True sampling distribution sample which is proportion to be approximately normal is "Both np and n(1 P) are at least 10".
For the sampling distribution of the sample proportion to be approximately normal, the sample size must be sufficiently large, and the sample proportion must be neither too small nor too large.
Specifically, the sample size multiplied by the sample proportion (np) and the sample size multiplied by one minus the sample proportion (n(1-P)) must both be at least 10. This is known as the "success-failure" condition.
Option b is not entirely accurate, as a sample size greater than 30 is a rule of thumb for the Central Limit Theorem to apply, but it is not a strict requirement for normality.
Option c is incorrect as a sample proportion greater than 0.5 means the distribution is skewed towards one end and not normal.
Option d and e are the mean and variance of the binomial distribution and are not directly related to normality.
The correct answer is option a. Both np and n(1-P) are at least 10.
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show all of your work, even though the question may not explicitly remind you to do so. clearly label any functions, graphs, tables, or other objects that you use. justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. your work will be scored on the correctness and completeness of your methods as well as your answers. answers without supporting work will usually not receive credit. unless otherwise specified, answers (numeric or algebraic) need not be simplified. if your answer is given as a decimal approximation, it should be correct to three places after the decimal point. unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number. the number of mosquitoes in a field after a major rainfall is modeled by the function m defined by m(t)
The function is defined as g(x) = f (√3x² + 4 ), where "f" is an unknown function.
A function is a mathematical object that assigns a unique output or value for each input. In other words, given an input, a function produces exactly one output.
To understand this function and its properties, we need to first identify and verify the domain and range of the function. The domain of a function is the set of all possible inputs for which the function produces a real output. In this case, the domain of "m" is the set of all real numbers "x" such that the expression √3x² + 4 is real.
Next, we need to understand the composition of functions. In this case, "m" is defined as the composition of two functions, "g" and "f."
The composition of two functions "f" and "g" is defined as "f(g(x))," which means that the output of "g" is used as the input for "f." In other words, we first evaluate "g" for a given value of "x," and then use the output of "g" as the input for "f."
Finally, we can evaluate the function "m" for a specific value of "x" by first evaluating "g" and then "f."
To do this, we simply substitute the value of "x" into the expression for "g" and then evaluate "f" with the resulting output.
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In plane P, lines m and n intersect at point A. If line k is perpendicular to line m and line n at point A, then line k is 1) contained in plane p 2) parallel to plane p 3) perpendicular to plane p 4) skew to plane p
Answer:
3)
Step-by-step explanation:
2 lines establish a plane (it is the same plane P as mentioned in the description).
a line being perpendicular (having a right angle = 90°) to 2 other lines means it is perpendicular to the plane these 2 lines are establishing.
as it is impossible for a line to be perpendicular to 2 other lines in the same plane, if these 2 other lines are intersecting. it would only be possible, if these 2 lines were parallel.
the set of all upper triangular n x n matrices is a subspace w of mnxn(f) (see exercise 12 of section 1.3). find a basis for w. vvhat is the dimension of w?
A basis for the set of all upper triangular n x n matrices is the set of matrix with all entries below the main diagonal equal to zero. The dimension of this subspace is n(n+1)/2.
A basis for the set of all upper triangular n x n matrices can be found by taking all n x n matrix with all entries below the main diagonal equal to zero. This basis has n(n+1)/2 elements, and so the dimension of this subspace is also n(n+1)/2.The set of all upper triangular n x n matrices is a subspace of mnxn(f), and a basis for this subspace can be found by considering all matrices with all entries below the main diagonal equal to zero. This basis is composed of n(n+1)/2 elements, and so this is also the dimension of the subspace. This means that the subspace is spanned by n(n+1)/2 linearly independent vectors. Each of the matrices in the basis is an upper triangular matrix, and all entries below the main diagonal are equal to zero. As such, each matrix in the basis can be used to represent one of the n(n+1)/2 coordinates of the subspace, and all of the matrices together span the entire space.
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Write the system first as a vector equation and then as a matrix equation. 3x^1 - x^2 = 4 10x^1 + 8x^2 = 2 6x^1 - x^2 = 1
The vector equation of system of equations is:
[tex]x_1\begin{bmatrix}a_1\\.\\.\\a_n\end{bmatrix}+x_n\begin{bmatrix}a_{m1}\\.\\.\\a_{mn}\end{bmatrix}=\begin{bmatrix}b_1\\.\\.\\b_n\end{bmatrix}[/tex]
And the matrix equation is,
[tex]\begin{bmatrix} 3 & -1\\10 & 8\\6 & -1\end{bmatrix}\begin{bmatrix}x_1\\x_2\end{bmatrix}=\begin{bmatrix}4\\2\\1\end{bmatrix}[/tex]
The system of eqyuations is:
3x₁- x₂ = 4
10x₁ + 8x₂ = 2
6x₁ - x₂ = 1
Consider the system of equations :
a₁x₁ + . . . + [tex]a_m x_m[/tex]= b₁
.
