Solve the triangle. Round answers to the nearest tenth

Answer:

The total amount of money Mr. Wong received from dividends is $118 * 2 = $236.

The total value of Mr. Wong's shares before the bonus was 5,000 * $1.60 = $8,000.

The bonus he received was 3.3% of $8,000 = $264.

So, the total amount of money Mr. Wong received from the investment was $236 + $264 + $9,100 = $9,600.

The return on investment for Mr. Wong is the total amount of money he received from the investment divided by the amount of money he initially invested, expressed as a percentage.

So, the return on investment is ($9,600 / $8,000) * 100% = 120%.

Therefore, the return on investment for Mr. Wong is 120%.

When booking a show for a future date, it is normal practice for the booking agent to collect a 50% advance fee when the advances are not given for shows. This is to ensure that the performer is fully committed to performing at the event and to cover any expenses that may be incurred in the process.

The advance fee is usually non-refundable and is paid by the promoter or venue operator to the booking agent. This is to show their commitment to the performer and to demonstrate that they are serious about booking them for the event. The remaining balance is then usually paid on the day of the performance or shortly after.

The booking agent should also ensure that all parties involved in the booking are aware of the terms and conditions and have signed a contract or agreement to confirm their agreement.

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Answer: AB=12

Los triangulos BCD y ADE son iguales por tener dos lados y el angulo comprendido respectivamente iguales. por tanto AE=DC=4

Luego AB = AE+EB = 4+8 = 12

Answer:

w= 25

Step-by-step explanation:

Cost of water= (w -1)¢

Cost of milk= (2w -11)¢

Let the certain number be x.

x(w -1)¢= 480¢ -----(1)

x(2w -11)¢= 780¢ -----(2)

From (1):

wx -x= 480 -----(3)

From (2):

2wx -11x= 780 -----(4)

(3) ×2:

2wx -2x= 960 -----(5)

(5) -(4):

(2wx -2x) -(2wx -11x)= 960 -780

Expand:

2wx -2x -2wx +11x= 180

9x= 180

Divide both sides by 9:

x= 180 ÷9

x= 20

Substitute x= 20 into (3):

w(20) -20= 480

20w -20= 480

20w= 480 +20

20w= 500

w= 500 ÷20

w= 25

1. The domain of \(V (h(r))\) is restricted to values of r greater than 0.

2. \(V(h(r)) = 3.5\pi r^3\)

3. The volume depends on the radius of the cylinder

A set of values for the decision variables that satisfy all the constraints and yields the best objective function value is a feasible solution that optimizes the objective function.

In optimization problems, decision variables are the quantities that we can control or adjust to achieve a desired outcome. Constraints are the limitations or conditions that these decision variables must satisfy. The objective function represents the goal or objective we want to optimize.

A feasible solution refers to a set of values for the decision variables that satisfy all the given constraints. This means that the solution meets all the specified requirements and does not violate any constraints. However, there can be multiple feasible solutions that meet the constraints.

Among these feasible solutions, the one that yields the best objective function value is the optimal solution. The objective function value is a measure of how well the solution aligns with the desired objective. The goal is typically to maximize or minimize this objective function value, depending on the problem.

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The number 713.49 is already written in standard form.

Standard form, also known as standard notation or scientific notation, is a way of writing numbers using digits and decimal places. In standard form, a number is written with one digit to the left of the decimal point and the remaining digits to the right of the decimal point.

For example, the number 7,134.9 would be written in standard form as 7,134.9. The number 713.49 is already written in this format, so there is no need to convert it to standard form.

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(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)

Answer:

umm its B cause i got it right hope this helped :)

Step-by-step explanation:

Therefore, the expression \(-3(2x - 8) + 4x\) is equivalent to option B, which is. \(-2x+24\).

To simplify an expression, you typically want to combine like terms and perform any necessary operations in the correct order. Here are the steps you can follow:

Identify any like terms in the expression. Like terms are terms that have the same variables raised to the same powers.

Combine the coefficients of like terms. If there are no like terms, leave the expression as is.

Simplify any operations in the expression, such as multiplication, division, addition, or subtraction, according to the order of operations.

Check if the expression can be simplified further. If it can, repeat steps 1-3 until the expression cannot be simplified further.

Here's an example of how to simplify the expression. \(3x + 2x^2 - 5x - x^2\):

Identify like terms: 3x and -5x are like terms, as are. \(2x^2\) and \(-x^2\).

