The probability of at most one accident in the next 2 hours is 82.15%.
Let X be the number of car accidents in the next 2 hours, and Y be the number of motorcycle accidents in the next 2 hours. Both X and Y follow Poisson distributions, with rates of λX = 0.12 = 0.2 and λY = 0.052 = 0.1, respectively.
To find the probability that there will be at most one accident (either car or motorcycle) in the next 2 hours, we need to find the probability of the events {X + Y = 0} and {X + Y = 1}:
P(X + Y ≤ 1) = P(X + Y = 0) + P(X + Y = 1)
To find these probabilities, we can use the joint Poisson distribution of X and Y:
P(X = i, Y = j) = e^-(λX+λY) * (λXᵃ /a!) * (λYᵇ / b!)
where a and b are non-negative integers.
For X + Y = 0, we have:
P(X + Y = 0) = P(X = 0, Y = 0) = e⁻⁽⁰ ²⁺⁰ ¹⁾ * (0.2⁰ / 0!) * (0.1⁰ / 0!) = e⁻⁰ ³ ≈ 0.7412
For X + Y = 1, we have:
P(X + Y = 1) = P(X = 0, Y = 1) + P(X = 1, Y = 0) = e⁻⁽⁰ ²⁺⁰ ¹⁾ * (0.2⁰/ 0!) * (0.1¹/ 1!) + e⁻⁽⁰ ²⁺⁰ ¹⁾ * (0.2¹/ 1!) * (0.1⁰ / 0!) = 20.20.1*e⁻ ⁰ ³ ≈ 0.0803
Therefore, the probability of there being at most one accident (either car or motorcycle) in the next 2 hours is:
P(X + Y ≤ 1) ≈ 0.7412 + 0.0803 ≈ 0.8215
So the probability of there being at most one accident in the next 2 hours is about 82.15%.
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0.67032
The given data is that car accidents and motorcycle accidents on a stretch of road occur independently and are described by the Poisson distribution at a rate of 0.1 and 0.05 per hour respectively. It is required to find the probability that there will be at most one accident in the next 2 hours.The number of car accidents along the stretch of the road in the next 2 hours is a Poisson distribution with a mean of 0.1 x 2 = 0.2. Similarly, the number of motorcycle accidents in the next 2 hours is a Poisson distribution with a mean of 0.05 x 2 = 0.1.The probability that there will be at most one accident in the next 2 hours is:P(at most one accident in the next 2 hours)=P(no accident in the next 2 hours)+P(one accident in the next 2 hours)= e^(-0.2) (0.2)^0 / 0! + e^(-0.2) (0.2)^1 / 1! + e^(-0.1) (0.1)^0 / 0! + e^(-0.1) (0.1)^1 / 1!= 0.67032Therefore, the probability that there will be at most one accident in the next 2 hours is 0.67032.
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Solve each inequality.
a. 9t-5(t - 5) ≤ 4(t - 3)
Answer:
No solution
Step-by-step explanation:
9t-5(t - 5) ≤ 4(t - 3)
9t - 5t + 25 ≤ 4t - 12
4t + 25 ≤ 4t - 12
0 ≤ -37
This is not true, so there is no solution to this inequality.
A table lamp emits light in the shape of a hyperbola. If the hyperbola is modeled by the equation 9x2 – 16y2 + 576 = 0, which of the following equations represents the boundaries of the light?
After answering the given query, we can state that The light's limits are equation therefore represented by the equations y = (3/4)x and y = -(3/4)x.
What is equation?A mathematical statement known as an equation demonstrates the equality of two expressions when they are joined by the equals symbol ('='). As an illustration, 2x - 5 = 13. 2x-5 and 13 are examples of expressions. The letter '=' joins the two phrases together. An equation is a mathematical formula with two algebraic expressions on either side of the equal symbol (=). It shows how the left and right formulas have an equivalent connection. In any formula, L.H.S. equals R.H.S. (left side = right side).
We must rewrite the provided equation in terms of y in order to ascertain the equation denoting the boundaries of the light.
Starting with the expression provided:
[tex]9x^2 - 16y^2 + 576 = 0\\-16y^2 + 576 = -9x^2\\y^2 - 36 = (9/16)x^2[/tex]
When both edges are squared:
y = ±(3/4)x
The light's limits are therefore represented by the equations y = (3/4)x and y = -(3/4)x.
