The relation O is not reflexive, symmetric, and not transitive is one of the following statements that is true about the relation O. which is option (C).
Given, [tex]\forall m, n \in Z, m O n \longleftrightarrow \exists k \in Z \mid(m-n)=2 k+1[/tex]
Let's verify for the following relations :
Reflexive relation:
[tex]\forall a\in Z, a O a \longrightarrow \exists k\in Z \mid (a-a)= 2k+1[/tex]
[tex]0\neq 2k+1[/tex] for all k [tex]\in[/tex] Z
Since 2k+1 can never be zero for any k [tex]\in[/tex] Z, hence we conclude that the relation O is not reflexive.
Symmetric relation:
Suppose a, b [tex]\in[/tex] Zsuch that a O b i.e. (a-b)=2k+1, where k[tex]\in[/tex] Z.
Now, we need to check whether b O a is true or not i.e. (b-a)=2j+1 for some j[tex]\in[/tex] Z
We have,
[tex](a-b) = 2k+1 \longrightarrow (b-a) = -2k-1 = 2(-k) - 1[/tex]
Let j=-k-1, then we have j[tex]\in[/tex] Z and 2j+1 = -2k-1
Hence, (b-a) = 2j+1, and we conclude that the relation O is symmetric.
Transitive relation:
Suppose a, b, c[tex]\in[/tex] Z such that a O b and b O c.
Now, we need to check whether a O c is true or not.
We have,
(a-b)=2k_1+1 and (b-c)=2k_2+1 for some k_1,k_2[tex]\in[/tex] Z
(a-b)+(b-c) = 2k_1+1 + 2k_2+1
a-c = 2k_1+2k_2+2
Let j=k_1+k_2+1, then we have j[tex]\in[/tex] Z and a-c=2j
Hence, (a-c) is even and we conclude that the relation O is not transitive.
Therefore, the relation O is not reflexive, symmetric, and not transitive. Hence, option (C) is the correct answer.
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Find an example of a 2×3 matrix A and a 3×2 matrix B such that, letting T(x)=Ax and U(x)=Bx, the composition T∘U is a reflection over the line y=x.
The example of 2×3 matrix A and a 3×2 matrix B such that, letting T(x)=Ax and U(x)=Bx is reflection Ab.
Matrices, the plural form of matrix, are the groupings of numbers, variables, symbols, or phrases in a rectangular table with varying rows and columns. These are rectangular arrays with specified operations such as addition, multiplication, and transposition. The elements of the matrix are the numbers or entries in it. The horizontal entries of matrices are referred to as rows, whereas the vertical elements are referred to as columns.
Let,
[tex]B = \left[\begin{array}{cc}0&1\\1&0&0&0\end{array}\right] , A = \left[\begin{array}{ccc}1&0&0\\0&1&0\\\end{array}\right][/tex]
Then,
[tex]AB =\left[\begin{array}{ccc}1&0&0\\0&1&0\\\end{array}\right] \left[\begin{array}{cc}0&1&1&0&0&0\\\end{array}\right] \\\\AB = \left[\begin{array}{cc}0&1&1&0\\\end{array}\right][/tex]
Therefore, Ab is reflection about y = x .
As U = Bx and T∘U
A matrix is a rectangular array of integers, variables, symbols, or expressions that are defined for subtraction, addition, and multiplication operations. The number of rows and columns in a matrix determines its size (also known as the order of the matrix).
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D. A population of rabbits is doubling every 3 months. If there were 2 rabbits to begin
with, how many will there be after 5 years?
There will be a population of 2,097,152 rabbits after 5 years.
What is exponential growth?A form of growth known as exponential growth occurs when a quantity's rate of expansion is proportionate to its present value. In other words, a quantity expands more quickly the greater it is. A prime example of exponential expansion is the rabbit population, which doubles in size every three months.
Given that, population of rabbits is doubling every 3 months.
That is,
5 years = 5 x 12 = 60 months
Number of doublings = 60 / 3 = 20
For every doubling, the population will be twice as large.
Thus,
P = 2 x 2²⁰ = 2 x 1,048,576 = 2,097,152 rabbits
Therefore, there will be approximately 2,097,152 rabbits after 5 years.