Combine the coefficients of like terms: \(3x - 5x = -2x\), and \(2x^2 - x^2\)= \(x^2\). So, the expression becomes:

\(-2x + x^2\)

To simplify the expression \(-3(2x - 8) + 4x\), we can start by using the distributive property to get:

\(-3(2x - 8) + 4x = -6x + 24 + 4x\)

Next, we can combine the like terms −6x and 4x to get:

\(-6x + 4x + 24 = -2x + 24\)

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In the last 10 presidential elections, the Democratic candidate has won six times in Michigan and four times in Ohio.

In the context of presidential elections, Michigan and Ohio are two key swing states that often play a crucial role in determining the outcome of the overall election. The statement indicates that in the last 10 presidential elections, the Democratic candidate emerged victorious six times in Michigan and four times in Ohio.

This information suggests that Michigan has been a more favorable state for the Democratic candidate compared to Ohio in recent election cycles. The Democratic candidate's success in Michigan for six out of the last 10 elections implies a higher level of support or electoral advantage in that state.

On the other hand, the Democratic candidate won four out of the last 10 elections in Ohio, indicating a relatively more balanced or competitive political landscape in that state. While the Democratic candidate has had some success in Ohio, the Republican candidate likely secured victories in the remaining six elections.

The varying electoral outcomes in these swing states highlight the importance of analyzing the political dynamics, demographics, and voting patterns within each state to understand the factors that contribute to election results. These results can provide insights into the electoral strategies, voter preferences, and overall political landscape of Michigan and Ohio.

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The option that indicates the appropriateness of using a two-sample z-interval for a difference in population proportions is I, II, and III. statements are relevant in determining a two-sample z-interval.

Statement I mentions that two populations of interest exist. This is crucial as the two-sample z-interval is used to compare two independent groups or populations.Statement II indicates that the variable of interest is categorical. A two-sample z-interval is suitable for categorical variables, specifically when comparing proportions.

Statement III states that the intent is to estimate a difference in sample proportions. This aligns with the purpose of a two-sample z-interval, which is to estimate the difference between population proportions based on sample data.Therefore, the combination of all three statements (I, II, and III) signifies the appropriateness of using a two-sample z-interval for a difference in population proportions.

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Answer:

y = (3/2)x + 3

Step-by-step explanation:

Point 1: (0, 3) Point: (2, 6)

            (x₁, y₁)          (x₂, y₂)

        y₂ - y₁        6 - 3            3

m = ------------ = ------------ = --------

        x₂ - x₁         2 - 0           2

y - y₁ = m(x - x₁)

y - 3 = (3/2)(x - 0)

y - 3 = (3/2)x

  +3               +3

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

y = (3/2)x + 3

I hope this helps!

Answer:

= 2 7/12

Step-by-step explanation:

We solve the above question using the operation of addition.

2 1/3 + 1/4

Lowest common denominator = 12

2 + ( 1/3 + 1/4)

2 + (4 × 1 + 3 × 1/12)

2 + (7/12)

= 2 7/12

Answer:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

15

Step-by-step explanation:

Hope it is helpful....

Answer:

The Square root of 225 is 15

It will take approximately 1.73 seconds for the object to fall 48 feet.

To solve this problem, we can use the concept of direct variation, which states that the distance (s) an object falls varies directly with the square of the time (t) of the fall.

Mathematically, this can be expressed as \(s = kt^2,\) where k is the constant of variation.

Given that the object falls 16 feet in one second, we can substitute these values into the equation to find the value of k.

So, we have \(16 = k\times 1^2,\) which simplifies to 16 = k.

Now, we can use the value of k to find the time it takes for the object to fall 48 feet. Let's denote this time as t2.

Using the equation again, we have \(48 = k \times t2^2.\)

To solve for t2, we can rearrange the equation as \(t2^2 = 48/k\)  and then take the square root of both sides to get t2 = √(48/k).  

Since we found earlier that k = 16, we can substitute this value into the equation to calculate t2.

Therefore, t2 = √(48/16) = √3 = approximately 1.73 seconds.

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The true statements about the arcs and angles in circle C are:

In Geometry, the sum of the measures of the interior angles in a quadrilateral is equal to 360°. Thus, we have:

m∠G + m∠GDC + m∠DCE + m∠GEC = 360°

60 + 90 + m∠DCE + 90 = 360

240 + m∠DCE = 360

m∠DCE = 360 - 240

m∠DCE = 120°.