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1. The table to the left shows the joint probability function for X and Y . a. Explain why this is a legitimate joint probability function for X and Y . X b. Find p(1,2) . c. Find P(X<1,Y≥2) . d Find p x (3)
The joint probability function for X and Y is legitimate because the sum of all probabilities is equal to 1 and the probabilities are non-negative. Each point in the domain has a corresponding probability.b. p(1,2) means the probability of X=1 and Y=2. p_x(3) = 0.1 + 0.05 = 0.15.
a. Probability function is considered legitimate when the sum of all the probabilities is 1, the probabilities are non-negative and each point in the domain must have a corresponding probability. Here, the joint probability function for X and Y is legitimate because the sum of all probabilities is equal to 1 and the probabilities are non-negative. Each point in the domain has a corresponding probability.b. p(1,2) means the probability of X=1 and Y=2. We can see from the table that p(1,2) = 0.04.c. P(X<1, Y≥2) means the probability of X being less than 1 and Y being greater than or equal to 2. We can find the probabilities by adding up all the probabilities in the cells that meet this condition. From the table, we can see that the cells (0,2) and (0,3) meet this condition. Therefore, P(X<1, Y≥2) = 0.01 + 0.01 = 0.02.d. We need to find p_x(3), which means the probability of X=3. We can find this by adding up all the probabilities where X=3. From the table, we can see that the cells (3,1) and (3,2) meet this condition. Therefore, p_x(3) = 0.1 + 0.05 = 0.15.
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thr radius of a circle is 1 meter, What is the length of a 45° arc?
Answer:
0.785
Step-by-step explanation:
formula = (a/360)2r π
if a plam tree grows 2.5 feet a year how many years from now will the plam tree be 30 feet tall
Answer: About 75 years
Step-by-step explanation:
2.5x30=75
After spending 2/3 of high salary on rent and food and 1/4of remaining of transportation. A man has rupees 6000 with him how much he pays on transportation.
Answer:
Step-by-step explanation:
Let's break down the information provided in the problem:
The man spends 2/3 of his high salary on rent and food.
This means that he has 1/3 of his salary remaining.
He then spends 1/4 of this remaining amount on transportation.
He has 6000 rupees left.
To solve for the amount he pays on transportation, we can use the following steps:
Calculate the amount of money he has left after spending 2/3 of his salary on rent and food:
Remaining amount = (1/3) * high salary
Calculate the amount he spends on transportation using the information that he spends 1/4 of the remaining amount:
Transportation cost = (1/4) * remaining amount
Substitute the value of remaining amount from step 1 into step 2:
Transportation cost = (1/4) * [(1/3) * high salary]
We are given that the man has 6000 rupees left, so we can set the equation above equal to 6000 and solve for high salary:
(1/4) * [(1/3) * high salary] = 6000
Simplifying the equation above:
(1/12) * high salary = 6000
Solving for high salary:
high salary = 6000 * 12 = 72000
Finally, substituting high salary from step 6 into step 3 to find transportation cost:
Transportation cost = (1/4) * [(1/3) * 72000] = 6000
Therefore, the man pays 6000 rupees on transportation.
Suppose that 10% of all homeowners in an earthquake-prone area of California are insured against earthquake damage. Four homeowners are selected at random; let x denote the number among the four who have earthquake insurance.
(a) Find the probability distribution of x. (Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with probability (.1)(.9)(.1)(.1) and associated x value of 3. There are 15 other outcomes.)
Value of x Probability
0 1 2 3 4 (b) What is the most likely value of x?
(a) 0
(b) 1
(c) 0 and 1
(d) 3
(e) 4
(C) What is the probability that at least two of the four selected homeowners have earthquake insurance?
P (at least 2 of the 4 have earthquake insurance) =
Answer: (a) The possible outcomes and their probabilities are:
Value of x Probability
0 0.6561 (0 F's and 4 S's)
1 0.2916 (1 F and 3 S's, or 2 F's and 2 S's, or 3 F's and 1 S)
2 0.0486 (2 F's and 2 S's)
3 0.0036 (1 S and 3 F's)
4 0.0001 (4 F's and 0 S's)
(b) The most likely value of x is the one with the highest probability, which is x = 0.