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Show that the lines with parametric equations given below are parallel, perpendicular, skew lines or neither. Line 1:x=t−3,y=3t+8,z=5−2tLine2:x=2s−1,y=s−1,z=s−4Refer: Relationship between lines parallel perpendicular skew neither
To check whether the given lines are parallel, perpendicular, skew or neither, we will find their direction vectors. If the direction vectors are parallel, then the lines are parallel. If the direction vectors are perpendicular, then the lines are perpendicular. If the direction vectors are neither parallel nor perpendicular, then the lines are skew. If the direction vectors of one line is parallel to the vector joining two points of the other line, then the lines are neither parallel nor perpendicular.
Line 1:x=t−3, y=3t+8, z=5−2tThis line can be written as(r_1): r= a_1+ t u_1where r_1 is the position vector of any point on the line. a_1 = i(-3) + j(8) + k(5) = -3i + 8j + 5k is the point of intersection of the line with the coordinate axis. And u_1 is the direction vector of the line.u_1 = i + 3j - 2k
Line 2: x=2s−1, y=s−1, z=s−4This line can be written as(r_2): r= a_2+ s u_2where r_2 is the position vector of any point on the line. a_2 = i(-1) + j(-1) + k(-4) = -i - j - 4k is the point of intersection of the line with the coordinate axis. And u_2 is the direction vector of the line.u_2 = 2i + j + k Now we will find the direction vectors of the two lines and then check their properties. The direction vectors of the lines areu_1 = i + 3j - 2ku_2 = 2i + j + kSince the direction vectors are not parallel, we need to check whether they are perpendicular or not.u_1.u_2 = (i + 3j - 2k).(2i + j + k) = 2 + 3 - 2 = 3Since u_1.u_2 is not equal to zero, the two lines are neither parallel nor perpendicular to each other. Therefore, the lines are skew lines.
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I need some help with this
Answer:
148.5 π
Step-by-step explanation:
Cone = 1/3 * base * height
1/3 * 22 * (9/2)^2 π = 148.5 π
Please some one help me solve this question.
George needs to take the route as follows .
6km on a bearing of 080° from A to B
5km on a bearing of 160°. From B to C
The scale is 1.5cm= 1km
However, George uses an incorrect scale of 1cm= 1km and ends up at D. What bearing and distance does he need to take to end up at the correct destination of C.
Multiple-choice questions each have five possible answers(a,b,c,d,e),one of which is correct. Assume that you guess the answers to 3 such problem:a. Use the multiplication rule to find the probability that the first 2 guesses are wrong and the 3rd is correct.b. Beginning with 2wrong and 1 correct,(WWC), make a complete list of all possibilities of 2 wrong and 1 correct, then find the probability for each.c. Based on the preceding results, what is the probability of getting exactly one correct answer when 3 guesses are made?
a. The probability of guessing a wrong answer is 4/5
Since there are three guesses, the probability of the first 2 guesses being wrong and the 3rd being correct can be calculated using the multiplication rule as follows: P(2 wrong and 1 correct) = (4/5)^2 * 1/5 = 0.128.
b. The complete list of possibilities for 2 wrong and 1 correct is: WWC, WCW, CWW.
The probability of each can be calculated using the multiplication rule as follows: P(WWC) = (4/5)^2 * 1/5 = 0.128, P(WCW) = (4/5) * (1/5) * (4/5) = 0.128, and P(CWW) = 1/5 * (4/5)^2 = 0.128.
c. The probability of getting exactly one correct answer when 3 guesses are made is the sum of the probabilities of the three possible outcomes of 2 wrong and 1 correct, which is 0.128 + 0.128 + 0.128 = 0.384.
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You have $3,200 to invest in stocks. You purchase shares for $11.95/sh. You decide to sell the stock at $11.87/sh?
How much did you net with this transaction?
A $21.36
B $30.71
C $11.87
D $0.08
Therefore, the net result of the transaction is a loss of $21.36. The answer is A) $21.36.
What is selling price?Selling price refers to the price at which a product or service is sold to customers or clients. It is the amount of money that a buyer pays to the seller in exchange for the product or service. The selling price is usually higher than the cost of producing or acquiring the product or service, and the difference between the selling price and the cost is the profit earned by the seller. In some cases, the selling price may also include additional charges such as taxes, shipping fees, or handling fees.
by the question.
