use the extended version of markov’s inequality stated above with φ(x) = (x c) 2 , where c is some positive constant, to show that
Answers
Using the extended version of Markov's inequality with the function φ(x) = (x^c)^2, where c is a positive constant, we can show that the probability of a random variable X being greater than or equal to a positive constant k can be bounded by E[X^(2c)]/k^(2c).
The extended version of Markov's inequality states that for a non-negative random variable X and any positive constant k, we have:
P(X ≥ k) ≤ E[X^c]/k^c
In this case, we are using the function φ(x) = (x^c)^2. Substituting this function into the inequality, we get:
P(X ≥ k) ≤ E[(X^c)^2]/k^(2c)
This inequality provides an upper bound on the probability that X is greater than or equal to k, based on the moment E[(X^c)^2]. The moment E[(X^c)^2] is a measure of the "spread" or variability of X raised to the power of c. By dividing this moment by k^(2c), we obtain an upper bound on the tail probability.
Overall, the extended version of Markov's inequality with the function φ(x) = (x^c)^2 allows us to establish an upper bound on the probability of a random variable X being greater than or equal to a positive constant k, based on its moment E[(X^c)^2]. This inequality provides a useful tool for bounding tail probabilities and studying the behavior of random variables.
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Related Questions
2. let x E Z(int)
a) prove that if x is even, then x^2 ? 0 or 4 (mod 8)
b) prove that if x is odd, then x^2 ? 1 (mod 8)
Answers
a) We have shown that if x is even, then \(x^2 = 0\) or 4 (mod 8).
b) We have shown that if x is odd, then \(x^2 = 1\) (mod 8).
a) To prove that if x is even, then\(x^2 = 0\) or 4 (mod 8), we can use the fact that any even integer can be written in the form 2k, where k is an integer. Then, we have:
\(x^2 = (2k)^2 = 4k^2\)
Since k^2 is also an integer, we can write \(4k^2\)as 8m or 8m + 4, where m is an integer. This can be simplified as:
\(4k^2 = 8m or 4k^2 = 8m + 4\\2k^2 = 4m or 2k^2 = 2m + 1\\k^2 = 2m or k^2 = (2m + 1)/2\)
In the first case, \(k^2\) is even and so\(x^2 = 0\) (mod 8). In the second case, \(k^2\)is odd and so \(x^2 = 4\) (mod 8).
b) To prove that if x is odd, then \(x^2 = 1\) (mod 8), we can again use the fact that any odd integer can be written in the form 2k + 1, where k is an integer. Then, we have:
\(x^2 = (2k + 1)^2 = 4k^2 + 4k + 1\)
Since \(k^2\)and k are integers, we can write \(4k^2 + 4k\) as 8m or 8m + 4, where m is an integer. This can be simplified as:
\(4k^2 + 4k = 8m or 4k^2 + 4k = 8m + 4\\2k^2 + 2k = 4m or 2k^2 + 2k = 2m + 1\)
k(k + 1) = 2m or k(k + 1) = (2m + 1)/2
In the first case, either k or k + 1 is even, so k(k + 1) is even and \(x^2 = 0\)(mod 8). In the second case, k and k + 1 are consecutive integers, so one of them must be even and the other odd. Therefore, k(k + 1) is even and x^2 ≡ 4 (mod 8).
Finally, we have:
\(x^2 = 4m + 1 or x^2 = 4m + 5\)
In either case, \(x^2 = 1\) (mod 8), since 4m + 1 and 4m + 5 are both congruent to 1 modulo 8.
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please help me its due soon
Answers
Answer:
it is 17.2 + 16.4
Step-by-step explanation:
because 8.6x2= 17.2
then 5.2x2=10.4
then 3+3=6
lastly 10.4+6= 16.4
so that makes it 17.2+16.4
In the first event, the eighth graders are running a baton relay race with three other classmates. The team’s top speed for each leg is 56.81 seconds, 59.22 seconds, 57.39 seconds, and 60.11 seconds. Use the information to predict the team’s best time for the race. (2 points)
Answers
in this excerpt from a short story published in 1914, a young
man arrives by train to take a position as an assistant
or secretary, to a certain Mrs. Culme. He di covers that
despite the winter weather, no one from her household has
come to meet him at the station
from "The Triumph of Night"
by Edith Wharton
It was clear that the sleigh from Weymore had
not come; and shivering young traveller
from Boston, who had so confidently counted
on jumping into it when he left the train at
Northridge Junction, found himself standing
alone on the open platform, exposed to the
full assault of nightfall and winter.
