(8 points) For each problem, select the best response. (a) Let A, B and C be mutually exclusive events such that S is equal to A union B union C. Which of the following statements is true A. One of A, B, or C must be a subset of the other two events B. A, B, and C must be independent events © c. P(S) = P(A) + P(B) + P(C) D. Probability of A given B must equal the probability of C E. S contains elements that are not in A or B or C F. None of the above.

Answer:

Step-by-step explanation:

The function is:

The 2005th term of the sequence is 55.

Given information,

The first term of a sequence is 2005.

It states that each succeeding term is the sum of the cubes of the digits of the previous term, then the 2005th term is;

First term = 2005

Second term = 2³ + 0³ + 0³ + 5³ = 8 + 0 + 0 + 125 = 133

Third term = 1³ + 3³ + 3³ = 1 + 27 + 27 = 55

Fourth term = 5³ + 5³ = 125 + 125 = 250

Fifth term = 2³ + 5³ + 0³ = 133

As we see the number obtained repeating, the 2005th term will be 55.

Hence, the 2005th term of the sequence is 55.

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The X-axis (horizontal axis) often represents a "class boundaries" of such an ogive, whereas the Y-axis (vertical axis) typically shows the frequency count.

A sort of frequency polygon that displays cumulative frequencies is an ogive, often known as a cumulative frequency polygon.

Thus, The X-axis (horizontal axis) often represents a class boundaries being measured of such an ogive.

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The probability that a randomly selected tire will fail before the 35,000 mile warranty mileage can be determined using the exponential distribution.

Given that the warranty mileage is the mean value (μ) of the exponential distribution, we can calculate the probability using the formula P(X < x) = 1 - e^(-x/μ), where X represents the random variable denoting the mileage at which the tire fails.

Using the given warranty mileage of 35,000 miles, we can plug in the values into the formula:

P(X < 35,000) = 1 - e^(-35,000/μ).

However, the value of μ, which represents the mean lifespan of the tire, is not provided in the given information. Therefore, it is not possible to determine the exact probability without knowing the specific value of μ. As a result, none of the provided answer choices can be selected as the correct probability.

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By the definition of lunar month, it can be inferred that-

If the moon were farther from earth than it is now, then lunar month will be more than 28 days.

What is lunar month?

Time taken by the moon to make one complete revolution around the earth is called lunar month.

If the moon were farther from earth than it is now, then the moon will have to travel a greater distance to make one complete revolution around the moon. So time taken by the moon to make one complete  revolution around the earth will increase. So lunar month will be more than 28 days.

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To solve the system of equations using Gaussian elimination, we can represent the given system in an augmented matrix form:

[ 3 -7 -2 | 46 ]

[ 1 -3 0 | 18 ]

To perform Gaussian elimination, we'll apply row operations to the augmented matrix to obtain row-echelon form.

First, let's perform the row operation R2 = R2 - (1/3)R1:

[ 3 -7 -2 | 46 ]

[ 0 2 (2/3) | 2 ]

Next, we'll perform the row operation R2 = (1/2)R2:

[ 3 -7 -2 | 46 ]

[ 0 1 (1/3) | 1 ]

Now, let's perform the row operation R1 = R1 + 7R2:

[ 3 0 1 | 53 ]

[ 0 1 (1/3) | 1 ]

Finally, let's perform the row operation R1 = R1 - (1/3)R2:

[ 3 0 0 | 52 ]

[ 0 1 (1/3) | 1 ]

The resulting row-echelon form gives us the following system of equations:

3x₁ + 0x₂ + 0x₃ = 52

0x₁ + 1x₂ + (1/3)x₃ = 1

From the row-echelon form, we can see that the system has a unique solution.

Therefore, the correct choice is A. The unique solution is x₁ = 52, x₂ = 1, and x₃ = 0.

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Answer:

8 minutes cause 32/8 = 4  then 4 x 2 = 8

Step-by-step explanation:

Answer:

6^2

Step-by-step explanation:

Answer:

\(6^{2}\)

Step-by-step explanation:

=\(\frac{6^{7} }{6^{5} }\)

=\(6^{7}\).\(6^{-5}\)

=\(6^{7-5}\)

=\(6^{2}\)

Answer:

4

Step-by-step explanation:

The solution to the system of equations f(x) = g(x) is:

x = -2, y = 3.

A system of equations is a set of equations that is related, and the solution of the system is found when the equations are equal, that is, when the equations all intersect.

In the context of this problem, the equations are given as follows:

The solution to the given system of equations is at the value of x for which f(x) = g(x), hence it is obtained as follows:

f(x) = g(x)

2x + 7 = -x + 1 (solve just line any equality, isolating the desired variable).

