what is ordered pair​

Answer:

\(a^2 - b^2\)

Step-by-step explanation:

1. \((a)(a)+(a)(b)+(-b)(a)+(-b)(b)\)

2. \(a^2 + ab - ab - b^2\)

3. \(a^2 - b^2\)

The value of the investment after a certain number of years can be calculated using the compound interest formula:

A = P(1 + r/n)^(nt),

where A is the final amount, P is the principal amount (initial investment), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

For part (a), after 6 years, the investment would grow to A = $10,000(1 + 0.04/2)^(2*6) = $12,167.88.

For part (b), after 12 years, the investment would grow to A = $10,000(1 + 0.04/2)^(2*12) = $14,851.39.

For part (c), after 18 years, the investment would grow to A = $10,000(1 + 0.04/2)^(2*18) = $18,061.13.

In these calculations, the interest rate of 4% per year is divided by 2 because interest is compounded semiannually. The exponent nt represents the total number of compounding periods over the given number of years. By substituting the values into the formula, we can find the value of the investment after each specified time period.

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Answer:

Step-by-step explanation: For example, if a 12 ounce can of corn costs 55 cents the rate is 55 cents for 12 ounces. The first term in ratio is measured in cents the second term in ounces

The tree should be 22.5 feet tall in the mural.

To determine the height of the tree in the mural, we can set up a proportion based on the scale ratio between Devon's height and the height of the tree.

Let's denote the height of the tree in the mural as 'x'.

According to the given information:

Devon's actual height: 6 feet

Devon's height in the mural: 4.5 feet

Tree's actual height: 30 feet

Setting up the proportion:

(Devon's height in the mural) / (Devon's actual height) = (Tree's height in the mural) / (Tree's actual height)

Substituting the given values:

4.5 feet / 6 feet = x / 30 feet

To solve for 'x', we can cross-multiply:

4.5 feet * 30 feet = 6 feet * x

135 feet = 6x

Divide both sides by 6:

x = 135 feet / 6

Simplifying the division:

x = 22.5 feet

Therefore, in the painting, the tree should stand 22.5 feet tall.

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The asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\) is f(n) ∈ Θ(g(n)). Therefore, the growth rates of f(n) and g(n) are primarily determined by the cubic terms, and they grow at the same rate within a constant factor.

To determine the asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\), we need to compare their growth rates as n approaches infinity.

Θ (Theta) Notation: f(n) ∈ Θ(g(n)) means that f(n) grows at the same rate as g(n) within a constant factor. In other words, there exists positive constants c1 and c2 such that c1 * g(n) ≤ f(n) ≤ c2 * g(n) for sufficiently large n.

o (Little-o) Notation: f(n) ∈ o(g(n)) means that f(n) grows strictly slower than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) < c * g(n) for all n > n0.

ω (Omega) Notation: f(n) ∈ ω(g(n)) means that f(n) grows strictly faster than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) > c * g(n) for all n > n0.

Now let's analyze the given functions:

\(f(n) = n^3 (8 + 2 cos 2n)\\g(n) = n^2 + 2n^3 + 3n\)

Since both functions have the same dominant term, we can say that f(n) ∈ Θ(g(n)) because they grow at the same rate within a constant factor. The other notations, o and ω, are not applicable here because neither function grows strictly faster nor slower than the other.

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Answer:

The answer is C

Step-by-step explanation:

(a) To show that the integral of f(z) dz over the unit circle C is equal to 0, we can parametrize C as z(t) = e^(it), where t ranges from 0 to 2π. Substituting this parametrization into f(z) = z^2, we get f(z(t)) = (e^(it))^2 = e^(2it). Now, dz = i e^(it) dt. Plugging these values into the integral, we have ∫[C] f(z) dz = ∫[0 to 2π] e^(2it) (i e^(it)) dt = i ∫[0 to 2π] e^(3it) dt. Evaluating this integral gives [e^(3it)/3i] from 0 to 2π. Substituting the limits, we get [e^(6πi)/3i - e^(0i)/3i].

Since e^(6πi) = 1, the expression simplifies to 1/3i - 1/3i = 0. Therefore, the integral of f(z) dz over C is indeed 0.

(b) By using the Cauchy's Integral Theorem, we can show that the integral of f(z) dz over C is 0. The theorem states that if f(z) is analytic inside and on a simple closed curve C, then the integral of f(z) dz over C is 0. In this case, f(z) = z^2, which is an entire function (analytic everywhere). Since C is the unit circle, which is a simple closed curve, we can apply the theorem. Thus, the integral of f(z) dz over C is 0.

Both methods, direct multivariable integration and the application of Cauchy's Integral Theorem, confirm that the integral of f(z) dz over the unit circle C is equal to 0.

