raj bought 300 mangoes at per 10 mangoes for RS 100 and sold them at a profit of 25% At what rate did he sell per 15 mangoes​

The value of the American put futures option using a one-time step tree is $0.

To value the American put futures option using a one-time step tree, we can follow these steps:

Step 1: Calculate the risk-neutral probability of an up move (p) and a down move (1-p) based on the volatility and time step. Given that the volatility is 25% and the time to maturity is 1 year, we can calculate the time step as √(1 year) = 1.

Since this is a one-time step tree, there are two possible outcomes: an up move or a down move. We need to find the risk-neutral probabilities of these moves.

To calculate p, we use the formula:

p =[tex](e^(r * t) - d) / (u - d)[/tex]

Where:

r is the interest rate per annum (6% = 0.06),

t is the time step (1),

u is the up move factor (1 + volatility) = (1 + 0.25) = 1.25,

d is the down move factor (1 - volatility) = (1 - 0.25) = 0.75.

Substituting the values, we get:

p =[tex](e^([/tex]0.06 * 1) - 0.75) / (1.25 - 0.75)

p = (1.06183 - 0.75) / 0.5

p = 0.31183 / 0.5

p = 0.62366

Step 2: Calculate the option values at each possible outcome. Since this is a put option, the payoff at each node is the difference between the strike price and the future price at that node.

At the up move node:

Option value (up) = max(strike price - future price (up), 0)

                = max(0.55 - 0.60, 0)

                = max(-0.05, 0)

                = 0

At the down move node:

Option value (down) = max(strike price - future price (down), 0)

                  = max(0.55 - 0.55, 0)

                  = max(0, 0)

                  = 0

Step 3: Calculate the expected option value at the current node by taking the risk-neutral weighted average of the option values at the next nodes.

Expected option value = p * option value (up) + (1 - p) * option value (down)

                    = 0.62366 * 0 + (1 - 0.62366) * 0

                    = 0

Therefore, the value of the American put futures option using a one-time step tree is $0.

for more such question on value visit

https://brainly.com/question/843074

#SPJ8

The expression "[tex]\sqrt[4]{9}^1^/^2[/tex]" simplifies to 81, but none of the given options represents this value.

The correct answer is option E.

The expression "[tex]\sqrt[4]{9}^1^/^2[/tex]" represents the fourth power of the square root of 9 raised to the power of one-half. Let's simplify this expression step by step.

First, let's simplify the square root of 9:

[tex]\sqrt{9}[/tex] = 3

Next, let's simplify the exponent one-half:

[tex]3^1/2 = \sqrt{3}[/tex]

Now, we have the expression "[tex]\sqrt[4]{3}[/tex]". This means we need to raise the square root of 3 to the fourth power.

[tex]\sqrt{(3)^4 }[/tex]= [tex](\sqrt{3})(\sqrt{3})(\sqrt{3})(\sqrt{3})[/tex]= 3*3*3*3 = 81

Therefore, "^[tex]\sqrt[4]{9}^1^/^2[/tex]" simplifies to 81.

Among the given options, none of them matches the simplified expression of 81.

Therefore, none of the options A, B, C, or D is equivalent to the expression "^[tex]\sqrt[4]{9}^1^/^2[/tex]".

For more such information on: expression

https://brainly.com/question/1859113

#SPJ8

The question probable may be:

Which is equivalent to [tex]\sqrt[4]{9}^1^/^2[/tex]?  

A.g2x

B. [tex]9^1/2[/tex]

C.[tex]\sqrt{9}[/tex]

D[tex]\sqrt[5]{9}[/tex]

E. None of the above

Answer:  (x² - 5)(x - 7)

Step-by-step explanation:

Grouping the terms, we have:

(x^3 - 7x^2) + (-5x + 35)

Now, let's factor out the common factors from each pair:

x^2(x - 7) - 5(x - 7)

Notice that we have a common factor of (x - 7) in both terms. We can factor it out:

(x^2 - 5)(x - 7)

Therefore, the resulting expression after factoring by grouping is (x^2 - 5)(x - 7).

