A small internet trading company estimates that each network blackout results in a $500 loss. Compute expectation and variance of this company’s daily loss due to blackouts.
x = 0, 1, 2
Px = 0.7, 0.2, 0.1
The expectation (mean) of the company's daily loss due to blackouts is $200, and the variance is $350.
To compute the expectation of the company's daily loss, we multiply each possible loss value by its corresponding probability and sum them up. In this case, we have three possible loss values (0, 1, and 2) with their respective probabilities (0.7, 0.2, and 0.1). Multiplying each loss value by its probability and summing them gives us the expected value of $200.
To calculate the variance, we need to find the squared differences between each possible loss value and the expected value, multiply them by their respective probabilities, and sum them up. Squaring the differences ensures that negative differences do not cancel out positive differences. In this case, the variance is calculated as (0 - 200)^2 * 0.7 + (1 - 200)^2 * 0.2 + (2 - 200)^2 * 0.1, resulting in a variance of $350.
The expectation and variance provide useful measures of the central tendency and variability, respectively, of the company's daily loss due to blackouts.
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pls help!
how to solve this?
identify the hypothesis and conclusion of the following statement: if 2 lines are perpendicular then they form 4 right angles.
Answer:
Step-by-step explanation:
The hypothesis needs to explain the certain conditions that need to exist in order for a specific conclusion to take place. Meaning that if these conditions are not present in the scenario, then the conclusion would be different or simply not exist. Based on this info we can say that the hypothesis is "2 lines are perpendicular" while the conclusion is "The lines form 4 right angles"
HELP WITH 5 & 6 DUE SOON!!!
Answer:
5: All triangles that share those three properties must be congruent.
6: All triangles that share those three properties must be congruent.
Hope this helps, have a great day :)
Determine the prime factorization of 88. 2^2• 3 • 5 2^3• 11 2 • 3^2• 5 2^2• 11
Answer:
2 three times or 2, 2, 2, and 11
Step-by-step explanation:
if you're writing/explaining in exponential form, this is how you write it out, 2³ x 11¹
YW.
What is the answer. Do anything begging for help
Answer:what’s the question?
Step-by-step explanation:
Which probabilities do you need in order to
calculate p(getting a on 2 or fewer spins)?
-p(0 successes)
-p(1 success)
-p(2 successes)
-p(3 successes)
-p(4 successes)
-p(5 successes)
answer: a,b, c
part b:
p(getting a on 2 or fewer spins)= answer: 0.79
Therefore , the solution to the problem of the probability comes out to be P(2 successes) thus , option C is correct.
How does probability work?The ability to occur is known as probability. The occurrence of random events is the subject of this branch of mathematics. The value is expressed as a number ranges between 0 and 1. The mathematical concept of likelihood has been used to predict how probable certain events are to occur. The definition of probability is essentially how likely it is that something will occur. This basic concept of probability serves as the foundation for the probability distribution.
Here,
compute p (getting a on 2 or fewer spins)
p (0 successes),p (One success) p (One success) p (Two successes) and p (3 successes)
-p(4 victories) -p (5 successes)
The likelihood that A will appear on two spins or fewer is what we're attempting to calculate.
You would need to be aware of the likelihood of two success sequences.
So, C. P. is your response (2 successes)
Therefore , the solution to the problem of the probability comes out to be P(2 successes) thus , option C is correct.
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THANK YOU :D
≈≈≈≈≈≈≈≈≈≈≈≈≈≈
Original Price Percent of Discount Sale Price
$
64% $72
The original price when 64% is applied to the item will be $200.
What is the percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentile in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value × 100
Let 'x' be the Original Price. Then the equation is given as,
(1 - 0.64) x = $72
0.36 x = $72
x = $200
The original price when 64% is applied to the item will be $200.
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suppose five students from the class are chosen at random. what is the probability that none are mechanical engineering majors?
The probability that none are mechanical engineering majors is 0.51.
The number of students who are not mechanical engineering majors is 100 - 49 = 51. The probability of choosing a student who is not a mechanical engineering major in one draw is 51/100. The probability of choosing five students in a row who are not mechanical engineering majors is (51/100)^5. Thus, the answer is (51/100)^5 = 0.1517816.
Probability refers to potential. From 0 to 1 is used to express the value. To determine how likely an event is to occur, probability has been introduced in mathematics. This is the fundamental theory of probability, which is also applied to the probability distribution, and from which you will discover the likelihood of results for a random experiment. The complete number of possibilities that can occur should be known before calculating the likelihood that a certain event will occur.
