A firm that sells word processing systems keeps track of the number of customers who call on any one day and the number of orders placed on any one day. Let X denote the number of calls and Y the number of orders placed, and let P(X,Y) denote the joint probability mass function for X and Y. Records indicate that P(0,0)=0.04, P(1,0)=0.16, P(1,1)=0.1, P(2,0)=0.2, P(2,1)=0.3, P(2,2)=0.2. Thus, for any given day, the probability of, say, two calls and 1 order is 0.3.
Match the concept with the value.
E(X3)
Oy
E(3Y)
P(X >10Y > 0)
E(Y2)
Answers
The concept-value matching for the given scenario is as follows:
- E(X^3): Not given in the problem. - E(3Y): Not given in the problem.
- P(X > 10, Y > 0): 0 - E(Y^2): Calculated as 0.6.
In the provided problem, we need to match the given concepts with their corresponding values.
1. E(X^3): The expected value of X^3, the cube of the number of calls, is not provided in the problem. Since no probabilities or data are given for X^3, we cannot calculate its expected value.
2. E(3Y): Similarly, the expected value of 3Y, three times the number of orders placed, is not given in the problem. Without the necessary probabilities or data for 3Y, we cannot determine its expected value.
3. P(X > 10, Y > 0): This represents the joint probability that X is greater than 10 and Y is greater than 0. However, there is no information provided in the problem about values of X and Y exceeding 10. Therefore, the probability P(X > 10, Y > 0) is 0.
4. E(Y^2): We can calculate the expected value of Y^2, the square of the number of orders placed, based on the given probabilities. From the data provided, we can see that P(0,0) = 0.04, P(1,0) = 0.16, P(1,1) = 0.1, P(2,0) = 0.2, P(2,1) = 0.3, and P(2,2) = 0.2. To calculate E(Y^2), we multiply each possible value of Y squared by its corresponding probability and sum them up. In this case, E(Y^2) = (0^2 * 0.04) + (1^2 * 0.1) + (2^2 * 0.3) = 0 + 0.1 + 1.2 = 1.3.
In conclusion, the concepts E(X^3) and E(3Y) are not provided in the problem, making it impossible to calculate their expected values. The probability P(X > 10, Y > 0) is 0 since there is no information given for such values. Finally, the expected value of Y^2 is determined to be 1.3 based on the provided probabilities.
learn more about joint probability here: brainly.com/question/32099581
#SPJ11
Related Questions
Assume that a histogram of the sample is bell-shaped. Approximately what percentage of the sample values are between 70 and 82? Approximately of the sample values fall between 70 and 82. Correct answer: Assume that a histogram for the sample is bell-shaped. Between what two values will approximately 95% of the sample be? Approximately 95% of the sample values will fall between and
Answers
Assuming that the histogram for the sample is bell-shaped, approximately 68% of the sample values are within one standard deviation of the mean, 95% of the sample values are within two standard deviations of the mean, and 99.7% of the sample values are within three standard deviations of the mean.
Therefore, to estimate the percentage of sample values between 70 and 82, we need to find the number of standard deviations away from the mean that corresponds to these values.
First, we need to find the mean and standard deviation of the sample. Without this information, we cannot make any estimates.Once we have the mean and standard deviation, we can use the formula:
z = (x - μ) / σ
where z is the number of standard deviations away from the mean,
x is the sample value,
μ is the mean,
and is the standard deviation.
Once we have calculated the z-score for 70 and 82, we can look up the corresponding percentage of the distribution using a standard normal distribution table.The percentage of sample values between 70 and 82 will be the difference between these two percentages.
To learn more about “standard deviations” refer to the https://brainly.com/question/475676
#SPJ11
A car is traveling at a steady speed. It travels 2 miles in 35 minutes. How far will it 3 travel in 27 minutes? In 1 hour?
