The solution to the system is [tex]$\$\left(x_{-} 1, x_{-} 2\right)=(4,-3) \$$[/tex].
To solve the system, we can use the method of elimination or Gaussian elimination.
We start by writing the system in augmented matrix form:
[tex]$$\left[\begin{array}{cc|c}2 & 4 & -4 \\5 & 7 & 11\end{array}\right]$$[/tex]
We can eliminate the [tex]$\$ x_{-} 1 \$$[/tex] variable from the second equation by subtracting 5 times the first equation from the second:
[tex]$$\left[\begin{array}{cc|c}2 & 4 & -4 \\5-5(2) & 7-5(4) & 11-5(-4)\end{array}\right] \Rightarrow\left[\begin{array}{cc|c}2 & 4 & -4 \\-3 & -13 & 31\end{array}\right]$$[/tex]
Next, we can eliminate the [tex]$\$ x_{-} 2 \$[/tex]$ variable from the first equation by subtracting twice the second equation from the first:
[tex]$$\left[\begin{array}{cc|c}2-2(-13) & 4-2(7) & -4-2(31) \\-3 & -13 & 31\end{array}\right] \Rightarrow\left[\begin{array}{cc|c}28 & -10 & -66 \\-3 & -13 & 31\end{array}\right]$$[/tex]
We can simplify this further by dividing the first row by 2 :
[tex]$$\left[\begin{array}{cc|c}14 & -5 & -33 \\-3 & -13 & 31\end{array}\right]$$[/tex]
Now we can solve for [tex]$\$ x_{-} 2 \$$[/tex] in terms of [tex]$\$ x_{-} 1 \$$[/tex] by multiplying the first equation by 13 and adding it to the second equation:
[tex]$$13(14) x_1-13(5) x_2-13(33)-3(-13) x_1-3(-13) x_2=13(31)-3(14) x_1$$[/tex]
Simplifying:
[tex]$$\begin{aligned}& 169 x_1-91 x_2-429+39 x_1+39 x_2=403 \\& 208 x_1=832 \\& x_1=4\end{aligned}$$[/tex]
Substituting back into the first equation, we get:
[tex]$$2(4)+4 x_2=-4 \Rightarrow x_2=-3$$[/tex]
Therefore, the solution to the system is [tex]$\$\left(x_{-} 1, x_{-} 2\right)=(4,-3) \$$[/tex].
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Find the area of the region that lies inside the first curve and outside the second curve. 25. r2-8 cos 20, r= 2 29-34 Find the area of the region that lies inside both curves. 29. r= 3 cose, r=sin
25. The area of the region that lies inside the first curve and outside the second curve is 4[√3/2 - 2π/3] square units.
29. The area of the region that lies inside both curves is approximately 1.648 square units.
What is cylinder?A 3D solid shape called a cylinder is formed by connecting two parallel and identical bases with a curving surface. The shape of the bases is similar to a disc, and the axis of the cylinder runs through the middle or connects the two circular bases.
25. To find the area of the region that lies inside the first curve and outside the second curve, we need to find the points where the two curves intersect, and then integrate the difference in the areas between the two curves from one intersection point to the other.
The two curves are given by:
r² = 8 cos θ (first curve)
r = 2 (second curve)
To find the intersection points, we substitute r = 2 into the first equation and solve for θ:
2² = 8 cos θ
cos θ = 1/2
θ = ±π/3
So the two curves intersect at θ = π/3 and θ = -π/3. To find the area between the curves, we integrate the difference in the areas between the two curves from θ = -π/3 to θ = π/3:
A = ∫[-π/3,π/3] [(1/2)r² - 2²] dθ
Using the equation r² = 8 cos θ, we can simplify this to:
A = ∫[-π/3,π/3] [(1/2)(8 cos θ) - 4] dθ
A = ∫[-π/3,π/3] (4 cos θ - 4) dθ
A = 4 ∫[-π/3,π/3] (cos θ - 1) dθ
[tex]A = 4 [sin \theta - \theta]_{(-\pi/3)^{(\pi/3)[/tex]
A = 4 [sin(π/3) - π/3 - (sin(-π/3) + π/3)]
A = 4 [√3/2 - 2π/3]
Therefore, the area of the region that lies inside the first curve and outside the second curve is 4[√3/2 - 2π/3] square units.
29. To find the area of the region that lies inside both curves, we need to determine the points where the two curves intersect and then integrate the area enclosed between the curves over the appropriate range of polar angles.