The complete question is:-
In a class of 100 students, 30 are computer science majors, 49 are mechaincal engineering majors, 13 are civil engineers and the rest are general engineering majors. Assume students only have one major.Suppose five students from the class are chosen at random what is the probability none are mechanical engineering majors?My info I know: The mechanical engineers account for 49% of the students, making 51% not mechanical engineers? Do I take five out of the 51, so 0.05 X 0.51?
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Identify the surface area of the composite figure.
Anwers:
S = 576 m2
S = 464 m2
S = 704 m2
S = 512 m2
Answer:
512 m^2
Step-by-step explanation:
surface area of the pyramid without the base=8×12×1/2×4=192
surface area of the square without one side=8×8×5=320
total surface area=192+320=512
Find vollume z=f(x,y) z=x2+y2;0⩽x⩽1,0⩽y⩽1 A) 32 ? b) Find volume of indicated region 9x+8y+10z=1 C) 240 ? C) Evaluate the integrals ∬RXydAR:7⩽x⩽9,4⩽y⩽7 C) 176??? ∫04∫016−x2xdydx B) 352??
A) The volume of the region defined by z = x² + y² over 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is 5/6.
B) The volume of the region defined by the equation 9x + 8y + 10z = 1 is infinite.
C) The volume of the region defined by ∬R XydA over 7 ≤ x ≤ 9 and 4 ≤ y ≤ 7 is 104.
D) The volume of the region defined by ∫(0 to 4) ∫(0 to 16-x²) x dy dx is approximately 341.33.
A) To find the volume of the region defined by z = f(x, y) = x² + y² over the given limits, we integrate the function with respect to x and y.
∫(0 to 1) ∫(0 to 1) (x² + y²) dy dx
Integration with respect to y:
∫(0 to 1) [xy² + (y³/3)] from 0 to 1 dx
Simplifying:
∫(0 to 1) (x + 1/3) dx
Integration with respect to x:
[ (x²/2) + (x/3) ] from 0 to 1
Substituting the limits:
[(1/2) + (1/3)] - [(0/2) + (0/3)]
= 1/2 + 1/3
= 3/6 + 2/6
= 5/6
Therefore, the volume of the region is 5/6 or approximately 0.8333.
B) To find the volume of the region defined by the equation 9x + 8y + 10z = 1, we need to express the equation in terms of z and solve for the bounds of z.
Rearranging the equation:
10z = 1 - 9x - 8y
z = (1 - 9x - 8y)/10
Now, let's examine the bounds for x and y. Since the equation does not provide any specific ranges for x and y, we can assume that they can take any real values.
Therefore, the volume of the region is infinite since it extends indefinitely in the x, y, and z directions.
C) To evaluate the integral ∬R XydA over the given region R, we integrate the function Xy with respect to x and y.
∫(7 to 9) ∫(4 to 7) Xy dy dx
Integration with respect to y:
∫(7 to 9) [ (xy²/2) ] from 4 to 7 dx
Simplifying:
∫(7 to 9) [ 7x - (x/2) ] dx
Integration with respect to x:
[ (7x²/2) - (x²/4) ] from 7 to 9
Substituting the limits:
[ (7(9)²/2) - (9²/4) ] - [ (7(7)²/2) - (7²/4) ]
Simplifying:
[ (7(81)/2) - (81/4) ] - [ (7(49)/2) - (49/4) ]
= [ (567/2) - (81/4) ] - [ (343/2) - (49/4) ]
= (1134/4 - 81/4) - (686/4 - 49/4)
= (1053/4) - (637/4)
= 416/4
= 104
Therefore, the volume of the region is 104.
D) To evaluate the integral ∫(0 to 4) ∫(0 to 16-x²) x dy dx, we integrate the function x with respect to y and then with respect to x.