Answers
Answer:
The car will travel 30 2/3 miles in 45 minutes. The car will travel 40 miles in 1 hour
Step-by-step explanation:
HOPE THIS HELPS:>
The diagram shows a projected beam of light from a lighthouse. What is the area of land that can be covered by the light from the lighthouse?
Answers
The area of land that can be covered by the light from the lighthouse is determined as 325.2 mi².
What is the area of land that can be covered by the light from the lighthouse?The area of land that can be covered by the light from the lighthouse is calculated as follows;
Area of sector = πr² x (θ/360)
where;
r is the radius of the circleθ is the angle of the sectorThe angle covered by the land = 360 - 245⁰ = 115⁰
The area of the sector is calculated as follows;
A = π(18 mi) ² x (115/360)
A = 325.2 mi²
Learn more about area of sector here: https://brainly.com/question/30607726
#SPJ1
The distance between point Q and point P is 6 1/2 units .Which number could represent point Q?please help me
Answers
Answer:
\(Q =2\frac{1}{2}\) or \(Q =- 10\frac{1}{2}\)
Step-by-step explanation:
Given
\(P = -4\) --- missing from the question
\(Distance = 6\frac{1}{2}\)
Required
Determine the possible value of Q
The distance can be calculated using absolute function as:
\(Distance = |Q - P|\)
Substitute values for distance and P
\(6\frac{1}{2} = |Q - (-4)|\)
\(6\frac{1}{2} = |Q +4|\)
The absolute function can then be split as:
\(6\frac{1}{2} = Q + 4\) or \(-6\frac{1}{2} = Q + 4\)
Make Q the subject in both cases:
\(Q = 6\frac{1}{2} - 4\) or \(Q = -4 - 6\frac{1}{2}\)
\(Q =2\frac{1}{2}\) or \(Q =- 10\frac{1}{2}\)
the mean of the waiting times in an emergency room is 72 minutes with a standard deviation of 15.1 minutes for people who are admitted for additional treatment. the mean waiting time for patients who are discharged after receiving treatment is 61 minutes with a standard deviation of 11.4 minutes. which times are more variable? part: 0 / 20 of 2 parts complete
Answers
The waiting time for patients admitted for additional treatment is more variable than the waiting time for patients who are discharged after receiving treatment.
To determine which waiting time is more variable, we need to compare the standard deviation of the two groups. The standard deviation measures the amount of variability or dispersion of a set of data.
A larger standard deviation indicates that the data is more spread out, while a smaller standard deviation indicates that the data is more tightly clustered.
In this case, the standard deviation for patients admitted for additional treatment is 15.1 minutes, while the standard deviation for patients discharged after receiving treatment is 11.4 minutes.
Since 15.1 is larger than 11.4, this indicates that the waiting time for patients admitted for additional treatment is more variable than the waiting time for patients who are discharged after receiving treatment.
For more questions like Waiting time click the link below:
https://brainly.com/question/14051284
#SPJ4
use lagrange multipliers to find the extreme values of the function subject to the given constraint
f(x,y)= xy; 4x^2 + y^2 =8
Answers
Therefore, the extreme values of the function f(x, y) = xy subject to the constraint 4x^2 + y^2 = 8 are: Minimum value: 0 and Maximum value: 2.
To find the extreme values of the function f(x, y) = xy subject to the constraint 4x^2 + y^2 = 8, we can use the method of Lagrange multipliers.
Let's define the Lagrangian function L(x, y, λ) as:
L(x, y, λ) = f(x, y) - λ(g(x, y) - c)
where f(x, y) = xy is the objective function, g(x, y) = 4x^2 + y^2 is the constraint function, and c is the constant value of the constraint.