To calculate the net result of the transaction, we need to determine how many shares were purchased with the $3,200 investment.
$3,200 divided by $11.95/sh = approximately 267.36 shares (rounded to the nearest hundredth)
Therefore, the total cost of purchasing 267 shares at $11.95/sh is:
267 shares x $11.95/sh = $3,195.65
The total revenue from selling 267 shares at $11.87/sh is:
267 shares x $11.87/sh = $3,174.29
To determine the net result of the transaction, we subtract the total revenue from the total cost:
$3,174.29 - $3,195.65 = -$21.36
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the length of a rectangle is 6in longer than its width. if the perimeter of the rectangle is 60in, find its length and width.
Angela took a general aptitude test and scored in the 87th percentile for aptitude in accounting. What percentage of the scores were at or below her score? (b) What percentage were above?
Angela's score is in the 87th percentile, which means that 87% of the scores were at or below her score.
To calculate the percentage of scores above her score, we subtract 87% from 100%. Therefore, the percentage of scores above Angela's score is 13%.
In summary, Angela's score is at or below 87% of the scores, and 13% of the scores are above her score. The percentile score indicates the percentage of scores that fall below a particular score. Therefore, Angela performed better than 87% of the test takers who took the aptitude test in accounting.
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Which function models the area of a rectangle with side lengths of 2x – 4 units and x + 1 units? What is the area when x = 3?
A. f(x) = 2x2 – 4x + 4; A = 10 B. f(x) = 2x2 + 8x – 4; A = 38 C. f(x) = 2x2 – 8x + 4; A = 2 D. f(x) = 2x2 − 2x − 4; A = 8
4. A parking lot in the shape of a trapezoid has an area of 2,930. 4 square meters. The length of one base is 73. 4 meters, and the length of the other base is 3760 centimeters. What is the width of the parking lot? Show your work
The width of the automobile parking space is 52.8 meters.
First, we want to convert the duration of the second one base from centimeters to meters
3760 cm = 37.6 m
Subsequent, we're suitable to use the system for the vicinity of a trapezoid
A = ( b1 b2) h/ 2
In which b1 and b2 are the lengths of the two bases, h is the height( or range) of the trapezoid, and A is the area.
Substituting the given values, we have
= (73.437.6) h/ 2
= 111h/ 2
Multiplying both angles through 2 and dividing by 111, we get
h = 52.8
Hence, the width of the automobile parking space is 52.8 meters.
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If 6 cans of tomatoes cost $9, how much would it cost to buy 8 cans?
Answer:
$12
Step-by-step explanation:
Cans : Dollars
6 cans : 9 dollars
DIVIDE BY 3
2 cans : 3 dollars
MULTIPLY BY 4
8 cans : 12 dollars
Hope this helps :)
Have a great day!
Can anyone help with this math problem please? Thanks!
New width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.
How to find reduced area?The area of the tennis court is given by:
A = lw
where l is the length of the court and w is the width of the court.
Substituting the given values, we have:
[tex]$$260.7569 = l \cdot 10.97$$[/tex]
Solving for l, we get:
[tex]$l = \frac{260.7569}{10.97} \approx 23.76 \text{ m}$$[/tex]
To find the area of the court without the white bands, we need to subtract the areas of the two white bands from the total area. Since the white bands are on the top and bottom, we need to subtract twice the product of the width of the court and the width of the white band. The width of the white band is not given, but we know that the width of the court will be reduced by 25%, so the new width of the court will be:
w' = w - 0.25w = 0.75w
Substituting the given values, we have:
[tex]$$\begin{aligned}A' &= lw' - 2(0.75w)(l) \ &= l(0.75w) - 1.5wl \ &= 0.5625lw\end{aligned}$$[/tex]
where A' is the new area of the court without the white bands. Substituting the values of l and w that we found earlier, we have:
[tex]$$A' = 0.5625 \cdot 23.76 \cdot 10.97 \approx 146.17 \text{ m}^2$$[/tex]
Therefore, the new area of the court is reduced by 25%.
To find out if the width of the land is also reduced by 25%, we need to compare the original width w with the new width w'. We have:
[tex]$w' = 0.75w$$[/tex]
Dividing both sides by w, we get:
[tex]$\frac{w'}{w} = 0.75$$[/tex]
This means that the new width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.
