The value of fraction in simplest form is, 1/1296.
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
We have to given that;
⇒ 1/6 with an exponent of 4.
Now, We can simplify as;
⇒ (1/6)⁴
⇒ 1 / 6⁴
⇒ 1/ 6×6×6×6
⇒ 1 / 1296
Thus, The value of fraction in simplest form is, 1/1296.
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describe all unit vectors orthogonal to both of the given vectors.
The unit vector orthogonal to both A and B is u = (0.23, -0.92, 0.15).
Given vectors:
A = (2, 3, 4)
B = (1, -1, 4)
A unit vector is a vector with a magnitude of 1. Two vectors are orthogonal if the angle between them is 90 degrees. In order to find unit vectors orthogonal to both A and B, we must first compute the cross product of A and B. The cross product of two vectors is a vector perpendicular to both of the given vectors and can be denoted by A × B.
The cross product of A and B is given by:
A × B = (3, -12, 2)
To normalize this vector and find the unit vector, we must divide the vector by its magnitude. The magnitude of the vector A × B is equal to the square root of the sum of the squares of its components. We can write this as:
|A × B| = √(3^2 + (-12)^2 + 2^2) = √(169) = 13
Therefore, the unit vector orthogonal to both A and B is given by:
A × B/|A × B| = (3/13, -12/13, 2/13)
This vector can also be written in terms of its unit components, as:
u = (0.23, -0.92, 0.15)
Therefore, the unit vector orthogonal to both A and B is u = (0.23, -0.92, 0.15).
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Aire du triangle sans avoir la base
Answer: 2A/H
Step-by-step explanation:
A = région
H = la taille
x = base
1/2*x*H = A
1/2*x = A/H
x = 2A/H
A store released a new DVD and sold 729 copies. Each day after that, the sales were one-third of the sales from the previous day.
The number of DVDs sold in any day is A. one-third, B. three more than, C. three less than, or D. three times
the number of DVDs sold the previous day and A. one-third, B. three more than, C. three less than, or D. three times
the number of DVDs sold the following day.
The function A. D(t) = 729 - (1/3)t, B. D(t) = 729 + (1/3)t, C. D(t) = 729 x t^(1/3), D. D(t) = 729 x 3^t, or E. D(t) = 729 x (1/3)^t
models the number of DVDs sold where t is the number of days since the release date and D(t) is the number of DVDs sold.
The number of DVDs sold in any day is one-third the number of DVDs sold the previous day three times the number of DVDs sold the following day.
The exponential function D(t) = 729(1/3)^t models the number of DVDs sold where t is the number of days since the release date and D(t) is the number of DVDs sold.
How to model the exponential function?The definition of an exponential function is given as follows:
y = ab^x.
In which:
a represents the initial value.b is the rate of change.For this problem, the parameter values are given as follows:
a = 729. -> number of copies on the first day.b = 1/3 -> each day, the copies sold are one third of the previous day.More can be learned about exponential functions at https://brainly.com/question/25537936
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How do you fully simplify (3)/(2x+12) - (x-15)/(x^2-2x-48)?
Answer:
Step-by-step explanation:
4564. 2 75444214///4222.-112
The fully simplified form of the expression is [tex]\frac{3}{2x+12}-\frac{-3}{x-8} +\frac{4}{x+6}[/tex]
What do you mean by quadratic equation?A quadratic equation is a type of polynomial equation that has the general form ax^2 + bx + c = 0, where a, b, and c are coefficients and x is an unknown variable. The equation has two solutions, which can be found using the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a, where the ± symbol indicates that there are two possible solutions.
