The figure below shows part of a circle, with central angle as marked. What part of
the full circle does the figure represent? Express your answer as a fraction in simplest
terms.
60°

The partial sum of the sequence {2, 3, 5, 8, 13, ...} for the first 8 terms is 761/2.

The sequence given is a Fibonacci sequence, where each term is the sum of the previous two terms. To find the partial sum for the first 8 terms, we can use the formula for the sum of a finite geometric series:

Sₙ = a(1 - rⁿ)/(1 - r),

where Sₙ is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 2, r = 3/2 (since each term is 1.5 times the previous term), and n = 8. Plugging these values into the formula, we get:

S₈ = 2(1 - (3/2)⁸)/(1 - (3/2))

Simplifying the expression, we get:

S₈ = 761/2

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Yes, the fractions 1/2 and 2/4 are proportional

A fraction can simply be defined as an expression that is used in the representation of the part of a whole.

This could be a whole number, a whole element, a whole material or a whole elemeent.

In mathematics, there are different types of fractions.

These fractions are enumerates thus;

From the information given, we have that;

If 1/2 and 2/4 are proportional, that is, if equal

2/4 = 1/2

Cross multiply the values

4 = 4

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The ROI (Return on Investment) for the above investment is 106.67%.

What is the Return on Investment?

ROI (Return on Investment) is one that is seen as a financial metric used to know the profitability of an investment relative to its cost.

The formula for ROI is:

ROI = (Net Profit / Cost of Investment) x 100%

Hence, the cost of investment is the sum of the price as well as the renovation cost, will be:

Cost of Investment = $100,000 + $50,000

                               = $150,000

Note that the The net profit from the sale of the house is $160,000.

So, the ROI can be calculated as:

ROI = (Net Profit / Cost of Investment) x 100%

= ($160,000 / $150,000) x 100%

= 106.67%

So, the ROI for the above investment is 106.67%.

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Answer:

[tex](3 + 2x)(2 + 2x) = 7[/tex]

[tex]6 + 10x + 4{x}^{2} = 7[/tex]

[tex]4 {x}^{2} + 10x - 1 = 0[/tex]

Answer:

4x2 + 10x − 1 = 0

Step-by-step explanation:

Answer:

c. -20x and 20x

Step-by-step explanation:

x² is the square of x.

100 is the square of 10 and of -10.

The middle term of (a + b)² is 2ab.

For b = 10:

2ab = 20x

for b = -10:

2ab = -20x

Answer: c. -20x and 20x

Answer:

Yes.

Step-by-step explanation:

8:120 = 4:60 = 2:30 = 1:15

You divide by two each time to simplify.

The Taylor series for f(x) = e^2x at x = 1 is option D. Σ2ⁿ e²ˣ/n! (x - 1)ⁿ

The Taylor series for a function f(x) centered at x = a is given by:

f(x) = f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...

f'(a), f''(a), f'''(a), ... depict the first, second, third, and higher derivatives of f(x) evaluated at x = a.

In this case:

f(x) = e^(2x)

The first derivative is:

f'(x) = 2e^(2x)

The second derivative is:

f''(x) = 4e^(2x)

The third derivative is:

f'''(x) = 8e^(2x) etc.

Finding the Taylor series for f(x) = e^(2x) at x = 1, evaluate each derivative at x = 1:

f(1) = e^(2)

f'(1) = 2e^(2)

f''(1) = 4e^(2)

f'''(1) = 8e^(2) etc.

Plug these values into the Taylor series formula:

f(x) = f(1) + f'(1)(x-1)/1! + f''(1)(x-1)^2/2! + f'''(1)(x-1)^3/3! + ...

f(x) = e^(2) + 2e^(2)(x-1)/1! + 4e^(2)(x-1)^2/2! + 8e^(2)(x-1)^3/3! + ...

Simplify:

f(x) = e^(2) + 2e^(2)(x-1) + 2e^(2)(x-1)^2 + 4e^(2)(x-1)^3/3 + ...

Therefore, the Taylor series for f(x) = e^(2x) at x = 1 is: Σ2ⁿ e²ˣ/n! (x - 1)ⁿ which is option D.

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Answer:

  (d)  A'(5, -1)

Step-by-step explanation:

You want the coordinates of A(1, 5) after it has been rotated 270° CCW about the origin.

The transformation for rotation 270° CCW is the same as that for rotation 90° CW:

  (x, y) ⇒ (y, -x)

For the given point, this is ...

  A(1, 5) ⇒ A'(5, -1)

The image of A is A'(5, -1), choice D.

