Answer:
16
Step-by-step explanation:
We can use the binomial distribution formula to find the probability of flipping three coins tails, four coins tails, and five coins tails. This is because the probability of P(x=3) is going to give the same result if we had defined the entire set, counted how many had 3, and then divided that by the entire set. So we can use this to find how much % of the data set is going to have at least 3.
So the binomial distribution formula is defined as: [tex]P_x=(^n_x)p^x(1-p)^{n-x}[/tex], where n=number of trials, x=how many successes (in this case it will be 3, 4, and 5) and p=probability of success.
The binomial coefficient is defined as: [tex](^n_x)=\frac{n!}{k!(n-x)!}[/tex].
So let's define the variables.
x = 3, 4, 5 since we want to find the probability of getting at least 3. This means we want the probability of getting 3, 4, or 5 tails, and then we simply add up these probabilities.
n = 5, since Paul is flipping the coin 5 times
p = 0.5 since the probability of flipping tails is 0.50
So let's plug the information in!
[tex]P_{x\ge3} = P_3 + P_4 + P_5[/tex]
[tex]P_3=\frac{5!}{3!2!}*0.5^30.5^2 = 0.3125[/tex]
[tex]P_4=\frac{5!}{4!1!}*0.5^4*0.5^1=0.15625[/tex]
[tex]P_5 = \frac{5!}{5!0!}0.5^50.5^0 = 0.03125[/tex]
Now let's add up all these probabilities to get:
[tex]0.3125 + 0.15625 + 0.03125 = 0.5[/tex]
This means 50% of the time Paul will flip three or more tails.
To translate this to the number of ways, we need to find how many combinations there are which can generally be defined as: [tex]options^{length}[/tex] and in this case options = tails and heads so 2, and the length is 5. So we get: [tex]2^5 = 32[/tex]
Now multiply the 32 by the 0.5 and you get 16, which is the amount of ways he can flip at least three tails
Answer:
16
Step-by-step explanation:
Rational functions v and w both have a point of discontinuity at x = 7. which equation could represent function w?
The correct option is C.
The formula that could be used to represent a function w is
= w(x)=v(x-7)+7
What is Rational function?A polynomial divided by another polynomial can be used to represent a rational function. Since polynomials are defined everywhere, the set of all numbers excluding the zeros in the denominator constitutes the domain of a rational function.
Example 1. x = f(x) (x - 3). The denominator, x = 3, only contains one zero. When the denominator is zero, rational functions are no longer defined.
According to the given Information:
Rational functions whose point of discontinuity is at x=7.
When a point of discontinuity exists for a rational function,
It occurs when:
q(x) = r(x-a), x=a
In this instance, we are required to notice the following relationship, which is a union of a parent rational function and a vertical translation:[tex]w(x)=v(x-a)+k\\ \forall k \in \mathbb{R}[/tex], (2)
If we are aware of a=7 and k=7 .
The equation that could be used to represent a function w is. w(x)=v(x-7)+7
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I understand that the question you are looking for is:
Rational functions v and w both have a point of discontinuity at x = 7. Which equation could represent function w?
A. w(x)=v(x-7)
B. w(x)=v(x+7)
C. w(x)=v(x-7)+7
D. w(x)=v(x)+7
As a fundraiser, the music boosters wrapped gifts at the mall one weekend. out of the 100 gifts they wrapped, 310 3 10 were for weddings, and 37100 37 100 were for baby showers. the rest of the gifts were for birthdays. what fraction of the gifts was for birthdays? enter your answer in the boxes.
For birthday events 33/100 gifts were packed by the music boosters at the mall.
Calculation of the fractionTotal number of gift items = 100
For the wedding purpose,out of 100 gifts, 3/10 number of gifts were boxed = 3/10*100 = 30
For the baby shower, out of 100 gifts, 37/100 gifts were packed = 37
The rest amount of the gift = 100-( wedding + baby shower)
= 100-(30+37) = 33
So, according to the question, these 33 numbers gift was for a birthday.
When it is expressed as a fraction,
The fraction should be = 33/100
Therefore, it is concluded that 33/100 gifts were packed for birthday occasions.
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Write an equation to represent the following statement.