Quadratic equations are used to model a variety of real-world phenomena, such as the motion of objects under the influence of gravity, the path of a projectile, and the growth of a population over time. They are also used to describe the parabolic shape of curves and to solve optimization problems, such as finding the maximum or minimum value of a function
We can simplify the expression as follows:
[tex]\frac{3}{2x+12} =\frac{x-15}{x^{2} -2x-48}[/tex]
First, we'll simplify the denominators. To do this, we can factor the quadratic expression x² - 2x - 48:
x² - 2x - 48 = (x - 8)(x + 6)
Now we can rewrite the denominators:
[tex]\frac{3}{2x+12}-\frac{x-15}{(x-8)(x+6)}[/tex]
Next, we'll simplify the fraction in the second term using partial fraction decomposition:
[tex]\frac{x-15}{(x-8)(x+6)} =\frac{A}{x-8}+\frac{B}{x+6}[/tex]
where A and B are constants that we can find by multiplying both sides by (x - 8)(x + 6) and equating the numerators:
x - 15 = A(x + 6) + B(x - 8)
Expanding both sides:
x - 15 = Ax + 6A + Bx - 8B
Comparing coefficients:
-15 = Ax + 6A + Bx - 8B
1 = A + B
8B = Ax + 6A + 15
-6A = -15 - Ax - 8B
-6A = -15 - (A + B)x - 8B
-6A = -15 - x + 7x
-6A = -15 - x + 7x
-6A = -15 + 6x
Solving for A and B, we have:
A = -3
B = 4
So, the second term can be written as:
[tex]\frac{x-15}{(x-8)(x+6)} =\frac{-3}{x-8}+\frac{4}{x+6}[/tex]
Putting everything together, we have:
[tex]\frac{3}{2x+12} -\frac{x-15}{(x-8)(x+6)} =\frac{3}{2x+12}-\frac{-3}{x-8} +\frac{4}{x+6}[/tex]
which is the fully simplified form of the expression.
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shaq is 85'' tal he cast a shadow 17''long if stephen curry cast a shadow 15''long how tall is he
Stephen Curry is 75 inches tall.
How to determine how long he isLet's call Stephen Curry's height h.
Since the shadow length of Shaq is proportional to his height,
we can write the following ratio:
shadow length of Shaq / Shaq's height = shadow length of Curry / Curry's height
This gives
17'' / 85'' = 15'' / h
Solving for h:
h = 15'' * 85'' / 17'' = 75''
So Stephen Curry is approximately 75 inches tall.
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The length of a basket is measured to be 13 inches, but the basket is actually 1 foot long. What is the percent error in the measurement?.
Percent error in the measurement is 8.3 % ( round to one decimal )
Percent of error show how big the error between measurement and actual value in comparison of actual value, and shown in percentage.
Simple formula to find percent of error is :
% error = | (T - E) / T | x 100%
Where :
T is actual value
E is estimated / measured value
From the question, we know following information :
1. Measured Value = 13 inches
--> E = 13 inches
2. Actual value = 1 foot. We know that 1 foot equal to 12 inches
--> T = 12 inches
% error = | (T - E) / T | x 100%
= | (12-13)/12 | x 100%
= | -1/12 | x 100%
= | -0.083 | x 100%
= 0.083 x 100%
= 8.3 %
Hence percent error of the measurement is 8.3%
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Answer: 9.2%
Step-by-step explanation: did the test and got it correct, hope this helps
unit 4 congruent triangles
homework 6
#4 and 6 ASAP
Triangle congruence: Two triangles are deemed to be congruent if all three of their matching sides and angles have the same magnitude.
How can the congruence of two triangles be established?
Slides, rotations, flips, and turns can be used to make these triangles appear identical.
One of the following conditions must be satisfied for two triangles to be considered congruent:The three equivalent side pairings are equal in all three cases. According to the question, there are four congruent triangles, and each of these triangles has equal-sized and length sides.
ASA, AAS, and HL make up the four triangles.
Divided by BD, ABCD.
BDA = BCD in the given context.
ST is parallel to UN and congruent to VU in the second.
That too is admitted
The FH divides the EHG in the third statement.
FRH and FGH are equivalent.