Since ∠DFE is an inscribed angle that is subtended by arc DE, we have:

m∠DFE =  m∠DCE

m∠DFE =  120

m∠DFE = 1/2 × 120

m∠DFE = 60°.

Therefore, ∠EFD ≅ ∠EGD.

From circle C, we can deduce that side ED is subtended by arc ED and side FD is subtended by arc FD (side ED ≅ side FD). Thus, arc ED ≅ arc FD and m arc FD is equal to 120°.

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Answer:

A C E

took quiz

Answer:  Angles are supplementary if and only if their sum is 180° is true.

Step-by-step explanation:

Test by making both parts negative: Angles are not supplementary if and only if their sum is not 180°  This is also true.

Answer:

31.6 or 31 6/10 or 31 3/5

39.5/1.25 = 31.6

Jack gets 31.6 miles per gallon.

.25 = 1/4

.5 = 1/2

The equation which can be used to represent each situation, in terms of x, is;

A = 80 + 2x

B = 45 + 3x

The interval of miles driven, x, for which Company A is cheaper than Company B is when x = 35 miles

Let

Company A:

A = 80 + 2x

Company B:

B = 45 + 3x

Company B > Company A:

45 + 3x > 80 + 2x

collect like terms

3x - 2x > 80 - 45

x > 35

In conclusion, the interval of miles driven, x, for which Company A is cheaper than Company B is 35 miles.

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Considering the technological advancement of the cell phone, customers perceive its value to be around $800. In this scenario, the economic value created is $450.

We can solve this by,

Cost: The expenses incurred by a firm while producing goods or providing services are known as cost.

Product: The item that is produced, processed, or delivered for sale is known as a product.

Value: The economic value of a product is determined by how much it is valued in the marketplace, which is a function of how much people are willing to pay for it. In the given scenario,

          Talkalot Corp. Incurs a cost of $350 to produce one unit of a cell phone. The company's management has priced the product at $600 in the market. Considering the technological advancement of the cell phone, customers perceive its value to be around $800.

       As per the scenario, the value created is:

          The value created = Perceived value - Cost Value created

                                          = $800 - $350

          The value created = $450

  Therefore, the economic value created in this scenario is $450.

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The value of c that makes the equation true is c = 64, when x = 6 and y = 3.

To find the value of c that makes the equation true, we can start by simplifying both sides of the equation using exponent rules and canceling out common factors.

First, we can simplify 3√(x^3) to x√x, and 3√y to y√y, giving us:

x√x/cy^4 = x/4y(y√y)

Next, we can simplify x/4y to 1/(4√y), giving us:

x√x/cy^4 = 1/(4√y)(y√y)

We can cancel out the common factor of √y on both sides:

x√x/cy^4 = 1/(4)

Multiplying both sides by 4cy^4 gives us:

4x√x = cy^4

Now we can solve for c by isolating it on one side of the equation:

c = 4x√x/y^4

We can substitute in the values of x and y given in the problem statement (x>0 and y>0) and simplify:

c = 4x√x/y^4 = 4(x^(3/2))/y^4

c = 4(27)/81 = 4/3 = 1.33 for x = 3 and y = 3

c = 4(64)/81 = 256/81 = 3.16 for x = 4 and y = 3

c = 4(125)/81 = 500/81 = 6.17 for x = 5 and y = 3

c = 4(216)/81 = 64 for x = 6 and y = 3

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Answer:The slope is m= 1/2

(0,-2) & (2,-1)

Step-by-step explanation:

(0,-2) & (2,-1)

m=y²-y¹/x²-x¹

m=(-1)-(-2)/2-0

m=1/2

The value of the exponent 5^2 is equivalent to 25

According to the equation, we are to write the expression 5^2 as a product

Since the exponent is 2, hence the value the base will be repeated twice.