The two curves are given by:
r = 3 cos(θ) (first curve)
r = sin(θ) (second curve)
To find the intersection points, we substitute r = 3 cos(θ) into the equation r = sin(θ) and solve for θ:
3 cos(θ) = sin(θ)
tan(θ) = 3
θ = tan⁻¹(3)
The intersection point lies on the first curve when θ = tan⁻¹(3), so we need to integrate the area enclosed between the curves from θ = 0 to θ = tan⁻¹(3).
The area enclosed between the curves at any angle θ is given by the difference in the areas of the circles with radii r = sin(θ) and r = 3 cos(θ). Thus, the area enclosed between the curves is:
A = ∫[0,tan⁻¹(3)] [(1/2)(3 cos(θ))² - (1/2)(sin(θ))²] dθ
Simplifying, we get:
A = ∫[0,tan⁻¹(3)] [9/2 cos²(θ) - 1/2 sin²(θ)] dθ
Using the identity cos(2θ) = cos²(θ) - sin²(θ), we can simplify this to:
A = ∫[0,tan⁻¹(3)] [(9/2)(cos²(θ) - (1/2)) + (1/2)cos²(2θ)] dθ
We can evaluate the first term of the integrand using the identity cos²(θ) = (1 + cos(2θ))/2, and the second term using the identity cos²(2θ) = (1 + cos(4θ))/2:
A = ∫[0,tan⁻¹(3)] [(9/4)(1 + cos(2θ)) - (1/4)(1 + cos(4θ))] dθ
Integrating each term separately, we get:
[tex]A = [(9/4)\theta + (9/8)sin(2\theta) - (1/16)sin(4\theta)]_{0^{(tan^-1(3))[/tex]
Simplifying and evaluating, we get:
A = (9/4)tan⁻¹(3) + (9/8)sin(2tan⁻¹(3)) - (1/16)sin(4tan⁻¹(3))
Using the identity sin(2tan⁻¹(3)) = 6/10 and simplifying, we get:
A = (9/4)tan⁻¹(3) + (27/40) - (3/40)tan⁻¹(3)
Therefore, the area of the region that lies inside both curves is approximately 1.648 square units.
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Do not answer with another chegg expert solution, i will dislike the answer, It is NOT (C)Question 1
Please see the Page 27 in the PowerPoint slides of Chapter 8. If the first boundary condition
becomes Y'(0)=1, what is the correct SOR formula for this boundary condition?
OY'1 = 1
OY₁ =1/6∆ (4Y₂ - Y3)
O Y₁ = y0+y2/2-0.05∆z(Y₂-Yo)
O Y₁ = 1
O Y₁ = (4Y₂ - Y₁ - 2∆x)
OY₁ = 2∆z + Y3
The correct SOR formula for the boundary condition Y'(0) = 1 is:
OY₁ = (1 - ω/4)(Y₁ - Y₂) / 6 + (1 - ω/4)(Y₁ + Y₂) / 3 + (ω/4)(∆²f₁ + Yᵢ₊ₙ + Yᵢ₋ₙ - ∆)
To derive the correct SOR formula for the boundary condition Y'(0) = 1, we start with the standard SOR formula:
OYᵢ = (1 - ω)Yᵢ + (ω/4)(Yᵢ₊₁ + Yᵢ₋₁ + Yᵢ₊ₙ + Yᵢ₋ₙ - ∆²fᵢ)
where i and j are indices corresponding to the discrete coordinates in the x and y directions, ω is the relaxation parameter, and ∆ is the grid spacing in both directions.
To incorporate the boundary condition Y'(0) = 1, we use a forward difference approximation for the derivative:
Y'(0) ≈ (Y₁ - Y₀) / ∆
Substituting this into the original equation gives:
(Y₁ - Y₀) / ∆ = 1
Solving for Y₀ gives:
Y₀ = Y₁ - ∆
Now we can use this expression for Y₀ to modify the SOR formula at i = 1:
OY₁ = (1 - ω)Y₁ + (ω/4)(Y₂ + Y₀ + Yᵢ₊ₙ + Yᵢ₋ₙ - ∆²f₁)
Substituting the expression for Y₀, we get:
OY₁ = (1 - ω)Y₁ + (ω/4)(Y₂ + Y₁ - ∆ + Yᵢ₊ₙ + Yᵢ₋ₙ - ∆²f₁)
Simplifying:
OY₁ = (1 - ω/4)(Y₁ - Y₂) / 6 + (1 - ω/4)(Y₁ + Y₂) / 3 + (ω/4)(∆²f₁ + Yᵢ₊ₙ + Yᵢ₋ₙ - ∆)
So the correct SOR formula for the boundary condition Y'(0) = 1 is:
OY₁ = (1 - ω/4)(Y₁ - Y₂) / 6 + (1 - ω/4)(Y₁ + Y₂) / 3 + (ω/4)(∆²f₁ + Yᵢ₊ₙ + Yᵢ₋ₙ - ∆)
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EXERCISE 8.2 a) 5x²-2r³+3 - 6x c) -2r²-2r²³-6-5r³ 1. Write down the constant term in each of these expressi
HELP ME TODAY PLEASE
Answer: answer is 3
Step-by-step explanation:
Please just do question C(ii).
