How do you write 7

11
/
18

as a whole number

The opportunity cost of washing a car for Ted is 4 cars, and the opportunity cost of washing a car for Ishana is 3 cars.

To determine each person's opportunity cost of washing a car, we need to compare the alternative activity they would have to give up in order to wash a car.

For Ted:

Ted can wax 4 cars or wash 12 cars. So, the opportunity cost of washing a car for Ted is the number of cars he could have waxed instead. In this case, Ted would have to give up waxing 4 cars to wash a car.

For Ishana:

Ishana can wax 3 cars or wash 6 cars. So, the opportunity cost of washing a car for Ishana is the number of cars she could have waxed instead. In this case, Ishana would have to give up waxing 3 cars to wash a car.

Therefore, the opportunity cost of washing a car for Ted is 4 cars, and the opportunity cost of washing a car for Ishana is 3 cars.

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Answer:

6-2= 4

4/4=1

Step-by-step explanation:

Hope this helps!

Answer:

1

Step-by-step explanation:

difference= subtract

so: 6-2=4

4/4=1

Hope this helps! Plz give brainliest!

The value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths is 13.11.

In algebra, we often deal with equations with unknown values ​​represented by variables. To solve such an equation, we need to find the values ​​of the variables.

A one-step equation is an algebraic equation that can be solved in just one step. Solve it and you've found the values ​​of the variables that make the equation true. To solve a one-step equation, perform the inverse (reverse) of the operation performed on the variable to get the variable itself.

For the given case, the  equation can be written as follows:

\(\frac{x}{5\frac{7}{10} }\) = \(2\frac{3}{10}\)

x = \(5\frac{7}{10}\) × \(2\frac{3}{10}\)

x = 5.7 × 2.3

x = 13.11

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a. The sequence that starts with 5 and ends with 8 is 5, 15, 3, 0, 0, 0, 8.

b. Since 8 is a single-digit number, it can be obtained by starting with any positive integer.

c. By systematically applying the sequence rules, we can construct a sequence that starts with 8 and ends with 999.

(a) To find a sequence that starts with 5 and ends with 8, we can follow these steps:

Start with 5.

Triple the current number: 5 * 3 = 15.

Delete the final digit: 15 -> 1.

Triple the current number: 1 * 3 = 3.

Delete the final digit: 3 -> 0.

Triple the current number: 0 * 3 = 0.

Triple the current number: 0 * 3 = 0.

Triple the current number: 0 * 3 = 0.

Add 8 to the sequence: 0, 0, 0, 8.

Therefore, the sequence that starts with 5 and ends with 8 is 5, 15, 3, 0, 0, 0, 8.

(b) Any positive integer can start a sequence that ends in 8 because of the following reasons:

Tripling a positive integer repeatedly will eventually lead to a number that is divisible by 3.

Dividing a number by 10 removes its final digit. By performing this operation repeatedly on a positive integer, we can reduce it to a single-digit number, at which point we cannot perform the operation anymore.

When a single-digit number is tripled, it becomes a number that is divisible by 3.

Since 8 is a single-digit number, it can be obtained by starting with any positive integer and following the sequence rules outlined above.

(c) To find a sequence that starts with 8 and ends with 999, we can follow this systematic process:

Start with 8.

Triple the current number: 8 * 3 = 24.

Delete the final digit: 24 -> 2.

Triple the current number: 2 * 3 = 6.

Delete the final digit: 6 -> 0.

Triple the current number: 0 * 3 = 0.

Add 9 to the sequence: 0, 0, 0, 9.

Triple the current number: 9 * 3 = 27.

Delete the final digit: 27 -> 2.

Triple the current number: 2 * 3 = 6.

Delete the final digit: 6 -> 0.

Triple the current number: 0 * 3 = 0.

Add 9 to the sequence: 0, 0, 0, 9, 0, 0, 0, 9.

Repeat steps 8-13 until the desired number is reached: 0, 0, 0, 9, 0, 0, 0, 9, 0, 0, 0, 9, ..., 0, 0, 0, 9, 99, 999.

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==================================================

Proof:

We'll break the proof into two cases which I'll label A and B

-----------

Case A: 'a' is even

k = some integer

a = 2k = some even integer

a+1 = 2k+1

a(a+1) = 2k(2k+1) = 2(2k^2+k) = 2*(some integer)

Since 2 is a factor of that last expression, this shows that a(a+1) is even when 'a' is even.

-----------

Case B: 'a' is odd

k = some integer

a = 2k+1 = some odd integer

a+1 = (2k+1)+1 = 2k+2

a(a+1) = (2k+1)(2k+2) = 2(2k+1)(k+1) = 2(some integer)

This shows that a(a+1) is even when 'a' is odd.

