What is the quotient of 5.67 x 107 and 2.7 x
104 expressed in scientific notation?

We have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

Let A and B be two sets in a generalized rectangle R, i.e., R = A x B. The boundary of R, denoted by bd(R), is defined as the closure of the set of points that are not in the interior of R. In other words, bd(R) = cl(R) \ int(R), where cl(R) is the closure of R and int(R) is the interior of R.

To show that bd(R) is the union of finitely many closed generalized rectangles with volume zero, we first note that the closure of R can be expressed as the union of R and its boundary, i.e., cl(R) = R ∪ bd(R). Therefore, it suffices to show that R can be expressed as the union of finitely many closed generalized rectangles with volume zero and that bd(R) can also be expressed as the union of finitely many closed generalized rectangles with volume zero.

Let (a,b) be a point in R. Then there exists an open ball B((a,b), r) around (a,b) that is contained in R, where r > 0. Without loss of generality, we can assume that r is small enough so that B((a,b), r) is a generalized rectangle. Since B((a,b), r) is open, it follows that int(R) is the union of all such generalized rectangles. Therefore, R can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such generalized rectangles.

Next, we show that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero. Let (a,b) be a point in bd(R). Then every open ball B((a,b), r) around (a,b) contains points both in R and in the complement of R. By definition of bd(R), the closure of B((a,b), r) intersects both R and the complement of R. Therefore, B((a,b), r) can be expressed as the union of two closed generalized rectangles, one contained in R and one contained in the complement of R. It follows that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such balls B((a,b), r) and their decompositions into closed generalized rectangles.

Therefore, we have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.

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The least scores Juan could have had in the two tests are 85 and 100

Let the test scores be x and y

Where x is the current test and y is the previous test

Using the interpretation of the parameters in the question, we have the following:

x = y + 15 --- the relationship between the test scores

The average test scores can be represented as

1/2(x + y) ≥ 92

Substitute x = y + 15 in 1/2(x + y) ≥ 92

1/2(y + 15 + y) ≥ 92

Evaluate the like terms

1/2(2y + 15) ≥ 92

So, we have

2y + 15 ≥ 184

This gives

2y ≥ 169

Divide by 2

y ≥ 84.5

From the question both numbers are integers

So, we can assume that y = 85

Substitute y = 85 in x = y + 15

x = 85 + 15

Evaluate

x = 100

Hence, the possible test scores are 85 and 100

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Answer:

c= 6103515625w/2187x

w= x in (c)/ in (3) + In (6561/ 6103515625)/ in (3)

no clue but I tryed

Answer:

The first blank is ‘the same’ the second blank is ‘proportional’

Step-by-step explanation:

how can i explain when the answer is already an explanation

Answer:

D. for the first one and B. for the second one i think

Answer:

Changing the point of view will cause completely different narrative of a story. You will never know the character's own thoughts, motifs of doing something and his/her perception of everything will not be that clear as it can be depicted in first point of view, when character tell you his story personally. If it was narrated in first person from other character you would never found out what is really true in the story.

Step-by-step explanation:

Answer:

i think it's c

Step-by-step explanation:

sorry if I'm wrong

The area and circumference to the nearest tenth include the following:

Area = 490.6 square meters.

Circumference = 78.5 meters.

In Mathematics, the area of a circle can be calculated by using this formula:

Area = πr²

Where:

r represents the radius of a circle.

Note: Radius = diameter/2 = 25/2 = 12.5 meters.

By substituting the radius into the formula for the area of a circle, we have the following;

Area of circle = 3.14 × 12.5²

Area of circle = 490.6 square meters.

In Mathematics, the circumference of a circle can be calculated by using the following mathematical expression:

Circumference of a circle, C = 2πr

Circumference of a circle, C = 2(3.14) × 12.5

Circumference of a circle, C = 78.5 m.

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Answer:

The outcome of rolling a set of 2 fair dice is a number between 2 and 12, and there is a probability of 1/9 for each outcome.

For the outcomes 4,5,6, you will lose $6, and for the other outcomes, you will win $3.

There are 3 outcomes 4,5,6, and 9-3 = 6 outcomes where you win $3.

So your expected gain/loss per roll is:

(3/9) * $3 + (3/9) * (-$6) = -$1

Therefore, on average, you will lose $1 per each throwing.

