Answer:
The answer is "between 0.10 and 0.05".
Step-by-step explanation:
For sample 1:
[tex]n_1 = 25\\\\\bar{x_1} = 90.00\\\\ s_1 = 9\\\\[/tex]
For sample 2:
[tex]n_2 = 25\\\\ \bar{x_2} = 95.08\\\\ S_2 = 12\\\\[/tex]
Calculating the null and alternative hypotheses:
[tex]H_O : \mu_1 = \mu_2 \\\\ H_Q : \mu_1 <\mu_2[/tex]
Calculating the test statistic:
[tex]Z= \frac{90-95.08}{ \sqrt{\frac{9^2}{25}+\frac{12^2}{25}}} \\\\ =\frac{-5.08}{ \sqrt{\frac{81}{25}+\frac{144}{25}}}\\\\=\frac{-5.08}{ \sqrt{\frac{81+144}{25}}}\\\\=\frac{-5.08}{ \sqrt{\frac{225}{25}}}\\\\=\frac{-5.08}{ \frac{15}{5}}\\\\=\frac{-5.08}{3}\\\\= -1.693[/tex]
Calculating the conservative degrees of freedom:
[tex]DF = min (n_1 -1, n_2 - 1) = min(25-1, 25-1) = 24[/tex]
by using Excel the p-value for left tailed test and for test statistic will be [tex]-1.693[/tex] with [tex]DF = 24[/tex].
[tex]\to p-value = TDIST(1.693, 24, 1) = 0.0517\ \ \ \ i.e, \bold{0.05 < p-value < 0.10}[/tex]
The clearing house has resistors that sell for $3.50 each and circuit boards that sell for $2.25 each. Write an inequality that represents how many of each type of electronic equipment can be bought with at most $7.
Answer:
3.50x + 2.25y smaller than or equal 7
Step-by-step explanation:
Let x represent the resistor and y represent the circuit board
Resistor: $3.50
Circuit board: $2.25
We know it can be bought at most for $7, so it will be smaller than or equal to $ 7. So, we have equation
3.50x + 2.25y smaller than or equal 7
The acceleration y, in meters per second squared, of an object after x seconds is given by y =. During the first 10 seconds, over which intervals is the acceleration increasing?.
During the first 10 seconds, in the intervals (0, 2) and (6, 10) the acceleration is increasing.
The acceleration is: y = 7*sin( x*pi/4).
Sin(θ) increases between -pi/2 and pi/2
Sin(θ) decreases between pi/2 and (3/2)*pi.
And so on.
Here we have:
θ = x*(pi/2)
When x = 0, θ = 0.
And sin(θ) is increasing in θ = 0.
Then we must choose one of the options that start with x = 0.
now it will stop increasing when:
θ = pi/2 = x*(pi/4)
x = 2.
So the acceleration is increasing in the segment (0,2)
And it will start increasing again when:
θ = (3/2)*pi = x*(pi/4)
(3/2)*pi*(4/pi) = 6 = x.
So at x= 6 the acceleration starts increasing again, and the acceleration is only defined until x = 10, then
the correct option is: (0, 2) and (6, 10)
Thus, during the first 10 seconds, in the intervals (0, 2) and (6, 10) the acceleration is increasing.
Complete question:
The acceleration y, in meters per second squared, of an object after x seconds is given by y = 7 sin (pi/4 x). During the first 10 seconds, over which intervals is the acceleration increasing?
(2, 6)
(4, 8)
(0, 2) and (6, 10)
(0, 4) and (8, 10)
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The acceleration is: y = 7*sin( x*pi/4).
Sin(θ) increases between -pi/2 and pi/2
Sin(θ) decreases between pi/2 and (3/2)*pi.
And so on.
Here we have:
θ = x*(pi/2)
When x = 0, θ = 0.
And sin(θ) is increasing in θ = 0.
θ = pi/2 = x*(pi/4)
x = 2.
θ = (3/2)*pi = x*(pi/4)
(3/2)*pi*(4/pi) = 6 = x.
