The inequality contain -12 in its solution is x + 5 ≤ -4.
What is inequality?
The phenomenon of an unfair and/or unequal distribution of opportunities and resources among the people who make up a society is referred to as inequality. To different people and in various contexts, the word "inequality" may mean different things.
We have to find from the given inequalities which inequality has -12 in its solution.
Consider, the given inequalities
(1) x + 6 < -8
⇒ x < - 8 - 6
⇒ x < -14
This inequality does not contain -12 in its solution.
(2) x + 4 ≥ - 6
⇒ x ≥ -6 - 4
⇒ x ≥ - 10
This inequality does not contain -12 in its solution.
(3) x - 3 > -10
⇒ x > -10 + 3
⇒ x > -7
This inequality does not contain -12 in its solution.
(4) x + 5 ≤ -4
⇒ x ≤ - 4 - 5
⇒ x ≤ -9
This inequality contain -12 in its solution.
Hence, the inequality contain -12 in its solution is x + 5 ≤ -4.
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Complete the car class by creating an attribute purchase_price (type int) and the method print_info() that outputs the car's information. Ex: if the input is: 2011 18000 2018 where 2011 is the car's model year, 18000 is the purchase price, and 2018 is the current year, then print_info() outputs:.
When an object is to be generated, classes are utilized as templates, whereas methods are functions that are called or invoked.
What is class?A class is a template specification of the method(s) and variable(s) of a certain sort of object in object-oriented programming. As a result, an object is a particular instance of a class; instead of variables, it holds real values. One of the fundamental concepts of object-oriented programming is the class.
How do you define a class?A class outlines the information included in the objects that are a part of it, including the actions and a collection of data fields known as instance variables (called methods). An object is an element (or instance) of a class, and objects exhibit the behaviors of the classes in which they belong.
We use the self keyword to declare the attribute purchase price (type int), initializing the value to 0.
Therefore, the purchase price attribute declaration is as follows:
self.purchase price equals zero
We just need to invoke the model year and purchase price variables to define the print info() function.
The print info() function is therefore defined as follows:
def print_info(self):
print("Car's information:")
print(" Model year:", self.model_year)
print("Purchase price:", self.purchase_price)
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What is the result when the number 48 is decreased by 75%?
Answer: 12
Step-by-step explanation: First turn 75% into its decimal form 0.75
Then multiply this by 48.
0.75 x 48 = 36
36 is 75% of 48
Then subtract 36 from 48. This will get you 12.
If you pay $25 per month for your cell phone and an additional $5 for each picture
you send, an equation to represent the cost of your phone would be
y = 5x + 25
y = 25x + 5
y = 3x + 1
y = x + 30
If you pay $25 per month for your cell phone and an additional $5 for each picture you send then y=25x+5 is the equation to represent the cost of your phone.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that you pay $25 per month for your cell phone
An additional $5 for each picture you send
We have to find the equation which represent the cost of your phone
Let x be the number of months.
The equation should be in the form of y=mx+b
in the given equation m is the slope and b is the y intercept or the additional fee.
y=25x+5 is the required equation
Hence, if you pay $25 per month for your cell phone and an additional $5 for each picture you send then y=25x+5 is the equation to represent the cost of your phone.
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You are given an integer n where 0 <= n <= 100, followed by another line of input which has a word w with length l where 1 <= l <= 50. Your task is to print n lines with the word w. The lines of your output should not have any trailing or leading spaces.
The Python program to print the value of the input string is as follows:N= int(input("Enter a integer variable N (0 <= N <= 100): ")), W = input("Enter the word W (length of 1 <= L <= 50): "), for n in range(N):, print(W)
A variable, what exactly do you mean?In a mathematical problem or experiment, a variable is a quantity that can change. To represent a variable, we typically use a single letter. Generic symbols used frequently for variables include the letters x, y, and z.
Program -
N= int(input("Enter a value of integer N (0 <= N <= 100): "))
W = input("Enter the word W (length of 1 <= L <= 50): ")
for n in range(N):
print(W)
Here,
defining the integer variable "N" that accepts a user-supplied integer value.
The user-end string value is input using another variable "W" that is declared in the next step.
A for loop using the range method and an integer variable is declared after all input values have been entered. This loop prints the string value.