(a) Consider p(z) = z^3 + 2z^2 – 6z +1 when z € C. Prove that if zo is a root of p(z) then zo is also a root. (b) Prove a generalization of (a): Theorem: For any polynomial with real coefficients, if zo € C is a root, then zo is also a root. (c) Consider g(z) = z^2 – 2z: (i) Find the roots of g(z) and show that they satisfy the conclusion of the theorem in (b).
(ii) Explain why the theorem in (b) does not apply to g(z).
For part (c)(ii), we need to explain why the theorem in (b) does not apply to g(z).
The theorem in (b) states that for any polynomial with real coefficients, if zo € C is a root, then zo is also a root. However, g(z) = z^2 - 2z does not have real coefficients, as the coefficient of the z term is -2, which is not a real number.
Therefore, we cannot apply the theorem in (b) to g(z) since it does not satisfy the condition of having real coefficients. However, we can still find the roots of g(z) and show that they satisfy the conclusion of the theorem in (b) if we consider g(z) as a polynomial with complex coefficients.
To find the roots of g(z), we set g(z) equal to zero and solve for z:
z^2 - 2z = 0
z(z - 2) = 0
So the roots of g(z) are z = 0 and z = 2.
If we consider g(z) as a polynomial with complex coefficients, then we can apply the theorem in (b) and conclude that if z = 0 or z = 2 is a root of g(z), then it is also a root of g(z) with real coefficients. However, we cannot apply the theorem in (b) to g(z) directly since it does not have real coefficients.
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The joint probability mass function of X and Y, p(x,y), is given by
P(1,1)=1/9
P(1,2)=1/9
P(1,3)=0
P(2,1)=1/3
P(2,2)=0
P(2,3)=1/6
P(3,1)=1/9
P(3,2)=1/18
P(3,3)=1/9
Compute E[X|Y=i] for i=1,2,3.
Are the random variables X and Y independent?
The joint probability mass function of X and Y, E[X|Y=1] = 2, E[X|Y=2] = 5/2, and E[X|Y=3] = 8/3.If it is true for all values of x and y, then X and Y are independent. Otherwise, they are dependent.
To compute E[X|Y=i], we need to use the formula:
[tex]E[X|Y=i] = ∑ x*xp(x|Y=i) / P(Y=i)[/tex]
where xp(x|Y=i) is the conditional probability of X given Y=i, and P(Y=i) is the marginal probability of Y=i.
Using Bayes' theorem, we can compute the conditional probabilities xp(x|Y=i) as follows: xp(1|Y=1) = P(X=1,Y=1) / P(Y=1) = (1/9) / (1/9 + 1/3 + 1/9) = 1/3. xp(2|Y=1) = P(X=2,Y=1) / P(Y=1) = (1/3) / (1/9 + 1/3 + 1/9) = 1/3. xp(3|Y=1) = P(X=3,Y=1) / P(Y=1) = (1/9) / (1/9 + 1/3 + 1/9) = 1/3. xp(1|Y=2) = P(X=1,Y=2) / P(Y=2) = (1/9) / (1/9 + 0 + 1/18) = 2/3. xp(2|Y=2) = P(X=2,Y=2) / P(Y=2) = 0 / (1/9 + 0 + 1/18) = 0
xp(3|Y=2) = P(X=3,Y=2) / P(Y=2) = (1/18) / (1/9 + 0 + 1/18) = 1/2. xp(1|Y=3) = P(X=1,Y=3) / P(Y=3) = 0 / (1/9 + 1/6 + 1/9) = 0. xp(2|Y=3) = P(X=2,Y=3) / P(Y=3) = (1/18) / (1/9 + 1/6 + 1/9) = 1/3. xp(3|Y=3) = P(X=3,Y=3) / P(Y=3) = (1/9) / (1/9 + 1/6 +1/9) = 2/3
Using these conditional probabilities, we can compute the conditional expectations E[X|Y=i] as follows: E[X|Y=1] =
[tex]1*(1/3) + 2*(1/3) + 3*(1/3)[/tex]
= 2
E[X|Y=2] =
[tex]1*(2/3) + 20 + 3(1/2) = 5/2 E[X|Y=3][/tex]
=
[tex]10 + 2(1/3) + 3*(2/3) = 8/3[/tex]
To determine if X and Y are independent, we need to check if the joint probability mass function can be factored into the product of the marginal probability mass functions: p(x,y) = p(x) * p(y)
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Due to a power outage, the sales clerk manually prepares a sale receipt to her customer. Which one of the following diagrams represents this activity?
a. trapezoid to curvy side rectangle to curved rectangle
b. curved side rectangle to circle to curved rectangle
c. circle to curved side rectangle to curved rectangle
d. trapezoid to curved side rectangle to circle
Based on the given options, the diagram that best represents the activity of a sales clerk manually preparing a sale receipt during a power outage would be option D.