So at x= 6 the acceleration starts increasing again, and the acceleration is only defined until x = 10, then
Thus, during the first 10 seconds, in the intervals (0, 2) and (6, 10) the acceleration is increasing.
(2, 6)
(4, 8)
(0, 2) and (6, 10)
(0, 4) and (8, 10)
What is the solution of the system of equations system?
The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect. To solve a system is to find all such common solutions or points of intersection.
A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
Calculating the unknown variables while keeping the equations balanced on both sides is the process of solving a system of equations. Finding the value of the variable that makes the condition of all the provided equations true is how we solve an equation system. There are several ways to solve a system of equations, including
graphical approachsubstitute techniqueElimination procedureCross-multiplication methodLearn more about system of equations to visit this link
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Ridgid motions to prove
Step-by-step explanation:
Kamla tablet in other developed its to the previous yield
pls help me again like this is hard
Answer:
10. Some of the class 4 children Amar, Bindu, Charisma, Danny are friends with some of the class 5 children Amar Diana Ekta Raghu Prem. The following table tells us which 2 children are friends with each other.
10. C11. A
12. 20 cm - 2(4cm) = 12
2(6cm length) + 2(4cm width) = 20 cm
12 + 8 = 20 cm
area = length * width
area = 6 * 4
area = 24 cm²
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-May I ask what’s the answer to this MC question because what I've calculated is 36 to the power 222 which giant matched the above choices
Answer:
B
Step-by-step explanation:
I just answered this question. you posted it multiple times ?
again
16 = 2⁴
9 = 3²
so, we have
(2⁴)¹¹¹ × (3²)²²² = 2⁴⁴⁴ × 3⁴⁴⁴ = (2×3)⁴⁴⁴ = 6⁴⁴⁴
remember, you can only combine either the exponents of the same base, or the bases of the same exponents (like in our case here).
What value of n makes the equation true?
Answer:
n=5
Step-by-step:
What divided by 10 equals 2? Well, 5 does. So, when you divide the exponents, it will equal the other side.
Sharonda uses a blend of dark chocolate and milk chocolate to make the ice cream topping at her restaurant. She needs to buy 120\,\text{kg}120kg120, start text, k, g, end text of chocolate in total for her next order, and her recipe calls for twice the amount of dark chocolate as milk chocolate. Let ddd be the number of kilograms of dark chocolate she buys and mmm be the number of kilograms of milk chocolate she buys. Which system of equations represents this situation?.
The equations m = 2d and m+d = 120 represent this situation.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
d = kilograms of dark chocolate
m =kilograms of milk chocolate
So, her recipe calls for twice the amount of dark chocolate as milk chocolate.
Mathematically speaking:
m = 2d
She needs to buy 120 kg, of chocolate in total. So;
m + d = 120
The following system of equations represents the situation:
m = 2d
m+d = 120
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The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
So, her recipe calls for twice the amount of dark chocolate as milk chocolate.
m = 2d
She needs to buy 120 kg, of chocolate in total. So;
m + d = 120
The following system of equations represents the situation:
m = 2d
m+d = 120
Find the circumference of a semicircle with diameter d cm
Answer:
Circumference of the semi-circle is d(π/2 + 1)
Step-by-step explanation:
Circumference of a semicircle is πr + 2r
So, since r = d/2,
therefore, π*d/2 + 2*d/2 = πd/2 + d = d(π/2 + 1).
i need help with this
Answer:
v = 6
w=13
Step-by-step explanation:
v = 6 because we know that both of the triangles are the same, they just rotate, but the measure is still the same.