.
[tex]a_n[/tex]x₁ + . . . + [tex]a_{nm} x_{nm}[/tex] = [tex]b_n[/tex]
We know that the vector form of above system of equations is:
[tex]x_1\begin{bmatrix}a_1\\.\\.\\a_n\end{bmatrix}+x_n\begin{bmatrix}a_{m1}\\.\\.\\a_{mn}\end{bmatrix}=\begin{bmatrix}b_1\\.\\.\\b_n\end{bmatrix}[/tex]
So, required vector equation would be,
[tex]x_1\begin{bmatrix}3\\10\\6\end{bmatrix}+x_2\begin{bmatrix}-1\\8\\-1\end{bmatrix}=\begin{bmatrix}4\\2\\1\end{bmatrix}[/tex]
and the required matrix equation would be,
[tex]\begin{bmatrix} 3 & -1\\10 & 8\\6 & -1\end{bmatrix}\begin{bmatrix}x_1\\x_2\end{bmatrix}=\begin{bmatrix}4\\2\\1\end{bmatrix}[/tex]
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Convert 39 gallons to liters using unit fractions
The conversion gives 39 Galloon = 147.63106 Liters
What is unit Conversion?The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.
Given:
We have to convert 39 galloon to liter
As, 1 Galloon = 3.7854118 Liters
Now, 39 Galloon= 39 x 3.7854118 Liters
= 147.63106 Liters
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·can someone please help
Answer:
2mn
Step-by-step explanation:
To solve the expression 14m^2n^2/7mn, we need to simplify the fraction.
First, we can simplify the numerator by combining the 14 and m^2:
14m^2 * n^2 / 7mn = (14m^2) * (n^2) / (7mn) = 14mn * mn / 7mn = 14mn / 7
Next, we can simplify the denominator by 7
14mn / 7 = 14 / 7 = 2mn
Let f : A → B be a function. Then, which of the following statements is/are equivalent to saying that f is onto
(a) 3x EA, Vy E B f(x) y
(b)y B, Vxe A f(x) y
(c) Vy e B, 3x A f(x) = y
(d) Væ E A, 3y B f(x) = y
(e) Vy e B, 3x E A, 3w E B f(x) = wɅy = w
Select all possible options that apply.
Let f : A → B be a function and the equivalent of stating that f is onto is statements (a), (c), and (e) and they are, (a) 3x EA, Vy E B f(x) y, (c) Vy e B, 3x A f(x) = y, and (e) Vy e B, 3x E A, 3w E B f(x) = wɅy = w.
(a) 3x EA, Vy E B f(x) y denotes that at least one element x in A must exist for f(x) to equal y for every element function y in B. The meaning of onto is as follows.
(c) According to the formula Vy e B, 3x A f(x) = y, there must be at least one element x in A such that f(x) = y for each element y in B. Simply put, this is the same as assertion (a).
(e) Vy e B, 3x E A, 3w E B f(x) = wy = w indicates that at least one element x in A exists for every element y in B such that f(x) = y. The further requirement that g (x)
It is not equivalent to claim that f is onto based on statements (b) and (d).
(b) y B, Vxe A f(x) y denotes that there is at least one element in A such that f(x) = y for every element y in B. This is different from stating that f is onto because it does not imply that every element in B must actually be mapped to by f.
(d) According to the formula Vae E A, 3y B f(x) = y, there must be at least one element y in B such that f(x) = y for every element x in A. According to this definition, a function is total if it is specified for each element in domain A. The fact that f is assigned to some elements in B does not imply that f is necessarily onto those elements.
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game show on a game show, you are given five digits to arrange in the proper order to form the price of a car. if you are correct, you win the car. what is the probability of winning, given the following conditions? (a) you guess the position of each digit. (b) you know the fir
Probability of winning, you guess the position of each digit is 0.00833 and Probability of winning when you know the first correct piece is 0.04167.
There are 5 pieces to form a car.
Total number of arrangement of these 5 pieces is 5! = 5×4×3×2×1 = 120 ways
Of these 120 arrangements only 1 arrangement will form a proper car
(a) Probability that each position's guess is correct is = 1/ 120
Thus, the probability of getting all the guesses correct is 0.00833 or 0.833%.