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adding and subtracting mixed numbers with like denominators worksheet
To add or subtract mixed numbers with like denominators, follow these steps:
Convert the mixed numbers to improper fractions.Add or subtract the numerators of the fractions and keep the denominator the same.Convert the result back to a mixed number if it is an improper fraction.How to explain the mixed numberFor example, Add: 1 ¾ + 1 ½
Convert to improper fractions:
1 ¾ = 7/4
1 ½ = 3/2 = 6/4
Add the numerators and keep the denominator the same:
7/4 + 3/2 = (7 + 6) / 4 = 13/4
Convert the result back to a mixed number:
13/4 = 3 1/4
So the answer is 3 1/4.
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parametrize the line segment passing through (1, 2, 1) and (2, 4, 3).
The parametrize line will be r(t)=(1,2,1)+t(1,2,2).
How to parametrize a line?
In order to parametrize a line, you need to know at least one point on the line, and the direction of the line. If you know two points on the line, you can find its direction. The parametrization of a line is r(t) = u + tv, where u is a point on the line and v is a vector parallel to the line. There are lots of possible such vectors u and v. To find one such vector v, find the difference between any two points on the line.
Example: If we want to parametrize the straight line passing through (1,1,1) and (4,6,2), we can take u = (1,1,1) and v = (4,6,2) - (1,1,1) = (3,5,1). So one possible parametrization for this line is r(t) = (1,1,1) + t(3,5,1). We can also write this as:
x(t) = 1 + 3t
y(t) = 1 + 5t
z(t) = 1 + t
Now,
For points (1, 2, 1) and (2, 4, 3)
u=(1,2,1)
v=(2,4,3)-(1, 2, 1)
v=(1,2,2)
so the parametrized line will be r(t)=(1,2,1)+t(1,2,2).
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How tall is 2 meters in feet and inches?
6.56168 feet and inches is around two metres.
What is the formula for converting metres to inches?Conversion from metres to inches Examples SolvedThe distance in inches must be determined. The distance in inches is calculated using the formula li=lm*39.36.The supplied value (in feet) is converted to inches by multiplying it by 12, as 1 foot is equivalent to 12 inches.3.28084 feet ,Converter from metres to feet3.28084 ft is about equivalent to one metre. Add 3.28084 feet to the given metre value to convert it to feet.2.56 metres is 6.56 ft. Convert decimal feet to inches in step two.To learn more about feet refer to:
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Sharon walked a total of 9. 52 mile in a walk a thon. If her average peed wa wa 2. 8 per hour, how long did it take Sharon to complete the walk?
Sharon completed a walkathon by walking a total of 9. 52 miles. Sharon would need 3.4 hours to complete the walk if she urinated on average 2. 8 times each hour.
What is meant by average?The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.Average By adding a collection of numbers, dividing by their count, and then summing the results, the arithmetic mean is determined. For instance, the sum of 2, 3, 3, 5, 7, and 10 is equal to 30 divided by 6, which equals 5. Median The central number in a set of numbers. The three primary average types are mean, median, and mode.Detailed explanation:
The distance that Shareen must travel is 9.52 miles.
Shareen travels at a mean speed of 2.8 mph.
We need to determine how long it took Shareen to finish the walk.
the average speed formula,
v = length/duration
[tex]$t & =\frac{d}{v} \\[/tex]
[tex]$t & =\frac{9.52}{2.8} \\[/tex]
[tex]$t & =3.4 \text { hour }[/tex]
As a result, the walk will take 3.4 hours to complete.
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Complete the equation of the line through
(-8,8) and (1,-10)
Use exact numbers.
Answer:
y = -2x-8
Step-by-step explanation:
1. (-8,8)
2. (1,-10)
first lets find the slope
m = y2-y1 / x2-x1
m = -10-8 / 1-(-8)
m = -18 / 9
m = -2
y = -2x+b
lets find b by plugging in point 2
-10 = -2(1)+b
-10 = -2+b
b = -8
our equation:
y = -2x-8
If the value of x is -1/4, order the expressions by value from least to greatest.
x
1-x
x-1
-2x
thx
The expressions by value from least to greatest are x-1, x, -2x, 1-x
What is an Algebraic Expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Given here: The value of x is -1/4
Thus evaluating for each expression by substituting value of x we get
1) x=-1/4
2) 1-x= 1+1/4
=5/4
3)x-1=-1/4-1
=-5/4
4)-2x= -2×-1/4
= 1/2
Hence, The answers are 1/4,5/4,-5/4,1/2
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Dylan is going to invest $95,000 and leave it in an account for 18 years. Assuming the interest is compounded monthly, what interest rate, to the nearest hundredth of a percent, would be required in order for dylan to end up with $251,000?.