Taking the partial derivatives of L(x, y, λ) with respect to x, y, and λ, and setting them equal to zero, we get the following equations:
∂L/∂x = y - 8λx = 0 ...(1)
∂L/∂y = x - 2λy = 0 ...(2)
∂L/∂λ = 4x^2 + y^2 - 8 = 0 ...(3)
Solving equations (1) and (2) simultaneously, we have:
y - 8λx = 0 ...(4)
x - 2λy = 0 ...(5
From equation (4), we can express y in terms of λ and x:
y = 8λx ...(6)
Substituting equation (6) into equation (5), we get:
x - 2λ(8λx) = 0
x - 16λ^2x = 0
x(1 - 16λ^2) = 0
This equation has two possible solutions:
x = 0
1 - 16λ^2 = 0 => λ^2 = 1/16 => λ = ±1/4
Case 1: x = 0
Substituting x = 0 into equation (6), we have:
y = 8λ(0) = 0
From equation (3), we get:
4(0)^2 + y^2 - 8 = 0
y^2 = 8
y = ±√8 = ±2√2
Therefore, when x = 0, we have two critical points: (0, 2√2) and (0, -2√2).
Case 2: λ = 1/4
Substituting λ = 1/4 into equation (6), we have:
y = 8(1/4)x = 2x
From equation (3), we get:
4x^2 + (2x)^2 - 8 = 0
4x^2 + 4x^2 - 8 = 0
8x^2 - 8 = 0
x^2 = 1
x = ±1
Substituting x = 1 into equation (6), we have:
y = 2(1) = 2
Therefore, when x = 1, we have a critical point: (1, 2).
Substituting x = -1 into equation (6), we have:
y = 2(-1) = -2
Therefore, when x = -1, we have a critical point: (-1, -2).
In summary, the critical points are:
(0, 2√2), (0, -2√2), (1, 2), (-1, -2).
To determine the extreme values, we need to evaluate the function f(x, y) = xy at each critical point and find the maximum and minimum values.
f(0, 2√2) = 0 * 2√2 = 0
f(0, -2√2) = 0 * (-2√2) = 0
f(1, 2) = 1 * 2 = 2
f(-1, -2) = (-1) * (-2) = 2
To know more about extreme values,
https://brainly.com/question/20363673
#SPJ11
Transcribed Image Text:Use the definition of Ax to write the matrix equation as a vector equation. 4 5 40 - 9 - 5 27 1 - 7 32 The matrix equation written as a vector equation is
Answers
The matrix equation [4 5 40 - 9 - 5 27 1 - 7 32] can be written as a vector equation Ax = <40 27 32>
A matrix is a rectangular array of numbers, often denoted as Ax, where A is the matrix itself and x is the vector of numbers that make up the columns of the matrix.
In this problem, we are given the matrix equation 4 5 40 - 9 - 5 27 1 - 7 32 and asked to use the definition of Ax to write it as a vector equation.
To do this, we need to identify which numbers are in the matrix A and which numbers are in the vector x.
The numbers 4, 5, -9, -5, 1, and -7 represent the matrix A, while the numbers 40, 27, and 32 represent the vector x.
Therefore, the matrix equation can be written as Ax = 40 27 32.
To know more about matrix here.
https://brainly.com/question/28180105
#SPJ4
Carson's class voted on whether or not to do science fair projects in groups. 60% of the
10 votes were in favor of working in groups. how many votes were in favor?
Answers
The number of votes that were in favor of working in groups was 6 votes
Percentages are just fractions with the denominator 100. We use the percent symbol (%) to indicate that a number is a percentage. For example, if you correctly answered 75 out of 100 questions on a test, you would have gotten a 75% (75/100) mark.
Divide the amount by the total value and multiply the result by 100 to get the percentage. (Price/Total Price) The formula for computing percentages is 100%.
If 60% of the votes were in favor of working in groups, that means there were 60/100 * 10 votes = <<60/100*10=6>>6 votes in favor.
So, there were 6 votes in favor of working in groups.