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2 + 4(2x-1) = 6.25x-26
with solution please
Answer:
x = -96/7 or -13.714285
Step-by-step explanation:
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in a class of 3000 students, the professor gives a multiple choice quiz with 4 questions, possible answers a,b,c, d or e. each student answers each question. among the 3000 students, at least how many students will turn in the exact same answers for the quiz questions?
Among the 3000 students, at least 5 students will turn in the exact same answers for the quiz questions.
What does at least mean in probability?
"At least" means as follows: equivalent to or less than. The bare minimum that should happen once a random event occurs is called the least mean in probability.
It will be the complement of the event never occurring to determine the likelihood of an event occurring at least once. In other words, there is a 100% chance that the event will occur regardless of its likelihood of never happening or happening at least once.
Solution Explained:
The quiz has 54=625 different possible outcomes. Given that 625 divided by four equals 2600 and 625 multiplied by five equals 3125, we deduce that 5 students will submit the same set of answers. This is due to the fact that there would be a maximum of 2600 students if only 4 students submitted each answer sheet.
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find the taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that rn(x) → 0.] f(x) = sin(x), a = ????
The taylor series of sin x at x= π is ∑( for n=0,∞) [tex]\frac{-1^{n+1}(x-\pi )^{2n+1} }{(2n+1)! }[/tex]
the Taylor series n of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.
since the function we are given is :
sin(x), since we need to find the Taylor series of sin(x) at x=π, which can also be written as : sin(x+π)
we can find find the Taylor series of sin(x+π) at x=0
sin(x+π)=−sin(x)
= ∑( for n=0,∞) [tex]\frac{(-1)^{n}x^(2n+1) }{(2n+1)!}[/tex]
= ∑( for n=0,∞) [tex]\frac{-1^{n+1}x^{2n+1} }{(2n+1)!}[/tex]
so sin (x)= ∑( for n=0,∞) [tex]\frac{-1^{n+1}(x-\pi )^{2n+1} }{(2n+1)! }[/tex]
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find the Taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that rn(x) → 0.] f(x) = sin(x), a = π????
How to solve 3(1+p)=-5(p+1)
The value of P in the equation is -1
Answer:
p=-1
Step-by-step explanation:
3(1+p)=-5(p+1)
Remove the parenthesis:
3+3p=-5p-5
Subtract 3 from both sides.
3p=-5p-5-3
Simplify:
3p=-5p-8
Rearrange:
3p=-8-5p
Add 5p to both sides:
8p=-8
Divide both sides by 8:
p=-1
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a company is placing an order for boxed lunches for a meeting of its executive board. there are 10 members of the board and each will have one lunch. the company is getting the lunches from a restaurant that has 25 varieties of boxed lunches. (a) how many different ways are there for the company to place the lunch order for the 10 lunches? note that it is not important who gets what lunch. all that matters is how many of each of the 25 possible varieties are purchased. (b) how many ways are there for the company to place the lunch order if the 10 lunches purchased are all different? (again, who gets what lunch is not important, just how many of each lunch are purchased).
a)
There are 3268760 different ways for the company to place the lunch order for the 10 lunches
b)
There are 11861676288000 ways for the company to place the lunch order if the 10 lunches purchased are all different
What is permutation and combination?
The process of placing all the components of a set into a certain sequence or order is known as permutation in mathematics. In other terms, the process of permuting is the reordering of the components of a set if the set is already ordered. Nearly all areas of mathematics include permutations in some form or another. They frequently appear when various orderings on certain finite sets are taken into account.
Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method. The number of combinations may be counted in simpler situatiThe combinationation is the taking together of n items, k at a time, without repetition. The terms k-selection or k-combination with repetition are frequently used to describe combinations where repetition is permitted.
a) total different ways are [tex]C^{25} _{10}[/tex]
= 25!/(25-10)!10!
= 25!/15! * 10!
= 3268760
b) total different ways are [tex]P^{25} _{10}[/tex]
= 25!/(25-10)!
= 25!/15!
= 11861676288000
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In triangle DEF, if mZD = (4x)°, mZE = (2x - 3)°, and mZF = (x + 8)°, what is the value of x?
O 51
0 29
026
O 25
The value of x, if In triangle DEF, if mZD = (4x)°, mZE = (2x - 3)°, and mZF = (x + 8)° is 25, so correct option is D.
What is triangle?One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices.