51 divided by 3 is k
Solve for k.
Answer:
K = 17
Based on the given conditions, formulate:
51 / 3 = k
Swap the sides : k = 51 / 3
Cross out the common factor: k = 17
determine which two of the three given triangles are similar. Find the scale factor for the pair.
Please help its confusing meeeeee
Answer:
p = 21.4 cm
∠P = 44°
Step-by-step explanation:
Apply the Pythagorean Theorem to solve for the length of p.
p² + 21² = 30²p² = 900 - 441p² = 459p = √459[tex]\fbox {p = 21.4 cm}[/tex]Now, take the inverse sine function to find angle P :
sin⁻¹ (opposite side / hypotenuse)sin⁻¹ (21/30)sin⁻¹ (0.7)[tex]\boxed {44^{o}}[/tex] (approximately)Answer:
a) 21.4 cm
b) 45.6°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between trig functions and sides of a right triangle. Here, two relevant function are ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
b) Angle PThe hypotenuse of the triangle, and the side adjacent to angle P are given, so we have ...
cos(P) = (21 cm)/(30 cm)
The angle value can be found using the inverse cosine function:
P = arccos(21/30)
P ≈ 45.6°
a) Side pNow, we know angle P and the side adjacent to it. We want to find the measure of side p, which is opposite the angle. This can be done using either the sine function or the tangent function. Here, we choose to use the tangent function.
tan(P) = p/21
p = 21×tan(P) = 21·tan(45.573°)
p ≈ 21.4 . . . . cm
__
Additional comment
In the attached, part of the calculator keypad is shown so you can see that the inverse cosine function is the 2ND function of the Cos key. The calculator mode is set to DEG (lower left of display) so that angles are in units appropriate to this problem.
Of course, you can always use the Pythagorean theorem to find the length of side p. More calculations are involved, so we used trig functions instead. Note that the angle P must be found first using the approach here, and its value must be retained with enough significant digits to ensure accuracy in the 'p' calculation.
Solve for m
-7+4m+10=15-2m−7+4m+10=15−2mminus, 7, plus, 4, m, plus, 10, equals, 15, minus, 2, m
m=
The value of m based on the given equation -7 + 4m + 10 = 15 - 2m is 2
Algebra-7 + 4m + 10 = 15 - 2m
collect like terms4m + 2m = 15 + 7 - 10
6m = 12
divide both sides by 6m = 12/6
m = 2
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Which equation is equivalent to the given equation?
−4x = x² + 3
x² - 4x +3=0
x² - 4x - 3=0
x² + 4x - 3=0
x² + 4x +3=0
Answer: x² + 4x +3=0
Step-by-step explanation:
Add 4x to both sides.
Arnold paid R2 599,99 for a car sound system in 1997 Assuming an average inflation rate of 7% per annum what did he pay for a sound system with the equivalent value in 2014
The value of the car in 2014 is 154709
How to determine the value?The given parameters are:
Initial, a = 599,99
Rate, r = 7%
The value of the car in t years is
Value = a * (1 + r)^t
This gives
Value = 59999 * (1 + 7%)^t
2014 is 17 years from 1997.
So, we have:
Value = 59999 * (1 + 7%)^14
Evaluate
Value = 154709
Hence, the value of the car in 2014 is 154709
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How can a right triangular cross-section be created from a right triangle ?
Answer:
in a triangle prism each cross section parallel to the triangular base is a triangle congruent to the base
A long oval is shown. Two lines are drawn where the sides are straight to form right angles.
How can you decompose the composite figure to determine its area?
as two semicircles and a rectangle
as two circles and a rectangle
as a circle and a square
as two semicircles and a trapezoid
The figure which is like a long oval can be decomposed to two semicircles and a rectangle so as to find the area.
Given a long oval and two lines are drawn where the sides are straight to form right angles.
We are required to find the way how we can decompose the composite figure to determine its area.
Area means the amount of space occupied by a two dimensional shape or object. The area of a figure can be decomposed to smaller figures so as to find the area.
The composed figure can be decomposed to two semicircles and a rectangle so as to find the area.
Hence the composite figure can be decomposed to two semicircles and a rectangle so as to find the area.