Integration with respect to y:
∫(0 to 16-x²) xy dy
= x(y²/2) from 0 to 16-x²
= x[(16-x²)²/2] - x(0/2)
= x[(256 - 32x² + x⁴)/2]
= (x/2)(256 - 32x² + x⁴)
Integration with respect to x:
∫(0 to 4) (x/2)(256 - 32x² + x⁴) dx
Expanding the expression:
∫(0 to 4) [(x/2)(256) - (x/2)(32x²) + (x/2)(x⁴)] dx
Simplifying:
∫(0 to 4) [128x - 16x³ + (x⁵/2)] dx
Integrating each term separately:
∫(0 to 4) 128x dx - ∫(0 to 4) 16x³ dx + ∫(0 to 4) (x⁵/2) dx
Taking the antiderivative of each term:
[64x²] from 0 to 4 - [4x⁴] from 0 to 4 + [(x⁶/12)] from 0 to 4
Substituting the limits:
[(64(4)²) - (64(0)²)] - [(4(4)⁴) - (4(0)⁴)] + [((4)⁶/12) - ((0)⁶/12)]
Simplifying:
[(64(16)) - (64(0))] - [(4(256) - 4(0))] + [(4096/12) - (0/12)]
= (1024) - (1024) + (4096/12)
= 0 + (4096/12)
= 4096/12
= 341.33...
Therefore, the simplified value of the integral ∫(0 to 4) (x/2)(256 - 32x² + x⁴) dx is approximately 341.33.
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The question is -
Find,
A) The volume of the region defined by z = f(x, y) = x² + y², where 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1, is 1/3.
B) The volume of the region defined by the equation 9x + 8y + 10z = 1.
C) The evaluation of the integrals ∬R XydA, where the region R is defined by 7 ≤ x ≤ 9 and 4 ≤ y ≤ 7, results in a volume of 176.
D) The integral ∫0 to 4 ∫0 to 16-x² x dy dx evaluates to a volume of 352.
Help me please asap!!! NOTE : PLEASE LOOK AT THE 3 PICTURES & I NEED A EXPLANATION
Step-by-step explanation:
3/5 - 1/3 = 4 /15
5/6 - 2/3 = 5/6 - 4/6 = 1/6
7/9 - 2/3 = 7/9 - 6/9 = 1/9
5/8 - 1/6 = (15 - 4) /24 = 11/24
(All the above ones I have taken common factor and subtracted them)
5 x 9/10 = 45/10 = 9/2 (simplified)
2/7 x 3 = 6/7
3 x 2/15 = 6/15
4x 2/6 = 8/6 = 4/3 (simplified form)
Hope this helps!!!
answer po plss plss plsss
Answer:
\( - 60\)
Step-by-step explanation:
\(( - 1)(5)( - 6)( - 2) \\ ( - 5)( + 12) \\ = - 60\)
Answer:
-60
Step-by-step explanation:
In ΔUVW, the measure of ∠W=90°, the measure of ∠U=27°, and WU = 9.7 feet. Find the length of VW to the nearest tenth of a foot.
Answer:
32.2
Step-by-step explanation:
esta es la respuesta correcta
Two fractions havedenominators of x^2+ 6x + 9and x^2. What is the LeastCommon Denominator?
The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. It's also known as the lowest common denominator.
The denominators of two fractions are given as:
\(x^2+6x+9\text{ and }x^2\)Factoring the first expression:
\(x^2+6x+9=(x+3)^2\)It's clear there is no common factor between both denominators. Such expressions and numbers are called to be coprime.
For example, 9 and 25 are coprime, but they are not prime numbers individually.
When two numbers or expressions are coprime, the LCD is just their product.
Therefore the Least Common Denominator is:
\(x^2(x+3\text{)}^2\)In the diagram, four squares of side length 2 are placed in the corners of a square of side length 6. Each of the points $W$, $X$, $Y$, and $Z$ is a vertex of one of the small squares. Square $ABCD$ can be constructed with sides passing through $W$, $X$, $Y$, and $Z$. What is the maximum possible distance from $A$ to $P$
In this problem, you have a square with side length 6 and four smaller squares with side length 2 placed in the corners. The points W, X, Y, and Z are the vertices of the smaller squares. The goal is to find the maximum possible distance between points A and P.
[asy] size(200); pair A,B,C,D,P,W,X,Y,Z; A=(0,4); B=(4,4); C=(4,0); D=(0,0); P=(2,2); W=(0,6); X=(6,6); Y=(6,0); Z=(0,0); draw(A--B--C--D--cycle); draw(W--X--Y--Z--cycle); draw(A--P--C); label("A",A,NW); label("B",B,NE); label("C",C,SE); label("D",D,SW); label("P",P,S); label("W",W,N); label("X",X,NE); label("Y",Y,S); label("Z",Z,SW); [/asy]
The point A is located on the bottom-left corner of the square with side length 6, and the point P is the center of the square $ABCD$. To find the maximum distance from A to P, we need to find the longest diagonal of the square $ABCD$.