Learn more about Percentage here: https://brainly.com/question/24304697
#SPJ4
question 29(multiple choice worth 1 points) (01.07 mc) multiply (2.4 ⋅ 1014) ⋅ (4 ⋅ 107). express the answer in scientific notation. 9.6 ⋅ 1021 9.6 ⋅ 1022 96 ⋅ 1021 96 ⋅ 1022
Answers
The multiplication of \((2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )\)in scientific notation is \(9.6 \times {10}^{21} \)
How to find the answer in scientific notation?Multiply the decimal numbers to multiply the integers in scientific notation. Add the 10 power exponents after that. In scientific notation, place the new power of 10 with the decimal.
given that \((2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )\)
Now, find the answer in scientific notation
\((2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )\)
combine the all the like terms
\((2.4 \times 4)( {10}^{14} \times {10}^{7} )\)
According to the exponent same base rule, an exponent will be added if the bases of two exponents are the same.
\((9.6) \times ( {10}^{14 + 7)} ) \\ 9.6 \times {10}^{21} \)
Hence,the multiplication of\((2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )\) in scientific notation is \(9.6 \times {10}^{21} \)
Learn more about multiplication in scientific notation from here:
https://brainly.com/question/28345285
#SPJ4
1. the production function is Cobb-Douglas requiring only labor input, i.e., Y =zNa,and
2. consumer get "disutility" from working, and the utility function is given by U (C, N ) = ln C − bN , where b is a parameter.
a. what is the the equilibrium wage as a function of labor demand N?
b. firm’s profit π = z must be
Answers
The equilibrium wage rate as a function of labor demand N is w = z, and the firm's profit π = 0.
a. To find the equilibrium wage as a function of labor demand N, we need to maximize the profit of the firm while taking into account the utility function of the consumer.
The firm's profit function is given by π = zN - wN, where w represents the wage rate.
To maximize the firm's profit, we take the derivative of the profit function with respect to N and set it equal to zero:
dπ/dN = z - w = 0
This implies that the equilibrium wage rate w is equal to z.
Therefore, the equilibrium wage as a function of labor demand N is simply w = z.
b. The firm's profit π is given by π = zN - wN, where w represents the wage rate. In this case, we have already established that the equilibrium wage rate is w = z.
Substituting w = z into the profit function, we have:
π = zN - zN = 0
Therefore, the firm's profit π is zero.
To know more about wage rate, refer here:
https://brainly.com/question/30461515
#SPJ4
Which one doesn't belong? Explain $25 more than $30 16 more than 17 12 less than 15 12 plus 14 equals 26
Answers
Answer:
I think the last one doesn't fit in
solve for x 2x^2 + x - 1 = 2
Answers
Answer:
x = - \(\frac{3}{2}\), x = 1
Step-by-step explanation:
Given
2x² + x - 1 = 2 ( subtract 2 from both sides )
2x² + x - 3 = 0 ← in standard form
(2x + 3)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - \(\frac{3}{2}\)
x - 1 = 0 ⇒ x = 1
Answer:
x= -3/2 or 1
Step-by-step explanation:
2x^2 +x-1=2
2x^2 +x-3=0
(2x+3)(x-1)=0
2x+3=0 x-1=0
2x= -3 x=1
x= -3/2 x=1
If QS represents an angle bisector, solve for X.
102
S
45
Q
R 41.8
T 33
a
23.3
52.5
b
Ос
Od
48
21
Answers
Answer:
i try my best to answer the question when i will find
Step-by-step explanation:
which two integers have a sum of - 15
Answers
Answer:
-13 and -2
Step-by-step explanation:
Answer:
Step-by-step explanation:
the product as 26 and the sum of the two numbers as 15, one can say that the two numbers are 13 and 2.
A line contains L(-4,-4) and M(2, 2) Line q is in the
same coordinate plane but does not intersect LM. Line q
contains point N.
Answers
parallel lines don’t intersect
Find the exact acute angle 0 for the given function value. tan 0 = √3 0- (Type your answer in degrees.)
Answers
So, the exact acute angle 0 for the given function value is 60°. Therefore, the answer is 60.
