A linear function is a polynomial function with a degree of 1, and a degree 4 polynomial function is a polynomial function with a degree of 4. The leading coefficient of a polynomial function is the coefficient of the term with the highest degree. The y-intercept of a graph is the point where the graph crosses the y-axis.
To create the linear function, h(x), we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. Since the y-intercept can not be 0, we can choose a value for b that is not 0. For example, b = 2. We can also choose a value for m that is not 0, so that h(x) is not a horizontal or vertical line. For example, m = 3. Therefore, h(x) = 3x + 2.
To create the degree 4 polynomial function, P(x), we can use the factored form: P(x) = a(x - r1)(x - r2)(x - r3)(x - r4), where a is the leading coefficient, and r1, r2, r3, and r4 are the zeros of the function. Since the leading coefficient can not be |1|, we can choose a value for a that is not 1 or -1. For example, a = 2. Since one of the factors must be repeated 2 times, we can choose a value for r1 and set r2 equal to r1. For example, r1 = 1 and r2 = 1. Since one of the zeros must be a fraction, we can choose a value for r3 that is a fraction. For example, r3 = 1/2. Since the zeros should have a mix of positive and negative numbers, we can choose a value for r4 that is negative. For example, r4 = -2. Therefore, P(x) = 2(x - 1)(x - 1)(x - 1/2)(x + 2).
To find the points of intersection between h(x) and P(x), we can set h(x) equal to P(x) and solve for x:
3x + 2 = 2(x - 1)(x - 1)(x - 1/2)(x + 2)
This equation can be solved algebraically by expanding the right-hand side and rearranging the terms to form a degree 4 polynomial equation. Then, we can use the Rational Root Theorem and synthetic division to find the possible rational roots of the equation. Once we find the rational roots, we can use them to factor the equation and find the remaining roots. The x-coordinates of the points of intersection are the roots of the equation.
To determine the intervals when h(x)≥P(x), we can use the points of intersection and the signs of h(x) and P(x) on either side of the points of intersection. If h(x) is greater than or equal to P(x) on an interval, then the graph of h(x) is above or coincident with the graph of P(x) on that interval. We can use a sign chart or a graph to determine the intervals when h(x)≥P(x).
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What does it equal?
-8=z/14
If you are solving for z:
-8=z/14
multiply by 14 on both sides:
z = -112
if you have any more questions let me know i need help
Answer:
x=6
My best attempt
Step-by-step explanation:
The ratio is 4:5.6 from top to bottom.
We have a ratio of x:8.4
We will make an equation.
4:5.6=x:8.4
Cross multiply:
5.6x=4x8.4
5.6x=33.6
Divide both sides by 5.6:
x=6
Wyatt plays a vides game called Rock Climber. He starts with 100 points. He loses 7 points each time he falls off a rock. Wyatt has fallen off 6 rocks. How many points does he have left? points Submit
The number of points Wyatt has left is 58.
If Wyatt loses 7 points every time he falls off a rock and he falls off 6 rocks, he will lose a total of 42 points (7 x 6 = 42). To find out how many points he has left, we can subtract 42 from his starting points of 100:
100 - 42 = 58
Therefore, Wyatt has 58 points left after falling off 6 rocks in the Rock Climber video game.
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Diameter of the tin on the picture = ? Height of the tin on the picture = ? Actual weight of coffee = 750 g 1.1 Measure the diameter of the tin in mm and write down the real diameter in mm 1.2 Hence, determine the circumference of the base of the tin in mm. You may us the formula: CС = 2πr Hint: radius = half of diameter MATHEMATICAL LITERACY GRADE 11, 2023 SBA GUIDELINE π = 3,142 Page 2 (3) (3)
Answer: 1.1 The diameter of the tin on the picture is approximately 90 mm.
1.2 The circumference of the base of the tin is approximately 565 mm (2πr = 2π(45) = 565).
Step-by-step explanation: math is stressful fr
We can write the diameter and circumferance of base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
Given is to find the diameter and height of the tin can.