To calculate w, we have the formula
2w + v + 11 = w - 3v +48
We already know v = 6, so put 6 in the v spot
2w + 6 + 11 = w -3(6) + 48
2w + 17 = w - 18 + 48
2w + 17 = w +30
Subtracted 17 from both sides
2w = w + 13
Subtract w from both sides
w= 13
Step-by-step explanation:
to add to the other correct answer :
the symbol means that both triangles are congruent.
and that means that when you turn then so that both can be laid on top of each other in the same direction, they would perfectly cover each other without any overlap whatsoever.
and that means that they must have the same angles and the same side lengths (and also other lengths like heights, bisectors, ...).
therefore,
v + 9 = 15
v = 6
and then
2w + v + 11 = w - 3v + 48
giving us w = 13
as the other answer already shows how.
and ED = QR, of course.
How can you describe the behavior of the graph of a polynomial function at its intercept with even number of multiplicities?
At its intercept with even number of multiplicities, the graph of a polynomial function will have a smooth curve that passes through the intercept point. The curve will loop around the intercept point, increasing and then decreasing in a cyclic manner, before repeating the pattern.
At its intercept with even number of multiplicities, the graph of a polynomial function will have a smooth curve that passes through the intercept point. This is because the multiplicities of the intercept point are even, meaning that the graph will not have a hard turn or corner at the intercept point. Instead, the graph will loop around the intercept point, gradually increasing until it reaches a peak before gradually decreasing and eventually reaching the same point it started at. This cyclic pattern will repeat itself as the graph moves away from the intercept point. The even number of multiplicities means the graph will not have any sharp turns or corners, only a smooth curve that passes through the intercept point.
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32 x 79 =
PLEASE HELP QUICK
Answer:
2528
Step-by-step explanation:
[tex]32\times79[/tex]
Multiply:
[tex]32\times79[/tex]
[tex]=\fbox{2528}[/tex]
I need to know how to find the answer to this question. -15 + n = -9
Answer:
n = 6
Step-by-step explanation:
-15 + n = -9
Add 15 to both sides
n = 6
So, the answer is 6
What is the formula for standard deviation of a sample in R?
For the sample provided, The formula for standard deviation is slightly different than the population standard deviation. The answer is
[tex]\sqrt \frac{\sum (x-\bar x)^2}{n-1}[/tex] .
What do you mean by sample?Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
sample size = n
sample standard deviation (s) = [tex]\sqrt \frac{\sum (x-\bar x)^2}{n-1}[/tex]
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The height of a triangle is 8 centimeters greater than three times its base. The area of the triangle is 128 square centimeters. What is the base of the triangle?
(Hint: area of triangle=12⋅base⋅height)
40 cm
8 cm
5 1/3 cm
16 cm
Answer:
To solve this problem, we can use the formula for the area of a triangle, which is A=1/2bh, where b is the base and h is the height. In this problem, we are given that the area of the triangle is 128 square centimeters, so we can set up the following equation:
A = 1/2bh
128 = 1/2bh
We are also given that the height of the triangle is 8 centimeters greater than three times the base, so we can set up the following equation:
h = 3b + 8
We can substitute the second equation into the first equation to get the following:
128 = 1/2bh
128 = 1/2(3b + 8)b
128 = 3/2b^2 + 4b
We can then use the quadratic formula to solve for b, the base of the triangle:
b = (-4 +/- sqrt(4^2 - 4(3/2)(128)))/(2(3/2))
b = (-4 +/- sqrt(64 - 192))/3
b = (-4 +/- sqrt(-128))/3
Since the square root of a negative number is not a real number, we know that there is no solution to this equation, which means that the given information is not sufficient to determine the base of the triangle.
Therefore, the correct answer is that the base of the triangle cannot be determined from the information given.
To solve this problem, we can use the formula for the area of a triangle, which is A=1/2bh, where b is the base and h is the height. In this problem, we are given that the area of the triangle is 128 square centimeters, so we can set up the following equation:
A = 1/2bh
128 = 1/2bh
We are also given that the height of the triangle is 8 centimeters greater than three times the base, so we can set up the following equation:
h = 3b + 8
We can substitute the second equation into the first equation to get the following:
128 = 1/2bh
128 = 1/2(3b + 8)b
128 = 3/2b^2 + 4b
We can then use the quadratic formula to solve for b, the base of the triangle:
b = (-4 +/- sqrt(4^2 - 4(3/2)(128)))/(2(3/2))
b = (-4 +/- sqrt(64 - 192))/3
b = (-4 +/- sqrt(-128))/3
Since the square root of a negative number is not a real number, we know that there is no solution to this equation, which means that the given information is not sufficient to determine the base of the triangle.