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Answer:

x(xy + 1)

Step-by-step explanation:

The two terms have the common factor x.

x²y + x = x(xy + 1)

A definite integral is said to be improper if one or both of the limits of integration are infinite, or if the integrand function has a vertical asymptote within the interval of integration.

In other words, an improper integral is one that cannot be evaluated using the usual techniques of integration, such as the fundamental theorem of calculus, because it involves infinite limits or a function that is not integrable over the interval.

For example, the definite integral of f(x) = 1/x from 1 to infinity is an improper integral because the upper limit of integration is infinity, which is not a finite number. Similarly, the definite integral of f(x) = ln(x) from 0 to 1 is an improper integral because the lower limit of integration is 0, and the function has a vertical asymptote at x=0.

To evaluate improper integrals, we use limit processes to determine whether the integral converges (has a finite value) or diverges (has an infinite value). If the integral converges, we can find its value by taking the limit of a related integral as one or both of the limits of integration approach infinity or zero.

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Answer:

the answer is 80

Step-by-step explanation:

or, angleAFE =angleBFD [V.O.A]

or, 125=45+DFC

or, 125-45=DFC

or, 80 =DFC

Using the concepts of straight angle, ∠DFC = 80°.

A straight angle is an angle equal to 180 degrees. It is called straight because it appears as a straight line.

Since AD is a straight line.

∠AFE + ∠EFD = 180°

125° + ∠EFD = 180°

∠EFD = 180° - 125° = 55°

Now, EB is a straight line.

∠EFD + ∠DFC + ∠CFB = 180°

55° + ∠DFC + 45° = 180°

∠DFC = 180° - 100° = 80°

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ANSWER

622.113821138 is the answer

Answer:

622.1138

Step-by-step explanation:

The economic significance suggested by the slope coefficient helps you determine whether the coefficient implies a "big" effect of X on Y.

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not. Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. 

Given

The slope coefficient suggests economic significance.

The economic significance suggested by the slope coefficient helps you determine whether the coefficient implies a "big" effect of X on Y.

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Let's solve the problems and provide the answers with the correct number of significant figures:

(4.307 × 10^4) × (6.2 × 10^-3)

Multiplying the numbers:

(4.307 × 6.2) × (10^4 × 10^-3) = 26.6974 × 10^1

Since the result is in scientific notation, we multiply the decimal part by the power of 10:

26.6974 × 10^1 = 266.974

To express the answer with the correct number of significant figures, we consider the least number of significant figures in the original values, which is three significant figures in this case.

Therefore, the answer is 267 with three significant figures.

26.127 + 3.9 + 0.0324

Adding the numbers:

26.127 + 3.9 + 0.0324 = 30.0594

To express the answer with the correct number of significant figures, we consider the least number of decimal places in the original values, which is one decimal place in this case.

Therefore, the answer is 30.1 with one decimal place.

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Answer:

Step-by-step explanation:

The dimension of the basis is {[1 0 0 2], [-1 1 0 0]}.

To find a basis for the subspace S = span {[1 -1 0 2], [3 -5 4 8], [0 1 -2 -1]}, we can use the same method as in the example. First, we put the vectors in a matrix and row-reduce it:

[1 -1 0 2]
[3 -5 4 8]
[0 1 -2 -1]

R2 - 3R1 -> R2
R3 -> R3 + 2R1

[1 -1 0 2]
[0 -2 4 2]
[0 1 -2 -1]

-1/2R2 -> R2

[1 -1 0 2]
[0 1 -2 -1]
[0 1 -2 -1]

R3 - R2 -> R3

[1 -1 0 2]
[0 1 -2 -1]
[0 0 0 0]

We can see that the last row is all zeros, so we have only two pivots and one free variable. This means that the dimension of the subspace S is 2. To find a basis, we can write the pivots as linear combinations of the original vectors:

[1 -1 0 2] = [1 0 0 2] + [-1 1 0 0]
[0 1 -2 -1] = [0 1 -2 -1]

Therefore, a basis for S is {[1 0 0 2], [-1 1 0 0]}.

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Answer:

65.5%

Explanation:

total number of students = 10+8+3+8 = 29

8+8+3 = 19 = number of students that did not choose football

(19/29)*100 = 65.51724138

rounded to nearest tenth = 65.5%

Answer:

65.5%

Step-by-step explanation:

To find the answer to this question, we have to find the number of people considering both attributes of the question. This is the number of people who do football and the number of people who do any type of sport in general.

The number of people who play any sport:

Wrestling = 8

Lacrosse = 3

Baseball = 8

Football = 10

8 + 3 + 8 + 10 = 29

The number of people who do not play football

29 - 10 = 19

Divide our values

19 ÷ 29 = 0.65517

Convert into percentage

To convert a decimal into a percentage we have to multiply the decimal by 100

0.65517 × 100 = 65.517

65.5 to the nearest tenth

Hope this helps, have a lovely day! :)

Answer:

A.