The longest diagonal of a square is the one that goes from one corner of the square to the opposite corner. In this case, the longest diagonal goes from point A to point C, which is a distance of 6 units. Therefore, the maximum possible distance from A to P is 6 units.
6 tons =______ pounds
Answer: 12,000 lbs is equal to 6 tons
The quotient of 38 times a number and -4
Answer:
140y
Step-by-step explanation:
35 times a number times -4 is 35×y×(-4) which is -140y
For what value of k, the following system of equations kx+2y=3, 3x+6y=10 has a unique solution ?
The given system of equations to have a Unique solution, the value of k must be any real number except 1 (k ≠ 1).
The value of k for which the given system of equations has a unique solution, we can use the concept of determinants. The system of equations is as follows:
kx + 2y = 3 -- (1)
3x + 6y = 10 -- (2)
To have a unique solution, the determinant of the coefficients of x and y must not be zero.
The determinant of the coefficient matrix for the system is:
D = | k 2 |
| 3 6 |
By calculating the determinant, we have:
D = (k * 6) - (2 * 3)
D = 6k - 6
For the system to have a unique solution, the determinant D must not equal zero.
6k - 6 ≠ 0
Simplifying the inequality:
6k ≠ 6
Dividing both sides by 6:
k ≠ 1
Therefore, for the given system of equations to have a unique solution, the value of k must be any real number except 1 (k ≠ 1).
In other words, if k is not equal to 1, the system of equations will have a unique solution. If k is equal to 1, the system will either have infinitely many solutions or no solution.
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The elevations of the 31 NFL stadiums range from 3 ft at Mercedes-Benz Superdome, New Orleans, Louisiana, to 5280ft at Sports Authority Field at Mile High, Denver, Colorado. The elevation of Sports Authority Field at Mile High is 275 ft higher than seven times the elevation of Lucas Oil Stadium in Indianapolis, Indiana. What is the elevation of Lucas Oil Stadium?
The elevation of the Lucas Oil Stadium is 40735ft
How to solve for the Elevation?We should know that elevation is defined as the Height of a geographic location above a fixed reference point
31 NFL stadium ranges from 3ft to 5280ft at Mecedez Benz Superdome, New Orleans, Louisiana
The elevation of the sports Authority field at mile high is 275
= 275+7(5280)ft
Multiplying the brackets, we have
275+40460ft
Adding up to get
40735ft
In conclusion, the elevation of Lucas Oil Stadium is 40730ft
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Emily is going to bake a cake. The recipe calls for 6 cups flour, 4 cups sugar
and 2 cups milk. If her cake pan only fits 10 cups of total ingredients how
much flour should she use?
Answer:
4 cups
Step-by-step explanation:
Seth is saving his money. He started with $75.00. If he adds
$25.00 to his savings each month, how much will he have
saved after 4 months?
You can earn S coins
Type here to search
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2
3
4
5
6
7
8
9
Answer:
$175
Step-by-step explanation:
\(75 + 25(4) = 75 + 100 = 175\)
statistics are used to: a. ask questions b. make estimates of population parameters c. form a basis for analysis d. theoretically specify grouping of study elements
Statistics are used to make estimates of population parameters. Therefore, the correct option is B.
Statistics are used for various purposes in data analysis. One important application of statistics is to make estimates of population parameters. Population parameters are characteristics or measures that describe an entire population. However, it is often impractical or impossible to collect data from the entire population, so statistics provide methods for estimating these parameters based on a sample of the population.
By collecting and analyzing data from a sample, statisticians can make inferences and draw conclusions about the larger population. These estimates help researchers understand the characteristics, patterns, and relationships within the population.
Additionally, statistics form the basis for analysis in many fields, including scientific research, business, social sciences, and more. They provide tools and techniques to summarize, interpret, and draw meaningful insights from data, enabling researchers and decision-makers to make informed choices and draw valid conclusions from their observations and experiments.
Therefore, the correct choice is option b. Statistics play a crucial role in estimating population parameters and providing insights for analysis and decision-making.
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Which word is associated with multiplication when computing probabilities? Choose the correct answer below Disjoint O And O Not
When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.
According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .
According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.
The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.
Therefore,
When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.