Assume the density of coffee as {ρ}. We can write the volume of the tin can as -
Volume = mass x density
Volume = 750ρ
We can write -
πr²h = 750ρ
r = √(750ρ/πh)
D = 2r
D = 2√(750ρ/πh)
Now, we can write the circumferance as -
C = 2πr
C = 2π√(750ρ/πh)
Therefore, we can write the diameter and circumferance of base as -
D = 2√(750ρ/πh)
C = 2π√(750ρ/πh)
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if there are 578 coyotes in 2003 with initial growth of 1.52. How many coyotes in 2028
If there are 578 coyotes in 2003 with initial growth of 1.52, there will be approximately 336113 coyotes in 2028.
The number of coyotes in 2028 can be found by using the formula for exponential growth:
[tex]A = P(1 + r)^t[/tex]
Where:
A = final amount
P = initial amount
r = growth rate
t = time in years
Plugging in the given values:
[tex]A = 578(1 + 1.52)^25[/tex]
Using a calculator, we get:
[tex]A = 578(1.52)^25[/tex]
[tex]A = 578(581.68)[/tex]
[tex]A = 336112.64[/tex]
Therefore, there will be approximately 336113 coyotes in 2028.
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The following linear system of equations is given x1, x2 and x3 are unknowns.
3x1-x3 = 3
x1-x2+x3 = 6
-x1+34+2x3 = 0
a) Apply Gaussian elimination to solve for the unknowns
b) Apply Gauss-Jordan elimination to solve for the unknowns.
c) Apply LU decomposition to solve for the unknowns
d) Use matrix-inverse based solution (x=A^-1b) to solve for the unknowns. Use elimination approach to identify matrix inverse.
a) To solve for the unknowns using Gaussian elimination, follow these steps:
1. Multiply the first equation by -1 and add it to the second equation to get x2 = 7 + x3.
2. Multiply the first equation by -3 and add it to the third equation to get x3 = 3.
3. Substitute x3 = 3 into the first equation to get x1 = 2.
b) To solve for the unknowns using Gauss-Jordan elimination, follow these steps:
1. Multiply the first equation by -1 and add it to the second equation to get x2 = 7 + x3.
2. Multiply the first equation by -3 and add it to the third equation to get x3 = 3.
3. Substitute x3 = 3 into the second equation to get x2 = 4.
4. Substitute x3 = 3 and x2 = 4 into the first equation to get x1 = 2.
c) To solve for the unknowns using LU decomposition, follow these steps:
1. Compute the LU decomposition of the coefficient matrix A.
2. Solve Ly = b using forward substitution to get y = [1, 4, 3]^T.
3. Solve Ux = y using backward substitution to get x = [2, 4, 3]^T.
d) To solve for the unknowns using matrix-inverse based solution, follow these steps:
1. Compute the inverse of the coefficient matrix A.
2. Multiply the inverse of A with b to get x = [2, 4, 3]^T.
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Problem: Suppose you start a business assembling and selling
scooters. It costs you $1500 for tools and equipment to get started,
and the materials for each scooter cost $200 for each scooter. Your
scooters sell for $300. (a) Write and solve a system of equations
representing the total cost and revenue of your business. (b)
Describe what the solution means in terms of the situation. (c) Give
an example of a reasonable number of scooters you could assembly
and sell in order to make a profit and find the profit you will make for
that number of scooters.
a) Tοtal cοst C(x) = 200x + 1500
Revenue cοst R(x) = 300x
What is equatiοn?The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns. Fοr instance, the equatiοn 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the 'equal' sign.
Let x be the number οf scοοters.
It cοsts yοu $1500 fοr tοοls and equipment tο get started, and the materials cοst $200 fοr each scοοter.
Here fixed cοst = $1500 and variable cοst = $200
We knοw that cοst functiοn = variable cοst per unit + fixed cοst
Cοst functiοn :
C(x) = 200x+1500
Yοur scοοter sell fοr $300
Revenue functiοn :
R(x) = 300x
(b) The sοlutiοn means
When yοu start a business assembling initial cοst is $1500 fοr tοοls and equipment.