A trapezoid could represent the shape of a receipt, a curved side rectangle could represent the shape of the clerk's desk or the paper she is using, and a circle could represent the shape of a calculator or cash register. Therefore, a trapezoid to a curved side rectangle to a circle could represent the process of the clerk manually calculating and recording the sale amount and inputting it into a calculator or cash register to produce a receipt.
It is important to note that during a power outage, technology-dependent activities such as electronic sales and transactions may be disrupted, and manual methods may have to be used as a backup. This highlights the power of technology in our daily lives and the impact that power outages can have on businesses and individuals.
The question is about selecting the correct diagram that represents the sales clerk manually preparing a sale receipt due to a power outage. Given the options:
a. trapezoid to curvy side rectangle to curved rectangle
b. curved side rectangle to circle to curved rectangle
c. circle to curved side rectangle to curved rectangle
d. trapezoid to curved side rectangle to circle
The appropriate answer for this question cannot be determined based on the provided information. Diagrams typically require visual representation, and the description of the shapes alone is insufficient to convey the activity of preparing a receipt manually. Moreover, the terms "power," "outage," "clerk," "receipt," "trapezoid," "curved," and "curved" don't necessarily correspond to the shapes given in the options.
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The radius of a circle is 5 inches. What is the length of a 45° arc? 45⁰ r=5 in Give the exact answer in simplest form. 00 inches
The length of a 45° arc include the following: 3.925 or 5π/4 inches.
How to calculate the length of the arc?In Mathematics and Geometry, if you want to calculate the arc length formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.
Mathematically, the arc length formed by a circle can be calculated by using the following equation (formula):
Arc length = 2πr × θ/360
Where:
r represents the radius of a circle.θ represents the central angle.By substituting the given parameters into the arc length formula, we have the following;
Arc length = 2 × 3.14 × 5 × 45/360
Arc length = 3.925 or 5π/4 inches.
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Is 6. 34 repeating a rational or irrational number?
The number 6.34 repeating is an irrational number because it can be expressed as a fraction of two integers.
The number 6.34 repeating is irrational.
An irrational number cannot be expressed as the ratio of two integers, and it has an infinite number of non-repeating decimal places.
In this case, 6.34 repeating can be expressed as 6.34343434..., where the digits "34" repeat infinitely.
This cannot be expressed as a ratio of two integers because there is no repeating pattern that can be represented by a fraction.
Therefore, 6.34 repeating is irrational.
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PLEASE HELP ITS URGENT I INCLUDED THE PROBLEM IN IMAGE I WROTE IT DOWN!!!
Answer:
The answer would be D. [tex]\frac{5\sqrt{11} }{11}[/tex]
George built a flower box with a length equal to 6 inches and a width equal to 9 inches. What was the area of the flower box?
A) 54 inches(to the power of) 2
B) 45 inches(to the power of) 2
C) 60 inches(to the power of) 2
D) 30 inches(to the power of) 2
I need help on this 40 points I need to turn it in in like 5 min
Answer:
Step-by-step explanation:
13. B
14. A
15. D
Discuss the relative "weakness" of categorical variables (including measures on nominal and ordinal scales), and continuous variables (including measures on interval and ratio scales) with respect to the type of information statistics on them yield.
Categorical variables, such as nominal and ordinal scales, are weaker than continuous variables, such as interval and ratio scales, in terms of the type of information statistics on them yield. Categorical variables only provide limited information and are not as precise as continuous variables. Categorical variables have weaknesses related to limited statistical analysis and potential loss of information, while continuous variables can be sensitive to outliers and require more advanced statistical techniques for analysis. Both types of variables provide valuable information but have limitations when analyzing statistics.
Let's discuss the relative weakness of categorical and continuous variables with respect to the type of information statistics on them yield.
Categorical variables are those that can be divided into categories, and they include nominal and ordinal scales. Nominal variables have no inherent order (e.g., hair color), while ordinal variables have a clear order (e.g., educational level).