-----------

Therefore, for any integer 'a', the expression a(a+1) is always even.

Some examples:

-----------

Here's a slightly different way to interpret why the proof works.

a(a+1) consists of factors 'a' and 'a+1'

Either way, we'll have 2 as a factor somewhere in a(a+1).

Answer:

4y+12x

Step-by-step explanation:

I dont have time to type sry

Step-by-step explanation:

3 + 9 = 12,

12 + 9 = 21,

21 + 9 = 30,

30 + 9 = 36.

The common difference is 9. (D)

Answer:

(d)-9

Step-by-step explanation:

12 – 3 = 9, 30 – 21 = 9, etc.

The expressions are solved below :

sinu = -3/5 3π/2 < u < 2π is [ 4th quadrant ]

Now we know that

By using trigonometric identities,

When there are trigonometric functions present in an expression or equation, trigonometric Identities come in handy. Every value of a variable appearing on both sides of an equation is valid in terms of trigonometric identities. These trigonometric functions of one or more angles, such sine, cosine, and tangent, are involved in these geometric identities.

sin²u + cos²u = 1

cos²u= 1-sin²u

cos²u = 1 -(-3/5)²

cos²u= 1 - 9/25

cosu = +4/5

:. u is in 4th quadrant

Now

1.  sin2u = 2 sinu cosu

= 2 (-3/5)(4/5) = -24/25

2. cos2u = 2cos²u- 1

       = 2(4/5)²- 1

       = 7/25

3. tan2u = sin2u /cos2u

              = -24/7

The exact values of the sine, cosine, and tangent of the angle are found.

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The mass of the fifth man is 153 kg.

The mean mass of five men is 76 kg.

The masses of four of the men are 72 kg, 74 kg, and 81 kg.

To solve this problem, we need to apply the concept of the mean of a set of data.

The mean is the average of all the values in a set of data.

It is calculated by adding up all the values and dividing by the total number of values in the set.

To find the mass of the fifth man, we need to use the mean of the entire set and the masses of the four men that are already given.

The formula to find the mean of a set of data is:

\(Mean = \frac{(sum of all the values)}{(total number of values)}\)

Let x be the mass of the fifth man.

Then we can write an equation using the given information:

\(Mean = \frac{(72 + 74 + 81 + x)}{5}\)

Substitute the given mean of 76 kg into the equation and solve for x:

\(76 = \frac{(72 + 74 + 81 + x)}{576 × 5} = 227 + x\)

Multiply both sides by 5:

\(380 = 227 + x\)

Subtract 227 from both sides:

\(153 = x\)

Therefore, the mass of the fifth man is 153 kg.

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Answer:

I'm 99.9% sure that x=4

Step-by-step explanation:

Answer:

Decimal: 2.65   Percentage: 265 %

Step-by-step explanation:

Answer:

2.65 is the answer you just round to 6 decimal place

The three double-angle identities are :

1.\($\cos(2\theta) = \cos^2\theta - \sin^2\theta$\)

2. \($\sin(2\theta) = 2\sin\theta\cos\theta$\)

3. \($\tan(2\theta) = \frac{2\tan\theta}{1-\tan^2\theta}$\)

The three double angle identities are equations that relate the cosine, sine, and tangent of twice an angle to the cosine, sine, and tangent of the original angle. these identities are useful in trigonometry, as they make it possible to express a double angle in terms of its simpler  angle components.

The first identity states that the cosine of twice an angle is equal to the square of the cosine of the original angle, minus the square of the sine of the original angle. the second identity, states that the sine of twice an angle is equal to twice the product of the sine and cosine of the original angle.

The third  identity states that the tangent of twice an angle is equal to twice the tangent of the original angle, over one minus the square of the tangent of the original angle,

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Answer:a

Step-by-step explanation:

The solution to the equation using three iterations of successive approximation is x≈35/16.

What is graph?

A graph is a structure that resembles a set of objects where some pairings of the objects are conceptually "connected" in discrete mathematics, more specifically in graph theory. Each connection between two adjacent vertices is referred to as an edge, and the items are symbolised by vertices, which are mathematical abstractions.

From the graph we get that at x=2.23 both graphs intersect each other.

17/8=2.125

35/16=2.1875

33/16=2.0625

19/8=2.375

35/16 is the nearest value to 2.23

Hence the correct answer is b,  x≈ 35/16

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A variable is any property, number, or quantity that can be measured or counted. Variables can also be referenced as data items.

Inference: Inference uses selected samples from a population to estimate the properties of unknown people.