The material cοst will increase $200 fοr each number οf scοοter increases.
The revenue will increase $300 fοr each number οf scοοter increases.
c) Let us take number οf scοοters x=50
Then cοst C(50)=200*50+1500 = 10000+1500=$11500
Revenue Cοst R(50)=300*50=$15000
Then prοfit = Revenue- cοst = 15000-11500 = $3500.
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iven the polynomial 4x^(2)y^(4) - 9x^(2)y^(6), rewrite as a product of polynomials
The polynomial 4x^(2)y^(4) - 9x^(2)y^(6) can be rewritten as a product of polynomials as:
x^(2)y^(4)(2y + 3)(2y - 3)
The polynomial 4x^(2)y^(4) - 9x^(2)y^(6) can be rewritten as a product of polynomials by factoring out the common factor of x^(2)y^(4). This leaves us with:
x^(2)y^(4)(4 - 9y^(2))
Now, we can factor the polynomial inside the parentheses as a difference of squares:
x^(2)y^(4)(2y + 3)(2y - 3)
Therefore, the polynomial 4x^(2)y^(4) - 9x^(2)y^(6) can be rewritten as a product of polynomials as:
x^(2)y^(4)(2y + 3)(2y - 3)
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A chemist wants to make 54 ml of 18% acid solution by mixing 11% acid solution and a 20% acid solution how many ml should the chemist use
The chemist must use 12 ml of the 11% acid solution and 42 ml of the 20% acid solution to make a solution of quantity 54 ml of 18% concentration acid solution.
It is already given that the chemist wishes to make a solution of 54 milliliters of 18 percent concentration using two different solutions of concentration 11% and 20% each.
Now let us consider that the quantity of acid to be present in the final solution is (18/100)×54 = 9.72 ml
If we consider that x ml of 11% solution and y ml of 20% solution are added, then following relations can be obtained:
Total volume of x and y in the final solution = x + y = 54 ...(1)
Considering the concentration of acid and its volume, the following equation is formed:
0.11x + 0.2y = 9.72 ...(2)
Solving the equations (1) and (2) for the value of x and y, we get:
x = 54 - y
∴ 0.11(54 - y) + 0.2y = 9.72
⇒ 5.94 - 0.11y + 0.2y = 9.72
⇒ 0.09y = 3.78
⇒ y = 42 ml
Putting the value of y in equation (1), we get
x = 54 - y
x = 54 - 42 = 12 ml
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Joey bought 5 plates of nachos and 2 2-liter sodas for him and his friends. The total bill came to $67.87 (before tax). The next day he bought one 2-liter of soda and 2 plates of nachos for him and his dad. That total bill came to $27.94 (before tax). How much does a plate of nachos cost? How much does a 2-liter of soda cost?
Therefore , the solution of the given problem of unitary method comes out to be a 2-liter soda costs $4.98 and a platter of nachos costs $11.99.
What is unitary method ?The measurements taken from this femtosecond section must be multiplied by two in order to complete the task using the unitary variable technique. In essence, the characterised by a group and the hue groups are both removed from the unit approach when a desired object is present. For example, 40 pens with a expression price will indeed cost Inr ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this. Almost every living creature has a distinctive quality.
Here,
Let's use "N" for the price of a platter of nachos and "S" for the price of a 2-liter soda.
The first aspect of the issue reveals that:
=> 5N + 2S = 67.87
The second component of the issue reveals the following to us:
=>2N + S = 27.94
=> S = 27.94 - 2N
When we use this expression in place of S in the first equation, we obtain:
=> 5N + 2(27.94 - 2N) = 67.87
When we simplify and account for N, we obtain:
=> 5N + 55.88 - 4N = 67.87\sN = 11.99
We can determine S by substituting this number for N in the second equation:
=> 2(11.99) + S = 27.94\sS = 4.98
As a result, a 2-liter soda costs $4.98 and a platter of nachos costs $11.99.