Given

5^2 = 5^1 * 5^1

5^2 = 5 * 5

5^2. = 25

Hence the value of the exponent 5^2 is equivalent to 25

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a) It would take Anya approximately 4 years to accumulate $40,000 with an annual interest rate of 12%. b) Anya must earn an annual rate of return of approximately 12.6% to save $40,000 in 3 years.

a) To calculate the number of years it would take Anya to accumulate $40,000, we can use the future value formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Where:

Future Value = $40,000

Present Value = $25,000

Interest rate = 12% = 0.12

n = number of years

Substituting the given values into the formula, we have:

$40,000 = $25,000 * (1 + 0.12)ⁿ

Dividing both sides of the equation by $25,000, we get:

(1 + 0.12)ⁿ = 40,000 / 25,000

(1.12)ⁿ = 1.6

To solve for n, we can take the logarithm of both sides of the equation:

n * log(1.12) = log(1.6)

Using a calculator, we find that log(1.12) ≈ 0.0492 and log(1.6) ≈ 0.2041. Therefore:

n * 0.0492 = 0.2041

n = 0.2041 / 0.0492 ≈ 4.15

b) To calculate the required rate of return for Anya to save $40,000 in just 3 years, we can rearrange the future value formula:

Future Value = Present Value * (1 + interest rate)ⁿ

$40,000 = $25,000 * (1 + interest rate)³

Dividing both sides of the equation by $25,000, we have:

(1 + interest rate)³ = 40,000 / 25,000

(1 + interest rate)³ = 1.6

Taking the cube root of both sides of the equation:

1 + interest rate = ∛1.6

Subtracting 1 from both sides, we get:

interest rate = ∛1.6 - 1

Using a calculator, we find that ∛1.6 ≈ 1.126. Therefore:

interest rate = 1.126 - 1 ≈ 0.126

To express the interest rate as a percentage, we multiply by 100:

interest rate = 0.126 * 100 = 12.6%

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Answer:

The value of \(m\) is -30.

Step-by-step explanation:

Let \(27\cdot x^{2}+m\cdot x +8 = 0\), we notice that expression is a second order polynomials. We can rearrange the polynomial and use factorization to calculate all roots:

\(x^{2}+\frac{m}{27}\cdot x + \frac{8}{27} = 0\) (1)

\(-x^{2}-x = \frac{m}{27}\) (2)

\(x^{3} = \frac{8}{27}\) (3)

From (3) we find the least root:

\(x = \sqrt [3]{\frac{8}{27}}\)

\(x = \frac{2}{3}\)

By (2) we have the value of \(m\):

\(m = -27\cdot (x^{2}+x)\)

\(m = -30\)

Applying the properties of kite, the measures are: SV = 41 units; QT = 21 units.

A kite is a quadrilateral that has 2 pairs of congruent adjacent sides, and has two diagonals where the longest one bisects the shorter one and divides it into equal segments.

The diagram given is a kite. Where TR = 17 units. Thus we would solve for x using the equation as shown below:

TR = RV [congruent adjacent sides of the kite]

Plug in the values

17 = 3x + 2

17 - 2 = 3x

15 = 3x

15/3 = x

x = 5

SV = TS = 9x - 4 [congruent adjacent sides of the kite]

Plug in the value of x

SV = 9(5) - 4

SV = 41 units

The length of segment QT is 41 units.

QT = QV = 4x + 1 [congruent adjacent sides of the kite]

Plug in the value of x

QT = 4(5) + 1

QT = 21 units

The length of segment QT is: 21 units.

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Answer:

SV: 41

QT:21

Step-by-step explanation:

To find the solution to the given boundary value problem, we can solve the corresponding second-order linear homogeneous ordinary differential equation. The characteristic equation associated with the differential equation is obtained by substituting y = e^(rt) into the equation:

r² - 7r + 6 = 0

Factoring the quadratic equation, we have:

(r - 1)(r - 6) = 0

This gives us two roots: r = 1 and r = 6.

Therefore, the general solution to the differential equation is given by:

y(t) = c₁e^(t) + c₂e^(6t)

To find the particular solution that satisfies the given boundary conditions, we substitute y(0) = 1 and y(1) = 6 into the general solution:

y(0) = c₁e^(0) + c₂e^(6(0)) = c₁ + c₂ = 1

y(1) = c₁e^(1) + c₂e^(6(1)) = c₁e + c₂e^6 = 6

We can solve this system of equations to find the values of c₁ and c₂. Subtracting the first equation from the second, we have:

c₁e + c₂e^6 - c₁ - c₂ = 6 - 1

c₁(e - 1) + c₂(e^6 - 1) = 5

From this, we can determine the values of c₁ and c₂, and substitute them back into the general solution to obtain the particular solution that satisfies the boundary conditions.

In conclusion, the solution to the given boundary value problem is y(t) = c₁e^(t) + c₂e^(6t), where the values of c₁ and c₂ are determined by the boundary conditions y(0) = 1 and y(1) = 6.

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Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

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