(b) It is given that we know the first correct piece.
That is we need to guess the other 4 from the 4 remaining pieces.
Total number of arrangement of these 5 pieces is 4!
= 4×3×2×1 = 24 ways
Of these 24 arrangements only 1 arrangement will form a correct arrangement with the known first piece.
Probability that each position's guess is correct = 1/24
Thus, the probability of getting all the guesses correct when we know the first correct piece is 0.04167 or 4.17%.
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What are the three major types of author's purpose?
Answer:
to inform, to persuade, and to entertain
Step-by-step explanation:
Can someone please help me with the math problem, ASAP? The math problem is in the picture below, THANK YOU!
Note: Please show how you go with your answer for decreasing on or increasing on, one of the other. If you know what I mean.
Answer:
Increasing: (-infinity, 1) and Decreasing: (1, -infinity)
Step-by-step explanation:
Increasing means as you go from left to right where the x values are increasing, the y values are also increasing.
Decreasing means as you go from left to right where the x values are increasing, the y values are decreasing.
A set of stairs is being made from concrete. A picture of the stairs is shown below.
2 feet
5 feet
$1 foot
8 feet
5 feet
What is the volume, in cubic feet, of the set of stairs?
The volume of the set of stairs is 65 cubic feet.
What is volume ?In mathematics, the volume of an object is the amount of three-dimensional space that it occupies. It is a measure of the total amount of space that a solid object or a container can hold.
The volume of an object is usually measured in cubic units such as cubic meters ([tex]m^3[/tex]), cubic centimeters ([tex]cm^3[/tex]), or cubic feet (ft³), depending on the units of measurement used for its dimensions. The formula for calculating the volume of an object varies depending on its shape.
For simple shapes like cubes, rectangular prisms, and cylinders, the formulas for calculating their volumes are:
Volume of a cube = length x width x height
Volume of a rectangular prism = length x width x height
Volume of a cylinder = π x radius² x height
Where π (pi) is a mathematical constant approximately equal to 3.14, and the dimensions are all measured in the same units.
For irregular shapes, the volume can be determined using mathematical equations, computer modeling, or physical measurements. In real-world applications, volume is used in a variety of fields such as engineering, architecture, physics, and chemistry to describe the size, capacity, or amount of a substance or material.
According to given information :To calculate the volume of the set of stairs, we need to find the volume of each rectangular block that makes up the stairs and then add them up. Let's first find the dimensions of each rectangular block:
The first block has dimensions 2 feet by 5 feet by 1 foot.
The second block has dimensions 8 feet by 5 feet by 1 foot.
To find the volume of each block, we multiply its length by its width by its height. So, the volume of the first block is:
Volume of first block = length x width x height
= 5 feet x 5 feet x 1 foot
= 25 cubic feet
The volume of the second block is:
Volume of second block = length x width x height
= 8 feet x 5 feet x 1 foot
= 40 cubic feet
Therefore, the total volume of the set of stairs is:
Total volume = volume of first block + volume of second block
= 25 cubic feet + 40 cubic feet
= 65 cubic feet
Therefore, the volume of the set of stairs is 65 cubic feet.
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Answer:
Step-by-step explanation:
Answer:
The volume of the set of stairs is 65 cubic feet.
What is volume ?
In mathematics, the volume of an object is the amount of three-dimensional space that it occupies. It is a measure of the total amount of space that a solid object or a container can hold.
The volume of an object is usually measured in cubic units such as cubic meters (), cubic centimeters (), or cubic feet (ft³), depending on the units of measurement used for its dimensions. The formula for calculating the volume of an object varies depending on its shape.
For simple shapes like cubes, rectangular prisms, and cylinders, the formulas for calculating their volumes are:
Volume of a cube = length x width x height
Volume of a rectangular prism = length x width x height
Volume of a cylinder = π x radius² x height
Where π (pi) is a mathematical constant approximately equal to 3.14, and the dimensions are all measured in the same units.
For irregular shapes, the volume can be determined using mathematical equations, computer modeling, or physical measurements. In real-world applications, volume is used in a variety of fields such as engineering, architecture, physics, and chemistry to describe the size, capacity, or amount of a substance or material.
According to given information :
To calculate the volume of the set of stairs, we need to find the volume of each rectangular block that makes up the stairs and then add them up. Let's first find the dimensions of each rectangular block:
The first block has dimensions 2 feet by 5 feet by 1 foot.
