The center of mass can be determined by dividing the moment of the solid with respect to each coordinate axis by the total mass.
In cylindrical coordinates, the paraboloid and the plane can be represented as z = 12r^2 and z = a, respectively. To find the mass, we integrate the density function k over the region of the solid, which is bounded by z = 12r^2, z = a, and the region in the xy-plane where the paraboloid intersects the plane z = a. The integral becomes M = k * ∭ρ dV, where ρ is the density function.
To find the center of mass, we calculate the moments of the solid with respect to each coordinate axis. The x-coordinate of the center of mass can be obtained by dividing the moment about the x-axis by the total mass. Similarly, the y-coordinate and z-coordinate of the center of mass can be calculated by dividing the moments about the y-axis and z-axis, respectively, by the total mass.
By evaluating the triple integral and performing the necessary calculations, we can determine the mass and center of mass of the given solid in cylindrical coordinates.
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For 1-4, a line has the points (-2,-9),
(3, 1), and (6, 7). Find the polnts for the
translation described.
1. 6 units to the left
2. 3 units down
3. 5 units to the right
4 2 units up
Answer:
3 units down
Step-by-step explanation:
got it right on edg
Find the slope of the line:
Maria made $192 for 12 hours of work.
At the same rate, how much would she make for 17
hours of work?
Answer:
192/12=16 per hour
16 x 17 = 272
Step-by-step explanation:
A quality control inspector selects 12 bottles of apple juice at random from a single day’s production. The mean amount of apple juice in the bottles is 298.3 milliliters, and the 95% confidence interval for the true mean amount of juice dispensed per bottle is (296.4, 300.2). Does this interval give the quality control inspector reason to believe that the mean amount of juice in today’s bottles differs from 300 milliliters, as the juice label promises?
Answer:
The juice label (300ml) is in the confidence interval.
So, the 95% CI does not give the inspector the reason to believe the amount of juice differs from 300ml
Step-by-step explanation:
Given
[tex]95\%\ CI = (296.4, 300.2)[/tex]
[tex]Juice\ label = 300ml[/tex]
From the 95% confidence interval value, we have: 296.4 to 300.2
Within this interval, we can find the juice label 300
i.e. 296.4 < 300 < 300.2
In other words, the juice label (300ml) is in the confidence interval.
So, the 95% CI does not give the inspector any reason to believe the amount of juice differs from 300ml.
it is now twenty-one minutes to ten. what time will it be in 5 hours and 17 minutes? write your answer using numbers and a colon (for example, 11:58).
The time after 21 minutes from 9:39 is 2:56am.
Given that it is now twenty-one minutes to ten, we need to determine the time in 5 hours and 17 minutes.
To find the answer, we can add 5 hours and 17 minutes to the current time, which is 9:39 PM. Let's first convert the hours to minutes:5 hours = 5 x 60 = 300 minutes.
Then, add 300 minutes and 17 minutes:300 minutes + 17 minutes = 317 minutes.
Since there are 60 minutes in an hour, we need to divide 317 by 60 to determine the number of hours:317 / 60 = 5 with a remainder of 17.
Therefore, the time in 5 hours and 17 minutes will be 2:56 AM.
To check our answer, we can work backward:
Start with 2:56 AM and subtract 5 hours and 17 minutes:2:56 AM - 5 hours = 9:56 PM9:56 PM - 17 minutes = 9:39 PMAs expected, we arrived back at the original time of 9:39 PM. Therefore, the final answer is 2:56.
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Which of the following are Statistical Inference methods?
• Significance Tests
• Confidence Intervals
• Normal and Binomal Summaries
• Sampling Distributions
• Graphs and Numerical Summarie
Statistical inference methods include significance tests, confidence intervals, and sampling distributions.
Statistical inference refers to the process of drawing conclusions and making predictions about a population based on sample data. It involves using various methods and techniques to make inferences and generalize findings to the larger population.
Significance tests are statistical inference methods that help determine if there is enough evidence to reject or accept a specific hypothesis about a population parameter. They involve calculating a test statistic and comparing it to a critical value to make a decision.