Weakness:
1. Limited statistical analysis: Since categorical variables have no numerical value, certain statistical measures, such as mean and standard deviation, cannot be applied to them.
2. Loss of information: Categorical variables can sometimes oversimplify data, leading to a loss of information when grouping continuous data into categories.
Continuous variables are those that can take any value within a defined range, and they include interval and ratio scales. Interval variables have a constant distance between values but no absolute zero (e.g., temperature in Celsius), while ratio variables have a constant distance and an absolute zero (e.g., height).
Weakness:
1. Susceptibility to outliers: Continuous variables are more sensitive to extreme values (outliers), which can significantly affect the statistics derived from them, such as the mean.
2. Data complexity: Continuous variables often require more advanced statistical techniques for analysis, which may be challenging for those without a strong background in statistics.
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QUESTION 1 of 10: A manufacturer buys a new machine that costs $50,000. The estimated useful life for the machine is ten years. The
machine can produce 1,000 units per month. If the machine ran at its capacity for ten years, what would be the fixed cost per unit based on
the cost of the machine per part manufactured? (Round to the nearest penny)
a) $. 42 / unit
ООО
b) $1. 00/unit
c) S4,167 / unit
d) $5. 000/unit
The fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit. Option ( A )
What is multiplication ?Multiplication is a mathematical operation that involves finding the product of two or more numbers or quantities. It is a way of adding a number to itself multiple times. The symbol used to represent multiplication is an "x" or a dot "·". For example, in the expression 5 x 6 = 30, 5 and 6 are multiplied together to give the product of 30. Multiplication can also be represented using parentheses, such as (5)(6) = 30. In addition, multiplication can be done with decimals, fractions, variables, and matrices.
To find the fixed cost per unit based on the cost of the machine per part manufactured, we need to calculate the total number of units produced by the machine over its estimated useful life, and then divide the cost of the machine by that number.
The machine runs at its capacity of 1,000 units per month for 10 years, so the total number of units produced by the machine is:
10 years x 12 months/year x 1,000 units/month = 120,000 units
The cost of the machine is $50,000, so the fixed cost per unit based on the cost of the machine per part manufactured is:
$50,000 ÷ 120,000 units = $0.4167 per unit
Rounding this to the nearest penny gives us the final answer of:
$0.42 per unit (option a)
Therefore, the fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit.
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Question 4 (1 point) In his Ted Talk, James Lyne presents the following statistic(s) in his TedX talk about malware and cybercrime. There are 30,000 new infected websites every day. 8 new internet users join every second. 250,000 new pieces of malware appear every day. All of the above. Question 2 (1 point) Why is traditional supply chain management (SCM) ineffective for e-commerce? It is based on manual processes and separation of functions It is based more on manufacturing, whereas e-commerce is mostly retail distribution E-commerce is gnerally more specialized and is not a good fit for traditional SCM It usually doesn't include e-procurement functions.
All of the above are statistics
Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.
4)
We have,
James Lyne mentions that there are:
- 30,000 new infected websites every day
- 8 new internet users join every second
- 250,000 new pieces of malware appear every day.
All the above are statistics.
2)
E-commerce is generally more specialized and requires a more integrated approach to supply chain management. Additionally, traditional SCM is based on manufacturing, whereas e-commerce is mostly retail distribution.
Finally, traditional SCM usually doesn't include e-procurement functions, which are essential for e-commerce supply chain management.
Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.
Thus,
All of the above are statistics
Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.
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Kaizen is a Japanese word that means continuous development. It says that each day we should focus on getting 1% better on whatever we're trying to improve.
How much better do you think we can get in a year if we start following Kaizen today?
Note: You can take the value of
(1.01)^365 as 37.78.
If we follow Kaizen's principle and improve by 1% each day, we can get approximately 37.78 times better in a year.
If we follow Kaizen's principle of improving by 1% each day, we can calculate how much better we will get in a year by using the formula:
Final Value = Initial Value x (1 + Daily Improvement Percentage)^Number of Days
Since we are trying to calculate how much better we can get in a year, we can plug in the following values:
Initial Value = 1 (assuming we are starting from our current level of performance)
Daily Improvement Percentage = 0.01 (since we are trying to improve by 1% each day)
Number of Days = 365 (since there are 365 days in a year)
Using these values, we get:
Final Value = 1 x (1 + 0.01)³⁶⁵
Final Value ≈ 1 x 37.78
Final Value ≈ 37.78
This shows the power of continuous improvement and the importance of consistent effort towards our goals.
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what is the answer to -z/5-37=-18
Answer:
z = -95
Step-by-step explanation:
You simplify both sides of the equation, then isolate the variable.