Mike comes to a stop 105.3 feet above sea level while trekking on a mountain. The vertical separation between Mike and the mountain's base is 101.5 feet .

Given that,

Mike comes to a stop 105.3 feet above sea level while trekking on a mountain. There are 3.8 feet of sea level below the mountain's base.

We have to find what is the vertical separation between Mike and the mountain's base.

The Mike comes to a stop 105.3 feet above sea level while trekking on a mountain.

3.8 feet of sea level below the mountain's base.

We just have to do the difference of the above sea level feet and below sea level feet.

=105.3-3.8

=101.5

Therefore, the vertical separation between Mike and the mountain's base is 101.5 feet .

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If the rectangle is not a square, then the sides must not be equal.

Thus, the rectangle can be cut horizontally, vertically, and diagonally. Therefore, it must be option D, which is "3 or more".

The general solution to the differential equation xy' + 3y = 0 is given by:

y = c/x^3

where c is a constant.

To verify that this is a solution, we can substitute it into the differential equation:

xy' + 3y = 0

\(x(d/dx)(c/x^3) + 3(c/x^3)\)= 0

-c/x^3 + 3(c/x^3) = 0

The last step follows from the fact that the derivative of \(x^(-n)\)is \(-nx^(-n-\)1).

This simplifies to:

\(2c/x^3\) = 0

which is true if and only if c = 0 or x = infinity. Since c can be any constant, this means that y = \(c/x^3\) is a family of solutions to the differential equation.

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The compound inequality describes the possible lengths for the third side, x is -4< c< 14.

A triangle is a three-sided polygon that is sometimes (but not always) referred to as a trigon. Every triangle has three sides and three angles, with some of them being the same.

A triangle with A, B, and C vertices is symbolized by ΔABC

The Triangle Inequality Theorem states that given two triangle side lengths, the length of the third side must be greater than the difference and less than the sum of the two provided sides. The third side c of a triangle must be the same as the first two sides a and b:

(a - b) < c < (a + b)

As a result, let a = 5 and b = 9

(5-9) <c (5+9)

-4< c< 14

As a result, the third side of the triangle must follow the inequality, which is -4< c <14

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The percentage that each expense has out of the total budgeted amount of $45,000  have been computed, where insurance has 8.00%, Utilities 7.00% and so on.

What is a percentage?

In this case, percentage refers to proportion of each expense from the total budgeted expense of $45,000, which means that in order to total budgeted expense of $45,000, which means that in order to compute the percentage of total budgeted for each expense category, we divide the expense by the total budgeted expense

Insurance=$3600/$45,000=8.00%

Utilities=$3150/$45,000=7.00%

Clothing=$2700/$45000=6.00%

Transportation=$1350/$45000=3.00%

Entertainment=$5400/$45000=12.00%

Savings=$4050/$45000=9.00%

Taxes=$7200/$45000=16.00%

Food=$7650/$45000=17.00%

Housing=$9900/$45000=22.00%

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Answer:

D

Step-by-step explanation:

cause Mary needs to know how much fencing to get.

Answer:

7.04

Step-by-step explanation:

2.27

2.27

2.50 equals 7.04

The expression csc(t)sin(t) can be simplified to 1/cos(t), which is equivalent to sec(t).

To simplify the expression csc(t)sin(t), we can rewrite csc(t) as 1/sin(t). Substituting this into the expression, we have (1/sin(t))sin(t). The sine functions cancel out, leaving us with 1. Therefore, csc(t)sin(t) simplifies to 1.

Alternatively, we can rewrite csc(t) as 1/sin(t) and sin(t) as cos(t)/sec(t). Substituting these into the expression, we have (1/sin(t))(cos(t)/sec(t)). The sin(t) and sec(t) terms cancel out, leaving us with cos(t)/1, which simplifies to cos(t). Therefore, csc(t)sin(t) is also equivalent to cos(t).

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(a) The range of c₁ (the objective coefficient of x₁) for which this BFS remains optimal is c₁ ≤ 2.

(b) The range of b₂ (the right-hand side of the second constraint) for which this BFS remains optimal is 3 ≤ b₂ < 4.

(c) The dual price of the second constraint is 0.

(a) The optimality condition for a linear programming problem requires that the objective coefficient of a non-basic variable (here, x₁) should not increase beyond the dual price of the corresponding constraint. In this case, the dual price of the second constraint is 0, indicating that increasing the coefficient of x₁ will not affect the optimality of the basic feasible solution. Therefore, the range of c₁ for which the BFS remains optimal is c₁ ≤ 2.