The equation that represents the given sentence "Don's score decreased by 23 is 43" is d - 23 = 43, where d represents Don's score.

To translate the given sentence into an equation, let's break it down:

"Don's score" can be represented by the variable d.

"Decreased by 23" indicates a subtraction operation. So we subtract 23 from Don's score.

"Is" signifies the equal sign in the equation.

"43" is the result or value that Don's score decreased by 23 should be equal to.

Combining all the information, we can write the equation:

d - 23 = 43

This equation states that when we subtract 23 from Don's score (represented by d), the result should be equal to 43. This equation accurately represents the given sentence.

To find the value of Don's score (d), we can solve the equation by isolating the variable:

d - 23 = 43

Adding 23 to both sides of the equation:

d - 23 + 23 = 43 + 23

Simplifying:

d = 66

Therefore, Don's score, represented by the variable d, is equal to 66 based on the given equation.

For more such questions on sentence into an equation, click on:

https://brainly.com/question/29475055

#SPJ8

Answer:

The graph representing the function f(x) = −|x − 2| − 1 is a downward-opening V-shaped graph that is shifted 2 units to the right and 1 unit downward from the standard absolute value function |x|.

Step-by-step explanation:

Here is a description of the graph and its key points:

The vertex of the graph is located at the point (2, -1), which represents the minimum point of the graph.

The graph approaches negative infinity as x approaches positive infinity and negative infinity as x approaches negative infinity.

The graph is symmetric with respect to the vertical line x = 2.

Please note that I cannot display images directly, but you can search for "graph of f(x) = −|x − 2| − 1" on an online graphing tool or use a graphing calculator to visualize the specific graph.

The two numbers are 20 and 32.

Let's assume the two numbers in the ratio 10:16 are 10x and 16x, where x is a common factor.

According to the given information, when 4 is added to each number, the ratio becomes 4:6. This means that the new numbers are (10x + 4) and (16x + 4).

To find the numbers, we can set up an equation based on the given ratios:

(10x + 4) / (16x + 4) = 4/6

To simplify the equation, we can cross-multiply:

6(10x + 4) = 4(16x + 4)

Expanding both sides:

60x + 24 = 64x + 16

Bringing like terms together:

60x - 64x = 16 - 24

-4x = -8

Dividing both sides by -4:

x = 2

Now that we have the value of x, we can substitute it back into the original ratios to find the numbers:

The first number = 10x = 10 * 2 = 20

The second number = 16x = 16 * 2 = 32

Therefore, the two numbers are 20 and 32.

To learn more about numbers

https://brainly.com/question/25734188

#SPJ8

Answer:

Let the two numbers be 10x and 16x.

When 4 is added to each, the resulting numbers are (10x + 4) and (16x + 4).

According to the problem, the ratio of (10x + 4) to (16x + 4) is 4:6.

We can write this as:

(10x + 4)/(16x + 4) = 4/6

Cross-multiplying, we get:

6(10x + 4) = 4(16x + 4)

Simplifying the equation, we get:

60x + 24 = 64x + 16

48 = 4x

x = 12

Therefore, the two numbers are:

10x = 120

16x = 192

So the two numbers are 120 and 192.

The expression "the product of 4 and g score is 72" in algebraic notation is 4g = 72

From the question, we have the following parameters that can be used in our computation:

The product of 4 and g score is 72

Represent the number with g

So the statement can be rewritten as follows:

the product of 4 and g is 72

So, we have the following

4g is 72

"is" means =

So, we have

4g = 72

Hence, the expression "the product of 4 and g score is 72" in algebraic notation is 4g = 72

Read more about expression at

brainly.com/question/4344214

#SPJ1

Alright, let's solve this system of equations whimsically, shall we?