(c) The probability that at least two of the four selected homeowners have earthquake insurance is equal to 1 minus the probability that 0 or 1 of them have earthquake insurance:
P(at least 2 of the 4 have earthquake insurance) = 1 - P(x = 0) - P(x = 1)
= 1 - 0.6561 - 0.2916
= 0.0523
Therefore, the probability that at least two of the four selected homeowners have earthquake insurance is 0.0523.
Enjoy!!!!!
Probability distribution of x is calculated by finding probabilities of each possible outcome, the most likely value of x is 0 with a probability of 0.6561, probability of at least two homeowners having earthquake insurance is 0.0523.
(a) The probability distribution of x can be found by calculating the probabilities of each possible outcome (0, 1, 2, 3, 4 homeowners with insurance) and associating them with their respective x values.
Value of x | Probability
--- | ---
0 | (.9)(.9)(.9)(.9) = 0.6561
1 | (.1)(.9)(.9)(.9) + (.9)(.1)(.9)(.9) + (.9)(.9)(.1)(.9) + (.9)(.9)(.9)(.1) = 0.2916
2 | (.1)(.1)(.9)(.9) + (.1)(.9)(.1)(.9) + (.1)(.9)(.9)(.1) + (.9)(.1)(.1)(.9) + (.9)(.1)(.9)(.1) + (.9)(.9)(.1)(.1) = 0.0486
3 | (.1)(.1)(.1)(.9) + (.1)(.1)(.9)(.1) + (.1)(.9)(.1)(.1) + (.9)(.1)(.1)(.1) = 0.0036
4 | (.1)(.1)(.1)(.1) = 0.0001
(b) The most likely value of x is 0, as it has the highest probability (0.6561).
(c) The probability that at least two of the four selected homeowners have earthquake insurance can be found by adding the probabilities of the outcomes with 2, 3, and 4 homeowners with insurance:
P (at least 2 of the 4 have earthquake insurance) = 0.0486 + 0.0036 + 0.0001 = 0.0523
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The difference quotient of a function is a formula that allows you to calculate the average rate of change on any interval. Each function has its own difference quotient. It is another variation of the slope formula. Average Rate of Change Difference Quotient AROC -f(x)-f(x) . on the interval xxldo-f(x+h)-f(x) x -X When finding the difference quotient (DQ) you should not assign numerical values to x and h. Only when you are asked to calculate the average rate of change should you plug in values for x and h, where x is the first endpoint of the interval and h is the length of the interval. * 4. a) Find the difference quotient for f(x)=x. Simplify as much as possible. xeh analyzemath.com b) Use the difference quotient from part a) to calculate the average rate of change of f(x) = x on the interval (1, 3).
The difference quotient for f(x)=x is (x+h-x)/h, which simplifies to 1/h. The average rate of change of f(x)=x on the interval (1,3) is 1/2, since h=2.
The difference quotient for f(x)=x can be found by taking the difference between f(x+h) and f(x) and then dividing by h. In this case, f(x+h) = x + h and f(x) = x, so the difference quotient is (x+h-x)/h, which simplifies to 1/h. To calculate the average rate of change of f(x)=x on the interval (1,3), we need to plug in the values of h and x. Here, x is the first endpoint of the interval, which is 1, and h is the length of the interval, which is 2. Thus, the average rate of change is 1/2.
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Please help step by step
Answer:
MARK BRIANLIST!!
The Public Utility Commission in a southern state is interested in describing the relationship between household monthly utility bills and the size of the house. A recent study of 30 randomly selected household resulted in thefollowing regression results:
Use the above output for answering the following questions:
Part a) (8 marks)
Interpret the slope of the regression line.
Write down the estimated linear regression line.
What is the value of coefficient of determination? Interpret this value
What is the value of the coefficient of correlation? Interpret this value.
Part b) (7 marks)
Based on the information provided, indicate what, if any, conclusions can be reached about the relationship between utility bill and the size of the house in square feet.
The slope of the regression line in this case is -0.0346. This means that as the size of the house increases by 1 square foot, the monthly utility bill decreases by $0.0346.
The estimated linear regression line can be written as: y = a + bx where y is the dependent variable (i.e. the monthly utility bill), x is the independent variable (i.e. the size of the house), a is the intercept, and b is the slope.Using the values from the regression output, we have:y = 142.5 - 0.0346x
R² = 0.6296 This means that about 62.96% of the variation in the monthly utility bill can be explained by the size of the house.
r = -0.7935 This means that there is a strong negative correlation between the size of the house and the monthly utility bill.
we can conclude that there is a statistically significant negative relationship between the size of the house and the monthly utility bill. This means that as the size of the house increases, the monthly utility bill tends to decrease.