The constant k is  0.08

The time taken is 40 minutes

The half-life of a specific radioactive substance is determined by its decay constant, which is a measure of how quickly the substance decays.

Given that;

P= Poe^-kt

P = population at time t

Po = initial population

k = rate of decay

t = time taken

Then;

100 = 500e^-k20

100/500 = e^-k20

0.2 = e^-k20

ln0.2 = e^-k20

k = ln0.2/-20

k = 0.08

We know that;

20 = 500e^-0.08t

20/500 = e^-0.08t

0.04 = e^-0.08t

ln 0.04 = e^-0.08t

ln0.04 = -0.08t

t = ln0.04/-0.08

t = 40 minutes

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An equation for which the solution is the height of a pyramid, in feet, when its volume is 48 cubic feet and the length of each side of its base is 4 feet is h = 3(48)/4².

In Mathematics and Geometry, the volume of a square pyramid can be calculated by using the following formula:

Volume of a square pyramid, V = 1/3 × a² × h

Where:

By making "h" the subject of formula, the side length of the base of a square pyramid can be determined as follows;

V = 1/3 × a² × h

3V = a²h

Height, h = 3V/a²

Height, h = 3(48)/4²

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The volume of the sphere as shown in the diagram is 904.3 cm³.

A sphere is a three-dimensional round-shaped object.

To calculate the volume of the sphere, we use the formula below

Formula:

Where:

From  the question,

Given:

Substitute these values into equation 1

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The velocity at pART a =  584

The velocity in answer B = 576

The change in time = 4

distance traveled using the 20 second interbval is

4[ 31 + 31 + 33 + 28 + 23 ]

= 4 * 146

= 584

At the end of the time periods the velocities would be:

4[31 + 33 + 28 + 23 + 29]

= 4 x 144

= 576

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The probability that Tuesday follows Monday in a week is 100%, or 1/1, since it is always true that Tuesday comes after Monday in a week. Expressed as a percentage, the probability is 100%.

Answer:

100%

Step-by-step explanation:

because according to our calendars, Tuesday is always after monday so the probability as percent is 100%.

Answer:

The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.

Step-by-step explanation:

We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is

 [tex]S_{n}[/tex]​ = 165000.

Let us find the amount as arithmetic series as follows:

4000 + 5000 + 6000

The arithmetic series being, first term is [tex]a_{1}[/tex] = 4000, second term is [tex]a_{2}[/tex] = 5000.

We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:

[tex]d = a_{2} - a_{1} = 5000 - 4000 = 1000[/tex]

The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex] ( ‘ d ‘ being the difference. )

Next we can substitute a = 4000, d = 1000 and [tex]S_{n}[/tex] = 165000 in “ [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex] “ which can be represented as:

Determining, [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex]

⇒ 165000 = [tex]\frac{n}{2}[/tex] [( 2 x 4000 ) + ( n - 1 ) 1000 ]

⇒ 2 x 165000 = n(8000 + 1000n - 1000 )

⇒ 330000 = n(7000 + 1000n)

⇒ 330000 = 7000n + [tex]1000n^2[/tex]

⇒ [tex]1000n^2[/tex] + 7000n - 330000 = 0

⇒ [tex]1000n^2[/tex] ( [tex]n^2[/tex] + 7n - 330 ) = 0

⇒  [tex]n^2[/tex] + 7n - 330 = 0

⇒ [tex]n^2[/tex] + 22n - 15n - 330 = 0

⇒ n( n + 22 ) - 15 ( n + 22 ) = 0

⇒ ( n + 22 )( n - 15 ) = 0

⇒ n = -22, n = 15

We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.

Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.

Let's call the two numbers we're trying to find x and y. We know that x + y = 12 and xy = 23. From the first equation, we can solve for one of the variables in terms of the other. So if we subtract x from both sides, we get y = 12 - x. Now we can substitute this expression for y into the second equation to get x(12 - x) = 23. Expanding this out, we get 12x - x^2 = 23. Rearranging, we get x^2 - 12x + 23 = 0. This quadratic equation can be factored as (x - 2)(x - 10) = 0. So either x = 2 and y = 10, or x = 10 and y = 2.

Answer:

The two numbers are 2 and 10.

The amount after 23 years on the investment plan is A = $358.20

Given data ,

$200 per month under a 4.5% annual percentage rate investing plan.

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

Where:

A is the total sum.

P stands for the initial deposit's principal.

The yearly interest rate is represented by the decimal r.

The yearly compounding rate of interest is determined by the number n.

The number of years is t.