To find the volume of each block, we multiply its length by its width by its height. So, the volume of the first block is:
Volume of first block = length x width x height
= 5 feet x 5 feet x 1 foot
= 25 cubic feet
The volume of the second block is:
Volume of second block = length x width x height
= 8 feet x 5 feet x 1 foot
= 40 cubic feet
Therefore, the total volume of the set of stairs is:
Total volume = volume of first block + volume of second block
= 25 cubic feet + 40 cubic feet
= 65 cubic feet
Therefore, the volume of the set of stairs is 65 cubic feet.
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Function A and Function B are linear functions.
Function A
Function B
y = 2x - 4
X
-5
-4
2
y
-11
-8
10
Which statements are true? Select all that apply.
The slope of Function A is greater than the slope of Function B.
The slope of Function A is less than the slope of Function B.
The y-intercept of Function A is greater than the y-intercept of Function B.
The y-intercept of Function A is less than the y-intercept of Function B.
Answer:
The true statements to be selected are the following:
"The slope of Function A is greater than the slope of Function B."
"The y-intercept of Function A is greater than the y-intercept of Function B."
Step-by-step explanation:
Based on the points that were provided for Function A: (-5, -11), (-4, -8), and (2, 10), we can create a linear function to represent the function. The slope of the function is 3, and the y-intercept would be 4, so the linear function of Function A would be y = 3x + 4. And the function of Function B is, as given, y = 2x - 4.
Now, we can compare the two functions and determine which statements are correct. Function A has a slope of 3 and a y-intercept of (0, 4), whilst Function B has a slope of 2 and a y-intercept of (0, -4). As both the slope and y-intercept of Function A is greater than the slope and y-intercept of Function B, the correct statements to select would be "The slope of Function A is greater than the slope of Function B." and "The y-intercept of Function A is greater than the y-intercept of Function B."
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.
The perimeter of a triangle is 104 units. The combined length of two of the sides of the triangle is 64 units.
What is the length of the third side of the triangle in units?
The equation that represents the third side of the triangle is x + 64 = 104 and its solution is 40 units.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The perimeter of the triangle is determined by adding together all of its sides.
The perimeter of a triangle is 104 units. The combined length of two of the sides of the triangle is 64 units.
Let the third side be 'x'. Then the equation is given as,
x + 64 = 104
x = 104 - 64
x = 40 units
The equation that represents the third side of the triangle is x + 64 = 104 and its solution is 40 units.
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find (-8-8\sqrt(3))^(1/4), express the roots in rectangular coordinates, exhibit them as the vertices of a certain square and point out which is the principal root g
The four roots form the vertices of a square in the complex plane. The side length of the square is √2. The vertices of the square complex number are: A = (-√2, -√2), B = (0, -2√2), C = (√2, -√2), D = (0, 0). The principal root is the one with the smallest argument, which is (-√2 - √2 i).
To find the fourth root of the complex number (-8-8√3), we can use the following steps:
We start by finding the modulus and argument of the number:
|(-8-8√3)| = 16
arg(-8-8√3) = arctan(-√3) = -π/3
Therefore, (-8-8√3) = 16(cos(-π/3) + i sin(-π/3)).
To find the fourth root, we take the square root twice. We can use De Moivre's theorem to simplify the calculation:
(-8-8√3)^(1/4) = (16(cos(-π/3) + i sin(-π/3)))^(1/4)
= 2(cos(-π/12) + i sin(-π/12))
= 2(cos(11π/12) + i sin(11π/12))
= 2(-√2/2 - √2/2 i)
We have expressed the roots in rectangular coordinates as (-√2, -√2), (0, -2√2), (√2, -√2), and (0, 0).
The four roots form the vertices of a square in the complex plane. The side length of the square is |(-√2) - (0)| = √2.
The vertices of the square are:
A = (-√2, -√2)
B = (0, -2√2)
C = (√2, -√2)
D = (0, 0)
The principal root is the one with the smallest argument, which is (-√2 - √2 i). This is the root corresponding to the first quadrant of the complex plane.
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A company is purchasing new computers for its new office. The expression below represents the total cost of the computers, including an
Installation charge for all the computers.
The constant of the expression represents the
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O
$115 + $100
Reset
Et
O
, and the coefficient of x represents the
The constant of the expression represents the installation charge, and the coefficient of x represents the number of computer.
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, an equation that the total cost of the computers, including an installation charge for all the computers:
y = $115x+$100
y is the total cost.
Here the constant of the expression $100 represents the installation charge and the coefficient of x represents the number of computer,
For 1 computer, the total cost be:
y = $215
For 2 computers the total cost be:
y = $330
Hence, the constant of the expression represents the installation charge, and the coefficient of x represents the number of computer.