The slope of the regression line gives us the rate of change of the dependent variable y (i.e. the monthly utility bill) with respect to a unit change in the independent variable x (i.e. the size of the house).The slope of the regression line in this case is -0.0346. This means that as the size of the house increases by 1 square foot, the monthly utility bill decreases by $0.0346.
The estimated linear regression line can be written as: y = a + bx where y is the dependent variable (i.e. the monthly utility bill), x is the independent variable (i.e. the size of the house), a is the intercept, and b is the slope.Using the values from the regression output, we have:y = 142.5 - 0.0346x
The coefficient of determination (R²) is a measure of the proportion of variation in the dependent variable that is explained by the independent variable. It is calculated as the` of the explained variation to the total variation.R² = 0.6296 This means that about 62.96% of the variation in the monthly utility bill can be explained by the size of the house.
The coefficient of correlation (r) is a measure of the strength and direction of the linear relationship between the two variables. It can take values between -1 and +1, with -1 indicating a perfect negative correlation, +1 indicating a perfect positive correlation, and 0 indicating no correlation.r = -0.7935 This means that there is a strong negative correlation between the size of the house and the monthly utility bill. This indicates that as the size of the house increases, the monthly utility bill decreases.
Based on the information provided, we can conclude that there is a statistically significant negative relationship between the size of the house and the monthly utility bill. This means that as the size of the house increases, the monthly utility bill tends to decrease. However, we should keep in mind that correlation does not imply causation, and there may be other factors that affect the monthly utility bill besides the size of the house.
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between which two benchmark fractions is 5/8?how do you know?
We can conclude that 5/8 is between the benchmark fractions 1/2 and 3/4.
What is fraction?A fraction represents a part of a whole or a ratio between two quantities. It consists of a numerator (the top number) and a denominator (the bottom number), separated by a horizontal line. The numerator represents the part or quantity being considered, while the denominator represents the whole or total quantity.
According to question:To determine between which two benchmark fractions 5/8 lies, we can compare it to the nearest benchmark fractions, which are 1/2 and 3/4.
We know that 1/2 is less than 5/8 because half of a whole is less than five-eighths of a whole.We also know that 3/4 is greater than 5/8 because three-fourths of a whole is greater than five-eighths of a whole.Therefore, we can conclude that 5/8 is between the benchmark fractions 1/2 and 3/4.To summarize, 1/2 < 5/8 < 3/4.
For example, the fraction 3/4 represents three parts out of a total of four parts, or a ratio of three to four. This can also be expressed as a decimal (0.75) or a percentage (75%).
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Which describes a possible independent variable for the given dependent variable?
Your monthly cell phone bill
1. Who you call most often each month
2. The amount of data you use each month
3. The color of your phone
4. The amount of money you spend for lunch each month
Answer:
1
explanation in head
A prism has a height of 6.1 meters. If the side of the base is 4.6 m and the apothem is 3.17 meters. Find the volume of the prism
The volume of the prism is 222. 4 m³
How to determine the volume of the prismThe formula for calculating the volume of a pentagonal prism is expressed as;
V = [1/2 x 5 x b x a] x h of the prism
Given that the parameters are;
V is the volume of the prismb is the base side of the prisma is the apothem of the prismh is the height of the prismNow, substitute the values, we get;
Volume , = ( 1/2 × 5 × 4.6 × 3.17) × 6.1
Multiply the values
Volume , V = (72.91/2) × 6.1
divide the values in the bracket
Volume = 36. 46 × 6.1
Multiply the values
Volume = 222. 4 m³
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E- Education is A new start-up that develops and markets MBA courses offered over the internet
The startup E-Education can go according to option 2 and option 3. Both the options are giving returns of $1500000 for 2 years.
There are three options available with E-Education to fulfill the company's need for additional space.
The decision tree for the available options is made below;
Option1 Option2 Option3
$ $ $
Cost of Moving to New Building 1000000 2000000
Leasing cost 1000000 1300000 1500000
Total Cost of the Option 2000000 1500000 1500000
Conclusion: The startup E-Education can go according to option 2 and option 3. Both the options are giving returns of $1500000 for 2 years.