B.

C.

Mean:

Median:

Mean ≠ median, not true

D.

Answer:

B

Step-by-step explanation:

Option B is correct because from the data it's visible that all the data are around 6 miles in other words clustered. In Class A half of them are on left and half are on right. Option A is wrong because there are 17 students in class A and 18 students in class B.

Option C is wrong because the mean is 8.2 and the median is 6.

To find mean add up all the miles the students chose and divide by total students (4+4+4+4+4+5+5+5+6+6+12+13+13+13+13+14+14)/17 = 8.2

To find the median line up all the numbers and find the one in middle. It's 6.

Option D is wrong because the range for class A is (14-4)=10

and class B is (9-3)=6. So the range of class A is greater than class B.

To find range maximum value-minimum value

Answer:

Step-by-step explanation:

1)  5

2)  63

????

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The Correct choice is C

The calculator will show an incorrect value, because she should have added 18 and 2 then entered 20 * 15 - 7 into the calculator.

I hope that explains it since we have to solve what's given in the bracket first.

the sacale factor is 1/2 because the sides are cut in half

The perimeter of the model is the product of thescale factor and the perimeter of the original rectangle. Because the origigale perimeter is 6+6+2+2=16 , and if multiply by 1/2 the perimeter is 8, this number is right because 3+3+1+1=8

The area of the reduced figure is 1/4 times the area of the original figure. because the original area is 6x2=12 and multiply by 1/4 is 3, the number is right because 3x1=3

Here is a two-way table that summarizes the information:

The marginal frequencies (totals) are shown in the last row and last column. The dealership has a total of 98 cars on its lot, which is the sum of the new and used cars. There are 55 new cars and 15 used cars, which is the sum of the domestic and foreign cars in each category.

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The domain and range of f(x) = -24 are given as follows:

The domain and range of f(x) = 0.5(x + 4)² - 11 are given as follows:

The range of y = -2x² + 12x - 13 is given as follows:

y <= 5.

The domain of a function is the set that contains all the input values that can be assumed by the function.

As neither of the functions in this problem have any restriction, the domain is all real values for the two of them.

The range of a function is the set that contains all the output values that can be assumed by the function.

The ranges are given as follows:

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Answer:

C(h) = 50h + 25

$425

Step-by-step explanation:

Et the plumber works for h hours.

Cost of one hour = $50

Therefore, cost of h hours = $50h

Total cost = cost of h hours + plumber service call charge

C(h) = 50h + 25 (required equation)

Plug h = 8

C(8) = 50* 8 + 25 = 400 + 25 = $425

you have a fair die, with six faces containing the numbers 1,2,3,4,5,6. are the two events a and b then A and B are exhaustive.

Given

A= { 1,2,4}

B= { 2,3,4,5,6}

C= { 3,4}

D= { 2,4,5}

Solving (a): The mutually exclusive events

These are events that have no common or mutual elements

Events A to D are not mutually exclusive because each of the events have at least 1 common element with one another.

Solving (b): Exhaustive events.

Two events X and Y are said to be exhaustive if:

S= P(X n Y)

i.e. if the sample space equals the intersection of X and Y

For events A to D, we have:

AnB= { 1,2,3,4,5,6}

and the sample space is:

S= {1,2,3,4,5,6}

By comparison;

A n B= S

Hence, A and B are exhaustive.

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Answer:

SW =XW and ST=XU and UW=TW

Step-by-step explanation:

All are true and correct since the two triangles are congruent

Answer:

The values of \(f\) and \(g\) are, respectively:

\(f = 6\,cm\), \(g = 8\,cm\)

Step-by-step explanation:

The area of the triangle ADE is:

\(A_{ADE} = 60\,cm^{2}-48\,cm^{2}\)

\(A_{ADE} = 12\,cm^{2}\)

The area of the triangle is defined by the following formula:

\(A_{ADE} = \frac{1}{2}\cdot AD\cdot DE\) (1)

If we know that \(A_{ADE} = 12\,cm^{2}\) and \(DE = 4\,cm\), then the length of the line segment \(AD\) is:

\(AD = \frac{2\cdot A_{ADE}}{DE}\)

\(AD = 6\,cm\)

And the area of the rectangle is:

\(A_{ABCD} = AD\cdot CD\) (2)

If we know that \(A_{ABCD} = 48\,cm^{2}\) and \(AD = 6\,cm\), then the length of the line segment \(CD\) is:

\(CD = \frac{A_{ABCD}}{AD}\)

\(CD = 8\,cm\)

Hence, the values of \(f\) and \(g\) are, respectively:

\(f = 6\,cm\), \(g = 8\,cm\)