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Exercise 3. Let \( n \in \mathbb{N} \) with \( n>2 \). Prove that there exists \( a \in \mathbb{Z}_{n} \) such that \( a^{2}=[1] \in \mathbb{Z}_{n} \) and \( a \neq[1] \).
\(a \in \mathbb{Z}_{n}\) such that \(a^{2} = [1] \in \mathbb{Z}_{n}\) and \(a \neq [1]\)
Let \(n \in \mathbb{N}\) with \(n>2\). We consider the set \( S = \{a \in \mathbb{Z}_{n} \ | \ a^{2} = [1] \in \mathbb{Z}_{n}\} \). We have to prove that \( S \neq \emptyset \).
We prove by contradiction. Suppose \( S = \emptyset \). This implies that for all \( a \in \mathbb{Z}_{n}, \ a^{2} \neq [1] \in \mathbb{Z}_{n}\). Thus, \( [1] \) is not a square in \(\mathbb{Z}_{n}\). But since \(n >2\), \([1]\) has at least two square roots in \(\mathbb{Z}_{n}\) which implies that \( S \neq \emptyset \).
Therefore, \(S \neq \emptyset\) and thus there exists \(a \in \mathbb{Z}_{n}\) such that \(a^{2} = [1] \in \mathbb{Z}_{n}\) and \(a \neq [1]\).
This proves that there exists an \(a \in \mathbb{Z}_{n}\) such that \(a^{2} = [1] \in \mathbb{Z}_{n}\) and \(a \neq [1]\).
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Determine if the given function is linear, quadratic, or exponential.
f(x) = 5 (2.3)^x
The given function f(x) = 5 (2.3)^x is an exponential function.
The given function is f(x) = 5 (2.3)^x.
To determine if the function is linear, quadratic, or exponential, we need to examine the form of the function.
A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept.
A quadratic function has the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
An exponential function has the form f(x) = ab^x, where a and b are constants.
The given function, f(x) = 5 (2.3)^x, is in the form of an exponential function, with a = 5 and b = 2.3. Therefore, the function is exponential.
In conclusion, the given function f(x) = 5 (2.3)^x is an exponential function.
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Find the values of a and b to express this recurring decimal as a fraction.
Simplify this fraction as much as possible before entering your answer.
0.727272... = [tex]\frac{a}{b}[/tex]
a=
b=
Answer: Let x = 0.727272...
Then, 100x = 72.727272...
Subtracting x from 100x gives:
100x - x = 72.727272... - 0.727272...
99x = 72
x = 72/99
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 9. Therefore:
x = (72/9) / (99/9) = 8/11
So, a = 8 and b = 11. Therefore, the recurring decimal 0.727272... can be expressed as the fraction 8/11.
Step-by-step explanation:
HELP MEEEEEE 20 EASY PONTSSSSS
The function that represents exponential growth is C. Of(x) = 0.3(1.05)^(x), where x is the input variable.
Exponential growth occurs when a quantity increases at a constant percentage rate over time, which is exactly what happens in the function C. As x increases, the term (1.05)^(x) grows larger and larger, leading to a corresponding increase in the value of the function. The coefficient 0.3 scales the rate of growth so that it starts at a manageable level.
Functions A, B, and D do not represent exponential growth. Function A decreases over time as the base is less than 1, function B represents a linear growth, and function D represents linear growth as well.
The function with Exponential growth is f(x) = 0.3 [tex](1.05)^x[/tex].
What is Exponential Function?An exponential function is a nonlinear function with the formula y = [tex]a(b)^x[/tex], where a = 0 and b = 1.
The function is an exponential growth function for a > 0 and b > 1. The function is an exponential decay function when a > 0 and 0 b 1.
First function, f(x) = 134 [tex](0.75)^x[/tex]
Here the value of b < 1 then it Exponential Decay.
Now, f(x) = 513 + 0.2x is linear function.
Now, f(x) = 0.3 [tex](1.05)^x[/tex]
Here the value of b > 1 then it Exponential Growth.