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Match each expression on the left with an equivalent expression on the right.
3⁄5 – 13⁄53x + 02x – 65⁄3 – x + 1⁄32x – 3−6.9 + 4.93x–6 + 2x–3⁄2x + 2 + 1⁄2xx – 3 + x
Answer:
3/5 - 13/5 => -6.9 + 4.9
2x - 3 => x - 3 + x
5/3 - x + 1/3 => -3/2x + 2 + 1/2x
2x - 6 => -6 + 2x
3x + 0 => 3x
Step-by-step explanation:
Hope it helps :)
PLEASE SOMEBODY HELP ME
Answer:
1. rhombus and square
2. rhombus, rectangle, square
3. rectangle and square
4. rectangle, squares, rhombus
5. same as 3
6. rhombus, rectangle, square
7. rhomus, rectangle, square
8. rectangle, square
Step-by-step explanation:
Harry, Jason and Sarah are taking the GMAT exam which is required by most applicants for admission to graduate schools of business. The three friends want to get admissions to three different business schools. Harry can get the admission if he gets a score above 650 in GMAT, Jason can get the admission if he gets above 630 and Sarah can get the admission if she gets above 670 . Scores on the GMAT are roughly normally distributed with a mean of 550 and a standard deviation of 115 . What is the probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one
The probability that Harry, Jason, and Sarah will all be accepted into their desired schools is;P(Harry, Jason, Sarah) = P(Harry) * P(Jason) * P(Sarah) = 0.1949 * 0.2413 * 0.1492 = 0.007 Possible answer: 0.007 (or 0.7%)
The solution to the question is given below; The mean score of the GMAT exam is μ = 550 and the standard deviation is σ = 115.There are three friends - Harry, Jason, and Sarah - who want to be admitted to business schools. Harry requires a score of 650 or above, while Jason requires a score of 630 or higher and Sarah requires a score of 670 or above. Because the admission procedure is independent for each of the friends, the joint probability can be calculated using the multiplication rule.
The probabilities that Harry, Jason, and Sarah will achieve the desired scores are calculated separately using the z-score equation, which is as follows;For Harry:Z = (650 - 550) / 115 = 0.87 Probability of Harry getting admitted = P(z > 0.87) = 0.1949 (using z-table)For Jason:Z = (630 - 550) / 115 = 0.7 Probability of Jason getting admitted = P(z > 0.7) = 0.2413 (using z-table)For Sarah:Z = (670 - 550) / 115 = 1.04 Probability of Sarah getting admitted = P(z > 1.04) = 0.1492 (using z-table)The probability that Harry, Jason, and Sarah will all be accepted into their desired schools is;P(Harry, Jason, Sarah) = P(Harry) * P(Jason) * P(Sarah) = 0.1949 * 0.2413 * 0.1492 = 0.007 Possible answer: 0.007 (or 0.7%)
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Fill in the blanks below in order to justify
whether or not the mapping shown
represents a function.
The mapping above represents a function since each element in Set A maps to exactly one element in Set B where there is no repetition or ambiguity in the mapping where there are no two distinct elements in Set A that map to the same element in Set B.
Describe Sets?Sets can be used to represent a wide range of mathematical and real-world concepts, such as the set of prime numbers, the set of colors in a rainbow, or the set of people who have visited a particular city.
Sets are usually described using set-builder notation, which uses a rule to define the set. For example, the set of even numbers can be described as {x | x is an integer and x is even}, where the vertical bar | means "such that" and the condition "x is an integer and x is even" specifies the elements of the set.
The mapping above represents a function since each element in Set A maps to exactly one element in Set B, where there is no repetition or ambiguity in the mapping.
To fill in the blanks:
The mapping above represents a function since each element in Set A maps to exactly one element in Set B where there is no repetition or ambiguity in the mapping where there are no two distinct elements in Set A that map to the same element in Set B.
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A rocket is launched from the top of a 40 foot cliff with an initial velocity of 150 feet per second. The height, h, of the
ocket after t seconds is given by the equation h= -16t² + 150t+ 40. How long after the rocket is launched will it be 10
feet from the ground?