Therefore, the correct answer is that the base of the triangle cannot be determined from the information given.
P(x)= 1/2x^2+3x-4x^3x+6x^4-1 write in standard form, is it polynomial, what degree, type, and leading coefficient is it?
Answer is 1. Polynomial Function is a quadratic, cubic, and of any degree function. It involves only a non - negative powers of x.
Find the solution ?Things to Remember: Leading coefficient is the numerical coefficient of the term with the highest degree.To write a polynomial function in standard form, simply arrange the terms according to the degree of the variable. The number of turning points/solutions of the polynomial function is based on the highest degree of the polynomial function.Polynomial Function is a quadratic, cubic, and of any degree function. It involves only a non - negative powers of x. The roots of the function are the values that when substituted equates the polynomial to 0.These are also the values that intercepts the x-axis with the graph. involves only non-negative integer powers or only positive integer exponents of a variable in a equation like the quadratic equation, cubic equation, and others.To learn more about Polynomial Function refer
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What is the median if there are 11 numbers?
The Median for n = 11 numbers will be 6th term of the Observation set.
One measure of central tendency is the median. The median is the number that lies in the middle of the specified range of integers. It separates the higher half from the lower half of a particular data sample. At least half of the observations are above or equal to the median, and at least half of the observations are below the median.
The median can be calculated as follows when there are odd numbers of observations in a data collection:
Step 1: Arrange the sample of data in ascending or descending order.
Step 2: If the number of observations (let's say n) is odd, the middle observation is the median of the given data.
Median = [tex](\frac{n+1}{2} )^{th}[/tex] term.
Here n = 11, So median will be 6th term of Observation set.
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If x = 6, y = 4 and z = 1, evaluate x(y to the power of 2 - z)
The solution to the evaluation of the expression x(y² - z) x = 6, y = 4 and z = 1 is 90
How to solve equationEvaluate:
x(y² - z)
When
x = 6, y = 4 and z = 1
x(y² - z)
substitute the value of x, y and z
= 6(4² - 1)
Applying PEMDAS:
P = parenthesis
E = Exponential
M = Multiplication
D = Division
A = Addition
S = Subtraction
= 6(16 - 1)
= 96 - 6
= 90
In conclusion, the expression x(y² - z) when evaluated gives 90.
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, if "y varies directly as x", find the constant of variation and write an equation of direct variation that
relates the two variables.
y = 12 when x = 1/4
Answer:
k = 48 , y = 48x
Step-by-step explanation:
given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 12 when x = [tex]\frac{1}{4}[/tex] , then
12 = [tex]\frac{1}{4}[/tex] k ( multiply both sides by 4 to clear the fraction )
48 = k
constant of variation is then k = 48 , so
y = 48x ← equation of variation
What is the total net worth if the banker pays off the student loans? $219,869 $247,517 $233,693 $252,304.
Given the credit union banker's assets and liabilities, their total net worth is C. $233,693.
The difference between a person's long-term and short-term assets and obligations is that person's net worth (long-term and short-term).
The equity of a company, or the net assets possessed by the stockholders after all obligations have been settled, is comparable to the net value of the company.
Assets:
Car Value = $29,850
Savings Accounts = $12,409
Treasury Bonds = $10,000
Checking Account Balance = $19,419
Home Value = $194,450
Total assets = $266,128
Liabilities:
Car loan = $10,560
Student Loans = $13,824
Credit Card Balance = $8,051
Total liabilities = $32,435
Net worth = $233,693 ($266,128 - $32,435)
Thus, the banker's net worth is $233,693.