Now, f(x) = 15+ 1.6x is linear function.
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What is 92199+20923+29290+83292+2819+99279+38471+378143
Answer:
744416
Step-by-step explanation:
Just add everything together
Use a vertical format to add the polynomials. -8x^(2)-9x-2 8x^(2)+10x-6 6x^(2)-4x+2
The sum of the polynomials is 6x^(2)-3x-6.
To add the polynomials using a vertical format, we will first write each polynomial in a column, lining up like terms vertically. Then, we will add the coefficients of each like term together to find the sum.
Here is the solution in a vertical format:
So, the sum of the polynomials is 6x^(2)-3x-6.
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Hi, Could you please show and explain the methods for
calculating Mean, Median and Mode?
Mean: The mean is the average of a set of numbers. To calculate the mean, you add up all the numbers in the set and then divide by the total number of numbers in the set.
Median: The median is the middle number in a set of numbers when they are arranged in ascending or descending order.
Mode: The mode is the number that appears most frequently in a set of numbers.
Hi there! Yes, I can certainly show and explain the methods for calculating Mean, Median, and Mode. These are all measures of central tendency, which are used to describe the center of a data set.
Mean: The mean is the average of a set of numbers. To calculate the mean, you add up all the numbers in the set and then divide by the total number of numbers in the set. For example, if you have the numbers 2, 4, 6, 8, and 10, the mean would be (2 + 4 + 6 + 8 + 10) / 5 = 6.
Median: The median is the middle number in a set of numbers when they are arranged in ascending or descending order. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. For example, if you have the numbers 2, 4, 6, 8, and 10, the median would be 6. If you have the numbers 2, 4, 6, 8, 10, and 12, the median would be (4 + 6) / 2 = 5.
Mode: The mode is the number that appears most frequently in a set of numbers. If there is more than one number that appears the same number of times, there can be more than one mode. For example, if you have the numbers 2, 4, 6, 8, 10, and 10, the mode would be 10 because it appears twice and the other numbers only appear once.
I hope this helps! Let me know if you have any other questions.
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jordan cut strips of border for a design for a triangular sign to put on a bulletin board. two of the strips were 15 inches long and the third was 30 inches long. determine if the design can be made.justify your response.
Given that Jordan cut strips of border for a design for a triangular sign to put on a bulletin board. Two of the strips were 15 inches long and the third was 30 inches long. We need to determine if the design can be made.
To determine whether the design can be made or not, we will check whether the sum of the lengths of any two sides of the triangle is greater than the length of the third side or not. Let a, b and c be the three sides of the triangle such that c is the longest side. According to the Triangle Inequality Theorem, For a triangle to be formed, the sum of the lengths of any two sides of the triangle should be greater than the length of the third side.Thus, a + b > cIf the above condition is satisfied, then the design can be made. If not, then the design cannot be made.
Let's check for the given design:
a + b > ca + b = 15 + 15 = 30 (Since two of the strips were 15 inches long)
Therefore, 30 > 30 (Since the third strip was 30 inches long)The given design satisfies the Triangle Inequality Theorem. Hence, the design can be made.
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20 points pls quick and mark brainly
American Eagle Outfitters is advertising 30% off all merchandise.
14A. Zoe wants to buy a sweater that originally costs $40. How much will she save if she buys it on sale? Show your work or explain in words how did you get the answer.
Answer:
Zoe will save 30% of the original cost of the sweater, which is $40. To calculate the amount saved, we must multiply 30% by the original cost of the sweater, which gives us 0.30 x $40 = $12. Therefore, Zoe will save $12 on the sweater with the 30% discount
Step-by-step explanation:
Answer:
She will save $12.00
Step-by-step explanation:
.3 x 40 = 12
30% as a decimal is .3.
The cost of the sweater on sale would be
.7 x 40 = 28
If we take 30% off, we are leaving 70% on.
28 + 12 = 40 the original cost.
Helping in the name of Jesus.
A die is rolled ten times. What is the probability that a prime
number will be rolled every time?
