The perimeter of the square is 256 m.
What ia area?Area is a measure of the amount of two-dimensional space enclosed by a closed figure or shape. It is usually measured in square units, such as square meters, square feet, or square centimeters.
What is a Square?A square is a regular quadrilateral with four equal sides and four right angles. It is a special case of a rectangle and a rhombus, and its properties are a combination of both.
In the given question,
We can start by using the formula for the area of a square, which is:
a = s²
where a is the area and s is the length of one side of the square.
If the area of the square is 64 m², then we have:
64 = s²
Solving for s, we get:
s = √64 = 8 m
Now, we can use the formula for the perimeter of a square in terms of its area:
P = 4a²
Substituting a = 64, we get:
P = 4(64) = 256 m
Therefore, the perimeter of the square is 256 m.
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Does someone mind helping me with this problem? Thank you!
the answer to the problem that you need to is 1024
Dakota earned $6.00 in interest in Account A and 30.00$ in interest in Account B after months. If the simple interest rate is 4% for Account A and 5% for Account B, which account has the greater principal? Explain.
the principal in Account B is 4.8 times the principal in Account A.
How to solve?
Let the principal in Account A be P and the principal in Account B be Q. Also, let n be the number of months.
From the given information, we have:
Interest earned in Account A = $6.00
Interest rate in Account A = 4%
Number of months = n
Using the formula for simple interest, we have:
Interest earned in Account A = (P × 4%× n) / 12
Substituting the given values, we get:
6.00 = (P × 4% × n) / 12
P× n = 150
Similarly, we have:
Interest earned in Account B = $30.00
Interest rate in Account B = 5%
Number of months = n
Using the formula for simple interest, we have:
Interest earned in Account B = (Q× 5% × n) / 12
Substituting the given values, we get:
30.00 = (Q× 5% ×n) / 12
Q × n = 720
To compare the principals, we can divide the equation for Account B by the equation for Account A:
(Q × n) / (P× n) = 720 / 150
Simplifying, we get:
Q / P = 4.8
Therefore, the principal in Account B is 4.8 times the principal in Account A.
Since the interest rate in Account B is higher than the interest rate in Account A, we can conclude that the principal in Account B is greater than the principal in Account A.
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At which values in the interval [0, 2π) will the functions f (x) = 2cos2θ and g(x) = −1 − 4cos θ − 2cos2θ intersect?
a: theta equals pi over 3 comma 4 times pi over 3
b: theta equals pi over 3 comma 5 times pi over 3
c: theta equals 2 times pi over 3 comma 4 times pi over 3
d: theta equals 2 times pi over 3 comma 5 times pi over 3
The values in the interval [0, 2π) for which the two points would intersect as required is; Choice C; theta equals 2 times pi over 3 comma 4 times pi over 3.
What values of θ make the two functions intersect?Recall from the task content; the given functions are;
f (x) = 2cos2θ and g(x) = −1 − 4cos θ − 2cos2θ
Therefore, for intersection; f (θ) and g(θ):
2 cos²θ = −1 − 4cos θ − 2cos²θ
4cos²θ + 4cosθ + 1 = 0
let cos θ = y;
4y² + 4y + 1 = 0
y = -1/2
Therefore; -1/2 = cos θ
θ = cos-¹ (-1/2)
θ = 2π/3, 4π/3.
Ultimately, the correct answer choice is; Choice C; theta equals 2 times pi over 3 comma 4 times pi over 3.
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8. Points P, Q, whose abscissae are 2 and 2+h, are taken on the curve y = 2x^2+1. Find the gradient of the chord PQ. To what value does this gradient approach as h decreases towards the value zero?
The gradient of the chord PQ is 2h + 8
What is the gradient of the chord?Let's first find the coordinates of points P and Q on the curve y = 2x^2+1.
Point P has an abscissa of 2, so its coordinates are (2, 2(2)^2+1) = (2, 9).
Point Q has an abscissa of 2+h, so its coordinates are (2+h, 2(2+h)^2+1) = (2+h, 2(4+4h+h^2)+1) = (2+h, 8+8h+2h^2+1) = (2+h, 2h^2+8h+9).
The gradient of the chord PQ is given by:
(m) = Δy /Δx
(m) = (2h^2+8h+9 - 9) / (2+h - 2)
(m) = (2h^2+8h) / (h)
(m) = 2h + 8
As h approaches zero, the gradient of the chord PQ approaches 8, because the term 2h becomes negligible compared to 8 when h is small. Therefore, the gradient of the tangent to the curve at point P is 8.