A record (or record) is a collection of data. For tabular data, a record corresponds to one or more database tables, each table column represents a specific variable, and each row corresponds to a particular record in that data set.

Therefore:

All the data collected in particular is referred to as Data Set.

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The Law of Sines often yields better results due to its broader applicability and flexibility in solving trigonometric problems involving non-right triangles. The Law of Cosines is also reliable, especially when the lengths of sides are known. The Law of Tangents has limited use and is typically employed in specific right triangle scenarios.

To compare the results of the verification of the Law of Sines, Law of Cosines, and Law of Tangents, we can create a table showcasing the findings and analyze which law had better results:

Law               |                         Results                                |                             Accuracy

--------------------------------------------------------------------------------------------------------------------------------------------------------

Law of Sines      |  Satisfied for various triangle scenarios   | Dependent on angle and side accuracy

Law of Cosines   | Satisfied for various triangle scenarios   | Dependent on side accuracy

Law of Tangents | Satisfied for specific triangle scenarios   | Dependent on angle accuracy

The Law of Sines may often have better results because it is applicable to a broader range of triangle scenarios, allowing for more flexibility in solving trigonometric problems. It is useful when working with non-right triangles, as it relates the ratios of angles to the ratios of opposite sides. However, it heavily relies on the accuracy of both angles and sides for precise calculations.

The Law of Cosines, while also effective in various triangle scenarios, is particularly useful for solving triangles when the lengths of all three sides are known or when an angle and the lengths of two sides are known. It is less dependent on angle accuracy but relies more on side accuracy.

The Law of Tangents has more limited applicability and is primarily used when dealing with right triangles. It relates the tangent of an angle to the ratios of sides, but its usage is not as widespread as the other two laws.

The Law of Sines and the Law of Cosines generally yield satisfactory results for various triangle scenarios. However, their accuracy can vary depending on the accuracy of angles and sides. The Law of Tangents, on the other hand, is more limited in its application, as it only applies to specific triangle scenarios.

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The standard deviation of the data given in this scenario would be 2.65

Given the data :

The mean of the squared data is 49. This means that the average squared deviation from the mean is 7.

The standard deviation, σ = √(49 / n) = √(7) = 2.65

Therefore, the standard deviation is 2.65

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61

Answer:

5²+6²=5*5+6*6=25+36=61 is a required answer.

Answer:

61 is the answer

Step-by-step explanation:

\( {5}^{2} = 5 \times 5 = 25 \\ {6}^{2} = 6 \times 6 = 36 \\ \\ {5}^{2} + {6}^{2} = 25 + 36 \\ = 61\)

The length of the diagonal of the rectangular prism drawn between the front bottom left vertex and the back top right vertex is about 9.5 feet

A rectangular prism is a six faced polyhedron in which the opposite faces are parallel and all faces are rectangles.

The dimensions (lengths of the sides of the rectangular prism are)

Length, l = 7 feet

Width, w = 4 feet

Height, h = 5 feet

The value of the diagonal of the base of the prism can be found as follows;

Length of the diagonal of base = √(7² + 4²) = √(65)

The diagonal of the base is a leg of the right triangle that has the diagonal of the prism as the hypotenuse side. The other leg of the right triangle formed by the diagonal of the prism is the height of the prism, therefore;

The diagonal of the rectangular prism, d = √(65 + 5²) = √(90) = 3·√(10)

The diagonal of the rectangular prism is therefore;

d = 3·√(10) ≈ 9.5

The diagonal of the rectangular prism is approximately 9.5 feet

The diagonal of a rectangular prism of length. l, width, w, and height, h, can also be obtained using the formula;

d = √(l² + w² + h²)

Therefore, d = √((7 feet)² + (4 feet)² + (5 feet)²) ≈ 9.5 feet

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Answer: 1,000 to 40,300

Step-by-step explanation:  Every major league stadium will let in fans to start the season, but capacities vary, ranging from just over 1,000 to 40,300.

The total revenue function, we integrate the marginal revenue function. The revenue from 125 gadgets is given as $21,217, so we can find the constant term in the total revenue function. Then, we can determine the number of gadgets needed to generate a revenue of at least $35,000 by solving for x in the total revenue function.

The total revenue function, we integrate the marginal revenue function R'(x) with respect to x. Integrating R'(x) = 4x(x^2 + 28,000)^(-2/3) gives us the total revenue function R(x).

The constant term in R(x), we can use the revenue from 125 gadgets. Since R(125) = $21,217, we substitute x = 125 into the total revenue function and solve for the constant term.