Confidence intervals are another statistical inference method that provides a range of plausible values for a population parameter. They estimate the parameter with a certain level of confidence and are based on sample data and the sampling distribution of the statistic.
Sampling distributions are fundamental to statistical inference as they describe the distribution of a statistic based on repeated sampling. They provide information about the variability and properties of the statistic under different sample scenarios.
Normal and binomial summaries, as well as graphs and numerical summaries, are tools and techniques used in statistical inference to summarize and analyze data but are not specific methods themselves. They help in understanding and visualizing data, which in turn informs the application of statistical inference methods.
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HELP PLS YALL HDHDGDUSHSHXHHXXHHXHXBXBXXHDBBDBDBDBDD
Answer:
with what?
Step-by-step explanation:
15. JAGUARUNDI A jaguarundi springs from a fence post to swat at a low flying bird.
Her height h in feet can be modeled by the equation h = -161? + 22.31 + 2,
where t is time in seconds. Use the discriminant to determine if the jaguarundi
will reach the bird if the bird is flying at a height of 10 feet. Explain.
Answer:
The discriminant, -14.71 < 0, shows that there is no solution of the equation, h = -16·t² + 22.3·t + 2, at the line 'h = 10' feet, therefore, the Jaguarundi height as she springs will not be up to 10 feet and therefore she will not reach the bird
Step-by-step explanation:
From the question, the equation that models the Jaguarundi's height, 'h', ma be written approximately as follows;
h = -16·t² + 22.3·t + 2
Where;
t = The time (duration) in seconds
The discriminant of the equation a·x² + b·x + c = 0 is b² - 4·a·c
When h = 10, we have;
10 = -16·t² + 22.3·t + 2
∴ 0 = -16·t² + 22.3·t + 2 - 10 = -16·t² + 22.3·t - 8
The discriminant of the given quadratic equation is given as follows;
The discriminant = 22.3² - 4 × (-16 × (-8)) = -14.71 < 0
Therefore, the function, h = -16·t² + 22.3·t + 2 has no real root at h = 10
The parabola does not reach or pass through the line h = 10 which is the height at which the bird is flying.
The Jaguarundi will not reach the bird flying at the height of 10 feet.
Answer:
No, the Jaguarundi will not reach the bird
Step-by-step explanation:
The equation is
[tex]h=-16t^2+22.3t+2[/tex]
When h = 10 feet
[tex]10=-16t^2+22.3t+2[/tex]
[tex]\Rightarrow -16t^2+22.3t-8=0[/tex]
[tex]a=-16[/tex]
[tex]b=22.3[/tex]
[tex]c=-8[/tex]
Discriminant is given by
[tex]b^2-4ac=22.3^2-4(-16)(-8)[/tex]
[tex]\Rightarrow b^2-4ac=-14.71[/tex]
[tex]\Rightarrow b^2-4ac<0[/tex]
So, the Jaguanrundi will not reach the bird as the roots will be imaginary.
Which way will the parabola open? Explain.
Please help!!
A school is constructing a rectangular play area against an exterior wall of the school
building. It uses 120 feet of fencing material to enclose three sides of the play area.
Answer:
Step-by-step explanation:
Question says that it uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides. Putting this into equation, we have something like this.
120 = L + 2W
Where
LW = area.
Again, in order to maximize the area with the given fencing, from the equation written above, then Width, w must be = 30 feet and length, l must be = 60
On substituting, we have
A = LW = (120 - 2W) W
From the first equation, making L the subject of the formula, we have this
L = 120 - 2W, which then we substituted above.
On simplification, we have
L = 120W -2W²
Differentiating, we have
A' = 120 - 4W = 0
Remember that W = 30
So therefore, L = 120 - 2(30) = 60 feet
The required length of the rectangular garden is 60 feet
Area of rectangular shapeAccording to the question, the school uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides.
Substitute into the perimeter of the rectangle will give:
120 = L + 2W
Area = LW
In order to maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60
On substituting, we have;
A = LW = (120 - 2W) W
L = 120 - 2W,
On simplification, we have
L = 120W -2W²
Differentiating, we have
A' = 120 - 4W = 0
Remember that W = 30
So therefore, L = 120 - 2(30) = 60 feet
Hence the required length of the rectangular garden is 60 feet
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A health psychologist wants to test the effectiveness of a new stress-reduction method. In the general population, stress level is normally distributed with μ = 40 and σ = 10. 40 randomly selected people are trained in the method; the mean score afterward is 36.