First, imagine these lines as threads of destiny. Each equation is like a thread weaving through the vast fabric of the cosmos, plotted on the 2D plane of our imagination.

So let's embark on this mathematical journey together!

Our first traveler is Line 1, or as we'll call him, "Sir L1." He struts along with the equation y = 3x + 1. His path is clear: for every step he takes in the x direction, he ascends 3 steps in the y. He's quite the climber!

Next, we meet Lady L2 with the equation y = 2x - 3. A bit more relaxed than Sir L1, she ascends 2 steps in the y direction for every step in the x. They clearly don't cross paths—they're too different in their inclinations. This means that Sir L1 and Lady L2 are consistent and independent.

Our third traveler is the mysterious Master L3. His equation is slightly different, written as 3y + x = 6. Let's write this in y = mx + c form to match our other travelers. With a little rearranging, we get y = -1/3x + 2. He's a bit of a downer, descending 1 step in y for every 3 steps in x. Observing him from afar, it's clear he never intersects with Lady L2 or Sir L1. They're all leading their independent lives.

Lastly, we have the young Miss L4, with her equation y = 1/3x - 1. She's a gentle traveler, ascending only a third of a step in y for every step in x. However, like the others, she doesn't cross paths with any of our other travelers.

So, in this whimsical world of equations, it appears that none of our travelers cross paths. Each one treads their own unique path. This means our system of equations is indeed consistent, but each line is independent, meaning they don't intersect, and each has a unique solution. There are no shared points of intersection. It seems our travelers are lone wolves in this cosmos of coordinates!

The statements that are correct about the function that have been shown are;A, B, C, F

A mathematical function called an exponential function has the independent variable in the exponent. Its general form is:

f(x) = a^x

where "x" is the variable and "a" is the base, a positive constant. The exponential function's appearance and behavior depend on the base "a".

The function grows exponentially when the base "a" is greater than 1. The function expands quickly as "x" grows in value. As "x" rises, the growth rate becomes steeper.

Learn more about exponential function:https://brainly.com/question/29287497

#SPJ1

The value of K is 4.

In a regular polygon, all interior angles are congruent, which means they have the same measure. Let's denote the measure of each interior angle as A.

The sum of the interior angles of a polygon with (2x + 1) sides can be found using the formula:

Sum of interior angles = (2x + 1 - 2) * 180°

Since the polygon is regular, each interior angle has the same measure A. Therefore, we have the equation:

(2x + 1 - 2) * 180° = (2x + 1) * A

Simplifying the equation:

(2x - 1) * 180° = (2x + 1) * A

Now, we are given that the size of each interior angle is 140°. Substituting this value into the equation:

(2x - 1) * 180° = (2x + 1) * 140°

Solving for x:

360x - 180° = 280x + 140°

80x = 320°

x = 4

Therefore, the value of K is 4.

For more questions on regular polygon, click on:

https://brainly.com/question/29425329

#SPJ8

The effect on the graph of f(x) = x² when it is transformed to h(x) = 3x² - 7 is described by option B. The graph of f(x) is vertically stretched by a factor of 3 and shifted 7 units down.

For more such questions on graph, click on:

https://brainly.com/question/19040584

#SPJ8

If the biased dice is rolled 150 times, we can expect to get approximately 45 ones

If the chance of getting a 1 on a biased dice is 0.3, it means that the probability of rolling a 1 on any given roll is 0.3 or 30%.

To determine how many ones you would get if rolled 150 times, we can multiply the probability of rolling a 1 (0.3) by the total number of rolls (150).

Number of ones = Probability of getting a 1 * Total number of rolls

Number of ones = 0.3 * 150 = 45

Therefore, on average, we would expect around 45 instances of rolling a one when using this biased dice over 150 rolls.

It's important to note that the actual number of ones obtained may vary due to the inherent randomness of dice rolls. However, if a biased dice has a 0.3 chance of getting a 1, when rolled 150 times, you would expect to get approximately 45 ones.