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Answer:
a
Step-by-step explanation:
A researcher records the hospital admission rates for coronary heart disease at 10 local hospitals. She finds that 2 different hospitals had the highest overall rates of hospital admissions. Which measure of central tendency did this researcher use to describe these data
The central tendency researcher use to describe these data is "mode".
What is mode?The value that appears most frequently in a data set is called the mode. One mode, several modes, or none at all may be present in a set of data. The mean, or average of a set, and the median, or middle value in a set, are two more common measurements of central tendency.
Calculation of mode is done by-
The number that appears the most frequently in a piece of data is its mode. Put the numbers in ascending order by least to greatest, then count the occurrences of each number to quickly determine the mode. The most frequent number is the mode.Simply counting how many times each number appears in the data set can help you identify the mode, which is the number that appears the most frequently in the data set. The figure with the largest total is the mode.Example: Since it happens most frequently, the mode for the data set [5, 7, 8, 2, 1, 5, 6, 7, 5] is 5.To know more about the mode of the data, here
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Representing a Graph with a Slope-Intercept Equation
-5-4-3-2
5
4
3
2
+
2345
y
2 3 4
X
5
A function f(x) is graphed.
What is the slope of the function?
m
What is the y-intercept of the function?
b = v
Which equation represents the graph of the function?
Answer:
1.) The slope is 2
2.) The y-intercept is (0,1)
3.) y = 2x + 1
Step-by-step explanation:
1.) you can either use rise over run or the slope formula. rise over run is quicker, but here's the formula:
you can use any two points on the line, i chose (2, 5) and (1, 3)
[tex]\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})} \\[/tex]
[tex]\frac{3-5}{1-2} \\\\\frac{-2}{-1} \\\\\frac{2}{1} \\\\2[/tex]
2.) for the y-intercept, you just look for the point where the graph crosses the y-axis and x = 0
3.) using the formula y = mx + b, m being the slope and b being the y-intercept, you take the information above and plug it in to get y = 2x + 1
i hope this helped!
If the hypotenuse has a length 7√2, then both legs have a length
Of what
Answer:
7
Step-by-step explanation:
this is probably a 45-45-90 triangle if its both legs
Type the correct answer in each box.
Find the elements of matrix A.
help PLS!!
Answer:
a = 2
b = 11
c = 11
d = -2
Step-by-step explanation:
[tex]\sf \left[\begin{array}{cc}a&b\\c&d \end{array}\right] *\left[\begin{array}{ccc} 22&11&7\\ 6&-9&-15 \end{array}\right] =\left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \end{array}\right][/tex]
[tex]\sf \left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \\ \end{array}\right] =\left[\begin{array}{ccc} 110&-77&-151\\230&139&107 \\ \end{array}\right][/tex]
On comparing to right side, we get,
22a + 6b = 110
Divide the entire equation by 2
11a + 3b = 55 ------------(I)
11a - 9b = -77 -------------(II)
Subtract equation (II) from (I)
11a + 3b = 55
11a - 9b = -77
- + + {Now subtract}
12b = 132
b = 132/12
[tex]\sf \boxed{\bf \ b = 11}[/tex]
Substitute the value of b in eqaution (I)
11a + 3*11 = 55
11a + 33 = 55
11a = 55 - 33
11a = 22
a = 22/11
[tex]\sf \boxed{\bf \ a = 2}[/tex]
22c + 6d = 230
Divide by 2
11c + 3d = 115 -----------------(III)
11c - 9d = -139 ------------------(IV)
Subtract (IV) from (III)
11c + 3d = 115
11c - 9d = 139
- + -
12d = -24
d = -24/12
[tex]\sf \boxed{\bf \ d = -2}[/tex]
Plugin d = - 2 in equation (III)
11c + 3*(-2) = 115
11c - 6 = 115
11c = 115 + 6
11c = 121
c = 121/11
[tex]\sf \boxed{\bf \ c = 11}[/tex]
Abe raises sheep. In his flock, there are 42 males and 56 females. What is the ratio of males to females in simplest form?
Answer:
3:4
Step-by-step explanation:
It's males to females. so we make 42:56 simplify that we get 3:4
Please help!!! due today. Find the surface area of the triangular prism.