6. Restate question as a research hypothesis and a null hypothesis about the populations.
Population 1:
Population 2:
Research hypothesis:
Null hypothesis:
7. Determine the characteristics of the comparison distribution.
8. Determine the cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01.
The cutoff sample score is therefore:40 - 2.326(1.5811) ≈ 36.59
The research hypothesis and null hypothesis about the populations can be restated as follows:Population 1: The population of people who have not received the new stress-reduction method training.Population 2: The population of people who have received the new stress-reduction method training.Research hypothesis: The new stress-reduction method training has reduced stress levels in the population that has received it compared to the population that has not.Null hypothesis: The new stress-reduction method training has not reduced stress levels in the population that has received it compared to the population that has not.7. The comparison distribution in this case is the distribution of means from samples of the population that has not received the new stress-reduction method training. This distribution has a mean (μ) equal to the population mean of 40 and a standard deviation (σ) equal to the population standard deviation divided by the square root of the sample size, which is σ/√n = 10/√40 = 1.5811.8. To determine the cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01, we need to find the z-score corresponding to a probability of .01 in the right tail of the distribution. This is given by:z = invNorm(0.99) ≈ 2.326Therefore, if the sample mean of the population that has received the new stress-reduction method training is more than 2.326 standard errors below the mean of the comparison distribution (which is 40), the null hypothesis can be rejected at the 0.01 level of significance.
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6. Restate question as a research hypothesis and a null hypothesis about the populations.
Population 1: The population of people who do not follow the stress-reduction method.
Population 2: The population of people who are trained in the stress-reduction method.
Research hypothesis: The mean score of population 2 is significantly less than the mean score of population 1, indicating that the stress-reduction method is effective in reducing stress levels.
Null hypothesis: There is no significant difference between the mean score of population 1 and population 2, indicating that the stress-reduction method is not effective in reducing stress levels.
7. The mean of the comparison distribution will be equal to the mean of the population of people who follow the stress-reduction method (which is 40), and the standard deviation of the comparison distribution will be equal to the standard deviation of the population of people who follow the stress-reduction method (which is 10 / sqrt(40) = 1.58).
8. The Z score of the sample mean is less than -2.33, we can reject the null hypothesis at p < .01. Since the Z score of the sample mean is -2.52, we can reject the null hypothesis at p < .01.
6. Restate question as a research hypothesis and a null hypothesis about the populations.
Population 1: The population of people who do not follow the stress-reduction method.
Population 2: The population of people who are trained in the stress-reduction method.
Research hypothesis: The mean score of population 2 is significantly less than the mean score of population 1, indicating that the stress-reduction method is effective in reducing stress levels.
Null hypothesis: There is no significant difference between the mean score of population 1 and population 2, indicating that the stress-reduction method is not effective in reducing stress levels.
7. To determine the characteristics of the comparison distribution.
The comparison distribution is the distribution of sample means if we drew all possible samples of the same size from the population of interest.
In this case, we have a sample of 40 people who were trained in the stress-reduction method, so the comparison distribution will be a distribution of sample means of size 40 from the population of people who follow the stress-reduction method.
The mean of the comparison distribution will be equal to the mean of the population of people who follow the stress-reduction method (which is 40), and the standard deviation of the comparison distribution will be equal to the standard deviation of the population of people who follow the stress-reduction method (which is 10 / sqrt(40) = 1.58).
8. To determine the cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01.
To find the cutoff sample score (or Z score), we need to calculate the Z score of the sample mean (36) using the formula:
Z = (X - μ) / (σ / sqrt(n))
Z = (36 - 40) / (10 / sqrt(40))
Z = -2.52
The cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01 is the Z score that corresponds to a probability of .01 in the upper tail of the distribution, which is equal to 2.33.
Therefore, if the Z score of the sample mean is less than -2.33, we can reject the null hypothesis at p < .01. Since the Z score of the sample mean is -2.52, we can reject the null hypothesis at p < .01.