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Reduce each expression to a polynomial
((y-b)^(2))/(y-b+1)+(y-b)/(y-b+1)
The given expression ((y-b)²/(y-b+1)+(y-b)/(y-b+1) after being reduced to a polynomial, can be represented as y-b.
In order to reduce the given equation to a polynomial, we are required to simplify and combine like terms. First, we can simplify the expression in the numerator by expanding the square:
((y-b)²/(y-b+1) = (y-b)(y-b)/(y-b+1) = (y-b)²/(y-b+1)
Now, we can combine the two terms in the equation by finding a common denominator:
(y-b)²/(y-b+1) + (y-b)/(y-b+1) = [(y-b)² + (y-b)]/(y-b+1)
Next, we can combine the terms in the numerator by factoring out (y-b):
[(y-b)² + (y-b)]/(y-b+1) = (y-b)(y-b+1)/(y-b+1)
Finally, we can cancel out the common factor of (y-b+1) in the numerator and denominator to get the polynomial:
(y-b)(y-b+1)/(y-b+1) = y-b
Therefore, the equation ((y-b)²)/(y-b+1)+(y-b)/(y-b+1) after being simplified, is equivalent to the polynomial y-b.
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How do you work this out?
Anyone help please .
Answer:
x=5/4 or x=5/9
pls mark me brainliest
Answer:
x=5/4 (for the first x),x=5/9 (for the second x)
a ball is dropped from a height of 6 ft. assuming that on each bounce, the ball rebounds to one-third of its previous height, find the total distance traveled by the ball.
A ball is dropped from a height of 6 ft. assuming that on each bounce, the ball rebounds to one-third of its previous height, the total distance traveled by the ball is approximately 11.926 feet.
How do we calculate the total distance?We have to calculate the distance traveled by the ball with the help of the given data, as shown below;The first height of the ball is 6 feet. Distance traveled by the ball at the first instance = 6 feet.The ball rebounds to one-third of its previous height, and the ball goes to a height of:6/3 = 2 feet.
Distance traveled by the ball after the first bounce = 6 + 2 + 2 = 10 feet.The ball rebounds again to one-third of its previous height, and the ball goes to a height of:2/3 = 0.6667 feet. Distance traveled by the ball after the second bounce = 10 + 0.6667 + 0.6667 = 11.3334 feet.
The ball rebounds again to one-third of its previous height, and the ball goes to a height of:0.6667/3 = 0.2222 feet. Distance traveled by the ball after the third bounce = 11.3334 + 0.2222 + 0.2222 = 11.7778 feet. The ball rebounds again to one-third of its previous height, and the ball goes to a height of:0.2222/3 = 0.0741 feet.
Distance traveled by the ball after the fourth bounce = 11.7778 + 0.0741 + 0.0741 = 11.926 feet. Therefore, the total distance traveled by the ball is approximately 11.926 feet.
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Write the equation of a line that is perpendicular to y=½x - 9 and passes through the point (3, -2).
Answer:
y = - 2x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{2}[/tex] x - 9 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (3, - 2 ) into the partial equation
- 2 = - 2(3) + c = - 6 + c ( add 6 to both sides )
4 = c
y = - 2x + 4 ← equation of perpendicular line
round 0.956 to one decimal place
Answer: 0.96
Step-by-step explanation:
To round 0.956 to one decimal place, we need to look at the second decimal place (the hundredths place), which is 5. Since 5 is greater than or equal to 5, we need to round up the first decimal place (the tenths place), which is 9. Therefore, the rounded number to one decimal place is:
0.956 rounded to one decimal place = 0.96
The probability distribution of the amount of memory X (GB) in a purchased flash drive is given below. x 1 2 4 8 16 p(x) .05 .10 .35 .40.10 Compute the following: E(X), E(X2), V(X), E(3x + 2), E (3X² + 2), V (3x + 2), E(X +1), V(X + 1).
To solve the question asked, you can say: Therefore, the final answers expressions are: E(X) = 5.8; E(X²) = 59.8; V(X) = 21.16 and E(3X + 2) = 20.4
what is expression ?In mathematics, an expression is a set of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation that represent quantities or values. Expressions can be as simple as "3 + 4" or as complex as they can contain functions like "sin(x)" or "log(y)" . Expressions can be evaluated by substituting values for variables and performing mathematical operations in the order specified. For example, if x = 2, the expression "3x + 5" is 3(2) + 5 = 11. In mathematics, formulas are often used to describe real-world situations, create equations, and simplify complex math problems.