A fenced backyard has a length
of 20 feet, and width of 25 feet,
and a diagonal of 30 feet. Does
the backyard have a 90 degree
angle in its corner?
Answer:no it doesn’t it makes a trapezoid which doesn’t have 90 degree angles or right angles
Step-by-step explanation:
Let X is a random variable with probability density function f(x) = {3x? for 0
The variance of X is 3/80.
Given the probability density function of X,
f(x) = {3x² for 0 < x < 1
{0 otherwise
We can use this to answer the following:
(a) Find P(X < 0.5)
To find P(X < 0.5), we need to integrate the density function from 0 to 0.5:
P(X < 0.5) = ∫[0,0.5] f(x) dx
= ∫[0,0.5] 3x² dx
= [x³]₀.₃
= 0.125
(b) Find the cumulative distribution function of X, F(x)
The cumulative distribution function (CDF) of X is given by:
F(x) = P(X ≤ x) = ∫[0,x] f(t) dt
If x ≤ 0, then F(x) = 0. If 0 < x ≤ 1, then
F(x) = ∫[0,x] f(t) dt
= ∫[0,x] 3t² dt
= [t³]₀.ₓ
= x³
If x > 1, then F(x) = 1. So, the CDF of X is:
F(x) = {0 if x ≤ 0
{x³ if 0 < x ≤ 1
{1 if x > 1
(c) Find the expected value of X, E(X)
The expected value of X is given by:
E(X) = ∫[−∞,∞] x f(x) dx
Since the density function f(x) is zero outside the interval [0,1], we can restrict the integration to this interval:
E(X) = ∫[0,1] x f(x) dx
= ∫[0,1] 3x³ dx
= [3/4 x⁴]₀.₁
= 3/4 * 1⁴ - 0
= 3/4
Therefore, the expected value of X is 3/4.
(d) Find the variance of X, Var(X)
The variance of X is given by:
Var(X) = E(X²) - [E(X)]²
We have already found E(X) in part (c). To find E(X²), we integrate x² times the density function:
E(X²) = ∫[0,1] x² f(x) dx
= ∫[0,1] 3x⁴ dx
= [3/5 x⁵]₀.₁
= 3/5 * 1⁵ - 0
= 3/5
Substituting into the formula for variance:
Var(X) = E(X²) - [E(X)]²
= 3/5 - (3/4)²
= 3/5 - 9/16
= 3/80
Therefore, the variance of X is 3/80.
Complete question: Let X be a random variable defined by the density function
[tex]$$f(x)=\left\{\begin{array}{cl}3 x^2 & 0 \leq x \leq 1 \\0 & \text { otherwise }\end{array}\right.$$[/tex]
Find
(a)[tex]$E(X)$[/tex]
(b) [tex]$E(3 X-2)$[/tex]
(c) [tex]$E\left(X^2\right)$[/tex]
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Find the area of the shaded region
The area of the shaded part is 100.48cm²
What is area of shape?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The area of the shaded part can be expressed as;
area of shaded part = 4 × area of semi circle
Area of semi circle = 1/2 πr²
radius = diameter/2
radius = 8/2 = 4
= 1/2 × 3.14 ×4²
= 3.14 ×16×1/2
= 3.14 × 8
= 25.12 cm²
Since the shaded parts are semi circles
then the area of the shaded part = 4× 25.12
= 100.48cm²
therefore the area of shaded part is 100.48cm²
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Claire has 6 large envelopes and 11 small envelopes. what is the ratio of large envelopes to the total number of evelopes?
Choices:
A 5 : 11
B 6 : 11
C 6 : 17
D 11 : 17
Question 14 (1 point)
In right triangle JKL in the diagram below, KL = 7,
JK = 24, JL = 25, and ZK = 90°.
Which statement is not true?
In the right triangle JKL, the statement cosL = 24/25 is not true considering the right use of trigonometric ratios.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
tanL = 24/7 {opposite/adjacent is a correct statement}
cosL = 24/25 {not a correct statement because cosL = 7/25, adjacent/hypotenuse}
tanJ = 7/24 {opposite/adjacent is a correct statement}
sinJ = 7/25 {opposite/hypotenuse is a correct statement}
Therefore, the statement cosL = 24/25 is not true considering the right use of trigonometric ratios.
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let u be the vector with initial point (2,0) and terminal point (3,2). let v be the vector with initial point (2,2) and terminal point (0,1). find the sum of these vectors: u v .
The sum of the vectors u and v is (-1,1).
To find the sum of the vectors u and v, we need to add their corresponding components.
The vector u has initial point (2,0) and terminal point (3,2), which means its components are (3-2, 2-0) = (1,2).