Given:
In triangle DEF, if mZD = (4x)°, mZE = (2x - 3)°, and mZF = (x + 8)°
Calculate the value of x as shown below,
The sum of triangles will be equal to 180°,
mZD + mZE + mZF = 180
4x + 2x - 3 + x + 8 = 180
7x = 180 - 5
x = 175 / 7
x = 25
Therefore, the value of x, if In triangle DEF, if mZD = (4x)°, mZE = (2x - 3)°, and mZF = (x + 8)° is 25.
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point is 9 units from the center of a circle of radius 15. how many different chords of the circle contain and have integer lengths?
Total number of different chords of the circle passing through point P with integer lengths is equal to 7.
As given in the question,
Radius of the circle = 15units
Longest chord of the circle 'diameter' = 2 × 15
= 30units
Point 'P' is 9 units away from the circle.
Consider shortest distance( perpendicular) of point P for shortest chord.
Half length of the chord , shortest distance and radius form right triangle.
(1/2) length of the chord = √15² - 9²
= √225 - 81
= 12units
Length of the chord = 2(12)
= 24 units
Different Chords with integer length = 24, 25, 26, 27, 28 , 29 , 30
Total number of different chords = 7
total number of chords = 6 original + 6 mirror image + 1 longest chord
= 13
Therefore, total chords with different integer length passing through the point P of the circle is 7.
The complete question is :
A point P is at the 9 unit distance from the center of a circle of radius 15 unit. How many total number of different chord of the circle passing through the point P and have the integer lengths?
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0.25r=0.5 how do i solve this please help.
Answer: r=2
Step-by-step explanation:
do .5/.25=2
(0.5- 0.3) power of 2?
Solving the Question
[tex](0.5- 0.3)^2[/tex]
⇒ Subtract inside the parentheses:
[tex]= (0.2)^2[/tex]
⇒ Evaluate the exponent by multiplying 0.2 by 0.2:
[tex]= 0.04[/tex]
Answer0.04
Answer:
0.04
Step-by-step explanation:
Calculate the unit rate for each option and determine which one is the BEST buy.
$160 for 10 books
$114 for 6 books
Answer:
$160 for 10 books is the BEST buy.
Step-by-step explanation:
To find which one is the best buy, we need to find the unit rate for the books (which is how much each book is worth). We do this by simply dividing the two numbers in each buy:
160 ÷ 10 = 16
114 ÷ 6 = 19
Since the first one is a smaller price, the first one is our answer.
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It would be $160 for 10 books
a coin is weighted so that the probability of obtaining a head in a single toss is 0.25. if the coin is tossed 45 times, what is the probability of obtaining between 9 and 14 heads, exclusive. a. 0.0537 b. 0.5051 c. 0.7201 d. 0.6975 e. 0.4836
The probability of obtaining between 9 and 14 heads is .0.0408
Probability:
in statistics, probability refers the possibility of the outcome of any random event.
Given,
A coin is weighted so that the probability of obtaining a head in a single toss is 0.25.
Here we need to find the probability of obtaining between 9 and 14 heads if the coin is tossed 45 times.
While we looking into the given question,
Probability of obtaining a head in a single toss = 0.25
Number of toss = 45
Here we need to find the probability of getting head between 9 and 14, is calculated as,
=> mean = 45 x 0.25 = 11.25
=> standard deviation = √11.25 x(1 - 0.25) = 2.9
Here the probability is written as,
=> P(9 < x < 14) = P(8.5 < x < 14.5)
Then the z score, is
=> z = (8.5 - 11.25)/2.9 = -0.9483
=> z = (14.5 - 11.25)/2.9 = 1.1207
So, the given probability is rewritten as,
=> P(9 < x < 14) = P(z < 1.1207) - P(z < 0.9483)
When we apply the value of z score on it then we get,
= > P(z < -0.9483) = 0.17149
=> P(z > 1.1207) = 0.13121
=> P(9 < x < 14) = 0.13121 - 0.17149
=> 0.0403
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Find the perimeter and area of triangle RST if each unit on the graph measures 1 centimeter. Round your answer to the nearest centimeter, if necessary.
y
8
S-4,5)-6
Q-6,1)
-876
R(-8,-3)
Perimeter
Area
4
-6
81
468x
7(6,-5)
cm²
jcm
The perimeter and the area of the triangle are given as follows:
Perimeter: 21 cm.Area: 16 cm².How to obtain the perimeter of the triangle?The perimeter of the triangle is given by the sum of the lengths of the outer edges of the triangle.