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List all prime numbers in the 2023 February calendar
Answer:
6 29 25
Step-by-step explanation:
those are the prime numbers on the 2023 feb calendar
A price was first decreased by 12%, then it was decreased again by an additional 5%. What is the percent of the total decrease?
The answer is not 17%.
Please help!!!!
10 PTS
Answer:
83.6%
Step-by-step explanation:
Let's say the original price is x
x decreased by 12% means 88% of x is left.
0.88x decreased by 5% means 95% of 0.88x is left.
This means the answer is: 0.88x * 0.95 = 0.836
The percent of the total decrease is 83.6%
Hope this helps :)
Have a great day!
which of the following is a characteristic of a reliable scientific poll? choose 1 answer: choose 1 answer: (choice a) small sampling error a small sampling error (choice b) required names for all respondents b required names for all respondents (choice c) entire population surveyed c entire population surveyed (choice d) open-ended questions d open-ended questions
The characteristic of a reliable scientific poll is small sampling error. The small sampling error is a characteristic of a reliable scientific poll.
What is a scientific poll?Scientific polls are surveys that gather and evaluate people's opinions or responses to questions. These surveys are done in a scientific way, implying that pollsters use scientifically proven techniques to gather responses and analyze data.A reliable scientific poll must have a small sampling error. A sampling error is the deviation of the sample mean from the population mean due to random error. The smaller the sample size, the more likely it is that the results will be imprecise. As a result, it's essential to conduct a reliable scientific poll with a sample size that is representative of the population as a whole.The option for the correct answer to this question is; (choice a) small sampling error.
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Mars candy company is testing one of its machines in the factory to make sure it is producing more than 98% high-quality candy (H0: p = 0. 98; Ha: p > 0. 98; α = 0. 05). The test results in a p-value of 0. 15. However, the company is unaware that it is actually producing 99% high-quality candy. What MOST likely happens as a result of the testing?
A. The company rejects H0, making a Type I error.
B. The company fails to reject H0, making a Type II error.
C. The company rejects H0, making a Type II error.
D. The company fails to reject H0, making a Type I error.
E. The company rejects H0 correctly
the correct answer is option C: The company rejects H0, making a Type II error. In this hypothesis test, the null hypothesis H0 is that the machine produces no more than 98% high-quality candy, and the alternative hypothesis Ha is that the machine produces more than 98% high-quality candy. The significance level is α = 0.05.
The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic, assuming that the null hypothesis is true. A p-value of 0.15 is greater than the significance level of 0.05, which means that the result is not statistically significant.
However, the company is unaware that the machine is actually producing 99% high-quality candy. This means that the null hypothesis is actually false, and the alternative hypothesis is true. In other words, the machine is producing more than 98% high-quality candy.
Based on these observations, the company failing to reject the null hypothesis (option B) would be a Type II error, as it would mean that the company is not detecting a significant difference in the candy quality when, in fact, the machine is producing candy of higher quality than the null hypothesis assumes.
Therefore, the correct answer is option C: The company rejects H0, making a Type II error.
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Dewayne missed four of the 30 problems on the problem set. What
percent of the problems did Dewayne answer correctly?
Answer:
75% correct
Step-by-step explanation:
Enter the correct answer for the box.
Making r the subject of formula in this equation A = V²/r gives r = V²/A.
How to calculate centripetal acceleration?In Mathematics and Science, the centripetal acceleration of a physical object (body) can be calculated by using the following mathematical expression:
A = V²/r
Where:
A represent the centripetal acceleration.r represent the distance (radius) from a circular track.V represent the velocity of a physical object (body).In this exercise, you are required to make radius (r) the subject of formula. Therefore, by making radius (r) the subject of formula, we have the following:
Radius, r = V²/A
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An equation y= a(x+2)(x-6) and passes through (7,27) what is the value of a
Answer:
a = 3
Step-by-step explanation:
since the parabola passes through (7, 27 ) then te coordinates of the point make the equation true.
substitute x = 7 and y = 27 into the equation and solve for a
27 = a(7 + 2)(7 - 6) = a(9)(1) = 9a ( divide both sides by 9 )
3 = a
a spinner has three sections. the table shows the results of spinning the arrow on the spinner 80 times. what is the experimental probability of the arrow stopping over section 1? responses 128 1 over 28 720 7 over 20 713 7 over 13 45 4 over 5 section 1section 2section 3 283616
The experimental probability of the arrow stopping over section 1 is 7/13, or 0.538.