To determine the number of gadgets needed to generate a revenue of at least $35,000, we set R(x) greater than or equal to $35,000 and solve for x. This involves rearranging the total revenue function and solving the inequality for x.

The first part involves finding the total revenue function by integrating R'(x) and determining the constant term. The second part involves solving the inequality R(x) ≥ $35,000 to find the minimum number of gadgets required to achieve that revenue.

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Vertically compressing the exponential parent function f(x) = 2^x by a factor of 3 means multiplying every function value by 1/3, resulting in a steeper and narrower curve closer to the x-axis.

If we vertically compress the exponential parent function f(x) = 2^x by a factor of 3, it means that every point on the graph of the function will be compressed closer to the x-axis. In other words, the function values will be multiplied by 1/3.

Let's consider a point on the original exponential function, (x, f(x)). After the vertical compression, this point will have the coordinates (x, (1/3)f(x)). For example, if f(x) = 8 for some x, after compression, the corresponding point will be (x, (1/3)(8)) = (x, 8/3).

This vertical compression affects all points on the graph uniformly, resulting in a steeper and narrower curve compared to the original exponential function.

The y-values of the compressed function will be one-third of the y-values of the original function for each x-value. Therefore, the graph will be squeezed vertically, with the y-values closer to the x-axis.

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Answer:

-7

Step-by-step explanation:

Answer:

1.5 pounds of beans are in each nag

The value of x is: x = 35.57.

Here, we have,

given that,

from the given diagram, we get,

it is a right angle triangle,

base = x

hypotenuse = 37

and angle = 16°

now, we know that,

cos θ = adjacent / hypotenuse

so, we get,

cos 16° = x/37

The value of cos 16° is equal to the x-coordinate (0.9613).

∴ cos 16° = 0.9613.

=> 0.9613 = x/37

=> x = 35.57

Hence, The value of x is: x = 35.57.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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6x4=24

24x1/2=12

12+3=15

15+2=17

17 is the answer

Using distance formula, the quadrilateral is a rhombus

To determine whether quadrilateral ABCD is a rectangle, rhombus, or square, we need to examine its properties. A rectangle is a quadrilateral with four right angles, a rhombus is a quadrilateral with four congruent sides, and a square is a quadrilateral that is both a rectangle and a rhombus.

To start, let's find the lengths of the diagonals of the quadrilateral. The diagonals of ABCD are AC and BD.

The distance formula between two points (x1, y1) and (x2, y2) is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

So the length of AC is:

d(AC) = sqrt((2 - (-6))^2 + (7 - 5)^2) = sqrt(64 + 4) = sqrt(68)

And the length of BD is:

d(BD) = sqrt((-1 - (-3))^2 + (2 - 10)^2) = sqrt(4 + 64) = sqrt(68)

So we know that AC and BD have the same length.

Next, let's find the slopes of the diagonals. The slope between two points (x1, y1) and (x2, y2) is:

m = (y2 - y1)/(x2 - x1)

The slope of AC is:

m(AC) = (7 - 5)/(2 - (-6)) = 2/8 = 1/4

And the slope of BD is:

m(BD) = (2 - 10)/(-1 - (-3)) = -8/4 = -2

Now, if ABCD is a rectangle, then AC and BD are perpendicular. That means the product of their slopes is -1:

m(AC) * m(BD) = (1/4) * (-2) = -1/2

Since -1/2 is not equal to -1, we know that ABCD is not a rectangle.

If ABCD is a rhombus, then all four sides are congruent. We can use the distance formula to find the lengths of the sides:

d(AB) = sqrt((-1 - (-6))^2 + (2 - 5)^2) = sqrt(25 + 9) = sqrt(34)

d(BC) = sqrt((2 - (-1))^2 + (7 - 2)^2) = sqrt(9 + 25) = sqrt(34)

d(CD) = sqrt((-3 - 2)^2 + (10 - 7)^2) = sqrt(25 + 9) = sqrt(34)

d(DA) = sqrt((-6 - (-3))^2 + (5 - 10)^2) = sqrt(9 + 25) = sqrt(34)

Since all four sides have the same length (sqrt(34)), we know that ABCD is a rhombus.

If ABCD is a square, then it is both a rectangle and a rhombus. We have already shown that it is a rhombus, so all we need to do is show that it is also a rectangle. A rectangle has opposite sides that are parallel and congruent, so we can use the slopes of the sides to check this. The slope of AB is:

m(AB) = (2 - 5)/(-1 - (-6)) = 3/5

And the slope of BC is:

m(BC) = (7 - 2)/(2 - (-1)) = 5/3

If AB and CD are parallel, then their slopes are equal.

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