2x + x = 1 - 7

3x = -6

x = -6/3

x = -2.

The y-coordinate of the solution of the system is given as follows:

y = -(-2) + 1 = 2 + 1 = 3.

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Answer:

85x(500-0.10x)

Step-by-step explanation:

The types of function that best models the number of books in Jamal's library as a function of time is A. increasing linear.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, it's important to note that this is a linear equation. Also, every month Jamal adds two new books to his library. This implies that it's increasing.

In conclusion, the correct option is A.

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Complete question

Every month Jamal adds two new books to his library. Which of the following types of functions

best models the number of books in Jamal's library as a function of time?

Increasing linear

Decreasing linear

Increasing exponential

Decreasing exponential

(a) The translation in coordinate notation is (x', y') = (x-4, y-3)

(b) The translation as a vector in component is \(\vec v = \vec w + ( -4\hat i -3\hat j)\).

The solution has been obtained by using the concept of transformation.

What is transformation?

A transformation is any operation that shifts a polygon or other two-dimensional object on a plane or coordinate system.

The two-dimensional shape that existing before any modification is referred to as the "inverse image" or "pre-image." The image is a representation of the altered shape.

From the given figure, we can see that the quadrilateral W'X'Y'Z' has been formed by translating quadrilateral WXYZ 4 units in x direction and 3 units in y direction.

So, the translation in coordinate notation is (x', y') = (x-4, y-3) and as a vector in component is \(\vec v = \vec w + ( -4\hat i -3\hat j)\).

Hence, the required solution has been obtained.

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The missing figure for the question has been attached below.

V can be expressed as a linear combination of vectors in S₁. This implies that S₁ U S₂ is linearly dependent.

To prove the statement, let's break it down into two parts and prove each part separately:

Part 1: If S₁ U S₂ is linearly dependent, then span(S₁) ∪ span(S₂) ‡ {0}.

Part 2: If span(S₁) ∪ span(S₂) ‡ {0}, then S₁ U S₂ is linearly dependent.

Part 1: If S₁ U S₂ is linearly dependent, then span(S₁) ∪ span(S₂) ‡ {0}.

Assume S₁ U S₂ is linearly dependent. This means there exist scalars c₁ and c₂, not both zero, such that c₁S₁ + c₂S₂ = 0

Since S₁ and S₂ are linearly independent, neither of them can be written as a linear combination of the other. Therefore, at least one of the scalars c₁ and c₂ must be non-zero. Without loss of generality, assume c₁ ≠ 0.

Now, rearranging the equation, we have c₁S₁ = -c₂S₂. Dividing both sides by c₁ (which is non-zero), we get S₁ = (-c₂/c₁)S₂.

This shows that S₁ is a scalar multiple of S₂. Therefore, span(S₁) ⊆ span(S₂).

Since c₁ ≠ 0, we also have -c₂/c₁ ≠ 0. Thus, the zero vector {0} can be expressed as a non-trivial linear combination of vectors in span(S₁) and span(S₂), i.e., span(S₁) ∪ span(S₂) ‡ {0}.

Part 2: If span(S₁) ∪ span(S₂) ‡ {0}, then S₁ U S₂ is linearly dependent.

Assume span(S₁) ∪ span(S₂) ‡ {0}. This means there exists a non-zero vector v such that v ∈ span(S₁) ∪ span(S₂).

Since v is non-zero, it can be expressed as a non-trivial linear combination of vectors in either span(S₁) or span(S₂). Without loss of generality, assume v is a linear combination of vectors in span(S₁).

Therefore, v can be expressed as a linear combination of vectors in S₁. This implies that S₁ U S₂ is linearly dependent.

By proving both parts, we have shown that S₁ U S₂ is linearly dependent if and only if span(S₁) ∪ span(S₂) ‡ {0}.

In summary, we have proven that if S₁ U S₂ is linearly dependent, then span(S₁) ∪ span(S₂) ‡ {0}, and conversely, if span(S_1) \cup span(S_2)) ‡ {0}, then S₁ U S₂ is linearly dependent.

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Answer:

31

Step-by-step explanation:

although we cannot see the whole graph, I assume it would be 31 because

2010-1979 is 31

and the x values are years after 1979

The linear function of  f(-10)= 4.5,f(-2)=4.5 is y = 4.5.