Complete question:
The assets and liabilities of a credit union banker are listed below.
What is the total net worth if the banker pays off the student loans?
A. $219,869
B. $247,517
C. $233,693
D. $252,304
(Refer to the image for the table)
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Car Value = $29,850
Savings Accounts = $12,409
Treasury Bonds = $10,000
Checking Account Balance = $19,419
Home Value = $194,450
Total assets = $266,128
Liabilities:
Car loan = $10,560
Student Loans = $13,824
Credit Card Balance = $8,051
Total liabilities = $32,435
Net worth = $233,693 ($266,128 - $32,435)
Thus, the banker's net worth is $233,693.
Tan 32 deg + tan 88 deg / 1 - tan32 tan88 = -√3
Answer:
Step-by-step explanation:
[tex]\displaystyle\\\frac{tan32^0+tan88^0}{1-tan32^0tan88^0} \ \ \ \ (1)\\\\Let\ \alpha =32^0\ and\ \beta =88^0\\\\Hence,\ expression\ (1)\ will \ look\ like\ this:\\\\\frac{tan\alpha +tan\beta }{1-tan\alpha tan\beta }\\[/tex]
The trigonometric formula for adding angles for a tangent is as follows:
[tex]\displaystyle\\\\\boxed {tan(\alpha +\beta )=\frac{tan\alpha +tan\beta }{1-tan\alpha tan\beta }}[/tex]
Thus,
[tex]\displaystyle\\\frac{tan32^0 +tan88^0 }{1-tan32^0 tan88^0 }=tan(32^0+88^0)\\\\\\\frac{tan32^0 +tan88^0 }{1-tan32^0 tan88^0 }=tan120^0[/tex]
Calculate the value of tan120°:
[tex]tan120^0=tan(90^0+30^0)\\\\tan120^0=-cot30&^0\\\\tan120^0=-\sqrt{3}[/tex]
So,
[tex]\displaystyle\\\frac{tan32^0 +tan88^0 }{1-tan32^0 tan88^0 }\equiv-\sqrt{3}[/tex]
What is a whole number called?
Answer:
they are called whole numbers
Step-by-step explanation:
How do you describe the relationship of a square root?
Therefore , the relationship of square root can be illustrated as [tex]y^{2}[/tex] = x.
What is square root ?A number's square root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as [tex]3^{2}[/tex] or as 3 x 3.
Here,
In math, the square root of a number x is a number y such that y2 = x, or a number y whose square
(the result of multiplication by itself, or y), is x.
As an illustration, 4 and 4 are the square roots of 16, since 42 = (4)2 = 16.
Therefore , the relationship of square root can be illustrated as [tex]y^{2}[/tex] = x
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Two piece of metal meaure1 1/6 yard and3/12 yard each. Three time the amount of metal i needed for a project. How many total yard of metal i needed?
The total number of yards needed is (4 + 1/4) yards of metal.
In this case, there are two pieces measuring (1 + 1/6) yard and (3/12) yard; adding the two, the total length is:
L = (1 + 1/6) yard + (3/12) yard
= (1 + 2/12) yard + 3/12yardd
= (1 + 5/12) yard
Since three times that amount of metal is needed, then the total amount of metal that is needed is found by multiplying the total length obtained above by three:
3×L = 3×(1 + 5/12) yard = (3 + 15/12) yard
Writing this as a mixed number:
(3 + 12/12yard + 3/12yard) = (4 + 3/12) yard = (4 + 1/4) yard
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How do you find potential rational zeros?
The leading coefficient and the constant term must both be divisible by the fraction's denominator in order to factor using the rational root theorem.
In plants, a stem's primary role is to aid in the transfer of water and minerals from the roots to the leaves and other sections of the plant. Additionally, it supports the buds, leaves, flowers, fruits, and branches of plants.
The rational root theorem, also known as the rational root test, is an algebraic principle that states that for a polynomial equation with one variable and integer coefficients to have a solution (root) that is a rational number, both the leading coefficient and the constant term must be divisible by the fraction's denominator.