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PLZ HELP I WILL GIVE BRAINLIEST Question 3
What are three different types of solutions you can get when you solve a system of
linear equations?
Answer:
Answer:
one solution
infinite number of solutions
no solutions
Step-by-step explanation:
i hope this helps :)
y=(2.5)^x graph and match function
Answer:
Step-by-step explanation:
Estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints. (Round your answers to four decimal places.)
R4 =
R4 ≈ 1.5535. The given function is f(x) = 5 cos(x).
We have to estimate the area under the graph of f(x) = 5 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints.
(Round your answers to four decimal places.)
Here is the given function graphically and the approximating rectangles: [tex]\text{graph}\left(5\cos\left(x\right),\ \left(0,\ \frac{\pi}{2}\right)\right)[/tex]
Now, let's find the value of ∆x:∆x = [b-a]/n, here n is the number of rectangles.
∆x = [π/2 - 0]/4= π/8
First, we will find the right endpoints of four approximating rectangles: x1 = ∆x+x0 = π/8+0 = π/8x2 = ∆x+x1 = π/8+π/8 = π/4x3 = ∆x+x2 = π/8+π/4 = 3π/8x4 = ∆x+x3 = π/8+3π/8 = π/2
Now, we will find the height of each rectangle: For rectangle 1: f(x1) = 5 cos(π/8) ≈ 4.8729
For rectangle 2: f(x2) = 5 cos(π/4) ≈ 3.5355For rectangle 3: f(x3) = 5 cos(3π/8) ≈ 1.4645
For rectangle 4: f(x4) = 5 cos(π/2) = 0
Therefore, the area under the curve using four approximating rectangles and right endpoints is:R4 = ∆x (f(x1) + f(x2) + f(x3) + f(x4))R4 = π/8(4.8729 + 3.5355 + 1.4645 + 0)≈ 1.5535 (rounded to four decimal places)
Hence, R4 ≈ 1.5535.
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a graph represents the perimeter y in units for an equilateral triangle
If the graph represents the perimeter (y) in units for an equilateral triangle, we can determine the relationship between the perimeter and the side length of the triangle.
In an equilateral triangle, all three sides are equal in length. Let's denote the side length of the equilateral triangle as x.
The perimeter (P) of an equilateral triangle is given by the formula:
P = 3 * x
Therefore, the relationship between the perimeter (y) and the side length (x) of the equilateral triangle is:
y = 3x
So, if the graph represents the perimeter (y) in units for an equilateral triangle, it would be a linear function with a slope of 3 and the side length (x) as the independent variable.
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Question 5 Multiple Choice Worth 5 por 03 01 LC) The social studies teacher wants to know whether the students in the entire school prefera model United Nations random sample from the following groups Al teachers in the school . Al boys in each grado • A students in each grado All students in the social studies club Which group best represents the population he should take a random sample from to get the best for ham O Al teachers in the school O All boys in each grade O All students in each grade O AB students in the social studios club
Answer:
D
Step-by-step explanation:
provide the missing information. the function f : = {(1, 5), (-2, 3), (-4, 2), (2, 5)} (is/is not) a one-to-one function. please respond only with: is or is not answer:
The function f: {(1, 5), (-2, 3), (-4, 2), (2, 5)} is a one-to-one function. It satisfies condition where each input value maps to unique output value, ensuring no repetition or multiple inputs leading to the same output.
A one-to-one function, also known as an injective function, is a type of function where each input value is uniquely mapped to an output value. In the given function f: {(1, 5), (-2, 3), (-4, 2), (2, 5)}, we can observe that each input value corresponds to a distinct output value. For example, the input 1 is mapped to the output 5, and no other input has the same output. Similarly, the inputs -2, -4, and 2 are associated with the outputs 3, 2, and 5 respectively, without any repetition.
This lack of repetition or duplication in the outputs demonstrates that the function is one-to-one. Each input has a unique correspondence with its output, and no two different inputs yield the same output value. Therefore, based on the provided set of mappings, we can conclude that the function f is indeed a one-to-one function.
