Answers
Answer:
13) F(-5, 0), so F' will be at (1, 2)
G(-1, -1), so G' will be at (5, 1)
H(-2, 3), soH' will be at (4, 5)
14) G(-2, 1), so G' will be at (-1, 3)
H(-1, 3), so H' will be at (0, 5)
I(3, 1), so I' will be at (4, 3)
J(2, -1), so J' will be at (3, 1)
Step-by-step explanation:
13) Add 6 to each original x-coordinate and add 1 to each original y-coordinate.
14) Add 1 to each original x-coordinate and add 2 to each original y-coordinate.
You may plot the new points to confirm my answer.
Related Questions
Lucia and Maria are business women who decided to invest money by buying farm land in Brazil. Lucia bought
11
1111 hectares of land in the first month, and each month afterwards she buys
5
55 additional hectares. Maria bought
6
66 hectares of land in the first month, and each month afterward her total number of hectares increases by a factor of
1. 4
1. 41, point, 4. They started their investments at the same time, and they both buy the additional land at the beginning of each month. What is the first month in which Maria's amount of land exceeds Lucia's amount of land?
Answers
Maria's amount of land first exceeds Lucia's amount of land after 3 months.
To solve this problem, we need to find out when Maria's total amount of land first exceeds Lucia's total amount of land. Let's start by writing out the formulas for the amount of land each woman has after n months
Lucia's land after n months = 11 + 5n
Maria's land after n months = 6 × 1.4^n
Now we want to find the month, n, when Maria's amount of land first exceeds Lucia's amount of land. So we need to solve the following inequality
6 × 1.4^n > 11 + 5n
We can solve this inequality by using a trial-and-error approach or by using a graphing calculator. Here's one way to solve it using trial-and-error
Let's start by plugging in n = 1 and see if Maria's land is greater than Lucia's land:
6 × 1.4^1 = 8.4
11 + 5 × 1 = 16
Since 8.4 < 16, we know that Maria's land is not greater than Lucia's land after 1 month.
Now let's try n = 2
6 × 1.4^2 = 11.76
11 + 5 × 2 = 21
Since 11.76 < 21, we know that Maria's land is still not greater than Lucia's land after 2 months.
Let's keep trying larger values of n until we find the first month when Maria's land is greater than Lucia's land:
n = 3
6 × 1.4^3 = 16.384
11 + 5 × 3 = 26
Since 16.384 > 26, we know that Maria's land is greater than Lucia's land after 3 months.
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The given question is incomplete, the complete question is:
Lucia and Maria are business women who decided to invest their money by buying farmland in Brazil. They started their investments at the same time, and each month they buy more land. Lucia bought 11 hectares of land in the first month, and each month afterwards she buys 5 additional hectares. Maria bought 6 hectares of land in the first month, and each month afterward her total number of hectares increases by a factor of 1.4. In which month will Maria's amount of land first exceed Lucia's amount of land?
Enter the correct answer for the box.
Answers
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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Dewayne missed four of the 30 problems on the problem set. What
percent of the problems did Dewayne answer correctly?
Answers
Answer:
75% correct
Step-by-step explanation:
Find the angle measures for m∠QRS and m∠SRT.
Answers
Answer:
its 126 and 54 hope this helps
This is Section 3.2 Problem 2: The cost function, in dollars, for producing $x$ items of a certain brand of barstool is given by C(x)-0.01x3-0.6x2+13x+200 (a) C(x).03r- .12x +13 (b) MC(50)-82 dollars per barstool . It approximately represents the cost of producing the 50 th barstool (c) The exact cost of producing the 51th barstool is C 51 -c50 28.91 dollars (d) Using C(50) and MC (50), the total cost of producing 53 barstools is approximately -Select
Answers
In the following question, the Total cost to production 50 barstools: $1,200 Total cost to produce 51 barstools: $1,228.91 "Total cost to produce 52 barstools: $1,258.44" Total cost to produce 53 barstools: $1,288.59 Therefore, the approximate total cost of producing 53 barstools is $559.15.
The cost function for producing $x$ items of a certain brand of barstool is given by C(x)=0.01x3-0.6x2+13x+200.
(a) C(x)=0.03x3- 0.12x2+13
(b) MC(50)=-82 dollars per barstool.
It approximately represents the cost of producing the 50th barstool.
(c) The exact cost of producing the 51st barstool is C51=C50+MC(50)=$28.91 dollars.
(d) Using C(50) and MC (50), the total cost of producing 53 barstools is approximately C50+(53-50) MC(50)=$229.82.
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Prove the following statement directly from the definition of divisibility. For all integers a, b, c, and d, if aſc and bld then ab|cd. Proof: Let a, b, c, and d be any integers such that alc and b|d. Then by definition of divisibilityq c= ar and d = bs for some integers r and s. Then cd equals the product of ab and a number that can be written in terms of r and s as follows: cd = ab: , which is an integer because products A of integers are integers. (Simplify your answer completely.) Thus cd = ab · (an integer), and so ablcd by definition of divisibility.