To calculate this, you need to take the number of times the arrow stopped on section 1 (45) and divide it by the total number of times the arrow was spun (80). This can be expressed as a fraction (45/80), which can be simplified to 7/13. To convert this fraction to a decimal, divide the numerator by the denominator (7/13 = 0.538).
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~~~~~~~~~~~~~~~~~~~~~~~~~~ Solve PLS ~~~~~~~~~~~~~~~~~~~~~~~~~~
Answer:
[tex]\frac{xa}{28}[/tex]
Step-by-step explanation:
[tex]\frac{4x^2}{y7a^3} * \frac{a^4}{16+8x}[/tex]
= [tex]\frac{2x(2+x)}{7a^3} * \frac{a^4}{8(2+x)}[/tex]
= [tex]\frac{xa}{28}[/tex]
[tex]\frac{x^{2}a }{28}[/tex]
Explination:
Factor the numerator and the denominator and cancel the common factors
determine the probability of drawing either a queen or a diamond? write your answer as a reduced fraction.
The probability of drawing either a queen or a diamond is 15/52
How do we calculate the probability?To determine the probability of drawing either a queen or a diamond, we have to find the sum of the probabilities of drawing a queen and drawing a diamond, then subtract the probability of drawing both a queen and a diamond. This is because the probability of drawing both a queen and a diamond has been added twice when we added the individual probabilities.
Thus, we have:P(queen or diamond) = P(queen) + P(diamond) - P(queen and diamond)
The probability of drawing a queen is 4/52, since there are four queens in a deck of 52 cards. The probability of drawing a diamond is 13/52, since there are 13 diamonds in a deck of 52 cards.
There are two ways to draw a card that is both a queen and a diamond, namely the queen of diamonds and the diamond queen. Thus, the probability of drawing both a queen and a diamond is 2/52. Therefore, P(queen or diamond) = 4/52 + 13/52 - 2/52 = 15/52 = 15/4 = 3.75 As a reduced fraction, this is 15/52.
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Problem 6-29 A quality-control inspector is testing sample outputfrom a production process for widgets wherein 89% of the items aresatisfactory (S) and 11% are unsatisfactory (U). Three widgets arechosen randomly for inspection. The successive quality events maybe assumed independent.
Find the probabilities for the following numbers of unsatisfactoryitems:
(1) Pr(none)=
.71
correct check mark
(2) Pr(exactly 2)= .0154
wrong check mark
(3) Pr(at least 1)= .29
correct check mark
(4) Pr(exactly 1)= .271
wrong check mark
(5) Pr(exactly 3)= .000275
wrong check mark
(6) Pr(at most 2)= .99
correct check mark
The probabilities for the given event is Pr(exactly 2) = 0.0283. Pr(exactly 1) = 0.2901, and Pr(exactly 3) = 0.001331.
What is probability and odds?The possibility of an event occurring can be expressed in terms of probability and odds, but they are not the same thing. The ratio of positive events to all conceivable outcomes, represented as a fraction or decimal, is known as probability. On the other hand, odds represent the proportion of good outcomes to those that are unfavourable. Odds can be stated as a ratio, fraction, or by dividing the favourable outcomes by the total number of outcomes to get their equivalent in probability.
The binomial probability is given as:
[tex]P(x) = (nCx) * p^x * (1-p)^{(n-x)}[/tex]
Here, n = 3, p = 0.11, and q = 1 - p = 0.89.
Thus,
[tex]Pr(exactly 2) = P(2) = (3C2) * 0.11^2 * 0.89^{(3-2)} = 0.0283\\Pr(exactly 1) = P(1) = (3C1) * 0.11^1 * 0.89^{(3-1)} = 0.2901\\Pr(exactly 3) = P(3) = (3C3) * 0.11^3 * 0.89^{(3-3)} = 0.001331[/tex]
Hence, the probabilities for the given event is Pr(exactly 2) = 0.0283. Pr(exactly 1) = 0.2901, and Pr(exactly 3) = 0.001331.