The interest rate required to end up with $251,000 is 6.9% to the nearest hundredth of a percent.
Compound interest is computed on the principal as well as the interest accumulated over the preceding period. It differs from simple interest in that interest is not added to the principal when computing interest for the next month.
The formula to calculate the compound interest is:
A = P * (1 + r/n)^(nt),
where:
A = final amount
P = principal amount ($95,000)
r = interest rate
n = number of compounding periods per year
t = time in years (18)
Rearranging the formula to solve for r:
r = (A/P)^(1/nt) - 1
Plugging in the given values:
r = ($251,000/$95,000)^(1/18*12) - 1
= 0.069 or 6.9%
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If xy = 13 and both x and y are positive integers, then what is the sum of x + y?.
The sum of x + y is always equal to 14.
What is positive integers?
Positive integers are the numbers that we use to count: 1, 2, 3, 4, and so on. A collection of positive integers excludes numbers with a fractional element that is not equal to zero and negative numbers.
Since x and y are positive integers, we can find the possible values of x and y by finding the factors of 13. The positive integer factors of 13 are 1 and 13. Therefore, the possible pairs of x and y are (1, 13) and (13, 1).
The sum of the two values for x and y in each pair is 14.
So, The sum of x + y is always equal to 14.
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Gillian has a board that is 2 meters long. She cuts the board into 5 equal pieces, and then measures them with a tape measure that only measures in customary units. To the nearest inch, what is the length of each piece?
The length of each piece to the nearest inch is 16 inches.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given that,
Total length of the board = 2 meters
Gillian cuts the board into 5 equal pieces.
Length of each piece of the board in meters = 2 / 5 = 0.4 meter
We know that,
1 meter = 39.37 inches
0.4 meter = 39.37 × 0.4
= 15.748 inches
≈ 16 inches
Hence the length of each piece of the board is approximately 16 inches.
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Find exact values or expressions for the six trigonometric functions of angle A.
a landscaper is designing a rectangular garden. the length of the garden is to be 5 55 feet longer than the width. if the area of the garden will be 104 104104 square feet, what will be the length, in feet, of the garden?
The length of the rectangular garden will be 13 feet.
Let x be the length of the rectangular garden.
If the length of the garden is to be 5 feet longer than the width, then the expression for the width should be "x - 5".
If the area of the garden will be 104 square feet, then the equation for the area will be:
A = x(x - 5) = 104 square feet
Simplify the equation and solve for the value of x.
x² - 5x - 104 = 0
(x + 8)(x - 13) = 0
x = -8 ; x = 13
(choose the positive value since dimensions should always be positive)
Therefore, the length of the rectangular garden is 13 feet.
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!NEED HELP ASAP!
will mark you the brainliest
The lateral surface area of the pyramid is 4√5 square inches.
What is a pyramid?A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.
We know the lateral surface area of a square pyramid when height is given is, [tex]\sqrt{\frac{a^2}{4} + h^2[/tex].
Given, A square pyramid has a height of 8 inches and the base is also 8 inches.
Therefore, the lateral surface area of the pyramid is,
= [tex]\sqrt{\frac{8^2}{4} + 8^2[/tex] square inches.
= [tex]\sqrt{\frac{64}{4} + 64[/tex] square inches.
= [tex]\sqrt{16 + 64[/tex] square inches.
= √80 square inches.
= 4√5 square inches.
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What Is Continuous Compounding Formula?
Continuous compounding is the process of calculating interest and reinvesting it into an account's balance over an infinite number of periods.