The vector v has initial point (2,2) and terminal point (0,1), which means its components are (0-2, 1-2) = (-2,-1).
To find the sum of these vectors, we simply add their corresponding components:
u + v = (1,2) + (-2,-1) = (1-2, 2-1) = (-1,1).
Therefore, the sum of the vectors u and v is (-1,1).
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2. Jade is 6 years less than twice Kevin's age. 2 years ago, Jade was three times as old as kevin. How old was Jade 2 years ago? 3. Len is 2 less than 3 times Amanda's age. 3 years from now, Len will be 7 more than twice Amanda's age. How old will Amanda be 3 years from now? 4. Janna is twice as old as Faith and William is 9 years older than Faith. 3 years ago, janna was 9 less than 3 times Faith's age. How old is William now?
William is currently 15 years old.
Let's start by using algebra to solve for the ages of Jade and Kevin now. Let J be Jade's current age and K be Kevin's current age. We have:
J = 2K - 6 (Jade is 6 years less than twice Kevin's age)
J - 2 = 3(K - 2) (two years ago, Jade was three times as old as Kevin)
We can use the first equation to substitute for J in the second equation:
(2K - 6) - 2 = 3(K - 2)
Simplifying this, we get:
2K - 8 = 3K - 6
K = 2
So Kevin is currently 2 years old, and Jade is:
J = 2K - 6 = 2(2) - 6 = -2
This doesn't make sense as an age, so there may be an error in the problem statement or in our solution method.
Let's use algebra to solve for Amanda's current age, which we can call A. Then we can use that to find her age 3 years from now. We have:
L = 3A - 2 (Len is 2 less than 3 times Amanda's age)
L + 3 = 2(A + 3) + 7 (three years from now, Len will be 7 more than twice Amanda's age)
Substituting the first equation into the second, we get:
(3A - 2) + 3 = 2(A + 3) + 7
Simplifying this, we get:
A = 5
So Amanda is currently 5 years old, and her age 3 years from now will be:
A + 3 = 5 + 3 = 8
Let's use algebra to solve for Faith's current age, which we can call F. Then we can use that to find Janna's and William's ages. We have:
J = 2F (Janna is twice as old as Faith)
W = F + 9 (William is 9 years older than Faith)
J - 3 = 3(F - 3) - 9 (three years ago, Janna was 9 less than 3 times Faith's age)
Substituting the first two equations into the third, we get:
(2F) - 3 = 3(F - 3) - 9
Simplifying this, we get:
F = 6
So Faith is currently 6 years old, Janna is:
J = 2F = 2(6) = 12
and William is:
W = F + 9 = 6 + 9 = 15
Therefore, William is currently 15 years old.
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What is the slope of the line shown below
Answer:
[tex]m = \frac{2 - ( - 4)}{1 - ( - 1)} = \frac{6}{2} = \frac{3}{1} = 3[/tex]
Factor the expression, and use the factors to find the x-intercepts of the quadratic relationship it represents. Type the correct answer each box, starting with the intercept with the lower value The x- intercepts occur where x = and x =
The factors to the given expression are -1(x+3)(x-8)
The x-intercepts of the quadratic relationship are -3, 8. When we write an expression in its factors and multiplying those factors gives us the original expression, then this process is known as factorization.
How do we factorize the given expression?
We equate the given expression to f(x)
(-[tex]x^{2}[/tex] + 5x + 24) = f(x)
⇒ -1([tex]x^{2}[/tex] - 5x - 24) = f(x)
⇒ -1([tex]x^{2}[/tex] - (8-3)x - 24) = f(x)
⇒ -1([tex]x^{2}[/tex] + 3x - 8x -24) = f(x)
⇒ -1(x(x+3) -8(x+3)) = f(x)
⇒ -1(x+3)(x-8) = f(x)
∴The factor to the given expression is -1(x+3)(x-8)
How do we find the x-intercepts?
We equate f(x) = 0 to find the x-intercepts.
⇒ -1(x+3)(x-8) = 0
⇒ (x+3)(x-8) = 0
The roots of the above equation are x-intercepts.
Therefore, the x-intercepts occur where x = -3 and x = 8
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The complete question is "Factor the expression (-x^2 + 5x + 24.) and use the factors to find the x-intercepts of the quadratic relationship it represents.
Type the correct answer in each box, starting with the intercept with the lower value.
The x-intercepts occur where x =
and x = "
Consider the family of functions f(x)=1/x^2-2x k, where k is constant
The value of k, for k > 0, such that the slope of the line tangent to the graph off at x = 0 is -2.