Linear function can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the linear function of f(-10)= 4.5, f(-2)=4.5 can be represented as follows:

Using y = mx + b

4.5 = -10m + b

4.5  = -2m + b

b = 4.5 + 10m

Hence, using substitution,

4.5  = -2m + 4.5 + 10m

4.5 - 4.5 = 8m

m = 0

Let's find b

4.5 = -10(0) + b

b = 4.5

Therefore, the linear function is y = 4.5

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To find the degree of a polynomial function, count the number of terms in the expression. To find the number of turning points, take the degree of the polynomial and subtract 1. The number of turning points will be equal to that number.

To find the degree of a polynomial function, the first step is to count the number of terms in the expression. For example, if the expression is 3x^2 + 4x + 2, then the degree is 2 because there are three terms.The second step is to subtract 1 from the degree of the polynomial. In the example, subtracting 1 from 2 gives us 1. Therefore, the polynomial has 1 turning point.A turning point is a point on the graph of the polynomial where the slope of the tangent line is 0. This means the graph changes direction at the turning point. In the example, the graph changes direction at the point (1, 5).In summary, to find the degree and the number of turning points in a polynomial function, count the number of terms in the expression to find the degree, then subtract 1 from the degree to find the number of turning points.

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The derivative of U with respect to x is A1 x/(x²+y²).

In order to find the value of dU/dx, we need to differentiate U with respect to x.

As A0 and A1 are constants, they will remain the same after differentiation.

Therefore, dU/dx = d/dx (A1 ln (√x²+y²))

Here, we will use the chain rule.

So, the derivative of ln(√x²+y²) is (1/√x²+y²) d/dx (√x²+y²).

Applying chain rule, d/dx (√x²+y²) = (1/2) (x²+y²)^(-1/2) .

2x = x/(√x²+y²)

Therefore, dU/dx

= d/dx (A1 ln (√x²+y²))

= A1 (1/√x²+y²) d/dx (√x²+y²)

= A1 (1/√x²+y²) . (x/(√x²+y²))

= A1 x/(x²+y²)

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Linear transformations have several properties, including mapping the zero vector to the zero vector, negating the image of a vector, and preserving the linearity of vector combinations.

In the context of linear transformations, where a linear transformation is denoted as L: V → W, the properties can be summarized as follows. Firstly, the zero vector in V, denoted as 0V, is mapped to the zero vector in W, denoted as 0W: L(0V) = 0W. This property ensures that the linear transformation preserves the concept of the zero vector.

Secondly, the negation of a vector v in V is reflected in the linear transformation: L(-v) = -L(v). This property demonstrates that the transformation of a negated vector is equal to the negation of the transformation of the original vector.

Lastly, the linearity property of linear transformations extends to vector combinations. For any real numbers a1, a2, ..., an and vectors v1, v2, ..., vn in V (where n is greater than or equal to 2), the linear transformation of their linear combination is equal to the linear combination of their individual transformations: L(a1v1 + a2v2 + ... + anvn) = a1L(v1) + a2L(v2) + ... + anL(vn). This property ensures that linear transformations preserve the linearity of vector combinations.

These properties are fundamental to understanding and working with linear transformations, as they provide rules and guidelines for their behavior and relationships between vectors in different vector spaces.

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Answer:

2 sqrt(2x-1)

Step-by-step explanation:

f(x) = sqrt( x+9)

g(x) = 8x-13

f(g(x))

place the function g(x) in for x in f(x)

f(g(x)) = sqrt(8x-13+9)

Combine like terms

f(g(x)) = sqrt(8x-4)

Factor out 4

f(g(x)) = sqrt(4*(2x-1)

           2 sqrt(2x-1)

\(\\ \sf\longmapsto f(x)=\sqrt{x+7}\)

\(\\ \sf\longmapsto g(x)=8x-11\)

\(\\ \sf\longmapsto f(g(x))=\sqrt{8x-11+7}\)

\(\\ \sf\longmapsto f(g(x))=\sqrt{8x-4}\)

\(\\ \sf\longmapsto f(g(x))=\sqrt{4(2x-1)}\)

\(\\ \sf\longmapsto f(g(x))=2\sqrt{2x-1}\)

Answer:

\(\textsf{C)}\quad \dfrac{5}{16}\; \sf yd^2\)

Step-by-step explanation:

The net of a square-based pyramid is made up of:

From inspection of the given net:

The area of a square is the square of one of its side lengths.

The area of a triangle is half the product of its base and height.

The total surface area of the pyramid is the sum of the area of the square base and the area of 4 congruent triangles.