For continuously compounded interest: FV = PV x e (i x t), where e is the mathematical constant approximated as 2.7183.
What is meant by process?
A process is a set of decisions and actions used to carry out work. Although we may not be aware of them, processes are present in every sphere of our lives, including work and pleasure. Several instances of processes might be: breakfast preparation. ordering something.To put it another way, a process is a single activity or a collection of related tasks that accepts inputs, adds value, and produces outputs for internal or external clients. A series of interconnected actions make up the process. The result of one procedure frequently serves as the starting point for another.The most widespread and straightforward mental abilities used by humans are the fundamental processes.To learn more about process refer to
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At Krysta's Swimwear, 25% of the 84 swimsuit styles are bikinis. How many bikini styles are there?
Answer:
21 Bikini Styles
Step-by-step explanation:
Hello!
If at Krysta's Swimwear 25% of the 84 swimsuit styles are bikinis there are 21 bikini styles.
Step-by-step explanation:
[tex]84[/tex] × [tex]0.25=21[/tex]
Hope this helps!
Which of the following statements is true?
a) Exactly one of these statements is false
b) Exactly two of these statements are false
c) Exactly three of these statements are false
d) Exactly four of these statements are false
None of the statements is true, as they all refer average to the false statement that exactly one, two, three, or four of the statements is false. This statement itself is false, and so none of the other statements can be true.
None of the statements is true because they all refer to the false statement that exactly one, two, three, or four of the statements is false. This statement itself is false, and so none of the other statements can be true. The statement that exactly one of the statements is false is false because it is referring to itself as the false statement, which means that it is not actually false. Similarly, the statement that exactly two of the statements are false is false because it is referring to itself as one of the two false statements, which means that it is not actually false. The statement that exactly three of the statements are false is also false because it is referring to itself as one of the three false statements, and the statement that exactly four of the statements are false is false because it is referring to itself as one of the four false statements. Therefore, none of the statements is true.
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Solved If sin (????)=8/17, where 0 < ???? < pi/2 and cos (????)=5/13 |
The value of θ is approximately equal to 0.92729522.
What do you mean by sine?The sine function is a basic trigonometric function used in mathematics to describe the relationship between the lengths of sides of a right triangle and its angles. The sine function is denoted by the symbol sin and is defined as the ratio of the side opposite a given angle to the hypotenuse of the triangle.
The sine function is periodic, meaning that it repeats its values over a certain interval, and its values range from -1 to 1.
If sin (θ)=8/17, where 0 < θ < pi/2 and cos (θ)=5/13, then θ can be found using the inverse sine function.
θ = sin⁻¹ (8/17) = sin⁻¹ (5/13) = arctan(8/5).
So, the value of θ is approximately equal to 0.92729522.
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The value of θ is approximately equal to 0.92729522.
What do you mean by sine?The sine function is a basic trigonometric function used in mathematics to describe the relationship between the lengths of sides of a right triangle and its angles. The sine function is denoted by the symbol sin and is defined as the ratio of the side opposite a given angle to the hypotenuse of the triangle.
The sine function is periodic, meaning that it repeats its values over a certain interval, and its values range from -1 to 1.
If sin (θ)=8/17, where 0 < θ < pi/2 and cos (θ)=5/13, then θ can be found using the inverse sine function.
θ = sin⁻¹ (8/17) = sin⁻¹ (5/13) = arctan(8/5).
Therefore, the value of θ is approximately equal to 0.92729522.
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help with this question please
The slope of this line is m = 1.
An equation of this line is y = x.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (0, 1).Points on y-axis = (0, 1).Substituting the given data points into the slope formula, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (1 - 0)/(1 - 0)
Slope (m) = 1/1
Slope (m) = 1
At data point (1, 1), an equation of this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represents the data points.Substituting the parameters, we have the following:
y - y₁ = m(x - x₁)
y - 1 = 1(x - 1)
y = x - 1 + 1
y = x
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prove that the function h(x)=(1-x^2) ^1/3 is its own inverse by showing that h(h(x)) =x.