Answers
The cd = ab · (an integer), and so ab | cd by definition of divisibility.
The question wants us to prove the following statement using the definition of divisibility. For all integers a, b, c, and d, if aſc and bld, then ab|cd.Definition of divisibility: Let a and b be integers. We say that b divides a or b is a divisor of a if there exists an integer k such that a = bk.
If b divides a, then we write b | a.Let a, b, c, and d be any integers such that alc and b | d. Then by definition of divisibility, c = ar and d = bs for some integers r and s. Then cd equals the product of ab and a number that can be written in terms of r and s as follows:cd = ab · rs, which is an integer because products of integers are integers.
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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
Answers
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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Suppose the entire pink arc measures 200 degrees and the entire blue arc measures 50 degrees, what would be measure of the manilla angle be?
Answers
Therefore, the measure of the manila angle is 110 degrees.
What is degree?The term "degree" can have several different meanings depending on the context. Here are a few possibilities:
Academic degree: This refers to the title or certificate awarded to a student upon the completion of a course of study at a college, university, or other educational institution. Examples of academic degrees include bachelor's degrees, master's degrees, and Doctoral degrees.
by the question.
Assuming that the pink, blue, and manila arcs are all part of the same circle, the sum of their measures must be 360 degrees.
Let's denote the measure of the manila arc as x degrees. Then we can set up an equation to solve for x:
200 degrees (pink arc) + 50 degrees (blue arc) + x degrees (manila arc) = 360 degrees
Simplifying the equation, we can solve for x:
x = 360 degrees - 200 degrees - 50 degrees
x = 110 degrees
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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?
Answers
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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List all prime numbers in the 2023 February calendar
Answers
1,2,3,5,7,11, 13,17,19,23 and 29, that is 11 in all.
Answer:
6 29 25
Step-by-step explanation:
those are the prime numbers on the 2023 feb calendar
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?
Answers
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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determine the probability of drawing either a queen or a diamond? write your answer as a reduced fraction.
Answers
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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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
Answers
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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Write the expression in complete factored
form.
b2(p + 3) + q(P + 3) =
Answers
b^2(p + 3) + q(p + 3) = (p + 3)(b^2 + q)
Therefore, the complete factored form of the expression is (p + 3)(b^2 + q).
I need help on these!
Answers
Three points that are solutions to the system are:
(0, -9)
(3, -5)
(4, -4)
b.
Three points that are solutions to the system are:
(3, 2)
(2, 1)
(1, 0)
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
Answers
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!
below is survey results describing the survival rate and life expectancy in a certain population. p(n) stands for the probability of a new-born to reach the age of n years. n 55 60 65 70 p(n) 0.903 0.882 0.742 0.657 according to the given survey, answer the following questions: what is the probability of a 65 years old man to reach the age of 70? you can express your answer as a fraction, decimal, or a percentage. if you asnwer in decimal, include at least 3 digits after the decimal point. if you answer is a percentage, make sure to include a % sign in your answer. symbolic expression given that the probability that a man who just turned 70 will die within the next 5 years is 0.176, what is the probability for a man to survive till his 75th birthday, i.e., what is p(75)? you can express your answer as a fraction, decimal, or a percentage. if you asnwer in decimal, include at least 3 digits after the decimal point. if you answer is a percentage, make sure to include a % sign in your answer.
Answers
The probability that a 65-year-old man will survive to reach the age of 70 is 88.4%, and also the probability man to survive till his 75th birthday is approx.59.952%.
The probability of a 65-year-old man reaching the age of 70 is the probability of surviving from age 65 to age 70, which is given as
p(70)/p(65) ⇒ 0.657/0.742 ≈ 0.88544 or 88.544%.
The probability of a man who just turned 70 dying within the next 5 years is 0.176.
Therefore, the probability of surviving for the next 5 years after turning 70 is
⇒ 1 - 0.176 ⇒ 0.824.
Thus, the probability of a man surviving till his 75th birthday is the probability of surviving from age 70 to age 75, which is given as
p(75)/p(70) ⇒ 0.657/0.903 × 0.824
≈ 0.59952 or 59.952%.
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Annie's Pie Shop has 12 pies for sale, including 4 chocolate cream pies.
What is the probability that a randomly selected pie will be a chocolate cream pie?
Write your answer as a fraction or whole number.
The best solution gets brainlist
Answers
Answer: 1/3
Step-by-step explanation:
The probability of selecting a chocolate cream pie can be found by dividing the number of chocolate cream pies by the total number of pies:
Probability of selecting a chocolate cream pie = Number of chocolate cream pies / Total number of pies
Probability of selecting a chocolate cream pie = 4 / 12
Simplifying this fraction by dividing the numerator and denominator by 4 gives:
Probability of selecting a chocolate cream pie = 1/3
Therefore, the probability of selecting a chocolate cream pie from Annie's Pie Shop is 1/3.