From the image given at the end of the answer, these lengths are of:
AB = 4.AC = 8.BC = 8.83 -> Pythagorean Theorem -> hypotenuse of a right triangle of sides 4 and 8.Hence the perimeter of the triangle is of:
P = 4 + 8 + 8.83 = 21 cm.
(rounded to the nearest cm, as each unit represents 1 cm).
How to obtain the area of the triangle?The triangle in this problem is a right triangle, hence the area is obtained by half the multiplication of the sides, as follows:
A = 0.5 x 4 x 8 = 16 cm².
Missing InformationThe problem is incomplete, hence a similar problem was given and solved, by the triangle in the image at the end of the answer.
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three women are selected from the audience of a style show to receive a purse, a pair of gloves, and a scarf. if 23 women are present, in how many different ways may the gifts be given?
The number of different possible ways in which the gifts can be given to 3 out of 23 women is 10626.
Each gift can be considered a position given to one of 23 women. The number of ways in which gift can be given to them is :
First gift : 23 possibilities
Second gift: 22 possibilities
Third gift: 21 possibilities
So, the gifts may be given in
23 * 22* 21
= 10626
We could encounter several patterns and number kinds in mathematics. Sequences are included in one of the number patterns.
Repetition is permitted and order is important in the sequence, which is a predetermined group of objects. Formally, a sequence is a function that connects the elements at each point to natural numbers. It has members, which are known as elements or words, just like a set.
The length of the sequence is determined by the number of items. In contrast to a set, the same items might appear more than once in a sequence at various points, and the order does important.
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Apply the distributive property to factor out the greatest common factor. 30+42=30+42=30, plus, 42, equals.
The greatest common factor of 30+42 according to the distributive property is 6×12.
What is distributive property?The distributive law, which states that equality is always true in elementary algebra, is generalized by the distributive principle of binary operations in mathematics.
For instance, addition is said to be more evenly distributed than multiplication in elementary mathematics.
So, here we wish to calculate the largest common factor between the numbers 30 and 42, which equals the total of 30 and 42.
Going one for one, the biggest divisor of 30 is 15, and since 42 cannot be divided by 15, this means that there isn't a frequent divisor of 30 and 42.
Since 10 is not a divisor of 42 and is the second largest divisor of 30 (10*3 = 30), it is not a common divisor of both 30 and 42.
6, which is also a divisor of 42 (6*7 = 42), is the third-largest divisor of 30 (6*5 = 30).
Then both 30 and 42 have 6 in common the most.
We may factor the total now by:
30 + 42 = 6*5 + 6*7 = 6*(5 + 7) = 6*12
Therefore, the greatest common factor of 30+42 according to the distributive property is 6×12.
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Correct question:
Apply the distributive property to factor out the greatest common factor. 30+42
solve the inequality
15t>180
Answer: t=12
Step-by-step explanation:
To isolate the t, divide both sides by 15. The 15 on the left cancels out, and 180 divided by 15 is 12.
Your team has contracted to design and build a 500 ft, square-based, open-top, rectangular steal holding tank for a paper company. The tank is to be made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weight as little as possible.
The first step is to calculate the approximate weight of the tank. This can be done by calculating the weight of the stainless steel plates and multiplying it by the surface area of the tank.
The surface area can be calculated by multiplying the length of the sides by the height. The weight of the stainless steel plates can be found online or by consulting a materials engineer.Once the approximate weight of the tank has been calculated, the base and height dimensions can be determined by trial and error. Start with a base length and a height and calculate the approximate weight of the tank. Then, adjust the base length and/or height and recalculate the weight. Continue this process until the lightest weight is achieved.It is important to consider the structural integrity of the tank when selecting the dimensions. A tank with too little height or too wide a base may not be able to withstand the pressure of the contents within. Consulting a structural engineer may be necessary to ensure that the tank is strong enough to withstand the pressure of the contents.
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(1 point) how many strings of four decimal digits (note there are 10 possible digits and a string can be of the form 0014 etc., i.e., can start with zeros.)
a) Four-digit strings with 10⁴ characters are available.
b) A string that finishes in an odd number has 10 options for the first three digits and 5 options for the last digit.
c) The fourth digit has nine alternatives.