To calculate these values, we first need to compute the mean (expected value) and variance of X, which are given by:
E(X) = ∑[x * p(x)]
= 1 * 0.05 + 2 * 0.10 + 4 * 0.35 + 8 * 0.40 + 16 * 0.10
= 5.8
E(X²) = ∑[x² * p(x)]
= 1² * 0.05 + 2² * 0.10 + 4² * 0.35 + 8² * 0.40 + 16² * 0.10
= 59.8
V(X) = E(X²) - [E(X)]²
= 59.8 - 5.8²
= 21.16
E(3X + 2) = 3E(X) + 2
= 3(5.8) + 2
= 20.4
E(3X² + 2) = 3E(X²) + 2
= 3(59.8) + 2
= 179.4
V(3X + 2) = V(3X)
= 9V(X)
= 9(21.16)
= 190.44
E(X + 1) = E(X) + 1
= 5.8 + 1
= 6.8
V(X + 1) = V(X)
= 21.16
Therefore, the final answers are:
E(X) = 5.8
E(X²) = 59.8
V(X) = 21.16
E(3X + 2) = 20.4
E(3X² + 2) = 179.4
V(3X + 2) = 190.44
E(X + 1) = 6.8
V(X + 1) = 21.16
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(a) In the figure below, m CED=50° and m AB = 140°. Find m CD.
(b) In the figure below, m VYW=36 and m VX = 62. Find m VW
a) Measurement of arcCD is 40°
b) Measurement of arcVW is 134°
Define the term Circle identities?The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.
a) Given that, ∠CED=∠AEC =50° arcAB=140° we have to find out arcCD
We know the formula for external angle as per given diagram,
∠AEC = [tex]\frac{1}{2} (arcAB-arcCD)[/tex]
50° = [tex]\frac{1}{2} *(140-arcCD)[/tex]
Simplify, arcCD = 140° - 100° = 40°
Therefore, measurement of arcCD is 40°
b) Given that, ∠VYW =36° arcVX=62° we have to find out arcVW
We know the formula for external angle as per given diagram,
∠VYW = [tex]\frac{1}{2} (arcVW-arcVX)[/tex]
36° = [tex]\frac{1}{2} *(arcVW-62)[/tex]
Simplify, arcVW = 72° + 62° = 134°
Therefore, measurement of arcVW is 134°
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According to the question the a) Measurement of arcCD is 40° and b) Measurement of arcVW is 134°
Define the term Circle identities?The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.
a) Given that, ∠CED=∠AEC =50° arcAB=140° we have to find out arcCD
We know the formula for external angle as per given diagram,
∠AEC = 1/2 (arcAB - arcCD)
50° = 1/2*(140 - arccd)
Simplify, arcCD = 140° - 100° = 40°
Therefore, measurement of arcCD is 40°
b) Given that, ∠VYW =36° arcVX=62° we have to find out arcVW
We know the formula for external angle as per given diagram,
∠VYW = 1/2(arcVW - arcVX)
36° = 1/2*(arcVW - 62)
Simplify, arcVW = 72° + 62° = 134°
Therefore, measurement of arcVW is 134°
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10 * x = 425
81729 / y = 898.12
What is X and Y?
I WILL GIVE BRAINLY IF U DONT USE CALCULATOR
The value of X is 42.5 and Y is 90.98.
How to solve equations?
To solve an equation, you need to perform the same operation on both sides of the equation until you isolate the variable on one side and have a numerical value on the other side. The process of solving an equation generally involves the following steps:
Simplify both sides of the equation by combining like terms and following the order of operations.
Add or subtract the same value from both sides of the equation to isolate the variable term.
Multiply or divide both sides of the equation by the same non-zero value to isolate the variable term.
Check your solution by plugging it back into the original equation and verifying that it satisfies the equation.
Solving the given equations :
To solve for X, we can use inverse operations to isolate the variable. Since 10 is multiplied by X, we can use the inverse operation of division by 10 to isolate X. So, dividing both sides of the equation by 10 gives:
[tex]10x/10 = 425/10[/tex]
Simplifying the left side of the equation gives:
[tex]x = 42.5[/tex]
Therefore, X is 42.5.