The probability of rolling a prime number every time
The probability of rolling a prime number on a single die is 3/6 or 1/2, since there are three prime numbers (2, 3, 5) out of six possible outcomes.
To find the probability of rolling a prime number ten times in a row, we need to multiply the probabilities together. This is because each roll is independent of the others, so the probability of rolling a prime number on each roll is the same.
So the probability of rolling a prime number ten times in a row is:
(1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 1/1024
Therefore, the probability of rolling a prime number every time a die is rolled ten times is 1/1024.
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Math Recommendations If h(v)=2v^(3)-25v+4, use synthetic division to find h(-4). Submit
Using synthetic division, the value of h(-4) is - 24.
To find h(-4) using synthetic division, we will use the following steps:
1. Set up the synthetic division grid with the divisor (-4) in the top left corner and the coefficients of the polynomial in the top row.
-4 | 2 0 -25 4
2. Bring down the first coefficient to the bottom row.
-4 | 2 0 -25 4
|
2
3. Multiply the divisor (-4) by the first number in the bottom row (2) and put the result (-8) in the second column of the top row.
-4 | 2 0 -25 4
| -8
2
4. Add the numbers in the second column (0 and -8) and put the result (-8) in the second column of the bottom row.
-4 | 2 0 -25 4
| -8
2 -8
5. Repeat steps 3 and 4 for the remaining columns.
-4 | 2 0 -25 4
| -8 32 -28
2 -8 7 -24
6. The last number in the bottom row (-24) is the remainder and the value of h(-4). The other numbers in the bottom row (2, -8, 7) are the coefficients of the quotient polynomial.
Therefore, h(-4) = 24.
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Reflect point A over the line to get point A', which point below is A'?
Reflect point A over the line to get point A', -1,2 is A'.
What is a graph?
A graph is a structure that fundamentally consists of a set of items where some pairs of the objects are "connected" in some way. This definition comes from discrete mathematics, more especially graph theory. The items are represented by mathematical abstractions called vertices, and each pair of connected vertices is known as an edge.
A graph is frequently depicted in a diagram by a collection of dots or circles for the vertices and lines or curves for the edges. Among the topics covered by discrete mathematics are graphs.
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Give an example of:
1. A vector space V, and a (non-empty) subset of V that is closed under addition but not under scalar multiplication.
2. A vector space V and a (non-empty) subset of V that is closed under scalar multiplication but not under addition.
1). W is closed under addition.
W is not closed under scalar multiplication
2. W is not closed under addition
W is closed under scalar multiplication
1. Let V be the vector space of all 2x2 matrices with real entries. Consider the subset W of V consisting of matrices of the form:
| a b |
| 0 c |
where a, b, and c are real numbers. Note that W is non-empty, since the matrix |0 0| is in W.
|0 0|
Now, let A and B be any two matrices in W, so that A has the form:
| a1 b1 |
| 0 c1 |
and B has the form:
| a2 b2 |
| 0 c2 |
Then the sum of A and B has the form:
| a1+a2 b1+b2 |
| 0 c1+c2 |
which is clearly also in W. Therefore, W is closed under addition.
However, W is not closed under scalar multiplication. Let A be any matrix in W, so that A has the form:
| a b |
| 0 c |
where a, b, and c are real numbers. Then, if we multiply A by a non-real scalar k = xi (where x is a real number and i is the imaginary unit), we get:
kA = xi * | a b | = | xia xib |
| 0 c | | 0 xc |
which is not in W, since the entry in the (1,2) position is non-zero. Therefore, W is not closed under scalar multiplication.
2. Let V be the vector space of all polynomials with real coefficients. Consider the subset W of V consisting of all polynomials of degree at most 2.
Note that W is non-empty, since the polynomial p(x) = 0 is in W.
Now, let c be any real scalar, and let p(x) be any polynomial in W.
Then cp(x) is a polynomial of degree at most 2, since multiplying a polynomial of degree at most 2 by a scalar does not change its degree. Therefore, W is closed under scalar multiplication.