Know more about probability here:

https://brainly.com/question/30390037

#SPJ8

Answer:

Step-by-step explanation:

The exponential equation for the volume v remaining after t hours can be written as ...

v(t) = (initial amount)×(decay factor)^(t/(decay time))

v(t) = 600,000×(1 -10%)^(t/3)

Then after 4 hours, the remaining volume is ...

 v(4) = 600,000×(0.90^(4/3)) = 521364.2677 gallons

[tex]\textit{Periodic/Cyclical Exponential Decay} \\\\ A=P(1 - r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &600000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=hours\dotfill &4\\ c=period\dotfill &3 \end{cases} \\\\\\ A=600000(1 - 0.10)^{\frac{4}{3}}\implies A=600000(0.9)^{\frac{4}{3}}\implies A\approx 521364[/tex]

Answer:

$5.76

Step-by-step explanation:

There are 16 US tablespoons inside a cup.

Since there are 2 pies, each needing 1/2 a cup, we can just class this as a full cup, as it is equivalent.

Since each lemon yields 2 tablespoons, we can do the following equation:

16/2=8

This gives us 8 lemons.

8 x 0.72 = 5.76

Therefore, this should cost $5.76

Hope this helps :D

In sampling distributions, the mean is consistently identical to the population mean. (Option C)

This concept is a fundamental property of sampling distributions and is rooted in the principles of probability and statistical theory. A sampling distribution is a theoretical distribution that represents the possible values of a statistic (such as the mean or proportion) calculated from different samples drawn from the same population. The mean of a sampling distribution is an average of the sample means, and it provides an estimate of the population mean.

When random samples are drawn from a population, the mean of each sample will vary due to random sampling variability. However, as the sample size increases, the distribution of sample means tends to converge around the population mean. This phenomenon is known as the Central Limit Theorem.

According to the Central Limit Theorem, as sample sizes become large (typically n > 30), the sampling distribution of the mean becomes approximately normal, with a mean that is identical to the population mean. In other words, on average, the sample means will be equal to the population mean. This property holds true regardless of the shape, spread, or other characteristics of the population distribution.

Therefore, the correct answer is C. Identical to.

Know more about the mean here:
https://brainly.com/question/1136789

#SPJ8

In this scenario, we can use the binomial distribution to calculate the probability of getting 2 frozen rain drops after defeating 20 Frigid Elements. The binomial distribution has four parameters: n, p, q, and x.

- n is the number of trials or attempts, which is 20 in this case.

- p is the probability of success on each trial, which is 0.019 (1.9%) in this case.

- q is the probability of failure on each trial, which is 1 - p = 0.981.

- x is the number of successes we are interested in, which is 2 in this case.

Using the formula for the binomial distribution, we can calculate the probability of getting exactly 2 frozen rain drops:

P(X = 2) = (20 choose 2) * (0.019)^2 * (0.981)^(20-2)

where (20 choose 2) = 20! / (2! * (20-2)!) = 190 is the number of ways to choose 2 Frigid Elements out of 20.

Simplifying the formula, we get:

P(X = 2) = 190 * 0.019^2 * 0.981^18 = 0.261

Therefore, the probability that 2 frozen rains will drop if 20 Frigid Elements are defeated is approximately 0.261.

Answer:

when y=0

2x=12

we divide by 2 on both sides

x= 6

There are a total of 45,144,000 (3 x 26 x 26 x 10 x 10) different character possibilities given the provided criteria.

To calculate the number of character possibilities, we'll break down each criterion and multiply the number of options for each position.

For the first position, we have 3 possibilities: the digits 1, 2, or 3.

For the second and third positions, we have 26 possibilities each, representing the 26 letters of the alphabet.

For the fourth and fifth positions, we have 10 possibilities each, representing the digits 0 through 9.