Given,
We have to find the number of strings of four decimal digits for the following conditions;
a) Do not use the same numeral more than once.
There are 10⁴ strings with four decimal digits.
We have 10 options for the first digit, 9 options for the second digit, 8 options for the third digit, and 7 options for the fourth digit when creating a string with 4 different digits. We deduce from the product rule that there are 10 9 8 7 = 5040 four decimal digits with no duplicate digits.
b) End with an odd digit
There are 10 choices (ranging from 0 to 1, 2,..., 9) for the first three digits of a string that ends in an odd number, and 5 possibilities (ranging from 1, 3, 5, 7,.., 9) for the last digit. According to the product rule, there are 5000 strings that terminate in an even number, or 10 × 10 × 10 × 5.
c) Have exactly three digits that are 8
There is one non-8 digit in the 4-decimal string, which includes exactly 3 digits that are 8. Therefore, there are 9 options for the fourth digit (ranging from 0 through 1, 2, 3, 4, 5, 6, and 9). The non-digit may appear in the string at positions 1, 2, 3, or 4. The sum rule leads us to the conclusion that there are 36 four decimal digits with exactly three 8s, which equals 9 + 9 + 9 + 9 = 36.
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Question is incomplete. Completed question is given below;
How many strings of four decimal digits
a) Do not contain the same digit twice
b) End with an odd digit?
c) Have exactly three digits that are 8
a dental student is conducting a study on the number of people who visit their dentist regularly. of the 520 people surveyed, 312 indicated that they had visited their dentist within the past year. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
For samples of size n = 60, the mean of the sampling distribution is 0.6
and the standard deviation of the sampling distribution is 0.0632
Here, N = 520 and X = 312
So, the population proportion is calculated as;
p = X / N
p = 312/520
p ≈ 0.600
So, the mean of the sampling distribution would be,
μ = 0.600
And for samples of size n = 60, the standard deviation of the sampling distribution would be,
σ = √[p(1 - p)] / n
σ = √[0.6(1 - 0.4)] / 60
σ = √[(0.6 * 0.4) / 60]
σ = √(0.004)
σ = 0.0632
Therefore, the mean of the sampling distribution = 0.6
and the standard deviation of the sampling distribution = 0.0632
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Given question is incomplete.
A complete question is:
a dental student is conducting a study on the number of people who visit their dentist regularly. of the 520 people surveyed, 312 indicated that they had visited their dentist within the past year. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n = 60
Find x in the right triangle. 324−−−√324
B 147−−−√147
C 63−−√63
D 175−−−√175
E 21−−√21
Answer:
I believe it is 3rd one but not 100% sure
Step-by-step explanation:
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10 points . Which graph shows Y=⌊x⌋+3? ... Picture provided
The graph that shows the function Y=⌊x⌋+3 is given by the image shown at the end of the answer.
How to obtain the graph of the function?The function in this problem is defined as follows:
Y=⌊x⌋+3.
The term ⌊x⌋ is the floor function of x, giving the greatest integer that assumes a value less than x.
The intervals to the function are given as follows:
Open on the left interval.Closed on the right interval.Then the translation is given as follows:
Y = y + 3.
Meaning that the function was shifted three units up.
Thus the correct graph is the bottom right graph, given by the image shown at the end of the answer, because:
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The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out to see whether this is the case. What conclusion is appropriate in each of the following situations? (a) n 15 t 1.66 a 0.05 o Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in o Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in o Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in o Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
The correct answer is 'Do not reject the null hypothesis as there is not sufficient evidence that the true diameter differs from 0.5 in.'
When the sample size is large and the standard deviation is known, the z-test is typically used.
The T-test is more flexible than the Z-test since the Z-test frequently needs particular circumstances in order to be reliable.
The t test is applied if the population standard deviation is unknown.
Test statistic for one sample t-test is, t = (X‾ - μ0) / (s / √n)
The formula of degrees of freedom for test is, df = n-1 here, n is sample size.
Decision rule:
1. If the P-value is less than the level of significance, the null hypothesis should be rejected; otherwise, it should not be.
2.The null hypothesis is rejected if the t-test statistic value is greater than the t tabulated value; otherwise, the null hypothesis is not rejected.
(a) From the given information, n=15, t=1.66, α =0.05 we can derive
degrees of freedom = df= n-1 which is 15-1 = 14
Thus, the critical value is, 2.145.