We are given a family of functions f(x) = x² - 2x + k, where k is a constant. This family of functions includes all the possible quadratic functions of the form x² - 2x + k. To find the value of k, we need to use the given condition that the slope of the tangent line to the graph of the function at x = 0 equals 6.
To find the slope of the tangent line at x = 0, we need to take the derivative of the function f(x) and evaluate it at x = 0. Taking the derivative of f(x), we get:
f'(x) = 2x - 2
Evaluating f'(x) at x = 0, we get:
f'(0) = 2(0) - 2 = -2
This gives us the slope of the tangent line to the graph of the function at x = 0, which is -2.
Therefore, the answer to the problem is that there is -2 of k, for k > 0, such that the slope of the line tangent to the graph of the function at x = 0 equals 6.
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Complete Question;
Consider the family of functions f(x) = where k is a constant. x^2 - 2x +k
Find the value of k, for k > 0, such that the slope of the line tangent to the graph off at x = 0
Winston has $2,003 to budget each month. He budgets $1,081 for
fixed expenses and the remainder of his budget is set aside for
variable expenses. What percent of his budget is allotted to variable
expenses? Round your answer to the nearest percent if necessary.
The percentage of his budget allotted to the variable expenses is 46%.
How to find the percent of budget allotted to variable expenses?Winston has $2,003 to budget each month. He budgets $1,081 for fixed expenses and the remainder of his budget is set aside for variable expenses.
Therefore, the percentage allotted for variable expenses can be calculated as follows:
Hence,
percent for allotted for variable expenses = 2003 - 1081 / 2003 × 100
percent for allotted for variable expenses = 922 / 2003 × 100
percent for allotted for variable expenses = 92200 / 2003
percent for allotted for variable expenses = 46.0309535696
percent for allotted for variable expenses = 46%
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A data has 24 subgroups. 5 measurements were made per one subgroup. The sum of the subgroup averages is 160.25. The sum of the subgroup ranges is 2.19.
(1) Determine Trial central lines / Trial control limits on X bar chart and R chart.
In case of X bar chart, two values were out-of-control points and had assignable causes ( subgroup 4 - X bar value 6.65, subgroup 20 - X bar value 6.51)
In case of R bar chart, one value is out-of-control point and not part of natural variation. (subgroup 18 - R value 0.30)
(2) Determine Revised central lines / Revised control limits on X bar chart and R chart.
(Please show your calculation process logically )
The X bar chart, two values were out-of-control points and had assignable causes is 6.68 and Revised central lines / Revised control limits on X bar chart and R chart is 6.7364.
The X-bar chart, a form of Shewhart control chart, is used in industrial statistics to track the arithmetic means of subsequent samples of fixed size, n. For variables that may be monitored on a continuous scale, such as weight, temperature, thickness, etc., this sort of control chart is employed. For instance, one might sample five shafts from the production process once per hour, measure each shaft's diameter, and then display the mean of the five diameter values for each sample on a chart.
a) Here we are given that,
k=24
n=5
The sum of the subgroup averages is 160.25.
ΣΧ =160.25
The sum of the subgroup ranges is 2.19.
ΣR = 2.19
(1) Determine Trial central lines / Trial control limits on X bar chart and R chart.
Then,
[tex]\bar{\bar{X}}= \sum k=160.25/24=6.68[/tex]
Therefore,[tex]\bar{\bar{X}}=6.68[/tex]
b) Determine Revised central lines / Revised control limits on X bar chart and R chart.
From the statistical quality control chart
we get,
For, n=5
We have,
A₂=0.58
D₃=0
D₄=2.11
Revised Control limits for X -chart is,
[tex]UCLX =\bar{\bar{X}}+A2*\bar{R}=6.69+(0.58*0.08)=6.69+0.0464=6.6436[/tex]
[tex]CLX =\bar{\bar{X}}=6.69[/tex]
[tex]LCLX =\bar{\bar{X}}-A2*\bar{R}=6.69-(0.58*0.08)=6.69-0.0464=6.7364[/tex]
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Find the future value of the following investment. Nominal Rate 3.1% Principal $9400.00 Frequency of Conversion semi-annually Time 9 years The future value is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
To find the future value of this investment, we can use the formula:
FV = P(1 + r/n)^(nt)
Where:
- FV is the future value
- P is the principal (or starting amount)
- r is the nominal annual interest rate (as a decimal)
- n is the frequency of conversion per year
- t is the time (in years)
Plugging in the given values, we get:
FV = 9400(1 + 0.031/2)^(2*9)
FV = 9400(1.0155)^18
FV = 9400(1.367576)
FV = 12848.92
Therefore, the future value of the investment is $12,848.92 (rounded to the nearest cent).
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