To find the total number of possibilities, we multiply the number of options for each position:

3 x 26 x 26 x 10 x 10 = 45,144,000.

Therefore, there are a total of 45,144,000 different character possibilities when considering the given criteria of having the options of 1, 2, or 3 for the first position, the 26 letters of the alphabet for the second and third positions, and the digits 0 through 9 for the fourth and fifth positions.

For more such questions on possibilities, click on:

https://brainly.com/question/25870256

#SPJ8

The length and the width of the garden are 12 and 13

from the question, we have the following parameters that can be used in our computation:

Length = Width + 1

So, we have

Area = 156

Represent the width with x

So, we have

Area = x(x + 1)

Recall that

Area = 156

So, we have

x(x + 1) = 156

When evaluated, we have

x = 12

Next, we have

Width = 12 + 1 = 13

Hence, the length and the width of the garden are 12 and 13

Read more about area at

https://brainly.com/question/24487155

#SPJ1

Answer:

Step-by-step explanation:

The expression 2x - 11x - 6 can be simplified as follows:

2x - 11x - 6 = -9x - 6

So, the equivalent expression is -9x - 6.

The answer is:

-9x - 6

Work/explanation:

To simplify this expression, we combine the like terms :

[tex]\huge\text{2x - 11x - 6} \\ \\ \\ \text{-9x - 6}[/tex]

There's nothing that we can do for this expression. It's been simplified as much as possible.

The inverse of the given function is: f⁻¹(x) = 4x² - 3 for x ≤ 0

The inverse of a function is defined as a function that serves to undo another function. That is, if f(x) produces y, then putting y into the inverse of f' produces the output x. A function f' that has an inverse is referred to as invertible and the inverse is denoted by f⁻¹.

The given function is:

f(x) = -¹/₂√(x + 3)

To find the inverse of the function we replace the value of x and y and then find y in terms of x which is the inverse of the function.

Let f(x) = y

Thus:

x = -¹/₂√(y + 3)

Multiply both sides by -2 to get:

-2x = √(y + 3)

Square both sides to get:

4x² = y + 3

y = 4x² - 3

Thus, the inverse of the function is:

f⁻¹(x) = 4x² - 3 for x ≤ 0

Read more about Inverse of Function at: https://brainly.com/question/3831584

#SPJ1

Vertically stretch the cubic parent function, we multiply the function by the vertical stretch factor, a. The new equation of the function is y = a(x^3).  

If you vertically stretch the cubic parent function, the equation of the new function is y = a(x^3) where a is the vertical stretch factor. A cubic parent function is a polynomial function with a degree of three and an equation of y = x^3.

A vertical stretch is a transformation that increases the distance between each point on a graph and the x-axis. This transformation does not change the shape of the graph, but it affects the height of the graph.

To vertically stretch the cubic parent function, we multiply the function by a vertical stretch factor, a. Therefore, the equation of the new function is y = a(x^3).

For example, let's say we want to vertically stretch the cubic parent function y = x^3 by a factor of 2. To do this, we multiply the function by 2, which gives us y = 2(x^3). This means that the new function is twice as tall as the original function.

On the other hand, if we want to vertically shrink the cubic parent function y = x^3 by a factor of 1/2, we divide the function by 1/2. This gives us y = (1/2)(x^3), which means that the new function is half as tall as the original function.

To learn more about : function

https://brainly.com/question/11624077

#SPJ8

The Inverse of ƒ(x) is given by y = 21x + 7 For the given function, the inverse is y = 21x + 7.

Given,ƒ(x) = 1/3 - 1/21x

To find the inverse of ƒ(x)

We can use the following steps,

Replace ƒ(x) with y, y = 1/3 - 1/21x

Swap x and y, then we get x = 1/3 - 1/21y

Solve for y

We have to isolate y on one side and other terms on the other side,

Add 1/21 y to both sides + 1/21 y = 1/3

Now, Multiply both sides by 21 to get rid of the denominator.21x + y = 7

Then the inverse of ƒ(x) is given by y = 21x + 7 For the given function, the inverse is y = 21x + 7.