The surface area of the shape is 168 square cm
Surface area of triangular prismThe surface area of a figure is the area of the faces of the given figure.
For the given figure, the area will be the sum of area of 2 triangles and 3 rectangles.
Area = (6*3) +(10*6)+(6+10) +(10*3)
Surface area = 18 + 120 + 30
Surface area = 168 square cm
Hence the surface area of the shape is 168 square cm
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If a wall is built in a room at a 36 degree angle. The angle formed in the other room by the wall is 144 degrees. What kind of angles are formed when they are added together
They form supplementary angles when they are added together.
Reason for Being Called Supplementary Angles
It is given that the angle made by the wall in one room is 36° and the angle formed by the same wall in the other room is 144°.
This implies that,
∠1 = 36°
∠2 = 144°
∠1 and ∠2 are adjacent angles and,
∠1 + ∠2 = 36° + 144°
⇒ ∠1 + ∠2 = 180°
Hence, these two adjacent angles make a straight-line angle. Hence, they are supplementary angles.
What are supplementary angles?
Two angles that form a straight line angle, that is, angle equal to 180°, when they are added together are said to be a pair of supplementary angles.
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Rule 1: Multiply by 2 then add 1 starting from 1.
Rule 2: Divide by 2 then add 4 starting from 40.
I need to make a sequence and I need help :)
PLease dont delete my question :(
Rule 1:
1, 3, 7, 15, 31, 63, 127, 255, 511, 1023 etc
Rule 2:
40, 24, 16, 12, 10, 9, 8.5, 8.25, 8.125, 8.0625 etc
Hope this helps!
A sporting goods store sells square exercise mats that are m on a side. Find the perimeter and area of the mat.
The perimeter of the mat is 4m and the area of the mat is [tex]m^{2}[/tex].
What is perimeter of the square?The complete length of a square's boundary is referred to as its perimeter. To get the perimeter of a square, we must add all of its sides.
Perimeter of square = sum of the length of all 4 sides.
In the question side of the mat is m.
Perimeter of the mat = m + m + m + m
= 4m.
Therefore, the perimeter of the mat is 4m.
What is the area of the square?
The total number of unit squares in a square's shape is used to calculate its area.
Area = (Side x Side)
Since, side of the mat is m.
Area of the mat = m x m
= [tex]m^{2}[/tex]
Therefore, the area of the mat is [tex]m^{2}[/tex].
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A customer who sees a pair of boots online but then decides to buy the same pair at Macy's after trying them on would be best classified as a(n)
The term used to describe a customer who sees a pair of boots online but then decides to buy the same pair at Macy's after trying them on would be best classified as a cross-channel shopper.
Who is a cross-channel shopper?A cross-channel shopper is a consumer who uses various combination of both several channels for the same purchase.
The customer has checked the pair of boots online but rather purchased the same boots at Macy's instead of purchasing online.
Therefore, a cross-channel shopper uses different purchasing channel to purchase a product.
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A Delivery service charges $25 per pound for making a delivery. If there is an additional 8% sales tax, what is the cost of delivering an item that weighs 4/5 of a pound?
The cost of delivering an item that weighs 4/5 of a pound?$21.60.
How to find the delivery cost?Let x = the number of pounds
Thus, we can say that;
Cost = 25x * 1.08
Since we want to find the cost of delivering an item that weighs 4/5 of a pound, the we will put 4/5 for x to get;
Cost = (25 * 4/5) * 1.08
Cost = 20 * 1.08
Cost = 21.6
The delivery cost would be $21.60.
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What is the length of an edge of a cube whose total surface area is equal to 150 square feet?
The length of an edge of a cube is 5 feet.
What is cube?In Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Total surface area of a cube = 6[tex]l^{2}[/tex]
Given that,
Total surface area of a cube = 150 square feet
Total surface area of a cube = 6[tex]l^{2}[/tex]
[tex]\Rightarrow[/tex] 150 = 6[tex]l^{2}[/tex]
[tex]\Rightarrow[/tex] [tex]l^{2}[/tex] = [tex]\frac{150}{6}[/tex]
[tex]\Rightarrow[/tex] [tex]l^{2}[/tex] = 25
[tex]\Rightarrow[/tex] l [tex]=\sqrt{25}[/tex]
[tex]\Rightarrow[/tex] l = 5 feet
Hence, the length of an edge of a cube is 5 feet.