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Write the expression in complete factored
form.
b2(p + 3) + q(P + 3) =
andrew is buying a cell phone that has a regular price of $485. the cell phone is on sale for 35% off the regular price. what will be the sale price?
the sale price of the cell phone after the 35% discount is $315.25.
How to solve and what is sale?
To find the sale price of the cell phone, we need to apply the discount of 35% to the regular price of $485. We can do this by multiplying the regular price by 0.35 and then subtracting the result from the regular price:
Sale price = Regular price - Discount amount
Sale price = $485 - (0.35 x $485)
Sale price = $485 - $169.75
Sale price = $315.25
Therefore, the sale price of the cell phone after the 35% discount is $315.25.
A sale is a temporary reduction in the price of a product or service. Sales are often used by businesses to attract customers and increase sales volume. Sales can be offered for many reasons, such as to clear out inventory, promote a new product, or attract customers during a slow period.
In a sale, the price of a product or service is discounted, either by a fixed amount or by a percentage of the regular price. For example, a store might offer a 20% discount on all clothing items, or a car dealership might offer a $5,000 discount on a particular model of car.
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If u dissolve 50 grams of sugar in 30 grams of water what would the sugar concentration be?
The sugar concentration would be approximately 62.5%.
To find the concentration of sugar in the solution, we need to use the formula:
Concentration = Mass of solute ÷ Volume of solutionIn this case, the solute is sugar and the solvent is water. We are given that the mass of sugar is 50 grams and the mass of water is 30 grams. However, we need to convert the mass of water to volume since we need the volume of the entire solution to calculate the concentration.
We can assume that the density of water is 1 g/mL, so the volume of water is 30 mL. The total volume of the solution is therefore 50 mL + 30 mL = 80 mL.
Now we can use the formula to find the concentration of sugar:
Concentration = 50 g ÷ 80 mL ≈ 0.625 g/mLSo the concentration of sugar in the solution is approximately 0.625 grams per milliliter.
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an actuary has discovered that policyholders are five times as likely to file two clams as to file four claims. if the number of claims filed has a poisson distribution, what is the variance of the number of claims filed?
The number of claims filed by the policyholders has a poisson distribution. Therefore, the variance of the number of claims filed will be about 2.5.
What is the variance?We need to use the Poisson Distribution for solving the question, which is as follows:
P(x) = (λˣ/x!) × [tex]e^(-lambda)[/tex]
where is the mean value of distribution and x is the number of events we want to calculate.
If a random variable follows a Poisson distribution, its variance is equal to its mean.
So, the mean will be λ.
Let the probability of filing four claims be p1.
Then, probability of filing two claims will be ⁵p₁
We know the sum of probabilities of different events of Poisson distribution will always be equal to 1.
So,
p₁ + ⁵p₁ = 1
p₁ = 1/6
The mean number of claims is λ, which is given by:
Now, the variance of the Poisson distribution is also λ.
So, the variance of the number of claims filed is 2.5.
Hence, the answer is variance of the number of claims filed is 2.5.
The mean number of claims is λ, which is given by:
λ = ⁴p₁ + 2⁵p₁ = 2.5
Now, the variance of the Poisson distribution is also λ.
So, the variance of the number of claims filed is 2.5.
Hence, the answer is variance of the number of claims filed is 2.5.
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To get the 10% discount, a shopper must spend at least $400.
Use d to represent the spending (in dollars) of a shopper who gets the discount.
The shopper must spend at least $444.44 to get the 10% discount.
Step-by-step explanation:If a shopper gets a 10% discount, it means they pay only 90% of the original price. Let's say the original spending is represented by x. Then the spending after the 10% discount would be:
d = 0.9x
Now, we know that the shopper must spend at least $400 to get the discount, so we can set up an inequality:
d ≥ 400
Substituting the expression we found for d, we get:
0.9x ≥ 400
Dividing both sides by 0.9, we get:
x ≥ 444.44
So the shopper must spend at least $444.44 to get the 10% discount.
The length of a rope is 0.05hm.Convert the length to cm
Answer: 500 cm
Step-by-step explanation:
multiply by 0.5 by 10000