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use double integration to calculate the area of the region r. you must sketch the region including all appropriate labels x 2y
9/16 square units is the calculated area of the region r using double integration.
The procedure where two variables, x and y, are involved and you must integrate with each of them is known as a double integral or double integration technique. The area of a given function beneath a curve is calculated using this integration method.
The area of a region, the volume below the surface, and the average value of a function of two variables over a rectangular region may all be determined using double integrals.
A two-variable function, f (x, y), integral over a region R is referred to as a double integral. Iterative integration may be used to get the double integral if R = [a, b] [c, d] (integrate first with respect to y, and then integrate with respect to x). The solution can be seen on the attached image below.
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Question correction:
See on the attached image.
Show that equation (5.3) is true by considering an investment in the asset combined with a short position in a futures contract. Assume that all income from the asset is reinvested in the asset. Use an argument similar to that in footnotes 2 and 4 of this chapter and explain in detail what an arbitrageur would do if equation (5.3) did not hold.
5.3 equation:
F0= S0e(r-q)T
Footnote 2:
For another way of seeing that equation (5.1) is correct, consider the following strategy: buy one unit of the asset and enter into a short forward contract to sell it for F0 at time T. This costs S0 and is certain to lead to a cash inflow of F0 at time T. Therefore S0 must equal the present value of F0; that is, S0= F0erT, or equivalently F0= S0erT
Equation 5.1 F0= S0erT.
Footnote 4:
For another way of seeing that equation (5.2) is correct, consider the following strategy: buy one unit of the asset and enter into a short forward contract to sell it for F0 at time T. This costs S0 and is certain to lead to a cash inflow of F0 at time T and an income with a present value of I. The initial outflow is S0. The present value of the inflows is I+ F0e-rT. Hence, S0=I + F0e-rT, or equivalently F0= (S0 – I)erT
Equation 5.2 F0= (S0 – I)erT
The futures price F0 must be equal to the present value of the expected future spot price, which is [tex]S0e^{(r-q)} T[/tex]. Hence, equation (5.3) is true.
We can use a similar strategy to Footnote 2 to show that equation (5.3) is correct.
Consider an investor who wants to invest in an asset with spot price S0, which pays a continuous dividend yield of q, and simultaneously take a short position in a futures contract with maturity T, which has a futures price of F0. The investor buys one unit of the asset for S0 and sells a futures contract for F0.
At maturity T, the futures contract will be settled at the spot price of the asset, ST. If ST > F0, the investor makes a profit of ST - F0 on the asset, but incurs a loss of F0 - ST on the futures contract. If ST < F0, the investor incurs a loss of F0 - ST on the asset, but makes a profit of ST - F0 on the futures contract.
Now, suppose that equation (5.3) does not hold, i.e., [tex]F0 \neq S0e^{(r-q)} T[/tex]. If [tex]F0 > S0e^{(r-q)} T[/tex], then the investor can buy the asset for S0, sell a futures contract for F0, and invest the difference [tex](F0 - S0e^{(r-q)} T)[/tex] at the risk-free rate r. At maturity T, the investor will receive ST from the asset, F0 from the futures contract, and [tex](F0 - S0e^{(r-q)} T)e^r(T-t)[/tex] from the investment. The total cash inflow will be [tex]ST + F0 + (F0 - S0e^{(r-q)} T)e^r(T-t).[/tex] But this is greater than the initial outflow of S0, which means that the investor can make a riskless profit, violating the no-arbitrage principle.
Similarly, if[tex]F0 < S0e^{(r-q)} T[/tex], then the investor can short-sell the asset for S0, buy a futures contract for F0, and borrow the difference [tex](S0e^{(r-q)} T - F0)[/tex] at the risk-free rate r. At maturity T, the investor will receive ST from the short sale, F0 from the futures contract, and [tex](S0e^{(r-q)} T - F0)e^r(T-t)[/tex]from the borrowing. The total cash inflow will be [tex]ST + F0 + (S0e^{(r-q)} T - F0)e^r(T-t)[/tex]. But this is greater than the initial outflow of S0, which means that the investor can make a riskless profit, violating the no-arbitrage principle.
Therefore, to avoid arbitrage opportunities, The futures price F0 must be equal to the present value of the expected future spot price, which is [tex]S0e^{(r-q)} T[/tex]. Hence, equation (5.3) is true.