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please help me im in a rush
Answer:
Step-by-step explanation:
A = 4 ft
B = 10 ft
C = 8 ft
D = 6 ft
b) Area of rectangle = length * width
Area of 2 triangle = base * height
Area of right triangular prism = area of 2 triangles +area of left rectangle + area of middle rectangle + area of right rectangle
= 6 * 8 + 4* 6 + 4 * 10 + 4 * 8
= 48 + 24 + 40 + 32
= 144 ft²
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Formulas:}[/tex]
[tex]\huge\text{Area of rectangle is: }\huge\boxed{\rm{\bold{w}idth \times \bold{h}eight = \bold{a}rea}}[/tex]
[tex]\huge\text{Area of triangle is: }\huge\boxed{\rm{\dfrac{1}{2} \times \bold{b}ase \times \bold{h}eight = \bold{a}rea}}[/tex]
[tex]\huge\textbf{Now, that we have that out of the}\\\\\huge\textbf{way, we can label your given equation:}[/tex]
[tex]\rm{A \rightarrow 4\ \boxed{\rm{ft}}}\\\\\rm{B \rightarrow 10\ \boxed{\rm{ft}}}\\\\\rm{C \rightarrow 8 \ \boxed{\rm{ft}}}\\\\\rm{D \rightarrow 6\ \boxed{\rm{ft}}}[/tex]
[tex]\huge\textbf{What should your equation look like?}[/tex]
[tex]\rm{6\times 8 + 4\times 6 + 4 \times 10 + 4 \times 8}[/tex]
[tex]\huge\textbf{What should it look like when we're}\\\huge\textbf{solving for the answer?}[/tex]
[tex]\rm{6\times 8 + 4\times 6 + 4 \times 10 + 4 \times 8}[/tex]
[tex]\rm{= 48 + 4\times6 + 4\times10 + 4\times8}[/tex]
[tex]\rm{= 48 + 24 + 4 \times 10 + 4\times8}[/tex]
[tex]\rm{= 72 + 4\times 10 + 4\times8}[/tex]
[tex]\rm{= 72 + 40 + 4\times8}[/tex]
[tex]\rm{= 112 + 4\times8}[/tex]
[tex]\rm{= 112 + 32}[/tex]
[tex]\rm{= 144}[/tex]
[tex]\huge\textbf{What is the answer?}[/tex]
[tex]\huge\boxed{\textsf{Answer: }\boxed{\frak{144\ ft^2}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
What is the denominator of the simplified expression? (startfraction 2 n over 6 n + 4 endfraction) (startfraction 3 n + 2 over 3 n minus 2 endfraction) 2 n 3n+2 3n-2
n/3n - 2.
The denominator of the given simplified expression is
The given expression is ( 2n/6n + 4 ) ( 3n + 2/ 3n - 2 )
To find the denominator of the simplified expression :
First, simplify the given expression as below ;
( 2n/6n + 4 ) ( 3n + 2/ 3n - 2 )
( 2n/2₍₃ₙ ₊ ₂₎ ( 3n + 2/ 3n - 2 ) ( here by taking the common term 2 outside the factor )
= (n/1) ( 1/ 3n - 2 ) ( here by simplifying the factors )
= n/3n - 2.
Therefore, ( 2n/6n + 4 ) ( 3n + 2/ 3n - 2 ) = n/3n - 2
Therefore the result of the given simplified expression is = n/3n - 2.
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A prism has volume 100cm^3 and length 8cm. If the cross-section is an equilateral triangle, find the length of a side of the triangle.
Answer:
5.373 cm
Step-by-step explanation:
Divide the volume by the length to find the area of the equilateral triangle
100/8 = 12.5
Area of equilateral triangle = sqrt(3) / 4 * s^2 = 12.5
s^2 = 12.5 *4 / sqrt3
s = 5.373 cm
Using the table below, find the mean and median of the set of data.
Note: Round all numbers to the nearest tenth
The mean of the data set is 81.6.
The median of the data set is 80.