Feng has a toy car collection he keeps 324 of the toy cars on his wall which is 81% of his entire collection what is the total number of toy cards in his collection
Answers
400 is the total number of toy cards in his collection. This will be the total number of toy cards in his collection if Feng keeps 324 of the toy cars on his wall which is 81% of his entire collection.
A fraction is a mathematical value that illustrates the components of a whole. In general, the whole can be any particular thing or value, and the fraction might be a portion of any quantity out of it. The top and bottom numbers of a fraction are explained by the fundamentals of fractions. The bottom number reflects the entire number of components, while the top number represents the number of chosen or coloured portions of the whole.
Based on the given conditions, formulate: 324/81%
Convert decimal to fraction: 324/81/100
Divide a fraction by multiplying its reciprocal 324 * 100 / 81
Reduce the expression to the lowest term: 4*100
Calculate the product or quotient: 400
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the mean height of men is about 69.2 69.2 inches. women that age have a mean height of about 63.7 63.7 inches. do you think that the distribution of heights for all adults is approximately normal? explain your answer.
Answers
Yes, the distribution of heights for all adults is approximately normal because normal distribution has a bell-shaped curve. The bell curve indicates that the majority of the data points are located around the mean, with fewer data points on either side. Furthermore, normal distribution has certain characteristics that are relevant to this question.
The average height of men is 69.2 inches, while the average height of women is 63.7 inches. Therefore, we can assume that the mean height for both genders would be approximately 66.45 inches, assuming the distribution is equal (i.e., half male, half female).
If we plot the data of both males and females together, the plot will likely resemble a bell curve as per the properties of normal distribution. Since most adults would fall within the average height range, the distribution of heights for all adults is considered approximately normal. Therefore, we can conclude that the distribution of heights for all adults is approximately normal.
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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?
Answers
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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a box contains 75 red marbles, 37 white marbles, and 19 blue marbles if a marble is randomly selected from the box, what's the probability that it is not blue
Answers
The probability that it the marble taken out of the box is not blue is [tex]\frac{112}{131}[/tex].
What is the probability?Probability is a branch of math that studies the chance or likelihood of an event occurring.
There are [tex]75[/tex] red marbles, [tx]37[/tex] white marbles, and [tex]19[/tex] blue marbles.
If a marble is randomly selected from the box, we have to find the probability that it is not blue.
Then the total number of marbles = [tex]75 + 37 + 19 = 131.[/tex]
The probability that a marble is not blue:-
[tex]P[/tex](Not blue) = [tex]P[/tex](Red or White)
[tex]P[/tex](Red or White) = [tex]\frac{(75 + 37)}{131}[/tex]
[tex]P[/tex](Red or White) = [tex]\frac{112}{ 131}[/tex]
[tex]P[/tex](Not blue) = [tex]1 - P[/tex](Blue)
[tex]P[/tex](Not blue) = [tex]1 - \frac{19}{131}[/tex]
[tex]P[/tex](Not blue) = [tex]\frac{112}{ 131}[/tex]
Therefore, the probability that a marble selected from the box is not blue is [tex]\frac{112}{131}[/tex].
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please help me I have attached a photo below. thanks for your time
Answers
Therefore, the slope of the line passing through the points (0,5) and (2,0) is -5/2.
What is slope?In mathematics, slope refers to the measure of steepness of a line. It is the ratio of the change in y (vertical change) over the change in x (horizontal change) between any two points on the line. The slope of a line is represented by the letter "m" and can be calculated using the slope formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Here,
To find the slope of a line, we use the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line.
Using the given coordinates, we have:
x1 = 0, y1 = 5
x2 = 2, y2 = 0
slope = (0 - 5) / (2 - 0)
slope = -5/2
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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
Answers
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 u dissolve 50 grams of sugar in 30 grams of water what would the sugar concentration be?
Answers
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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I would like to know the answer
Answers
Answer:
[tex] \frac{3}{2} {x}^{8} [/tex]
Step-by-step explanation:
[tex] \frac{9 {x}^{16} }{6 {( {x}^{2} )}^{3}{x}^{2} } = \frac{9 {x}^{16} }{6 {x}^{6} {x}^{2} } = \frac{9 {x}^{16} }{6 {x}^{8} } = \frac{3}{2} {x}^{8} [/tex]
I need some help with this
Answers
Answer:
148.5 π
Step-by-step explanation:
Cone = 1/3 * base * height
1/3 * 22 * (9/2)^2 π = 148.5 π
An equation y= a(x+2)(x-6) and passes through (7,27) what is the value of a
Answers
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
In each expression below the numbers under the root sign all add to the same number, 10. Determine which expression is greatest. How?
a) √7+ √3
b) √6+ √4
c) √8+ √2
Answers
Answer:
Step-by-step explanation:
I think a calculator is the only way to solve this question:
[tex]\sqrt{7} +\sqrt{3} = 2.96\\\\\sqrt{6} +\sqrt{4} = 2.54\\\\\sqrt{8} +\sqrt{2} =3.07[/tex]
So (c) is the greatest.
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?
Answers
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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