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Let S be a set. Consider the algebraic structure (℘(S),∪,∩). Taking union to be the additive operation and intersection to be the multiplicative operation, investigate whether or not this algebraic structure is a commutative ring. That is, either prove or provide a counterexample for each property of a commutative ring.
Bonus: Does this structure have zero divisors?
The algebraic structure (℘(S),∪,∩) is a commutative ring.
To prove that the algebraic structure (℘(S),∪,∩) is a commutative ring, we need to show that it satisfies the following properties:
Addition is commutative: A ∪ B = B ∪ A for any A, B ∈ ℘(S)
Addition is associative: (A ∪ B) ∪ C = A ∪ (B ∪ C) for any A, B, C ∈ ℘(S)
There exists an additive identity: there exists a set 0 ∈ ℘(S) such that A ∪ 0 = A for any A ∈ ℘(S)
There exists an additive inverse: for any A ∈ ℘(S), there exists a set -A ∈ ℘(S) such that A ∪ -A = 0
Multiplication is commutative: A ∩ B = B ∩ A for any A, B ∈ ℘(S)
Multiplication is associative: (A ∩ B) ∩ C = A ∩ (B ∩ C) for any A, B, C ∈ ℘(S)
There exists a multiplicative identity: there exists a set 1 ∈ ℘(S) such that A ∩ 1 = A for any A ∈ ℘(S)
Distribution property: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) for any A, B, C ∈ ℘(S)
Addition is commutative: This property is true, as the union operation is commutative. Therefore, A ∪ B = B ∪ A for any A, B ∈ ℘(S).
Addition is associative: This property is also true, as the union operation is associative. Therefore, (A ∪ B) ∪ C = A ∪ (B ∪ C) for any A, B, C ∈ ℘(S).
There exists an additive identity: The empty set ∅ is the additive identity, as A ∪ ∅ = A for any A ∈ ℘(S).
There exists an additive inverse: The additive inverse of any set A is its complement -A, as A ∪ -A = ∅ for any A ∈ ℘(S).
Multiplication is commutative: This property is true, as the intersection operation is commutative. Therefore, A ∩ B = B ∩ A for any A, B ∈ ℘(S).
Multiplication is associative: This property is also true, as the intersection operation is associative. Therefore, (A ∩ B) ∩ C = A ∩ (B ∩ C) for any A, B, C ∈ ℘(S).
There exists a multiplicative identity: The set S is the multiplicative identity, as A ∩ S = A for any A ∈ ℘(S).
Distribution property: This property is also true, as the intersection operation distributes over the union operation. Therefore, A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) for any A, B, C ∈ ℘(S).
Therefore, we have shown that the algebraic structure (℘(S),∪,∩) is a commutative ring.
Bonus: This structure does not have zero divisors. A zero divisor is an element a of a ring that is not zero and that has a product with some nonzero element b that is equal to zero. However, in
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Can someone please help me with this math problem, ASAP? It is in the picture below, Thank You!
The average rate of change from x = 4 to x = 9 is given as follows:
-1.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output divided by the change in the input.
The numeric values are given as follows:
f(4) = 25, f(9) = 20.
Hence the change in the output is of:
20 - 25 = -5.
The change in the input is of:
9 - 4 = 5.
Hence the rate is given as follows:
r = -5/5
r = -1.
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Fort Hood is 0.8 miles from Tom's house. Tom's workplace is 0.35 times as far from Fort Hood as Tom's House. What is the distance in miles from Tom's workplace to Fort Hood?
Tom's workplace is 0.28 miles from Fort Hood.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Fort Hood from Tom's house distance = 0.8 miles
Now,
Tom's workplace is 0.35 times as far from Fort Hood as Tom's House.
This means,
Tom's workplace from Fort Hood distance.
= 0.35 x 0.8
= 0.28 miles
Thus,
Tom's workplace is 0.28 miles from Fort Hood.
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What is an equation of the line that passes through the point (-7,-6)(−7,−6) and is parallel to the line x-y=5x−y=5?
Answer:
y = x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
x - y = 5 ( subtract x from both sides )
- y = - x + 5 ( multiply through by - 1 )
y = x - 5 ← in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes , then
y = x + c ← is the partial equation
to find c substitute (- 7, - 6 ) into the partial equation
- 6 = - 7 + c ( add 7 to both sides )
1 = c
y = x + 1 ← equation of parallel line
5.) Which point satisfies the following system
of inequalities?
y=-x+2
-2x+y<-2
Á.(1,-1) B.(0,0) C. (2,2) D.(3,3)
The point satisfies the given system of inequalities is (1, -1)
What a system of inequalities?A system of inequalities is a set of two or more inequalities in one or more variables.