42
Step-by-step explanation:
42-7=69z3
Answer: To find out how long after the rocket is launched will it be 10 feet from the ground, we need to solve for t in the equation:
h = -16t^2 + 150t + 40
We know that when the rocket is 10 feet from the ground, h = 10:
10 = -16t^2 + 150t + 40
Subtracting 10 from both sides:
0 = -16t^2 + 150t + 30
Dividing both sides by -2:
0 = 8t^2 - 75t - 15
Using the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 8, b = -75, and c = -15.
Plugging in these values:
t = (-(-75) ± sqrt((-75)^2 - 4(8)(-15))) / 2(8)
Simplifying:
t = (75 ± sqrt(5715)) / 16
Therefore, the rocket will be 10 feet from the ground approximately 0.26 seconds and 8.05 seconds after it is launched.
Your welcome (:
Step-by-step explanation:
would appreciate any help on this
The correct graph of f(x) include the following: D. Graph D.
Domain format: (-∞, -2) U (2, ∞).
Range format: (1, ∞).
What is a piecewise-defined function?In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.
Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. On the other hand (conversely), the range of any piecewise-defined function simply refers to the union of all of the ranges of each sub-function over its entire sub-domain.
By critically observing the graph of the piecewise-defined function g shown in the image attached below, we can logically deduce that the range and domain are as follows;
Range = (1, ∞).
Domain = (-∞, -2) U (2, ∞).
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Work out
25% of 401. 16m
Give your answer rounded to 2 DP
The 25 percent of 401.16m is equal to 100.29m, rounded to 2 decimal places as 100.30m.
To calculate 25% of 401.16m, we can use the formula:
percentage × value = result
where the percentage is 25%, the value is 401.16m, and the result is what we want to find.
So, we can write:
25% × 401.16m = (25/100) × 401.16m = 0.25 × 401.16m = 100.29m
Therefore, 25% of 401.16m is equal to 100.29m.
To round this to 2 decimal places, we need to look at the third decimal place, which is 9. Since 9 is greater than or equal to 5, we round up the second decimal place, which is 0. Therefore, the final answer rounded to 2 decimal places is:
100.29m rounded to 2 decimal places is 100.30m.
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Anybody know how to do the following?.. Which Similarity statement can you write relating the three triangles in the diagram below?
Answer:
I believe the answer is D
Step-by-step explanation:
if you want an explanation let me know and have a great day and I'm 100% sure that D is the right answer
An article reports that the amount of a certain antifungal ointment that is absorbed into the skin can be modelled with a lognormal distribution. Assume that the amount (in ng/cm2) of active ingredient in the skin two hours after application is lognormally distributed with μ = 2.6 and σ = 2.1. 1) Find the 80th percentile of the amount absorbed. Round the answer to one decimal place. 2) Find the standard deviation of the amount absorbed. Round the answer to one decimal place.
The standard deviation of the amount absorbed is 1819.9 ng/cm² rounded to one decimal place.
1. 80th percentile of the amount absorbed
Given that the amount (in ng/cm²) of active ingredient in the skin two hours after application is lognormally distributed with μ = 2.6 and σ = 2.1. The 80th percentile of the amount absorbed is to be found. Let X be the random variable representing the amount of active ingredient absorbed. We know that X follows a log-normal distribution with parameters μ = 2.6 and σ = 2.1. We are to find the value x such that P(X ≤ x) = 0.8We know that for a log-normal distribution X ~ log N (μ, σ). Then we can obtain the corresponding normal distribution with mean and variance of ln(X) as follows:µ1 = ln(X) = µ, σ1^2 = ln(1 + (σ^2/µ^2)) = σ^2From the normal distribution, we can use the standard normal tables to determine the required probability. Thus Z = (ln(x) - µ)/σ and P(X ≤ x) = P(Z ≤ (ln(x) - µ)/σ) = 0.8We can use the standard normal tables to determine the z-score for P(Z ≤ z) = 0.8, which is 0.84. Then we can find ln(x) using:0.84 = (ln(x) - 2.6)/2.1 or ln(x) = 2.6 + (0.84)(2.1) = 4.374x = e^4.374 = 79.1 ng/cm²Therefore, the 80th percentile of the amount absorbed is 79.1 ng/cm² rounded to one decimal place.2. Standard deviation of the amount absorbedThe standard deviation of a lognormal distribution is given by σx = [(e^(σ^2) - 1)(e^(2μ + σ^2))]^(1/2)From the given data, we have μ = 2.6 and σ = 2.1. Therefore,σx = [(e^(2.1^2) - 1)(e^(2(2.6) + 2.1^2))]^(1/2) = 1819.9 ng/cm² rounded to one decimal place. Therefore, the standard deviation of the amount absorbed is 1819.9 ng/cm² rounded to one decimal place.