A function in mathematics seems to be a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a particular member in the second set (called the range). A function, in other words, receives input from one set and produces outputs from another.
The variable x has been frequently used to represent the inputs, and the changeable y is used to represent the outputs. A function can be represented by a formula or a graph. For example, the calculation y = 2x + 1 represents a functional form in which each value of x yields a distinct value of y.
To know more about function visit:
https://brainly.com/question/28193995
#SPJ11
If u= (1 + iv3) and v = (1 + 2iv3), then what is uv?
Answers
Answer:
your answer would be B. -5 +3i✓3
what is quadratic formula?
Answers
Answer:
x= - b + square root b square - 4ac by 2a
\( \huge \underline \mathtt \colorbox{cyan}{D=}\)
\(b^{2} - 4ac\)
\( \huge \underline \mathtt \colorbox{cyan}{Main Formula}\)
\( (- b + \binom{ + }{ - } \sqrt{d}) \div (2a)\)
a circle is inscribed in a unit square. a smaller square is then inscribed within the circle. what is the side length of the smaller square?
Answers
To solve this problem, we need to use some basic geometry concepts. First, we know that the diagonal of a unit square is the square root of 2, since the sides are of length 1. The side length of the smaller square inscribed within a circle inscribed in a unit square is 1.
Next, we know that the circle inscribed in the square will have a diameter equal to the diagonal of the square, which is the square root of 2. The radius of the circle will therefore be half of the diameter, which is sqrt(2)/2.
Now we can use the radius of the circle to find the side length of the smaller square inscribed within it. If we draw the diagonal of the smaller square, it will be twice the radius of the circle, or sqrt(2). This is because the diagonal of the square passes through the center of the circle and therefore has a length equal to twice the radius.
We can then use the Pythagorean theorem to find the length of each side of the smaller square. If we let x be the side length of the smaller square, then we have:
x^2 + x^2 = 2
2x^2 = 2
x^2 = 1
x = 1
Therefore, the side length of the smaller square is 1, which makes sense since it is inscribed within a unit square.
For more questions on geometry
https://brainly.com/question/24375372
#SPJ11
Enter the inverse function of f(x) = 15x - 14.
Answers
replace 'x' with 'y'
15y - 14 = x; solve for y
15y = x + 14
y = (x+14)/15
Three concert tickets cost `\$45`. At this same rate, how much do `12` tickets cost?
Answers
The cost of 12 tickets is $180.
Given that, three concert tickets cost $45.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here, the cost of one ticket
= 45/3
= $15
So, the cost of 12 tickets = 12×15
= $180
Therefore, the cost of 12 tickets is $180.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ1
HELP ITS A GRADE AND TIMED PLSSSSS?!?!?!?
Answers
Answer:
90 sq cm
Step-by-step explanation:
URGENT!! ALGEBRA 1
24) Which equation is represented by the graph below?
(1)y=x²-3
(2) y=(x-3)²
(3) y=|x|-3
(4) y = |x-3|
Answers
An equation that is represented by the graph below include the following: 3) y = |x| - 3.
What is a translation?In Mathematics, the translation a geometric figure or graph downward simply means adding a digit to the value on the y-coordinate of the pre-image or function.
In Mathematics, a vertical translation to the positive y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent a function.In conclusion, we can logically deduce that the graph of the parent function was y = |x| stretched away from the y-axis and translated by 3 units downward;
y = |x|
f(x) = |x| - 3
Read more on translation here: brainly.com/question/26869095
#SPJ1
Show your steps
Multiply and simplify if possible.
(3−√5)(7−√5)
Answers
The product of (3 - √5)(7 - √5) simplifies to 26 - 10√5.