What is mean?The mean is the average of a data set. Therefore,
Mean = (70 x 2 + 75 x 8 + 80 x 6 + 85 x 3 + 90 x 9) / 28 = 81.6.
Hence,
mean = 81.6
What is a median?Median is a statistical measure that determines the middle value of a dataset listed in ascending order .
Therefore,
28 / 2 = 14
median = 80 + 80 / 2 = 160 / 2 = 80
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The equation table below represents Lavaughn's earnings in dollars and
cents, y, for working a hours. Find the rate of change.
The rate of change is also known as the slope. The formula to find the slope of a line is (y2 - y1) / (x2 - x1).
You can use any two points, as long as both are on the line.
Point 1 = (2, 55)
Point 2 = (8, 220)
slope = (220 - 55) / (8 - 2)
slope = 165 / 6
slope = 55 / 2 = 27.5 / 1
Lavaughn earns $27.50 for working one hour.
Hope this helps!
POSSIBLE OUTCOMES!!!
A bag contains 1 white (W), 3 blue (B1, B2, B3), and 2 red (R1, R2) marbles.
Use a tree diagram to list all the possible outcomes for tossing a coin and then drawing a marble from the bag.
The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL
How to determine the possible outcomes?The given parameters are:
Coin = Head (H) and Tail (T)
Marble = W, B, B, B, R, R
See attachment for the tree diagram
From the tree diagram, we have the following possible outcomes
WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL
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Find RS.
A. 12
B. 5
C. 10
D. 9
Answer:
5
Step-by-step explanation:
(2x - 6) + 1 + (x - 4) = 18
3x - 9 = 18
3x = 27
x = 9
RS = x - 4 = 9 - 4 = 5
Answer:
B. 5
Step-by-step explanation:
Pls mark brainiest if helpful!!
PQ + QR + RS = 18
This statement is equivalent to the following:
(2x - 6) + 1 + (x - 4) = 18.
This is because we substitute the line segments with their values.
Now that we have an equation to work with, we will solve it. We start by removing the parenthesis as they are not necessary here.
2x - 6 + 1 + x - 4 = 18
Next, we will make it, so x is alone on the left. We will do this by adding 6 and 4 to both sides
2x - 6 (+6) + 1 + x - 4 (+4) = 18 (+6) (+4)
After doing this we are left with the following equation:
2x + 1 + x = 28
Now we will subtract 1 from both sides to make x alone of the left side of the equation.
2x + 1 (-1) + x = 28 (-1)
After we solve this, we get the following:
2x + x = 27
We can add 2x and x and get 3x because 2 + 1 = 3.
3x = 27
We now simplify this equation by dividing both sides by 3.
[tex]\frac{3x}{3}[/tex] = [tex]\frac{27}{3}[/tex]
We again simplify the equation to the following:
x = 9
BUT THATS NOT THE ANSWER!
Now that we know what x is, we can solve for the value of RS.
We input 9 for x in the equation x - 4.
When we do this, we get 9 - 4 which is 5.
And this is our final answer!!
I hope I could help! Have an amazing day and good luck on your homework!
"You can't predict the future, but you can create it"
-Juliana Palazzolo, 2022
Pls mark brainiest if helpful!!
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The probability of winning on an arcade game is 0.568. If you play the arcade game 22 times, what is the probability of winning more than 15 times
The probability of winning 15 out of the 22 games is [tex]P = 0.099[/tex]
what is the probability of winning more than 15 times?We know that the probability of winning on the arcade game is 0.568.
Then the probability of losing is:
P = 1 - 0.568 = 0.432
The probability of winning 15 out of 22 games is given by the equation:
[tex]P = C(22, 15)*(0.568)^{15}*(0.432)^{7}[/tex]
Where C(22, 15) is the number of combinations of 15 elements that we can make with a set of 22 elements, given by:
[tex]C(22, 15) = \frac{22!}{(22 - 15)!*15!} = \frac{22!}{7!*15!} = \frac{22*21*20*19*18*17*16}{7*6*5*4*3*2*1} = 170,544[/tex]
Then the probability is:
[tex]P = 170,544*(0.568)^{15}*(0.432)^7 = 0.099[/tex]
If you want to learn more about probability:
https://brainly.com/question/25870256
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