Now, since the test statistic value is less than the critical value, do not reject the null hypothesis.
Here, the test statistic value do not lie in the critical region. The null hypothesis cannot be rejected. There is insufficient evidence that the true diameter differs from 0.5 in.
(b) From the given information, n=15, t = -1.66, α =0.05 we can derive
degrees of freedom = df= n-1 which is 15-1 = 14
Thus, the critical value is, -2.145.
Now, since the test statistic value does not lie in the rejection region, do not reject the null hypothesis.
Here, the test statistic value does not lie in the critical region. The null hypothesis cannot be rejected. There is insufficient evidence that the true diameter differs from 0.5 in.
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5(2t -3) - 7.5t = 0.5 (12-t) Show your work
Answer:7
Step-by-step explanation:
Can write it as
10t -15 - 7.5t = 6 - 0.5t
2.5t -15 = 6 - 0.5
3t - 15= 6
3t = 21
t= 7
when solving the equation, which is the best first step to begin to simplify the equation? negative 2 (x 3)
Answer:
Negative one-half (negative 2) (x + 3) = negative 10 (negative one-half
ashley wants to crochet a blanket for her new baby cousin. her pattern calls for 900 yards of thick, soft wool. she already has 200 feet of wool left from another project. at the craft store, she notices that each ball has 500 feet of wool. how many balls of wool should she buy?
By using the concept of subtraction and multiplication, it can be calculated that
Ashley should buy 5 balls
What is subtraction and division?
To find how big or small one number is from the other, then the operation used is called subtraction
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a word problem on subtraction and division
Total length of Wool Ashley required = 900 [tex]\times[/tex] 3 = 2700 ft
Length of wool Ashley has = 200 ft
Length of wool Ashley still needed = 2700 - 200 = 2500 ft
Length of wool in each ball = 500
So Number of balls required = 2500 [tex]\div[/tex] 5 = 5
Ashley should buy 5 balls
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a femur 18 inches long is placed in traction with an elevation of 6.2 inches. what is the angle of elevation of the femur?
The angle of elevation of the femur is 71°.
The angle of elevation:
The angle is formed by the line of sight and the horizontal plane for an object above the horizontal.
Here we have to find the angle of elevation of the femur.
Data given:
length of femur = 18 inches
elevated = 6.2 inches
Formula to calculate the angle of elevation:
Tangent of the angle of elevation = height of the object/distance from the object
tan Ф = 18/ 6.2
tan Ф = 2.903
Ф = [tex]tan^{-1}[/tex]( 2.903)
= 71°
Therefore the angle of elevation is 71°.
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let x denote the number of canon slr cameras sold during a particular week by a certain store. the pmf of x is x 0 1 2 3 4 px(x) 0.1 0.2 0.3 0.25 0.15
the value of P(X=4,Y=2) is 0.0518.
Given that, X denote the number of Canon SLR cameras sold during a particular week by a certain store.
The probability mass function (pmf) of X is,
X 0 1 2 3 4
PX(x) 0.1 0.2 0.3 0.25 0.15
Let Y denote the number of purchasers during this week who buy an extended warranty.
The value of P(X=4,Y=2) is the probability that 4 cameras are sold and 2 extended warranties are sold in a week.
P(X=4,Y=2)=p(4,2)=P(Y=2|X=4)×P(X=4)
The number of purchasers purchasing the extended warranty can be 0, 1, ……, x.
Here x is cameras are sold.
Assuming that each customer buys at most 1 camera.
Considering that the event “a purchaser buys extended warranty” as “success” and the event “a purchaser does not buy extended warranty” as “failure”.
In that case, all the customers purchasing cameras buy extended is 60%.
The probability of failure is 0.4.
This follows the binomial distribution, where total number of trials is the number of purchasers of camera and x is the probability of success is 0.6.
The probability that 2 out of 4 cameras purchasers buys extended warranty with probability of success 0.6 is,
P(Y=2|X=4)=4C2(0.6)2(0.4)4−2=6×0.36×0.16=0.3456
Given that,
P(X=4)=0.15
Therefore,
P(X=4,Y=2)=P(Y=2|X=4)×P(X=4)=0.3456×0.15=0.0518
Therefore, the value of
P(X=4,Y=2) is 0.0518.
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