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Rates and Ratios 1. A motorist covers a distance of 360 km in .exactly 4 hour Appropriately how far did the motorist drive in one hour
The motorist drove covered a distance of 90 kilometers in one hour.
How far did the motorist drive in one hour?Speed is simply referred to as distance traveled per unit time.
Mathematically, it is expressed as;
Speed = Distance ÷ time.
To determine how far the motorist drove in one hour, we need to divide the total distance covered by the total time taken:
distance in one hour = total distance / total time
Given that;
distance covered = 360 kmtime taken = 4 hoursSubstituting the given values, we get:
distance in one hour = 360 km / 4 hours
distance in one hour = 90 km/hour
Therefore, the motorist drove at a speed of 90 kilometers per hour.
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i need help[ i dont understand this
a) The theoretical probability of a fair coin landing on heads is 1/2
b) The experimental probability of landing on heads is 40%. Note that the experimental probability is lower than the theoretical probability.
What is the explanation for the above?Part A: The theoretical probability of a fair coin landing on heads is 1/2 or 0.5. Thus, it is possible for either of the teams to get the ball first.
Part B: The frequency of each outcome after flipping the coin 10 times may vary, but for example:
Heads: 4
Tails: 6
The experimental probability of landing on heads can be calculated by dividing the frequency of heads by the total number of flips: 4/10 = 0.4 or 40%.
Comparing the experimental probability of 0.4 to the theoretical probability of 0.5, we can see that the experimental probability is lower than the theoretical probability.
This difference may be due to random chance or factors such as the way the coin is flipped, the surface it lands on, or the wind. As more flips are made, the experimental probability should approach the theoretical probability.
Note that Theoretical probability is the likelihood of an event occurring based on reasoning or calculation, without actually performing the event.
Experimental probability is the probability of an event occurring based on actual repeated trials or experiments. It is determined by dividing the frequency of the event by the total number of trials.
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[tex]2^{3x} =11[/tex]. Find the value of x.
Answer:
[tex] \frac{ log_{2}(11) }{3} [/tex]
Step-by-step explanation:
[tex]3x = log_{2}(11) [/tex][tex]
x = \frac{ log_{2}(11) }{3} [/tex]
DIG DEEPER! You use a crowdfunding website to raise money. The website keeps 5% of each donation. Five of your friends each donate the same amount. The total funding you receive is $47.50. How much does each friend donate?
Question 11 Find the average rate of change of g(x)=5x^(3)+(9)/(x^(2)) on the interval -1,1. Question Help: Video Submit Question
The average rate of change of g(x) on the interval [-1, 1] is 5.
The average rate of change of a function over a given interval is the difference between the values of the function at the endpoints of the interval, divided by the length of the interval. Here, we have to Find the average rate of change of g(x) = 5x³ + 9/x² on the interval [-1, 1].Now we'll apply the formula: (g(1) - g(-1)) / (1 - (-1)) (g(1) - g(-1)) / 2 We have g(x) = 5x³ + 9/x². Hence g(1) = 5(1)³ + 9/(1)² = 5 + 9 = 14 g(-1) = 5(-1)³ + 9/(-1)² = -5 + 9 = 4 Therefore, the average rate of change of g(x) on the interval [-1, 1] is: (14 - 4) / 2 = 10 / 2 = 5 Therefore, the average rate of change of g(x) on the interval [-1, 1] is 5.
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The distribution of all registered nurses' salaries on the Treasure Coast is known to be normally distributed
with a mean of $50, 650 and a standard deviation of $1,000. Use this information to determine the
following two probabilities. Round solutions to four decimal places, if necessary.
The probability that a single randomly selected nurse's salary is greater than $50,516 is 0.5533 and the probability that a random sample of 95 nurses have a salary greater than $50,516 is 0.9098.
What is the probability that a single randomly selected nurse's salary is greater than $50,516a. To find the probability that a single randomly selected nurse's salary is greater than $50,516, we need to standardize the value using the mean and standard deviation of the distribution, and then use a standard normal table or calculator to find the probability.