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Solve the linear system as a matrix equation. [Solve by finding the inverse] (5x + 7y + 4z = 1 3x - y + 3z = 1 (6x + 7y + 5z = 1
To solve the linear system as a matrix equation using the inverse, we can represent the system of equations in matrix form as AX = B, where A is the coefficient matrix, X is the column matrix of variables (x, y, z), and B is the column matrix of constants.
The coefficient matrix A is:
A = [[5, 7, 4],
[3, -1, 3],
[6, 7, 5]]
The column matrix B is:
B = [[1],
[1],
[1]]
To find the inverse of matrix A, we calculate A^(-1), if it exists.
After performing the necessary calculations, we find that the inverse of matrix A is:
A^(-1) = [[1/5, 1/5, -1/5],
[2/25, -3/25, 1/25],
[-3/25, 4/25, 1/25]]
Now, to solve for X, we multiply both sides of the equation AX = B by A^(-1):
X = A^(-1) * B
Performing the matrix multiplication, we obtain:
X = [[1/5, 1/5, -1/5],
[2/25, -3/25, 1/25],
[-3/25, 4/25, 1/25]] * [[1],
[1],
[1]]
Simplifying the expression, we have:
X = [[1/5],
[0],
[1/5]]
Therefore, the solution to the linear system is x = 1/5, y = 0, z = 1/5.
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pls help........................................................
Answer:
6 i think
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
You order all the numbers from least to greatest and the center number/s is the median.
If two numbers are in the center, you add them up and divide by 2
The median for this set was 4 and 4. We add those numbers (4+4=8) and divide the sum by 2. We get 4 as the answer
Revenue given by R(q)=600q and cost is given C(q)=10,000+5q2. At what quantity is profit maximized? What is the profit at this production level? 4= Proft =S
At the production level of 40 units, profit is maximized and the profit at this production level is $64,000.
Revenue is given by R(q) = 600q and cost is given by C(q) = 10,000 + 5q2. Profit is given by P(q) = R(q) - C(q).Therefore, P(q) = 600q - (10,000 + 5q2) or P(q) = -5q2 + 600q - 10,000. The profit is maximized at the production level where the derivative of P(q) is equal to zero.The derivative of P(q) is given by P'(q) = -10q + 600. Setting this to zero, we get -10q + 600 = 0 or q = 60. However, this is the maximum point of the revenue function R(q) and not the profit function P(q).To determine the maximum point of P(q), we need to find the second derivative of P(q) which is given by P''(q) = -10. Since P''(q) is negative, the maximum point of P(q) occurs at the production level q = 40. At q = 40, P(q) = -5(40)2 + 600(40) - 10,000 = $64,000.
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True/False
1) The nullspace of a 3x4 matrix cannot consist of only the zero vector.
2) The nullspace of a 4x3 matrix cannot consist of only the zero vector.
3) The set of all vectors of the form 1
x
y
where x and y range over all real numbers, is a subspace of R^3.
4) 3) The set of all vectors of the form 0
x
y
where x and y range over all real numbers, is a subspace of R^3.
Null space is defined as the set of vectors 'x' in Rn that are solutions to the matrix equation A*x = 0. False: The set of all vectors of the form 1 x y where x and y range over all real numbers is a subspace of R3. True: The set of all vectors of the form 0 x y where x and y range over all real numbers is not a subspace of R3.
1) False Null space can consist of zero vector only. A null space is defined as the set of vectors 'x' in R^n that are solutions to the matrix equation A*x = 0.
2) True The number of columns can never be less than the number of rows of the matrix in order for a null space to exist, hence a 4x3 matrix may have the null space of only the zero vector.
3) True The set of all vectors of the form 1 x y where x and y range over all real numbers, is a subspace of R^3. This set contains zero vector because for x=0 and y=0, we get the vector as [0,0,0]. Hence it is a subspace of R^3.
4) False The set of all vectors of the form 0 x y where x and y range over all real numbers, is not a subspace of R^3 as it doesn't contain zero vector. To have a subspace of R^3, it should contain a zero vector.
So, the correct options are:1) False2) True3) True4) False
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What is a difference between distance and displacement? a Distance takes into account direction, and displacement does not. b Distance is only concerned with the first part of the journey; displacement takes into account the entire journey. c Displacement accounts for the direction being traveled, and distance does not. d There are no differences between distance and displacement.
Answer:
Step-by-step explanation:
the distance is how close i am to kssing your mom
Find the solution(s) of the system of equations.
y = –x2 + 2
y = x2 + 4x + 4