However, W is not closed under addition. Let p(x) and q(x) be any two polynomials in W of degree at most 2. Then the sum p(x) + q(x) may have degree greater than 2, and hence may not be in W. For example, if p(x) = x^2 + 2x + 1 and q(x) = -x^2 + x - 1, then p(x) + q(x) = 3x, which is not in W. Therefore, W is not closed under addition.
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You are sailing from your lakeshore cabin to a marina 60º north of east and 0.5 miles across the lake. On your return trip, you decide to sail directly south and then west to get back to your cabin.
A right triangle. The hypotenuse is 0.5, and an angle is 60 degrees.
How far would you now have to sail?
a.
0.68 miles
b.
0.43 miles
c.
0.25 miles
d.
0.5 miles
Since you sailed 0.5 miles 60º north of east to reach the marina, the distance you sailed eastward is 0.5cos(60º) = 0.25 miles and the distance you sailed northward is 0.5sin(60º) = 0.433 miles.
To return to your cabin, you sailed directly south for 0.433 miles, forming the adjacent side of a right triangle, and then sailed directly west for 0.25 miles, forming the opposite side of the same right triangle.
Therefore, the distance you sailed on your return trip is the hypotenuse of the right triangle, which can be found using the Pythagorean theorem:
distance = sqrt((0.433)^2 + (0.25)^2) ≈ 0.51 miles
Rounded to the nearest hundredth, the distance you sailed on your return trip is 0.51 miles, which is closest to option (a) 0.68 miles.
Iteration = 5000
Random: =RAND()
Demand: =ROUND ( NORM.INV ( RAND(), Mean, Standard Deviation),0)
Revenue: = Unit Price x MIN (Demand, Order Quantity)
Cost: = Order Quantity x Unit Cost
Refund: = Unit Refund x MAX(0, Order Quantity - Demand)
Profit: = Revenue - Cost + Refund
The Bin is the given, how should I get the chart that I had circled in the second picture with all these given?
To get the chart that you have circled in the second picture, you need to create a table using the given formulas and then create a chart using the table. Here are the steps:
1. Create a table with the following columns: Iteration, Random, Demand, Revenue, Cost, Refund, and Profit.
2. In the first row of the table, enter the given formulas in the respective columns. For example, in the first row of the Random column, enter =RAND(), in the first row of the Demand column, enter =ROUND ( NORM.INV ( RAND(), Mean, Standard Deviation),0), and so on.
3. Copy the formulas down to the 5000th row to get the values for all 5000 iterations.
4. Select the entire table and click on the Insert tab in the Excel ribbon.
5. In the Charts group, click on the type of chart that you want to create. In this case, it looks like you want to create a scatter chart.
6. In the Chart Design tab, click on the Select Data button in the Data group.
7. In the Select Data Source dialog box, click on the Add button in the Legend Entries (Series) section.
8. In the Edit Series dialog box, enter a name for the series, select the Profit column for the Series X values, and select the Demand column for the Series Y values.
9. Click on the OK button to close the Edit Series dialog box and then click on the OK button to close the Select Data Source dialog box.