It is proved that the function h(x)=(1-x^2) ^1/3 is its own inverse by showing that h(h(x)) =x.
The inverse of a function f is denoted by f-1 and it exists only when f is both one-one and onto function. Note that f-1 is NOT the reciprocal of f. The composition of the function f and the reciprocal function f-1 gives the domain value of x.
(f o f-1) (x) = (f-1 o f) (x) = x
For a function 'f' to be considered an inverse function, each element in the range y ∈ Y has been mapped from some element x ∈ X in the domain set, and such a relation is called a one-one relation or an injunction relation. Also the inverse f-1 of the given function has a domain y ∈ Y is related to a distinct element x ∈ X in the codomain set, and this kind of relationship with reference to the given function 'f' is an onto function or a surjection function. Thus the inverse function being an injunctive and a surjection function, is called a bijective function.
The given function is h(x) = (1-x²)^1/3
We have to find h(h(x)).
Put h(x) in place of x in above function:
h(h(x)) = (1-((1-x²)^1/3)²)^1/3
After solving the above equation, we get
h(h(x)) = x
Thus, it is proved that the function h(x)=(1-x^2) ^1/3 is its own inverse by showing that h(h(x)) =x.
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11. It's the middle of a season, and Bill James has calculated the Pythagorean Winning Percentage (W%) of a team as .562. What does this mean?
O A. The team will win exactly 56.2% of their future games.
O B. The team has won 56.2% of the games they've played so far.
O C. The team has a 56 2% chance of winning the next game they play
OD. The team is predicted to win 56.2% of their games this season.
The team is predicted to win 56.2% of its games this season.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. The probability can also be expressed as in form of a percentage as we multiply it by 100.
It's the middle of a season, and Bill James has calculated the Pythagorean Winning Percentage (W%) of a team as .562.
To convert, the probability to percentage just multiply by 100 =.562*100
= 56.2%.
Hence The team is predicted to win 56.2% of their games this season.
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question is in image
answer choices
42%
65%
18%
39%
The value of p is obtained as follows:
p = 18%.
How to obtain the value of p?The value of p is obtained applying the proportions in the context of this problem.
A proportion is applied as a percentage is given by the division of the number of desired outcomes by the number of total outcomes, which is then multiplied by 100%.
The outcomes for this problem are given as follows:
Total: 750 students.Desired: 12th graders and like cold drinks: 137 students.Hence the percentage is given as follows:
p = 137/750 x 100%
p = 18%.
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Standard form through the given point with given slope
Answer:
x=2
Step-by-step explanation:
undefined slope means the line is vertical
Find the value of x. 72 Degree x+4
on july 1 a one year non interest bearing note for 110250 was accepted in exchange for an unpaid accounts receivable for 105000 time was5%
joe placed his pencil on point a of the hexagon below. he flipped a coin 4 times and recorded the sequence of heads and tails. each time he flipped heads, he moved his pencil along one edge clockwise to the next vertex. each time he flipped tails, he moved his pencil along one edge counter-clockwise to the next vertex. how much greater is the probability that he will end up with his pencil back on point a than the probability that he will end up with his pencil on point c? express your answer as a common fraction
The probability of each possible outcome has been calculated and the most likely joe placed his pencil on point a of the hexagon below. is zero
The task provides a context to calculate discrete probabilities and represent them on a bar graph. It could also be used to create a class activity where students gather, represent, and analyze data, running simulations of the random walk and recording and then displaying their results.
If we denote by H an outcome of heads and by T and outcome of tails, then the possible outcomes for the four coin flips can be represented by a sequence of four letters, with each letter being either a T or an H. For example HHHH would represent the case where all four coin tosses come up heads. There are two choices for each letter and four letters so this gives 2^4=16possible outcomes.
To see more clearly why the two possibilities for the first toss need to be multiplied by the two possibilities for the second toss observe that each outcome, H or T for the first toss, leads to two possible outcomes when paired with the second toss: H leads to HH and HT while T leads to TH and TT. This reasoning for multiplying by two for each additional coin toss leads to 2^4 possibilities if the coin is tossed four times.
