combinations here:
https://brainly.com/question/11732255
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