To solve for Y, we can use similar steps. Since 81729 is divided by Y, we can use the inverse operation of multiplication by Y to isolate Y. So, multiplying both sides of the equation by Y gives:
[tex]81729 = 898.12 \times Y[/tex]
Simplifying the right side of the equation gives:
[tex]Y = 81729 / 898.12[/tex]
[tex]Y = 90.98[/tex]
Therefore, Y is 90.98.
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Suppose the number of water people drink in a week is normally distributed with a mean of 50 and a standard deviation of 5 glasses of water. Find the value 1 standard deviation below the mean
Answer:
Step-by-step explanation:
.
If John had 3 apples then Droped 2 then found 4 then gave one to his friend how many apples does he have now
Answer:
4 apples
Step-by-step explanation:
We know
John had 3 apples, then Dropped 2, found 4, then gave 1 to his friend.
How many apples does he have now?
3 - 2 + 4 - 1 = 4 apples
So, he has 4 apples now.
Answer:
4 apples
Step-by-step explanation:
We know that John had 3 apples
but then he had dropped 2 of them
he then found 4
then he gave 1 to his friend
3-2=1
1+4=5
5-1=4
The answer is 4
Hope this helps!
It takes 120 unit cubes to completely fill a rectangular prism. The prism is 10 unit cubes high. What are the other possible dimensions of the rectangular prism?
the possible dimensions of the rectangular prism are:
1 unit by 12 units by 10 units
2 units by 6 units by 10 units
3 units by 4 units by 10 units
Let the length and width of the rectangular prism be represented by l and w, respectively. Since the height of the prism is 10 unit cubes, we know that the volume of the prism is:
V = l × w × 10
We are also given that the prism requires 120 unit cubes to fill completely, which means:
V = l × w × 10 = 120
Dividing both sides by 10, we get:
l × w = 12
Now we need to find pairs of positive integers l and w that multiply to 12. These are:
1 × 12
2 × 6
3 × 4
Therefore, the possible dimensions of the rectangular prism are:
1 unit by 12 units by 10 units
2 units by 6 units by 10 units
3 units by 4 units by 10 units
Note that these dimensions are not unique, as we can also obtain different dimensions by exchanging the length and width, or by rotating the prism.
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how many yard are in 10 meters
Answer:
10.936 yards
Step-by-step explanation:
A triangle has a base that measures 6.4 feet. Its height measures 5 feet. How many square feet is the area of the triangle?
Answer:
16 feet
Step-by-step explanation:
Area of triangle = 1/2(a x b)
A = 1/2(6.4 x 5)
A = 32/2
A = 16 feet
Calvin ordered scissors. Each pair of scissors weighs 0. 34 kg. A box of scissors weighs
64. 6 kg. How many pairs of scissors come n each box?
190 pairs of scissors came in each box.
This is an example of a word problem. As a model, a word problem depicts circumstances from the actual world that may be converted into phrases.
Weight of each pair of scissors = 0.34 kg
Weight of a box of scissors = 64.6 kg
Therefore, pairs of scissors in each box = Weight of a box of scissors ÷
Weight of each pair
= 64.6 ÷ 0.34
= 190 pairs.
Hence, 190 pairs of scissors came in each box.
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A barista mixes 12lb of his secret-formula coffee beans with 15lb of another bean that sells for $18 per lb. The resulting mix costs $20 per lb. How much does the barista's secret-forumula means cost per pound?
Answer:
The baristas secret formula beans cost per pound is $19.2.
Step-by-step explanation:
Given is that a barista mixes 12 lb of his secret-formula coffee beans with 15 lb of another bean that sells for $18 per lb.The cost of 1 pound of another bean as -$(15/18) = $(5/6)Assume that 1 pound of secret coffee costs ${x}. So, we can write -x + 5/6 = 20x = 20 - 5/6x = 19.2Therefore, the baristas secret formula beans cost per pound is $19.2.
Answer:
Find 5 rational numbers between 4/5 - and * 3/7
Whatis the value of # y_ When y = 5 and x = 10?
The value of y when x=36 is 31/3.
According to the question,
x varies directly with 3y+5
Thus,
[tex]x = k(3y+5)[/tex]
where K is any positive integer.