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Calculate (1/x1)+(1/x2)+(1/x3), where x1,x2,x3 are the solutions of the eq. x^3 -3x +1=0
The expression can be evaluated using the property of zeros as 0.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given equation is x³ - 3x + 1 = 0.
Its zeros are given as x₁, x₂ and x₃.
As per the properties of zeros of a cubic equation, the following expressions can be written as,
x₁x₂x₃ = Constant term ÷ Coefficient of x³
⇒ x₁x₂x₃ = 1.
And, x₁x₂ + x₂x₃ + x₁x₃ = Coefficient of x² ÷ Coefficient of x³
⇒ x₁x₂ + x₂x₃ + x₁x₃ = 0.
Now, the given expression 1/x₁ + 1/ x₂ + 1/x₃ can be evaluated as below,
(x₁x₂ + x₂x₃ + x₁x₃)/x₁x₂x₃ = 0/1
⇒ 0
Hence, the given expression can be evaluated as 0.
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How do you solve algebraic expressions Grade 7?
Algebraic expressions can be solved by using the order of operations. The order of operations is PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
To solve an algebraic expression, start by simplifying any parts inside parentheses, then move on to the exponents. Next, perform any multiplications and divisions from left to right. Finally, complete any additions and subtractions from left to right.How solve algebraic expressions Grade 7?The best way to solve algebraic expressions in Grade 7 is to use the Order of Operations (also known as PEMDAS) or BEDMAS. The Order of Operations states that you must first complete any operations inside parentheses, followed by Exponents, Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right). Once you have completed the operations in the correct order, you will have the solution to the algebraic expression.
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Who found zero in maths?
Answer:
Mohammed ibn-Musa al-Khowarizmi
Given that D(x) = 2x, select all of the following that are true statements. D( x) is a direct variation. D( x) is a function. D( x) is a rule for the set of points (5, 10), (6, 12) and (-2, -4). x is the dependent variable. D(6) = 3
Answer:
Step-by-step explanation:
I reformatted the question to clarify the statements. Please check for accuracy.
Given that D(x) = 2x, select all of the following that are true statements.
1. D( x) is a direct variation.
2. D( x) is a function.
3. D( x) is a rule for the set of points (5, 10), (6, 12) and (-2, -4).
4. x is the dependent variable.
5. D(6) = 3
----------
1. D( x) is a direct variation. YES. D(x) will always be 2 times x.
2. D( x) is a function. YES. Each calculated D(x) will have a unique point.
3. D( x) is a rule for the set of points (5, 10), (6, 12) and (-2, -4). YES. Each (x,y) shows a value of y that is 2 times x, as per the equation's instructions.
4. x is the dependent variable. YES. y depends on what value is chosen for x.
5. D(6) = 3 NO. d(6) = 2*(6) or 12
y is the number of tickets purchased for a randomly chosen olympic event. is the random variable y discrete or continuous?
The number of tickets purchased for a randomly chosen Olympic event. is the continuous random variable.
y is the number of tickets purchased for a randomly chosen Olympics event. is the random variable y discrete or continuous?
A random variable is a numerical quantity that is generated by a random experiment.
A random variable is called discrete if it has either a finite or a countable number of possible values. A random variable is called continuous if its possible values contain a whole interval of numbers.
A random variable is a number generated by a random experiment.
A random variable is called discrete if its possible values form a finite or countable set.
A random variable is called continuous if its possible values contain a whole interval of numbers.
In Olympics , number of event are there . that are not countable.
therefor, the number of tickets purchased for a randomly chosen Olympic event. is the continuous random variable.
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A random variable is a numerical quantity that is generated by a random experiment.
A random variable is called discrete if it has either a finite or a countable number of possible values. A random variable is called continuous if its possible values contain a whole interval of numbers.
A random variable is called continuous if its possible values contain a whole interval of numbers.
The number of tickets purchased for a randomly chosen Olympic event. is the continuous random variable.