For f(6) to be zero, there need to be the same number of steps to the left as to the right. So there must be 3 heads and 3 tails. We can make a list of the possibilities. To simplify the list, we will list the possibilities for which tosses came up heads so that 123 will mean that the first, second, and third tosses were heads while the fourth
123,124,134,234.
There are four possibilities so the probability that f(4)=0 is 4/ 16.
A word is worthwhile regarding the way in which the possible ways three heads could occur was listed above. The list is long and so to avoid duplication and to make sure the list is complete a method is useful. The list above has been formed by choosing the smallest first number (this is why the first ten numbers in the list begin with a 1), then the smallest possible second number, and finally the smallest third number.
In order for f(4) to be one there would need to be one more occurrence of heads than tails. But this means that the total number of coin tosses would have to be odd: if n is any whole number then n+(n+1)=2n+1 is an odd number. Therefore the probability that f(4)=1 is 0. The argument for why f(4) can never equal 1 is essentially the same as the argument in ''Random Walk II'' for why it is not possible for f(5) to be equal to 2.
Finally for the probability that f(4)=4. This means that Scott must have moved in the positive direction after each of the six coin tosses so all six coin tosses must have been heads. So this can happen in only one way while there are 2^4=16 different possible outcomes for the four coin tosses so the probability that f(4)=4 is 1/16.
The probability of each possible outcome has been calculated and the most likely joe placed his pencil on point a of the hexagon below. is zero.
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The probability of each potential result has been evaluated, and the most likely result is zero, where Joe set his pencil on point an of the hexagon.
The assignment gives you a context for computing discrete probabilities and visualizing them as bars. It might also be used to develop a lesson plan where students acquire, depict, and evaluate data, simulate the random walk, then record, analyze, and present their findings. The four coin flips' various outcomes can be represented by a string of four letters, each of which can be either a T or an H. If we signify by H an outcome of heads and by T an outcome of tails. For instance, the circumstance when all four coin tosses result in heads would be represented by HHHH. Each letter and the four letter combination has two options. so this gives [tex]2^4=16[/tex] possible outcomes.
For a clearer understanding of why the two possibilities for the first toss must be multiplied by the two possibilities for the second toss, consider the fact that each of the two possible outcomes for the first toss, H or T, leads to two additional outcomes when paired with the second toss: H leads to HH and HT while T leads to TH and TT. This reasoning for multiplying by two for each additional coin toss leads to [tex]2^4[/tex] possibilities if the coin is tossed four times.
There must be exactly as many steps to the left as there are to the right in order for f(6) to be zero. The result is that there must be three heads and three tails. A list of the possibilities can be created. To make the list shorter, we will list the possibilities for which tosses resulted in heads. For example, 123 would indicate that the first, second, and third tosses were all heads, but the fourth
123,124,134,234.
There are four possibilities so the probability that f(4)=0 is 4/ 16.
An explanation of how the potential causes of three heads were given above is important. The list is lengthy, thus a method is helpful to prevent duplication and ensure the list is full. The first 10 digits on the list above start with a 1, which was chosen as the smallest first number, followed by the smallest second number and, ultimately, the smallest third number.
There would have to be one more head than tail occurrences for f(4) to be one. However, this necessitates that the total number of coin tosses be odd: if n is any whole integer, then [tex]n(n+1)=2n+1[/tex] is an odd number. Consequently, there is no chance that f(4)=1 at all. Similar to the justification in "Random Walk II" for why f(5) cannot equal 2, the justification for why f(4) can never equal 1 is basically the same.
Finally, we have the likelihood that f(4)=4. This implies that Scott must have walked in the right direction after each of the six coin flips, proving that all six flips resulted in heads. Given that there are [tex]2^4=16[/tex] possible outcomes for the four coin flips, there is only one way that this may happen, making the chance that f(4)=4 1/16. The likelihood of each potential result has been evaluated, and the most likely value is zero.
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