A = 200(1 + 0.045/1)¹ˣ²³

A = 200(1.045)²³

A ≈ 200(1.791)

A ≈ $358.20

After 23 years, the investment plan will contain approximately $358.20

Total deposits = Monthly deposit amount x Number of months

Total deposits = $200 x (12 months/year) x 23 years

Total deposits = $200 x 12 x 23

Total deposits = $55,200

Consequently, $55,200 would be the total amount of deposits made during the 23-year period.

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Answer m+6=b

Step-by-step explanation:

m means Moby since Moby is being added by six compared to Tim, we put a 6 after m to show how many more books Tim has, then we use b for book.

Answer: The number of books belonging to Tim is m+6

Step-by-step explanation: Here variable "m " represents the number of books Moby owns.

Let "b" be the variable representing the number of books owned by Tim.

The question directs that Tim has 6 more books than Moby.

To find the number of books belonging to Tim, one has to add six more books than that of Moby

Therefore by the simple addition of these variables, we will get to know the solution

So, the number of books belonging to Tim (b) will be m+6,

that is m+6=b

Hence proved.

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The motivations for producers and consumers in the black market are largely driven by financial incentives and a desire to avoid legal consequences.

The black market refers to the illegal trade of goods and services that are not permitted by law, such as drugs, counterfeit items, and stolen goods. Producers and consumers in the black market are motivated by a variety of factors, including:

High profits, Producers in the black market can earn higher profits than they would in legal markets due to the lack of regulation and taxes.

Escaping legal consequences: Producers and consumers may participate in the black market to avoid legal consequences, such as fines or imprisonment, for engaging in illegal activities.

Limited availability, Some goods and services are only available on the black market due to legal restrictions or limited supply.

Low prices, Consumers in the black market can often purchase goods and services at lower prices than in legal markets due to the lack of taxes and regulations.

Desire for anonymity, The black market can provide anonymity for both producers and consumers, allowing them to engage in illegal activities without fear of detection or retribution.

However, participating in the black market also comes with significant risks, including the possibility of arrest, fines, and even violence.

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Basd on the information about the triangle, DF is approximately 5.68 units long.

First, let's find the length of EF using the sine function:

sin 20° = EF / DE

cos 20° = 6 / DE

DE = 6 / cos 20°

Now that we know DE, we can solve for EF:

sin 20° = EF / DE

EF = DE * sin 20°

EF = (6 / cos 20°) * sin 20°

EF ≈ 1.95

DF^2 = DE^2 - EF^2

DF^2 = (6 / cos 20°)^2 - (1.95)^2

DF ≈ 5.68

DF is approximately 5.68 units long.

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Assuming that a fair coin was tossed twice, the probability that exactly one of the tosses is a head and the other toss is a tail is 1/2.

The probability of a certain event happening is the number of ways that event can occur, divided by the total number of possible outcomes. In this case, we are interested in finding the probability that exactly one of the two coin tosses results in a head and the other results in a tail.

There are two possible outcomes that satisfy this condition: HT and TH. Since the coin is fair, each of these outcomes has a probability of 1/4. Therefore, the total probability of getting exactly one head and one tail is:

P(HT or TH) = P(HT) + P(TH) = 1/4 + 1/4 = 1/2

In other words, there is a 50-50 chance of getting exactly one head and one tail when a fair coin is tossed twice.

To see why this is the case, we can think of each toss as an independent event with two possible outcomes (head or tail). There are four possible outcomes when we toss a coin twice, and two of these outcomes satisfy the condition of exactly one head and one tail. Therefore, the probability of getting exactly one head and one tail is 2/4, which simplifies to 1/2.

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Answer:

[tex](x - \frac{4}{9} )(x - \frac{9}{2} ) = 0[/tex]

[tex] {x}^{2} - \frac{89}{18} x + 2 = 0[/tex]

Answer:

$8.92 each

Step-by-step explanation:

Answer:

First, you need to calculate the total cost of the loan. The monthly payment is $260, and there are 72 payments over 6 years. The total cost of the loan is 72 months * $260/month = $18,720

Next, you calculate the total cost of owning the car for 6 years. The insurance will cost $960 per year, so over 6 years it will cost $960/year * 6 years = $5,760

The registration will cost $240 per year, so over 6 years it will cost $240/year * 6 years = $1,440

The gas and maintenance will cost $175 per month, so over 6 years it will cost $175/month * 72 months = $12,600

Now you can add up all the costs to find the total cost of owning the car over the life of the loan:

Loan cost + insurance cost + registration cost + gas/maintenance cost

= $18,720 + $5,760 + $1,440 + $12,600

= $38,520

Therefore, the car will cost Brooke $38,520 over the life of the loan, including all additional costs of owning the car.