1 2 3 4 5 6 7
Toward the end of the story, starting on page 5,
Faxon encounters a man in furs. What function
does Faxon's interaction with this character
serve?
It provides character details that indicate Mrs.
Culme may be an unpleasant person.
It provides setting details that suggest that Faxon
is in danger from the cold.
It provides suspense by implying that the youth
may not be what he seems.
It provides exposition by explaining that Mrs. Culme
will send a sleigh soon.
Answers
It provides character details that indicate Mrs. This function Faxon's interaction with this character serve in the given excerpt. Therefore, the correct option is option A.
An excerpt is indeed a quotation from that other resource that the author introduces with fresh language in a sentence. This phrase is taken from Thomas Jefferson's 1801 inaugural speech: As he warned his audience, "I may often go wrong by defect of judgement," Jefferson admitted the fallibility of human nature. "I shall frequently err through lack of judgement" is the excerpt. It provides character details that indicate Mrs. This function Faxon's interaction with this character serve.
Therefore, the correct option is option A.
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In a recent school newspaper survey, 3,000 randomly selected teenagers were asked to cite their primary transportation method to school. Fifteen of 20 teenagers said they use their own car to get to school. A 90% confidence interval to estimate the true proportion of teenagers who drive their own car to school is found to be (0.5907, 0.9093). Which of the following is a correct interpretation of the confidence level?
Ninety percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who drive their own car to school.
Ninety percent of all samples of this size would yield a confidence interval of (0.5907, 0.9093).
There is a 90% chance that the true proportion of teenagers who drive their own car to school will be (0.5907, 0.9093).
Ninety percent of all the samples of size 3,000 lie in the confidence interval (0.5907, 0.9093).
Answers
The correct interpretation of the 90% confidence interval is given as follows:
There is a 90% chance that the true proportion of teenagers who drive their own car to school will be (0.5907, 0.9093).
What is the interpretation of a x% confidence interval?It means that it is x% likely that the true population parameter(mean/proportion/standard deviation) is between a and b, which are the bounds of the confidence interval.
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If YZ is the requested side and XZ is the given side, which ratio amongst sin 35,3° or cos 35,5° will be used to calculate YZ
Answers
The answer of the given question based on the trigonometry is , to calculate YZ, we should use the cosine function with the angle 35.5°.
What is Sine function?The sine function is a mathematical function that relates the ratios of the lengths of two sides of a right triangle with the measure of one of its non-right angles. Specifically, the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse.
To use trigonometry to calculate YZ, we need to find a trigonometric ratio that involves the given side XZ and the angle opposite the requested side, which is angle YXZ. We don't have the measure of this angle, but we know that it is supplementary to the given angle 35.5°, so it must measure:
180° - 35.5° = 144.5°
We can use this angle and the given side XZ to find the length of YZ using the sine or cosine function.
In this case, the length of the opposite side is YZ, the length of the hypotenuse is XZ, and the measure of the angle is 144.5°. So we can write:
sin(144.5°) = YZ / XZ
Solving for YZ, we get:
YZ = XZ * sin(144.5°)
On the other hand, the cosine function , this case, the length of the adjacent side is YZ, the length of the hypotenuse is XZ, and the measure of the angle is 35.5°. So we can write:
cos(35.5°) = YZ / XZ
Solving for YZ, we get:
YZ = XZ * cos(35.5°)
Therefore, to calculate YZ, we should use the cosine function with the angle 35.5°.