Now, from the question,
y=5/3 when x=10
Thus,
[tex]10 = k(3(\frac{5}{3} )+5)\\10 = k(10)\\k = 1[/tex]
Now we can use k to find the value of y when x=36:
[tex]36 = 1(3y+5)\\31 = 3y\\y = \frac{31}{3}[/tex]
In mathematics, an integer is a whole number that can be positive, negative, or zero. Integers are a fundamental concept in number theory and are used in a variety of applications across many fields. Integers can be represented using the symbol "Z" and are denoted by an integer value like -3, 0, 1, 2, 3, etc. They are used to count and measure quantities in real-life situations, such as the number of apples in a basket or the distance between two cities.
Integers are closed under addition, subtraction, and multiplication, meaning that if you add, subtract, or multiply any two integers, the result will also be an integer. However, the division is not always closed under integers, as dividing by zero is undefined, and dividing two integers can result in a non-integer value.
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Complete Question:
If x varies directly with 3y+5 and y=5/3 when x=10, then what is the value of y when x=36
Step 1 of 3
a.
About 180,000 terawatts of solar power reaches Earth’s surface.
Out of which about 0.06% is used by plants for photosynthesis.
Thus 108 terawatts of solar power is used by plants for photosynthesis.
Of this energy, about ends up stored in plant matter
Thus 1.08 terawatts of energy get stored in plant matter.
Consider the following facts
Therefore,
Therefore joules of energy get stored in plant matter each second.
The amount of energy stored in plant matter each second is 1.08 × 10^12 Joules.
Step 1: Calculation of joules of energy stored in plant matter each secondGiven that, 1.08 terawatts of energy gets stored in plant matter for photosynthesis in a second.Therefore, 1.08 × 1012 watts of energy gets stored in plant matter each second. Also, the energy stored in plants matter in Joules = Watts × seconds (Joule is the unit of energy)1.08 × 1012 watts of energy stored in plant matter in a second.1 watt-second = 1 JouleEnergy stored in plant matter in a second = 1.08 × 1012 watts × 1 second = 1.08 × 1012 Joules Answer: The amount of energy stored in plant matter each second is 1.08 × 10^12 Joules.
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the graph represents the number of different tacos ordered for an office lunch. in total, how many tacos were ordered?
Answer:
do you have the graph to solve it?
use the relationships in the diagram to solve for t. Justify your solution with a definition or theorem
Answer:
The value of t = 18
Step-by-step explanation:
202 = 2t + 5 + t + 3t - 2 + 5t +1 Combine like terms
202 = 11t + 4 Subtract 4 from both sides
198 = 11[tex]\frac{11x}{11}[/tex]x Divide both sides by 11
[tex]\frac{198}{11}[/tex] = 18
Is the question the value of t or the length of each side?
Each side
2t + 5
2(18) + 5
41
T
18
3T - 2
3(18) - 2
52
5T + 1
5(18) + 1
91
91 + 52 + 18 + 41 = 2002
Helping in the name of Jesus.
in exercises 1-8 solve the inequality graph the solution
1. 6x < -30
Step-by-step explanation:
x<-5 is the answer
1.
6x=-30
2.
x=-5
3.
x<-5
A package is delivered 3 hours 25 minutes after it is collected, it is collected at 15:39
at what time is the package delivered
Given the data in the question we calculate that the package is delivered at 18:44.
If the package is collected at 15:39 and delivered 3 hours and 25 minutes later, we can add that amount of time to the collection time to find the delivery time.
First, we need to convert 3 hours and 25 minutes to just minutes. To do this, we multiply 3 by 60 (to convert hours to minutes) and then add 25:
3 hours and 25 minutes = (3 × 60) + 25 = 185 minutes
Now we can add 185 minutes to the collection time of 15:39:
15:39 + 185 minutes = 18:44
Therefore, the package is delivered at 18:44. The delivery time of a package is the time it takes for the package to be transported from the sender to the receiver. In this case, the package was collected at 15:39 and delivered 3 hours and 25 minutes later. To find the delivery time, we added the duration of 3 hours and 25 minutes to the collection time. It is important to keep track of delivery times to ensure timely and efficient shipping, especially for time-sensitive or perishable items. Timely delivery is crucial for businesses that rely on shipping to meet customer expectations and maintain customer satisfaction.