Therefore:

\(\begin{aligned}\sf Total\;surface\;area&=\sf Area_{square}+4 \cdot Area_{triangle}\\\\&=s^2+4 \cdot \dfrac{1}{2}bh\\\\&=\left(\frac{1}{4}\right)^2+4 \cdot \frac{1}{2} \cdot \frac{1}{4} \cdot \frac{1}{2}\\\\&=\dfrac{1^2}{4^2}+\dfrac{4 \cdot 1 \cdot 1 \cdot 1}{2 \cdot 4 \cdot 2}\\\\&=\dfrac{1}{16}+\dfrac{4}{16}\\\\&=\dfrac{1+4}{16}\\\\&=\dfrac{5}{16}\; \sf yd^2\end{aligned}\)

Therefore, the surface area of the pyramid is 5/16 yd².

$240 is saved by Isaiah from his allowance within the space of 20 weeks.

An equation is used to show the relationship between two or more variables. Equations may involve the use of mathematical operations.

Isaiah is saving $12 per week from his allowance

The amount of money saved by Isaiah in 20 weeks is:

Money saved = $12 per week * 20 weeks

Money saved  = $240

Hence $240 is saved by Isaiah from his allowance within the space of 20 weeks.

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In the given boundary-value problem, we are asked to set up the set of equations required to solve the problem using the finite difference method. The equation is y" = 2x²y + xy + 2, and we are given the boundary conditions y(1) = -1 and y(4) = 4.

To solve the problem using the finite difference method, we can approximate the second derivative y" using the central difference formula: y" ≈ (yₙ₊₁ - 2yₙ + yₙ₋₁) / h². Substituting this approximation into the original differential equation, we obtain the finite difference equation: (yₙ₊₁ - 2yₙ + yₙ₋₁) / h² = 2xₙ²yₙ + xₙyₙ + 2.

For the given boundary conditions, y(1) = -1 and y(4) = 4, we can use these values to form additional equations. At x₀ = 1, we have the equation y₀ = -1. At xₙ = 4, we have the equation yₙ = 4.

In summary, the set of equations required to solve the boundary-value problem by the finite difference method, with the given boundary conditions, would be:

(y₂ - 2y₁ + y₀) / h² = 2x₁²y₁ + x₁y₁ + 2,

(y₃ - 2y₂ + y₁) / h² = 2x₂²y₂ + x₂y₂ + 2,

...

(yₙ₊₁ - 2yₙ + yₙ₋₁) / h² = 2xₙ²yₙ + xₙyₙ + 2,

y₀ = -1,

yₙ = 4.

These equations form a system of equations that can be solved numerically to obtain the solution to the boundary-value problem.

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Answer:

(5, 3)

Step-by-step explanation:

\(x = 17 - 4y \\ y = x - 2\)

Substitute x into y:

\(y = (17 - 4y) - 2 \\ y = 15 - 4y \\ y + 4y = 15 \\ 5y = 15 \\ y = 3\)

Substitute y into x:

\(y = x - 2 \\ 3 = x - 2 \\ 3 + 2 = x \\ x = 5\)

Therefore your answer is (5, 3).

Answer:

Step-by-step explanation:

You want to know the amount borrowed at 10%, 12%, and 14% if the total borrowed was $21000, the total interest was $2580, and the total of amounts borrowed at 10% and 14% was double the amount borrowed at 12%.

The relations give rise to three equations. If we let x, y, z represent the respective amounts borrowed at 10%, 12%, and 14%, we have ...

  x + y + z = 21000 . . . . . . total borrowed

  0.10x +0.12y +0.14z = 2580 . . . . . . total interest

  x + y = 2z . . . . . . . . . . . relationship between amounts

Writing the last equation as ...

  x -2y +z = 0

we can formulate the problem as a matrix equation and use a solver to find the solution. We have done that in the attachment. It tells us the amounts borrowed are ...

__

Additional comment

Recognizing that the amount at 12% is 1/3 of the total, we can use that fact to rewrite the other two equations. The interest on the $7000 at 12% is $840, so we have ...

These two equations have the solution shown above. (It is usually convenient to solve them by substituting for x in the second equation.)

<95141404393>

Answer:

Slope is 1/5 and equation is  4-2 / 10-0  

Step-by-step explanation:

Its equation is             4-2 / 10-0  

-2/-10       =         1/5 Slope is 1/5

Answer:

The answer is y=1/5x+2

Step-by-step explanation:

The slope is 1/5

and the y is 2

Answer:

lines tx and vs are perpendicular

Answer:

I think it is the 2 one don't blame me if I am wrong

Answer:

fraction: 3 1/5  

Step-by-step explanation:

The following are the offered rational exponents in expression form:

• (A) the fourth root's tenth root = \(\sqrt[10]{4}\)

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: The following rational exponents are expressed in the expression form (Math Operator, Number/Variable, Math Operator): (A) the tenth root of four= \(\sqrt[10]{4}\)

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