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how many different four-digit ID tags can be made if repeats are allowed
Answer:
4!Explanation:
4! = 4×3×2×1 = 24
here's an example:
123412431324134214231432213421432314234124132431312431423214324134123421412341324213423143124321What is the percent of change? Round to the nearest whole percent if necessary. State whether the percent of change is an increase or decrease. $99 to $74
Help, I don't want to lose my answer streak.
Answer:
[tex]4\frac{5}{12}[/tex]
Step-by-step explanation:
[tex]4\frac{3}{4} -\frac{1}{3} \\\\\frac{19}{4} -\frac{1}{3} \\\\\frac{57}{12} -\frac{4}{12} \\\\\frac{53}{12} \\\\4\frac{5}{12}[/tex]
Answer:
leon's older brother is 4 5/12 feet tall
Step-by-step explanation:
4 3/4 - 1/3
= 4 5/12
During a blind taste test of 8 different sodas, some people were asked to choose a favorite. Each dot represents one person. If the ratio of people choosing B to people choosing H stays the same, he many people will choose H if the number of people who choose B increases to 20
Answer:
20:5
Step-by-step explanation:
1. What is the ratio for B and H?
Ratio = 4 to 1 or 4:1
2. What is the question asking?
The question is increasing 5 to 20. What is the quotient of 20 and 5? 4! The question is basically multiplying B by 5. Now, since math is a very jealous subject, it needs to be done on the other side too! So you need to multiply the B, which is 1, by 5.
3. 1 x 5?
5
4. Answer
So, since B is 20 and H is 5, the ratio would be 20:5!
Hiii, so I REALLY want to rank up, and I just need 4 more Branliests, so if you liked my answer, can you please give me one? Thank you so much, and thanks for the points!!
Answer:
Step-by-step explanation:
J
Answer this question to get marked as barinliest!!!!
3.14 × 16 = 50.24
C is ur answer
now gimme brainliest
Answer:
B or the second one i did my math
Step-by-step explanation:
The box plots show data about test
scores for two classes.
Test Scores
Class 1
Class 2.
+
t
60
70
90
100
80
Score
Which statement is best supported by the
information in the box plots? (7.1A, 7.18,
7.1E, 716)
Answer:
t = r n − 2 1 − r 2 = 0.45 25 − 2 1 − 0.45 2 = 2.417 The critical value for α = 0.05 for a two-tailed test using the t 24 distribution is 2.064. Your value is greater than this, so you reject the null hypothesis and conclude that the study produced evidence that the variables are significantly correlated
Step-by-step explanation:
Use the provided dropdown menus to construct a translation of the given compound statement into propositional logic notation. Enter a sentence letter, a propositional operator, or a parenthetical mark into each blank space. By convention, parentheses () go inside brackets [], if more than one level of parentheses are needed.
Statement: Today is Thanksgiving Day, but I will eat the turkey if and only if the turkey is free range and it has not been tortured.
Key: E = I will eat the turkey.
F = The turkey is free range.
O = The turkey has been tortured.
T = Today is Thanksgiving Day.
The translation of the compound statement into propositional logic notation is as follows: T ∧ (E ↔ (F ∧ ¬O)).
In propositional logic notation, the compound statement is broken down into individual propositions using sentence letters and logical operators. Here, T represents "Today is Thanksgiving Day," E represents "I will eat the turkey," F represents "The turkey is free range," and O represents "The turkey has been tortured." The compound statement can be translated as T ∧ (E ↔ (F ∧ ¬O)), where ∧ represents the logical AND operator, ↔ represents the logical biconditional operator (if and only if), and ¬ represents the logical NOT operator (negation). This notation captures the conjunction of the conditions and the relationships between them.
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if h(x)=3^x then h (-4) =
Answer:
1/81
Step-by-step explanation:
In h(x)=3^x, replace each instance of x with -4:
h(-4) = 3^(-4), or
1
h(-4) = ----------- = 1/81
3^4
[tex]\huge{\mathbb{\tt { PROBLEM:}}}[/tex]
if h(x)=3^x then h (-4) =
[tex]\huge{\mathbb{\tt { ANSWER:}}}[/tex]
[tex] \frac{1}{81} [/tex]
[tex]\huge{\mathbb{\tt { EXPLANATION:}}}[/tex]
In h(x) = 3^x , you must replace each instance of with -4:
h(-4)=3^(-4)
[tex]h(4)= \frac{1}{3^4} = \frac{1}{81} [/tex]
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→X x K i m 0 2 x XDetermine the value of x in the triangle shown.