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Solve the inequality 2x + 3 > 19
Answers
Answer:
x > 8
Step-by-step explanation:
Given
2x + 3 > 19 ( subtract 3 from both sides )
2x > 16 ( divide both sides by 2 )
x > 8
The solution of the inequality 2x + 3 > 19 is x>8.
The relationship between the two values that are not equal to each other, either they are greater or less than each other, is called as inequality.
A collection of constants, variables connected using one or more arithmetic operator is called an expression
Example = 4y, 3x+4.
The inequality of the expression 2x + 3 > 19 is calculated as:
2x + 3 > 19
Subtract 3 from both the sides,
2x > 19 -3
2x > 16
Divide both side by 2, to get the inequality,
\(x > \dfrac{16}{2}\)
Where, x> 8.
The inequality of the expression 2x + 3 > 19 is x> 8.
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What is the range of y=3sin(x)?
Answers
Answer:
The range is -3≤y≤3 - 3≤y≤3.
Step-by-step explanation:
I hope this helps! :)
in herrnstein's matching equation, the letters and numbers to the left of the equals sign refer to what?
Answers
In Herrnstein's matching equation, the letters and numbers to the left of the equals sign refer to behaviour.
THE MATCHING LAW
Herrnstein's Experiment Herrnstein (1961) conducted an experiment with pigeons in a room with two response buttons, red and white. Each key was assigned its own VI gain schedule. For example, under one condition, the left button pick was boosted on a VI 135 second schedule, and the right button pick was boosted on a VI 270 second schedule.
After the birds have learned as much as possible about this electoral situation, how do they distribute their responses? We trained them for days and then measured their reactions. As is often the case with VI schedules, birds returned many responses for each reinforcer received. Most interesting, however, is that in this condition, where two-thirds of the reinforcers came from the left button, the birds performed about two-thirds of the responses with the left button. That is, the proportion of left button responses equaled or matched the proportion of reinforcers delivered by the left button. In another condition, two birds received only about 15% of reinforcers from the left key and responded about 15% to that key.
Based on these results, Herrnstein proposed the following general principle for individual behavior when presented with alternative sequences. So, what you think makes sense rather than other options available at that particular moment.
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Luke and Liam wash their clothes on a schedule. Luke
washes his clothes every 7 days and Liam washes his
clothes every 9 days. How long will it be before they
both wash their clothes on the same day
Answers
Answer:
2......... ..... ..m.......... ..
ILL GIVE BRAINLY THING
Your class raised funds for an end of the year trip to an amusement park. It costs $150.00 to rent a school bus for the day plus $33.00 per student admission ticket. If your class raised $1000.00, how many students can attend?
Write an equation and solve
Answers
Answer:
25
Step-by-step explanation:
1000≥150+33(s)
1000-150=850
850≥33(s)
850/33=25.(numbers that don't matter because you can't have a decimal of a student)
You can take at most 25 students because you cant have a half a student.
What is an equation that represents a non proportional relationship???
I really need help(I know nothing about proportional and non proportional equations)
Answers
y=mx+b
Please help!! I already missed two!
Answers
Answer:
30,40,50
Step-by-step explanation:
We use the Pythagorean theorem to find out if they would be sides of a right triangle
the Pythagorean theorem states that the two shorter sides squared added together equal the longest side square
for 30, 40 , 50
\(30^2=900\\40^2=1600\\1600+900=2500\\50^2=2500\\2500=2500\)
2500=2500 therefore that is the correct answer
find the volume of this cyilindar
Answers
Answer:
Formula =
\(\pi \: {r}^{2} h\)
But there is no picture !!
Answer:
Formulas for calculating the volume of the cylinder:
1) The volume of the cylinder is equal to the production of the base area to a height. 2) The volume of the cylinder is equal to the pi (3.1415) per square of the base radius to height.
the radius of a circle is increasing at a certain instant the rate of increase in the area of the circle is numericallt equa to twice the rate of increase in its circumference. what is the raduis of teh circle at that instant
Answers
So the radius of the circle at that instant is 1.
Let's call the radius of the circle at that instant "r."
The formula for the area of a circle is A = pi * r^2 and the formula for the circumference of a circle is C = 2 * pi * r.