10. Your chart should now be created and should look like the one that you have circled in the second picture.
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I need help on any of these please
The center of the circular track with the equation x² - 18x + y² - 22x = -177 is (20, 0). See below for other solutions
Points on the circleThe equation of a circle that passes through the origin is represented as
x² + y² = r²
Where
r = radius
For circle 13, we have
Point = (0, 6)
So, the radius is
0² + 6² = r²
r = 6
This gives
x² + y² = 6²
For the point (√11, 5), we have
(√11)² + 5² = 6²
36 = 36 --- true
The point (√11, 5) is on the circle
For circle 14, we have
Point = (-7, 0)
So, the radius is
-7² + 0² = r²
r = 7
This gives
x² + y² = 7²
For the point (√14, 6), we have
(√14)² + 6² = 7²
50 = 49 --- falsee
The point (√14, 6) is not on the circle
Error in Andy's solutionAndy's error is that he did not square 12 in (√23)² + (11)² ≠ 12
The correct solution is
(√23)² + (11)² = 12²
144 = 144
The point (√23, 11) is on the circle
Equations of the circles
The equation of a circle is represented as
(x - a)² + (y - b)² = r²
For circle 16, we have
Center = (-1, 5)
Radius, r = 4
So, we have
Equation: (x + 1)² + (y - 5)² = 4²
For circle 17, we have
Center = (2, 0)
Point = (-2, 3)
So, we have
Equation: (x - 2)² + (y - 0)² = (-2 - 2)² + (3 - 0)²
Equation: (x - 2)² + y² = 25
The center of a circular trackGiven that
x² - 18x + y² - 22x = -177
This gives
x² - 40x + y² = -177
Factorize
(x - 20)² + y² = -177 + 400
Evaluate
(x - 20)² + y² = 223
From the above, we have
Center = (20, 0)
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Figure E is dilated from point, the center of dilation.
Which figure is a dilation of figure E?
figure G
D
H
G
F
E
A figure which is a dilation of figure E include the following: A. figure F.
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape. This ultimately implies that, the size of the geometric shape would be increased (enlarged) or decreased (reduced) based on the scale factor applied.
What is a scale factor?In Geometry, a scale factor is the ratio of two corresponding length of sides or diameter in two similar geometric figures such as equilateral triangles, quadrilaterals, and other types of polygons.
Based on the image (see attachment), we can logically deduce that only figure E and figure F share the same (common) line of symmetry.
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Determine y when x = 18 if y = 20/3 when x = 30
x = 18 ...... y = 20/3
x = 30 ..... y = ?
____________
[tex]y = \dfrac{30 \cdot 20}{3 \cdot 18} = \dfrac{100}{9}[/tex]
Mara is draining her swimming pool. The depth of the water in the pool
changes by -__3
4 foot every hour. The depth of the water was 5 feet when
she started draining. What is the depth of the water after 5 hours?
After 5 hours of draining, the depth of the water in Mara's swimming pool will be 11/4 feet
The depth of the water variations via- 3/ 4 foot each hour, this means that the depth decreases by employing 3/4 foot every hour.
Still, also after one hour of draining, the intensity of the water might be
If the primary depth of the water was five bases.
5-(3/4) = 41/4 ft
After hours, the depth might be
-(3/4) = 31/2 fr
After three hours
-(3/4) = 23/4 ft
After 4 hours
-(3/4) = 2 ft
After five hours
2-(3/4) = 11/4 bases
Thus, after 5 hours of draining, the depth of the water in Mara's swimming pool will be 11/4 feet
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A pilot flies in a straight path for 1.5 hrs. She then makes a course correction, heading 20 degrees to the right of her original course, and flies 2 hrs in the new direction. If she maintains a constant speed of 685 mi/h, how far is she from her starting position?
Ans - The pilot is 1868.08 mi from her starting position, To find the distance the pilot is from her starting position, we can use the law of cosines. The law of cosines states that for any triangle with sides a, b, and c, and angle C opposite side c:
[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]
In this case, the pilot's original path is one side of the triangle (a), her new path after the course correction is another side of the triangle (b), and the distance she is from her starting position is the third side of the triangle (c). The angle between the two paths is 20 degrees (C).
First, we need to find the length of sides a and b. The pilot flew for 1.5 hrs at a speed of 685 mi/h on her original path, so:
a = 1.5 hrs * 685 mi/h = 1027.5 mi
She then flew for 2 hrs at the same speed on her new path, so:
b = 2 hrs * 685 mi/h = 1370 mi
Now we can plug these values into the law of cosines to find the distance the pilot is from her starting position (c):
[tex]c^2 = 1027.5^2 + 1370^2 - 2*1027.5*1370*cos(20)[/tex]
[tex]c^2 = 3,488,806.25[/tex]
[tex]c = sqrt(3,488,806.25)[/tex]
[tex]c = 1868.08 mi[/tex]
Therefore, the pilot is 1868.08 mi from her starting position.
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