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Don bought the furniture listed below he paid $500 and will make monthly payments of $85 for the remaining amount how long will it take to pay for the furniture
Answer:
it will take approximately 5.88 months for Don to pay off the remaining amount of $R = $85t = $85(5.88) = $499.80
Step-by-step explanation:
Don paid $500 upfront and will make monthly payments of $85 for the remaining amount. Let's assume the remaining amount he needs to pay is $R. The total cost of the furniture is the sum of the amount paid upfront and the remaining amount:
Total Cost = $500 + $R
Since he will be paying $85 per month, we can set up an equation to determine the time it will take to pay off the remaining amount:
$R = $85t
where t is the number of months it will take to pay off the remaining amount.
Substituting $R = $85t in the total cost equation, we get:
Total Cost = $500 + $85t
Since we want to find the time it will take to pay off the furniture, we need to solve for t. We can equate the total cost to the amount Don will pay at the end of the payment period, which is:
Total Cost = Amount Paid
$500 + $85t = $500 + $85t + $R
$85t = $R
$500 + $85t = $500 + $85t + $85t
$500 + $170t = $500 + $R
$170t = $R
Substituting $R = $85t, we get:
$170t = $85t
t = $500/$85
t = 5.88 (rounded to two decimal places)
An unfair coin with Pr[H]=23 is flipped. If the flip results in a head, then a marble is selected from an urn containing 6 red, 9 white, and 10 blue marbles. If the flip results in a tail then a marble is selected from an urn containing 10 red and 1 white marbles. If the marble selected is white, then what is the probability that a flip resulted in a head?
The probability that the flip results in a head is given as Pr[H] = 23. Therefore, the probability that the flip results in a tail is Pr[T] = 1 - Pr[H] = 1 - 23 = 13.
Let A be the event that a white marble is selected. We need to find the conditional probability Pr[H|A], i.e., the probability that the flip resulted in a head given that a white marble was selected.
Using Bayes' theorem, we have:
Pr[H|A] = (Pr[A|H]*Pr[H]) / Pr[A]
Pr[A|H] is the probability of selecting a white marble given that the flip resulted in a head. This is given by (9/25), since there are 9 white marbles out of 25 in the first urn.
Pr[A] is the total probability of selecting a white marble, which can be found using the law of total probability:
Pr[A] = Pr[A|H]*Pr[H] + Pr[A|T]*Pr[T]
= (9/25)*0.23 + (1/11)*0.13
= 0.0888 + 0.0118
= 0.1006
Pr[A|T] is the probability of selecting a white marble given that the flip resulted in a tail. This is given by (1/11), since there is only 1 white marble out of 11 in the second urn.
Therefore,
Pr[H|A] = (9/25 * 0.23) / 0.1006 = 0.6508
Hence, the probability that the flip resulted in a head given that a white marble was selected is 0.6508 (or approximately 0.65).
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suppose that each day the price of a stock moves up 1/8th of a point with probability 1/3 and moves down 1/8th of point with probability 2/3. if the price fluctuations from one day to another are independent, what is the probability that after 6 days the stock has its original price?
After 6 days, the probability that the stock has its original price is 5/16.
There are two possible scenarios that can take place when the stock price fluctuates from one day to the next. Either the price goes up by 1/8th of a point with probability 1/3 or it goes down by 1/8th of a point with probability 2/3.
The price of the stock after six days can be denoted as S6. The price of the stock after the first day can be represented as S0.
Since the price fluctuates either up or down by 1/8th of a point on each day, the price after six days can be represented as follows:S6 = S0 + (up, up, up, up, up, up), (up, up, up, up, up, down), (up, up, up, up, down, up), ... , (down, down, down, down, down, down)
In order to return to the original price, the stock must go up and down by the same amount. As a result, there must be an equal number of ups and downs in the six-day period.
As a result, we must calculate the probability of obtaining an equal number of ups and downs over six days.
Let's represent an increase in the stock price as 'U' and a decrease as 'D.'
The total number of ways in which the stock can go up and down over six days is [tex]2^6 = 64[/tex].
The total number of ways in which the stock can return to its original price can be calculated as follows: [tex]N(UUUDDD) = 6! / (3! * 3!) = 20[/tex]
The probability of the stock returning to its original price after six days can be calculated as:
[tex]P = N(UUUDDD) / 64 = 20 / 64 = 5 / 16[/tex]
Therefore, the probability that after 6 days the stock has its original price is 5/16.
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What is 0.83333333333 as a fraction?
Answer: 41666666669 / 50000000003
Step-by-step explanation:
Select THE TWO values of that are solutions to the equation (* - 5) (7x - 21) = 0.