If the rate of increase in the area of the circle is numerically equal to twice the rate of increase in its circumference, we can set up the following equation:
2 * (2 * pi * r) = (pi * r^2)
Solving this equation for r, we find that the radius of the circle at that instant is r = 1.
So the radius of the circle at that instant is 1.
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find the circumference and the area of the circle with a diameter of 15ft
Answers
Answer:
Circumference is pi times diameter so that would equal 15 pi. The formula to find the area of a circle is A=pi * r^2 So you divide 15 by 2 to find the radius. r=7.5 Then you square it and multiply it by pi and get 56.25pi which is about equal to 176.715
(b) Given the matrix D = k 0 0 3 k² k³ 0 kª k³ kº k k k 0 0 0 k¹⁰ Find all possible value(s) of k if det(D) = 1024."
Answers
To find the possible values of k, we need to calculate the determinant of matrix D and set it equal to 1024.
Given matrix D:
D = | k 0 0 |
| 3 k² k³ |
| 0 kª k³ kº |
| k k k |
| 0 0 0 |
| k¹⁰ |
The determinant of D can be calculated by expanding along the first row or the first column. Let's expand along the first row:
det(D) = k(det | k³ k k |
| 0 k³ kº |
| 0 0 k¹⁰ |)
- 0(det | 3 k² k³ |
| 0 kª k³ |
| k k k |)
+ 0(det | 3 k² k³ |
| k k k |
| k k k |)
Simplifying further, we have:
det(D) = k(det | k³ k k |
| 0 k³ kº |
| 0 0 k¹⁰ |)
Now, we can calculate the determinant of the 3x3 submatrix:
det | k³ k k |
| 0 k³ kº |
| 0 0 k¹⁰ |
This determinant can be found by expanding along the first row or the first column. Expanding along the first row gives us:
det = k(k³(kº) - 0(k)) - 0(0(k¹⁰)) = k⁴kº = k⁴+kº
Now, we can set det(D) equal to 1024 and solve for k:
k⁴+kº = 1024
Since we are looking for all possible values of k, we need to solve this equation for k. However, solving this equation may require numerical methods or approximations, as it is a quartic equation.
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translate and solve: 12 less than m is no less than 132. give your answer in interval notation.
Answers
The problem states that 12 less than a variable, represented by 'm,' is no less than 132. The solution to the inequality is that 'm' is greater than or equal to 144.
To translate the given statement into an inequality, we can express "12 less than m" as "m - 12" and "no less than 132" as "≥ 132". Combining these expressions, we have the inequality: m - 12 ≥ 132. To solve for 'm,' we can add 12 to both sides of the inequality: m - 12 + 12 ≥ 132 + 12, which simplifies to m ≥ 144. Thus, the solution to the inequality is that 'm' is greater than or equal to 144. In interval notation, this can be written as [144, +∞), indicating that 'm' lies between 144 (inclusive) and positive infinity.
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A population of pheasants is declining over time. The number of adults per hectare has decreased from 1,832 in 2012 to 422 in 2016. In which year will the population fall below the minimum viable density, 100 pheasants per hectare?
Answers
The number of pheasants in 2012 was 1832. The number of pheasants in 2016 was 422. The minimum viable density is 100 pheasants per hectare.
So, we need to find out the year in which the population will fall below 100 pheasants per hectare.
First, we need to find out the rate of decline per year which can be calculated as follows: Rate of decline per year = (1832 - 422) / (2016 - 2012)= 1410 / 4= 352.5 per yearNow, let the number of pheasants per hectare be y after t years from 2012.
Then, y = 1832 - 352.5t (as we know the rate of decline per year)We need to find the year in which the population will fall below 100 pheasants per hectare. So, we need to solve the equation:1832 - 352.5t = 100⇒ 352.5t = 1732⇒ t = 1732 / 352.5⇒ t = 4.91 Therefore, the population will fall below the minimum viable density of 100 pheasants per hectare after 4.91 years from 2012, which is around 2017 or 2018.