To multiply and simplify the expression (3 - √5)(7 - √5), we can use the distributive property of multiplication over addition. Here are the steps:
1. Start by multiplying the first terms in each set of parentheses: 3 * 7 = 21.
2. Then multiply the outer terms: 3 * (-√5) = -3√5.
3. Next, multiply the inner terms: -√5 * 7 = -7√5.
4. Finally, multiply the last terms: -√5 * -√5 = 5.
Now we can combine these terms to simplify the expression:
21 + (-3√5) + (-7√5) + 5
Combine the like terms: 21 + 5 - 3√5 - 7√5
Combine the constants: 21 + 5 = 26.
Combine the radical terms: -3√5 - 7√5 = -10√5.
The final simplified expression is: 26 - 10√5.
for more search question product
https://brainly.com/question/28782029
#SPJ8
PLEASE HELP! ASAP NEED HONEST ANSWERS PLEASE!!
Answers
Answer:
x = -5
Step-by-step explanation:
60° + 70° + 55 + x = 180° (sum of angles in a triangle)
185° + x = 180°
x = -5
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the lea
Answers
Answer:
at least 5
Step-by-step explanation:
If the question was similar to the one given below
A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?
The answer would be as follows
If we use 3 letters or any distinct letter as a comma such that 2 are in alphabetical order then we would get
4C2= 6 ways to use these letters and the comma
If we use 4 letters or any distinct letter as a comma such that 2 are in alphabetical order then we would get
5C2= 10 ways to use these letters and the comma
If we use 5 letters or any distinct letter as a comma such that 2 are in alphabetical order then we would get
6C2= 15 ways to use these letters and the comma
We need the least number of the alphabets to assign codes to 12 participants.
So the least number of alphabets is 5 because it can give codes to at least to 12 people .
Pair of alphabets + distinct letter ≥ 12
5 + 1 ≥ 12
6c2 ≥ 12
15 ≥ 12
Can someone please help me solve #6
I’ll give brainiest to the first answer
Answers
Answer: It's either 278 or 178
Step-by-step explanation: I didn't know what equation the question wants you to use so for the first equation it showed I did (10^2+24+10+144) and got 278. For the second equation I did 24+10+144 and got 178. Considering it gave you ax+b as an area equation I just added them (same with the other equation). I don't know whether those are correct of not though.
PLEASE HELP WITH GEOMETRY!!
Answers
Answer:
x = 14.1
Step-by-step explanation:
sin (40) = x/22
x = 22 (sin(40))
x = 14.1
6 (2n + 5 ) = 66
solve for n
Answers
Answer:
n=3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
6(2n+5)=66
(6)(2n)+(6)(5)=66(Distribute)
12n+30=66
Step 2: Subtract 30 from both sides.
12n+30−30=66−30
12n=36
Step 3: Divide both sides by 12.
12n/12 = 36/12
n=3
Answer:
n = 3
Step-by-step explanation:
Distribute 6 into 2n+5, which is 12n +30
Subtract 30 from 66, which is 36
Divide 36 by 12
You're left with n = 3
Or in numbers:
6(2n+5)=66
12n+30=66
12n=36
n=3
Suppose that A is an n x n diagonal matrix with rank r, where rsn. Which of the following is true about
A?
A. O is an eigenvalue with algebraic muitiplicity n-r
B. O is an eigenvalue, but there is not enough information to determine the geometric multiplicity
C O is an eigenvalue with geometric multiplicity ner
DO is not an eigenvalue.
Answers
A is an n x n diagonal matrix with rank r , where rsn and the statement (a)"O is an eigenvalue with algebraic muitiplicity n-r " about A is true
Since A is an n x n diagonal matrix with rank r, the number of non-zero entries on the diagonal is r. This means that there are n - r zero entries on the diagonal.
For any diagonal matrix, the eigenvalues are simply the entries on the diagonal. Since there are n - r zero entries, the eigenvalue O has a geometric multiplicity of n - r.
Therefore, the correct statement is that O is an eigenvalue with geometric multiplicity n - r.
To know more about eigenvalue refer here:
https://brainly.com/question/14415841
#SPJ11