The standardized value (z-score) is:
z = (x - μ) / σ = (50,516 - 50,650) / 1,000 = -0.134
Using a standard normal table or calculator, we can find the probability that a randomly selected nurse's salary is greater than $50,516:
P(x > 50,516) = P(z > -0.134) = 0.5517
Therefore, the probability that a single randomly selected nurse's salary is greater than $50,516 is 0.5533.
b. To find the probability that a random sample of 95 nurses have a salary greater than $50,516, we need to use the central limit theorem, which states that the distribution of the sample means approaches a normal distribution with mean μ and standard deviation σ/√n, where n is the sample size.
The mean of the sample means is still μ = 50,650, but the standard deviation of the sample means is now:
σ/√n = 1,000 / √95 = 102.06
We want to find the probability that the sample mean is greater than $50,516:
P(x > 50,516) = P(z > (50,516 - 50,650) / (1,000 / √95)) = P(z > -1.335)
Using a standard normal table or calculator, we can find the probability:
P(x > 50,516) = P(z > -1.335) = 0.9098
Therefore, the probability that a random sample of 95 nurses have a salary greater than $50,516 is 0.9098.
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A survey found that 10% of people believe that they have seen a UFO. Choose a sample of 15 people at random. Find the probability of the following. Round intermediate calculations and final answers to at least three decimal places.
(a) At least 3 people believe that they have seen a UFO.
(b) 3 or 4 people believe that they have seen a UFO.
(c) Exactly 4 people believe that they have seen a UFO
(a) Prοbability οf at least 3 peοple believe that they have seen a UFO 0.857.
(b) Prοbability οf 3 οr 4 peοple believe that they have seen a UFO 0.181.
(c) Prοbability οf Exactly 4 peοple believe that they have seen a UFO 0.00049 (rοunded tο 3 decimal places).
What is prοbability?Prοbability is a branch οf mathematics that deals with the study οf randοmness and uncertainty in events. It is the measure οf the likelihοοd οr chance that an event will οccur. Prοbability is expressed as a number between 0 and 1, where 0 indicates that the event will nοt οccur and 1 indicates that the event will οccur with certainty.
This is a binοmial prοbability prοblem, where the prοbability οf success (p) is 0.1 and the sample size (n) is 15.
(a) At least 3 peοple believe that they have seen a UFO:
Using the cοmplement rule, the prοbability οf having less than 3 peοple whο believe they have seen a UFO is:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = (0.9)¹⁵ + 15(0.1)(0.9)¹⁴ + (105)(0.1)²(0.9)¹³
where X is the number οf peοple whο believe they have seen a UFO in the sample. Therefοre, the prοbability οf having at least 3 peοple whο believe they have seen a UFO is:
P(X ≥ 3) = 1 - P(X < 3) = 1 - [(0.9)¹⁵ + 15(0.1)(0.9)¹⁴ + (105)(0.1)²(0.9)¹³] = 0.170
Sο the prοbability οf at least 3 peοple believing they have seen a UFO is 0.170.
(b) 3 οr 4 peοple believe that they have seen a UFO:
Using the binοmial prοbability fοrmula, we can calculate the prοbabilities fοr 3 and 4 peοple believing they have seen a UFO and then add them tοgether:
P(X = 3) = (15 chοοse 3)(0.1)³(0.9)¹² = 0.185
P(X = 4) = (15 chοοse 4)(0.1)⁴f(0.9)¹¹ = 0.099
Therefοre, the prοbability οf having 3 οr 4 peοple whο believe they have seen a UFO is:
P(3 οr 4) = P(X = 3) + P(X = 4) = 0.185 + 0.099 = 0.284
Sο the prοbability οf 3 οr 4 peοple believing they have seen a UFO is 0.284.
(c) Exactly 4 peοple believe that they have seen a UFO:
Using the binοmial prοbability fοrmula, we can calculate the prοbability fοr 4 peοple believing they have seen a UFO:
P(X = 4) = (15 chοοse 4)(0.1)⁴ (0.9)¹¹ = 0.099
Sο the prοbability οf exactly 4 peοple believing they have seen a UFO is 0.099.
Hence,
(a) P(X ≥ 3) = 0.857
(b) P(3 ≤ X ≤ 4) = 0.181
(c) P(X = 4) = 0.00049 (rοunded tο 3 decimal places)
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