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With regularly distributed data, what percentage of the data points will fall within one standard deviation from the mean?.
Answers
Answer:
68%
Step-by-step explanation:
The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.
sing horizontal analysis, the increases and decreases are shown as a.amounts and percentages for each line item. b.amounts for the highest three lines. c.amounts only for each line item. d.percentages only for each line item.
Answers
Answer: D. percentages only for each line item.
Horizontal analysis, also known as trend analysis, is a method of financial statement analysis that compares line items over time by expressing them as a percentage of a base year. The base year is typically the most recent year, and the comparison is typically made to the prior year. In horizontal analysis, the increases and decreases are shown as percentages for each line item, so that the changes in the line items can be easily compared and analyzed. This is different from vertical analysis, which shows the line items as a percentage of a total, such as total assets or total revenue.
Step-by-step explanation:
Suppose that there are 400 students taking a biology course. 50 of the students are computer science majors. 213 of the students are biology majors and 44 of the students are double majoring in both computer science and biology. How many of the students taking the biology course are neither of these majors
Answers
225 students taking the biology course are neither computer science nor biology majors.
To find out how many students taking the biology course are neither computer science nor biology majors, we can use the following steps:
Determine the total number of students majoring in computer science, biology, or both.
- Computer science majors: 50 students
- Biology majors: 213 students
- Double majors (both computer science and biology): 44 students
Subtract the double majors from the individual major counts to find the unique number of students in each major.
- Unique computer science majors: 50 - 44 = 6 students
- Unique biology majors: 213 - 44 = 169 students.
Add the unique number of students in each major.
- Total unique majors: 6 (computer science) + 169 (biology) = 175 students
Subtract the total unique majors from the total number of students taking the biology course to find the number of students who are neither of these majors.
- Neither major: 400 (total students) - 175 (unique majors) = 225 students.
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Helpppppppppppppppp!!!!!!!!!!!!!!!!
Answers
CA^2 = 17^2 + 9^2
CA^2 = 289 + 81
CA^2 = 370
To find the value of CA, we need to take the square root of both sides of the equation:
CA = √370
CA is approximately equal to 19.24cm (rounded to two decimal places). Therefore, the length of the unknown side of this right-angled triangle is approximately 19.24cm
Answer:
See below
Step-by-step explanation:
Using the Pythagorean theorem, we can find the length of the unknown side CA.
AC^2 = AB^2 + BC^2
AC^2 = 9^2 + 17^2
AC^2 = 290
AC = √290
Therefore, the length of side CA is approximately 17 cm (rounded to whole).
Jesse has $3.40 in quarters and nickels. The number of nickels is 5 more than 2 times the number of quarters. How many quarters does Jesse have?
Answers
Answer:
9 quarters
Step-by-step explanation:
From the question
Jesse has $3.40 in quarters and nickels
Quarters = q = number of quarters
1 quarter = $0.25
nickels = n = number of nickels
1 nickel = $0.05
Hence,
0.25q + 0.05n = $3.40 .......Equation 1
The number of nickels is 5 more than 2 times the number of quarters.
n = 2q + 5
0.25q + 0.05n = $3.40 .......Equation 1
0.25q + 0.05(2q + 5) = 3.40
0.25q + 0.10q + 0.25= 3.40
0.35q = 3.40 - 0.25
0.35q = 3.15
q = 3.15/0.35
q = 9
Therefore, Jessie has 9 quarters.
Use vertical angles to find the value of x. Use pencil and paper. Is it possible to find the value of x without using vertical angles? Explain your reasoning.
Answers
Answer:
40=(x/6)
40×6=240
x=240?
The value of x is 204 degree.
What is vertical opposite angle?The point where they meet is called a vertex. When two lines intersect, the opposite (X) angles are equal.
As line UM and FQ is intersecting at point x.
Using Vertical opposite angle,
x/6= 40
x=40*6
x=240
Hence, the vertically opposite angle is 240.
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a bank pin is a string of seven digits, each digit 0-9. five of the digits {0, 2, 4, 6, 8} are even and five of the digits {1, 3, 5, 7, 9} are odd. how many pins are there in which exactly four of the digits are even?