(b) The range of b₂ for which the BFS remains optimal is determined by the allowable range of the corresponding dual variable. In this case, the dual price of the second constraint is 0, implying that the dual variable associated with that constraint can vary within any range. As long as 3 ≤ b₂ < 4, the dual variable remains within its allowable range, and thus, the BFS remains optimal.

(c) The dual price of a constraint represents the rate of change in the objective function value per unit change in the right-hand side of the constraint, while keeping all other variables fixed. In this case, the dual price of the second constraint is 0, indicating that the objective function value does not change with variations in the right-hand side of that constraint.

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Answer:

B

Step-by-step explanation:

Answer:

I think its D.

Step-by-step explanation:

Im taking the quiz right now. But as far as i have seen most people are saying D too.

Answer:

a) 5x + x AND 6x

b) 5 + 40y

Step-by-step explanation:

Answer:

is 2/3 times - 13/12=- 5/12 times

Step-by-step explanation:

Answer:

just add all of the numbers that are around the shape and you will have your answer!

Answer:

so far if u add everything it should equal to 126

The two given theorems are as follows:

a) The square root of every positive number less than one is greater than the number itself.

c) Every real number besides 0 has a multiplicative inverse.

To restate these theorems, we can write:

a) If a number is positive and less than one, then its square root is greater than the number itself.

c) For every real number x ≠ 0, there exists a real number y such that xy = 1.2.2.2 Determine whether the statement is true or false by direct proof or counterexample

The second part of the question asks to determine whether the given statement is true or false by direct proof or counterexample.

The statement is as follows:b) If x + y is an even integer, then x and y are both even integers.

To prove that the statement is true, we need to show that if x + y is an even integer, then x and y are both even integers. Let x = 2a and y = 2b, where a and b are integers. Then x + y = 2a + 2b = 2(a + b), which is even.

Hence, the statement is true.To show that the statement is false, we need to give a counterexample. Let x = 2 and y = 3.

Then x + y = 2 + 3 = 5, which is odd. However, x = 2 is even.

Hence, the statement is false.

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Answer:

Step-by-step explanation: I hypothesize

that I'm going to choose a defective light bulb

The equivalent expression when x² - 81 is factored is (x - 9)(x + 9)

From the question, we have the following expression that can be used in our computation:

x² - 81

Start by expressing as the square of 9

So, we have the following expression

x² - 9²

Solving further, we apply the difference of two squares to each term of the expression

This gives

(x - 9)(x + 9)

This cannot be solved further

Hence, the solution to the expression is (x - 9)(x + 9)

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So, the last three digits of m*n is 001.

Let p be the probability that Alfred wins given that he goes first. Then, the probability that Bonnie wins given that she goes first is 1-p. Therefore, the probability that Alfred wins the second game given that Bonnie went first in the first game is 1-p. Similarly, the probability that Alfred wins the third game given that he went first in the second game is p, and so on.

Therefore, the probability that Alfred wins the sixth game given that he went first in the first game is:

p(1-p)(1-p)(p)(p)(p) = p^4 (1-p)^2

Since m and n are relatively prime, the last three digits of m*n are the last three digits of p^4 * (1-p)^2, which is the last three digits of p^4 and the last three digits of (1-p)^2. Since p is the probability of winning given that you go first, it is a number between 0 and 1. Therefore, the last three digits of p^4 and (1-p)^2 are 001, resulting in the last three digits of the final answer being 001.

Therefore, the last three digits of m*n is 001.

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Answer:

2/3

Step-by-step explanation:

I am not sure

Answer:

Step-by-step explanation:

\(Let \:the \: unknown \: fraction \: be \: x\\\\\frac{5}{3} -x = 1\\\\\frac{5}{3}-x=1\\\\\mathrm{Subtract\:}\frac{5}{3}\mathrm{\:from\:both\:sides}\\\\\frac{5}{3}-x-\frac{5}{3}=1-\frac{5}{3}\\\\\frac{5}{3}-x-\frac{5}{3}=-x\\\\1-\frac{5}{3}=-\frac{2}{3}\\-x=-\frac{2}{3}\\\\x=\frac{2}{3}\\\)