Given is a system of inequalities y < -x+2 and -2x+y < -2,
We know that, the solution set of a system of inequalities is given by studying the graph of the system, The solution set the region covered by lines of the both inequalities.
Plotting the graphs, of the system of inequalities, we get, the set of solution is the area covered with purple shade,
In that area only, (1, -1) lies.
Therefore, the point (1, -1) is the solution of the given system of inequalities
Hence, the point satisfies the given system of inequalities is (1, -1)
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While preparing his budget sheet, John Drake noticed that his annual
expenses were $17,700 while his monthly living expenses were $300 more than
his monthly fixed expenses. If John's total monthly expenses were $3,250, find his
monthly fixed expenses and his monthly living expenses.
Answer:
Step-by-step explanation:
The relationship between the Fahrenheit (F) and Celsius (C) temperature scales is given by the linear function F = 9/5 C + 32. a. Sketch a graph of this function. b. What is the slope of the graph? What does it represent? The slope means that F increases 32 degrees for each increase of 1 degree c. What is the F-intercept? What does it represent? The F-intercept of 212 is the Fahrenheit temperature corresponding to a Celsius temperature of
a. To sketch the graph of the function F = 9/5 C + 32, we can plot a few points and connect them with a straight line.
For example, when C = 0, F = 32, so we can plot the point (0, 32). When C = 100, F = 212, so we can plot the point (100, 212). Connecting these two points gives us the following graph
b. The slope of the graph is 9/5. This represents the rate of change of F with respect to C. Specifically, it means that for every 1 degree Celsius increase in temperature, there is a corresponding increase of 9/5 degrees Fahrenheit.
c. The F-intercept is 32. This represents the Fahrenheit temperature when the Celsius temperature is 0. In other words, it is the point where the graph crosses the y-axis.
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What is the height h for the base that is 5/4 units long?
The measure of the height of the triangle is 3 / 8 units.
What are trigonometric identities?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that the triangle has sides, 3 / 4 cm, 1 cm, and 5 / 4 cm.
The angle of the triangle is,
tanθ = ( 1 ) / ( 3 / 4 )
tanθ = 1.33
θ = 53.6°
The height will be,
h = ( 3 / 4 ) x sin53.4
h = 0.6
h = 4 / 5 cm
Therefore, the measure of the height of the triangle is 3 / 8 units.
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NO LINKS!!! URGENT HELP PLEASE !!!
#1-3
Find the shaded area of each figure, and round your answer to one decimal place if necessary.
You posted a lot of questions. I'll do the first three to get you started.
==================================================
Problem 1
Answer: 55 square inchesExplanation:
Draw a vertical line to enclose the un-shaded region. Think of it like adding fencing to enclose a paddock or backyard.
What results are two rectangles. The larger rectangle has area = length*width = 8*10 = 80 square inches.
The smaller unshaded rectangle inside has area of 5*5 = 25 square inches.
The difference of those areas is: 80-25 = 55
You have the correct answer. Nice work.
==================================================
Problem 2
Answer: 486 square feetExplanation:
Follow the same set of steps as done in the previous problem. Draw a vertical line to form a larger rectangle.
The larger rectangle has area of 18*31.5 = 567 square feet.
The smaller unshaded rectangle has area of 9*9 = 81 square feet.
Subtract those results to get the shaded region only: 567-81 = 486
==================================================
Problem 3
Answer: 5.6 square cmExplanation:
This time we don't have to add any extra lines to enclose the figure.
A = larger area = 6*2.4 = 14.4
B = smaller unshaded area = 2*4.4 = 8.8
C = A-B = 14.4-8.8 = 5.6 square cm
You have the correct answer. Nice work.
Answer:
1) 55 in²
2) 486 ft²
3) 5.6 cm²
Step-by-step explanation:
To calculate the area of each given figure, subtract the area of the cut-out rectangle (marked in blue on the attached diagram) from the area of the larger rectangle.
[tex]\boxed{\begin{minipage}{5cm}\underline{Area of a rectangle}\\\\$A=w\cdot l$\\\\where:\\ \phantom{ww} $\bullet$ \quad $w$ is the width.\\ \phantom{ww} $\bullet$ \quad $l$ is the length.\\\end{minipage}}[/tex]
Question 1[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&=8 \cdot 10- 5\cdot 5\\&=80-25\\&=55\; \sf in^2\end{aligned}[/tex]
Question 2[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&= 31.5\cdot 18- 9\cdot 9\\&=567-81\\&=486\; \sf ft^2\end{aligned}[/tex]
Question 3[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&= 6\cdot 2.4- 4.4\cdot2 \\&=14.4-8.8\\&=5.6\; \sf cm^2\end{aligned}[/tex]
Fill in the table using this function rule.
y=3x-1
X Y
1
4
5
7
The completed table using this function rule is,
Input (x) 1 4 5 7
Output (y) 2 11 14 26
What is the function rule?Function rule is the rule of writing the relationship between the two variables, one is dependent and another is independent.