Answers
The total number of choices is 5000, and the total number of choices is 2520.
We have 10 digits(0 to 9)
In the first place, second place, and third place we can put 0-9 means a total of 10 numbers.
In fourth place, we can only put 1, 3, 5, 7, and 9 means a total of 5 digits.
So total number of choices = 10×10×10×5 = 5000
When repetition is not allowed
When we put 1 at last place, then a number of choices:
=9×8×7×1 = 505
Similarly for 3, 5, 7, and 9 the number of choices same as placing 1 at last place, then a number of choices:
= 505+505 +505+505+505
= 2520.
Thus, the total number of choices is 5000,.
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2. Assume f(x) = g(x). Which of the following functions may be used to represent the equation 3x+2 = 7x + 6? A. f(x) = x + 2, g(x) = 7x + 6 B. f(x) = 37x+6, g(x) = 7(3x+2) + 6 C. f(x) = 3x+2, g(x) = 7x + 6 D. f(x) = 7*+2, g(x) = 3x + 6
Answers
Answer:
C. f(x) = 3·x + 2, g(x) = 7·x + 6
Step-by-step explanation:
The given equations relates to the property of equality of values;
The given formula for the association between f(x) and g(x) is f(x) = g(x)
The given equation of two expressions is 3·x + 2 = 7·x + 6
By transitive property of equality, the two above equations are correct when f(x) = 3·x + 2 and g(x) = 7·x + 6
Therefore, the function that may be used to represent the equation is option C; f(x) = 3·x + 2, g(x) = 7·x + 6.
Develop the B&B tree for each of the following problems. For convenience, always select x₁ as the branching variable at node 0. Maximize z = 3x₁ + 2.8% subject to 2x + 5.x₂ = 18 4.x₁ + 2x₂ = 18 X₁, X₂0 and integer
Answers
To develop the Branch and Bound (B&B) tree for the given problem, follow these steps:
1. Start with the initial B&B tree, where the root node represents the original problem.
2. Choose \($x_1$\) as the branching variable at node 0. Add two child nodes: one for
\($x_1 \leq \lfloor x_1 \rfloor$ \\(floor of $x_1$) and one for $x_1 \geq \lceil x_1 \rceil$ (ceiling of $x_1$).\)
3. At each node, perform the following steps:
- Solve the relaxed linear programming (LP) problem for the node, ignoring the integer constraints.
- If the LP solution is infeasible or the objective value is lower than the current best solution, prune the node and its subtree.
- If the LP solution is integer, update the current best solution if the objective value is higher.
- If the LP solution is non-integer, choose the fractional variable with the largest absolute difference from its rounded value as the branching variable.
4. Repeat steps 2 and 3 for each unpruned node until all nodes have been processed.
5. The node with the highest objective value among the integer feasible solutions is the optimal solution.
6. Optionally, backtrace through the tree to retrieve the optimal solution variables.
Note: The specific LP problem and its constraints are missing from the given question, so adapt the steps accordingly.
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Given the original statement "If a number is negative, the additive inverse is positive,” which are true? Select three options. If p = a number is negative and q = the additive inverse is positive, the original statement is p → q. If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q. If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is ~q → ~p. If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q. If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q → p.
Answers
Answer:
A. If p = a number is negative and q = the additive inverse is positive, the original statement is p → q.
B. If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.
D. If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.
Step-by-step explanation:
(not 100% sure if these are correct but if they are, then I hope they helped you!)
have a nice day/night!
Answer:
abd
Step-by-step explanation:
Find the equation of the line use exact numbers.
Y=|____|x+|____|
Answers
Answer:
\(y=\frac{3}{4} x-2\)
Step-by-step explanation:
The line has a positive slope, that much is clear. If we just count from the y-intercept up to the next clear point, we can see that it is 3 up and 4 to the right. That gives us a rise over run of 3 over 4, or \(\frac{3}{4}\).
The y-intercept is -2, so that is the latter half of the equation.