Question 3 options:
132°
228°
42°
48°
Answer:
x = 132°
Just add the opposite interior angles
Determine the p-value for the two-tailed t-test with df = 19 (remember, H_1: µ ≠ µo) and sample t = -0.36. At a significance level of α = .01 do you reject or retain the null hypothesis?
The p-value for the two-tailed t-test with degrees of freedom (df) = 19 and a sample t-value of -0.36 is greater than the significance level of α = 0.01. Therefore, we retain the null hypothesis.
In a two-tailed t-test, the null hypothesis (H₀) states that there is no significant difference between the population mean (µ) and a hypothesized mean (µo). The alternative hypothesis (H₁) states that the population mean is not equal to the hypothesized mean.
To determine the p-value, we compare the absolute value of the sample t-value (-0.36 in this case) with the critical t-value for the given degrees of freedom (df = 19). Since the sample t-value falls within the acceptance region, we find the probability of obtaining a t-value as extreme as -0.36 (or more extreme) assuming the null hypothesis is true.
If the p-value is less than the significance level (α = 0.01), we reject the null hypothesis. However, if the p-value is greater than the significance level, we retain the null hypothesis. In this case, since the p-value is greater than 0.01, we do not have sufficient evidence to reject the null hypothesis. Therefore, we retain it.
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Consider the situation where the maximum temperature in degrees Farenheit for the seven successive days in a certain week is the vector random variable, (T1,..., 77), where T₁ ~ N(75,0² = 4), Tj+1=14+0.87, +3Xj, j = 1,...6, where X₁,..., X6 i.i.d. U[-1,1]. A weather derivative pays $100 if there are two or more days with maximum temperatures below 70 degrees. Using Monte Carlo simulation com- pute the fair price of this derivative with n= 105 sample paths. Ignore the time value of money for a week. [Hint: Generate the sample temperature paths using the iterative formula step by step. Create a matrix to store sample temperature paths using command "ma- trix(NA,nrow-n,ncol=7)", then fill in each column (each day) of the sample paths. Think about how to write the code to check the number of days with maximum temperature below 70. The option price is estimated using the sample mean of payoffs.]
To determine the fair price of a weather derivative, use Monte Carlo simulation to generate sample temperature paths, count the number of days below 70 degrees for each path, calculate the payoffs, and estimate the derivative price using the sample mean.
To compute the fair price of the weather derivative using Monte Carlo simulation, you can follow these steps:
Generate n sample paths for the maximum temperature using the given iterative formula and the specified distribution of X₁,...,X₆. Create a matrix to store the sample temperature paths.
For each sample path, count the number of days with a maximum temperature below 70 degrees.
Calculate the payoff for each sample path: If the number of days below 70 degrees is two or more, the payoff is $100; otherwise, the payoff is $0.
Estimate the option price by taking the sample mean of the payoffs.
Here's a summary of the steps to determine the fair price of the derivative:
Generate n sample paths for maximum temperature using the iterative formula and the specified distribution.
Count the number of days below 70 degrees for each sample path.
Calculate the payoff for each sample path: $100 if the count is two or more, $0 otherwise.
Estimate the fair price of the derivative by taking the sample mean of the payoffs.
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Deon wants to replace a glass window in his restaurant. The window is in the shape of a square. Its side lengths are 8 feet. Suppose glass costs $6 for each square foot. How much will the glass cost to replace the window?
Answer:
is 84 dollars
Step-by-step explanation:
Teresa wants to replace a glass window in her restaurant. The window is in the shape of a square. Its side lengths are 6 feet. Suppose glass costs $7 for each square foot. How much will the glass cost to replace the window? Please I really need help ASAP!!!
please answer the question
Answer:
I think it is 25÷8
Step-by-step explanation:
this is because the circumference is found by π multiplied by the diameter. So the inverse would be the circumference divided by the diameter.