The table given in the problem is;
Input (x) 1 4 5 7
Output (y)
Thus we need to write such a function, which gives the value of (y).
y=3x-1
Complete the table using the above function rule;
At (x) equal to 1,
y=3x-1
y=3(1)-1
y = 2
At (x) equal to 4,
y=3x-1
y=3(4)-1
y = 11
At (x) equal to 5,
y=3x-1
y=3(5)-1
y = 14
At (x) equal to 7,
y=3x-1
y=3(7)-1
y = 26
Hence, the completed table is,
Input (x) 1 4 5 7
Output (y) 2 11 14 26
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Explain why the graph of a linear equation in the form of y = c is the horizontal line, parallel to the x-axis passing through the point (0,c).
The linear equation in the form of y = c is the horizontal line, parallel to the x-axis passing through the point (0,c), because in this equation the x-intercept is 0.
What are linear equations?A linear equation is an equation in which the highest power of the variable is always 1.
The line y = c, is always parallel to x-axis because here if we compare to general equation of a line y = mx+c, the m is zero that means the slope is zero and also the x-intercept is zero.
Therefore, the line y = c is the horizontal line, parallel to the x-axis.
Hence, the linear equation in the form of y = c is the horizontal line, parallel to the x-axis passing through the point (0,c), because in this equation the x-intercept is 0.
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4. How many terms will be in the expansion of (2x + 3y)?
There will be 6+ 1 = 6 terms in the expansion.
There will be 6-1 = 5 terms in the expansion.
There will be 6-1 = 6 terms in the expansion.
O There will be 6+1=7 terms in the expansion.
The solution is, In the binomial expansion (2x + 3)^5 , there are 6 terms.
What is binomial expression ?The formula for expanding the exponential power of a binomial expression is provided by the binomial theorem, sometimes referred to as the binomial expansion. The following is the binomial expansion of (x + y)n using the binomial theorem:
(x+y)n = nC0 xny0 + nC1 xn-1y1 + nC2 xn-2 y2 + ... + nCn-1 x1yn-1 + nCn x0yn
here, we have,
According to the question, given that
Binomial expansion (2x + 3)^5
Number of terms in a binomial expansion of (x + y)^n is
N = n + 1 words in total
In the binomial expansion (2x + 3)^5
n = 5
N = 5 + 1 = 6
Therefore, In Binomial expansion (2x + 3)^5 there are 6 terms.
The algebraic expression (x + y)n can be expanded according to the binomial theorem, which represents it as a sum of terms using separate exponents of the variables x and y. Each word in a binomial expansion has a coefficient, which is a numerical value.
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Consider the matrix A = [ 3 -2 -4 -5 -2 3 ] and the vector x = [5 2 -4] When multiplying A by z on the right, the result Az is a linear combination of three vectors vi, v2, v3, where the entries of x play the role of the coefficients in front of those vectors, as follow (5)vi (2)02 + ( - 4)vs What are these vectors? v1 =v2 =v3 =
The entries of x, 5, 2, and -4, are the coefficients in front of the vectors v1, v2, and v3 respectively.
To find the vectors v1, v2, and v3, we need to perform the matrix-vector multiplication Az = A * x.
A = [3 -2 -4 -5 -2 3]
x = [5 2 -4]
Az = [3 -2 -4 -5 -2 3] * [5 2 -4] = [35 -8 -52 -34 -12 22]
So, the vectors v1, v2, and v3 can be represented as follows:
v1 = [35]
v2 = [-8]
v3 = [-52 -34 -12 22]
These vectors represent the components of the result Az in the same order as they appear in the multiplication. The values of x, 5, 2, and -4, are the coefficients in front of the vectors v1, v2, and v3 respectively.
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____ The given question is incomplete, the complete question s given below:
Consider the matrix A = [ 3 -2 -4 -5 -2 3 ] and the vector x = [5 2 -4] When multiplying A by z on the right, the result Az is a linear combination of three vectors v1, v2, v3, where the entries of x play the role of the coefficients in front of those vectors, as follow (5)v1 + (2)v2 + ( - 4)v3. What are these vectors v1, v2, v3.