For more questions on Inverse .

https://brainly.com/question/3831584

#SPJ8

I think 5x but I'm not sure

The expression (1 - x)(125 + 80y) gives us the final cost for Hector after applying the coupon, taking into account the surfboard rental fee and the fee per hour for the surfing classes with the instructor.

(1 - x): This represents the remaining percentage after applying the coupon. If the coupon offers a discount of x percent, then (1 - x) represents the percentage of the total cost that Hector has to pay.

(125 + 80y): This represents the original cost without any discounts or coupons. The term 125 represents the surfboard rental fee, and 80y represents the fee per hour that Hector works with the instructor (where y is the number of hours).

(1 - x)(125 + 80y): Multiplying the two terms together gives us the cost after applying the coupon. The expression (1 - x)(125 + 80y) represents the product of the remaining percentage after the coupon and the original cost.

Therefore, the expression (1 - x)(125 + 80y) gives us the final cost for Hector after applying the coupon, taking into account the surfboard rental fee and the fee per hour for the surfing classes with the instructor.

for such more question on percentage

https://brainly.com/question/24877689

#SPJ8

Answer: D=[tex]\sqrt{53}[/tex]

Step-by-step explanation:

The distance between two points in a plane can be calculated using the distance formula, which is derived from the Pythagorean Theorem. The distance between points (x1, y1) and (x2, y2) is given by:

[tex]D=\sqrt{(x2-x1)^{2} } +\sqrt{(y2-y1)^{2} }[/tex]

Use this formula to find the distance between points C and D.

C: x1 = -6, y1 = -4

D: x2 = 1, y2 = -6

[tex]D=\sqrt{[(1-(-6)]^{2} } +\sqrt{[(-6-(-4)]^{2} }[/tex]

[tex]D=\sqrt{49+4}[/tex]

[tex]D=\sqrt{53}[/tex]

If a + 2b + 3 = 0, then the statement could imply that the expression evaluates to zero.

If a + 2b + 3 > 0, then the statement could indicate that the expression is greater than zero.

If a + 2b + 3 = c, then the statement could suggest that the expression is equal to some value c.

If a + 2b + 3, then the statement is incomplete. It does not provide any specific condition or outcome that follows the "then" part of the statement.

A conditional statement typically follows the form "If [condition], then [outcome]." In this case, we have the expression a + 2b + 3, but it is not clear what condition or outcome is being referred to.

To complete the conditional statement, we need additional information to specify the condition and the corresponding outcome. For example:

If a + 2b + 3 = 0, then the statement could imply that the expression evaluates to zero.

If a + 2b + 3 > 0, then the statement could indicate that the expression is greater than zero.

If a + 2b + 3 = c, then the statement could suggest that the expression is equal to some value c.

Without further context or specific instructions, it is not possible to determine the exact completion of the conditional statement.

For more questions on expression

https://brainly.com/question/1859113

#SPJ8

The line segment is calcilated by  the formula  represented mathematically as (x1+x2/2, y1+y2/2), The midpoint is (5,5).

The midpoint of a line segment is the point on the line that is halfway between the endpoints of the line.

To find the midpoint of a line segment, you need to average the x-coordinates of the endpoints and the y-coordinates of the endpoints.

In other words, the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.

The midpoint formula can be represented mathematically as (x1+x2/2, y1+y2/2)

Where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.

Let's illustrate this with an example:

Suppose we have a line segment with endpoints (2,3) and (8,7).

To find the midpoint of the line segment, we use the formula (x1+x2/2, y1+y2/2)(2+8/2, 3+7/2)(10/2, 10/2)

The midpoint is (5,5).

For more related questions on midpoint:

https://brainly.com/question/28224145

#SPJ8