Answer:

$38,520

Step-by-step explanation:

To calculate the total cost of the car, we need to consider the following expenses:

Monthly payments:

$260/month x 72 months = $18,720

Insurance:

$960/year x 6 years = $5,760

Registration:

$240/year x 6 years = $1,440

Gas and maintenance:

$175/month x 12 months/year x 6 years = $12,600

Therefore, the total cost of the car over the life of the loan is:

$18,720 (monthly payments) + $5,760 (insurance) + $1,440 (registration) + $12,600 (gas and maintenance) = $38,520

So, while Brooke may think she's getting a good deal with zero down and low monthly payments, the total cost of the car over the life of the loan is quite high. It's important to consider all the additional costs associated with owning a car before making a decision to purchase one.

The surface areas of the figures are:

10.To find the surface area of this rectangular prism, find the area of each face and then add them together.

Face 1: The front and back faces both have dimensions of 12 ft by 14 ft, so the area of each is:

12 ft × 14 ft = 168 ft²

Two of these faces, so the total area is:

2 × 168 ft² = 336 ft²

Face 2: The top and bottom faces both have dimensions of 20 ft by 14 ft, so the area of each is:

20 ft × 14 ft = 280 ft²

Two of these faces, so the total area is:

2 × 280 ft² = 560 ft²

Face 3: The left and right faces both have dimensions of 12 ft by 20 ft, so the area of each is:

12 ft × 20 ft = 240 ft²

Two of these faces, so the total area is:

2 × 240 ft² = 480 ft²

Now add up the areas of all the faces:

336 ft² + 560 ft² + 480 ft² = 1,376 ft²

11. To find the surface area of the figure, add the areas of all six faces.

Find the area of the rectangular faces:

The front and back faces both have dimensions of 14 in by 14 in, so each has an area of 14 in x 14 in = 196 in².

The top and bottom faces both have dimensions of 13 in by 8.9 in, so each has an area of 13 in x 8.9 in = 115.7 in².

Find the area of the triangular faces. Use the Pythagorean theorem to find the length of the third side of each triangle:

The two side faces are congruent triangles with legs of 14 in and 13 in.

Using the Pythagorean theorem, find the length of the hypotenuse to be √(14² + 13²) ≈ 19.14 in. The area of each triangle is then 1/2 base x height = 1/2 x 19.14 in x 8.9 in ≈ 85.3 in².

Using the Pythagorean theorem, find the length of the hypotenuse to be √(8.9² + 13²) ≈ 15.8 in. The area of each triangle is then 1/2 base x height = 1/2 x 15.8 in x 14 in ≈ 110.6 in².

Finally, add up the areas of all six faces:

Front and back faces: 2 x 196 in² = 392 in²

Top and bottom faces: 2 x 115.7 in² = 231.4 in²

Side faces: 2 x 85.3 in² = 170.6 in²

End faces: 2 x 110.6 in² = 221.2 in²

The total surface area is the sum of these areas:

392 in² + 231.4 in² + 170.6 in² + 221.2 in² ≈ 1,015.2 in²

Therefore, the answer is B. 1,058.4 in².

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The solution to the exponential equation 10^(-x - 1) = 36 is given as follows:

x = -2.5563.

The exponential equation in the context of this problem is defined as follows:

10^(-x - 1) = 36

The log10 operation is the inverse of the power of 10 operation, hence we can isolate the variable x as follows:

-x - 1 = log10(36)

-x - 1 = 1.5563

x = -1.5563 - 1

x = -2.5563.

Which is the solution to the exponential equation in the context of the problem.

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The diameter of the racetrack in feet is 1,681.53 feet.

In Mathematics and Geometry, the circumference of a circle can be determined by using the following mathematical equations:

C = πD or C = 2πr

Where:

Conversion factor;

1 mile = 5280 feet

By substituting the given parameters into the formula for the circumference of a circle, we have the following;

5280 = 3.14 × D

Diameter, D = 5280/3.14

Diameter, D = 1,681.53 feet.

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The set X/Y is the same as saying the set of all elements that are in X but not in Y and the answer is {3, 12}.

A set is a collection of distinct objects, called elements and are usually enclosed within braces { }.

An example of a set is the set of even numbers between 1 and 10 which can be written as {2, 4, 6, 8, 10}.

Types of set

Finite and Infinite Sets: A finite set is a set that has a specific number of elements, whereas an infinite set has an unlimited number of elements.

Empty Set: The empty set, denoted by ∅ or {} is a set that has no elements.

Singleton Set: A singleton set is a set that contains only one element. For example, {5} is a singleton set.

Subset: A subset is a set whose elements are all members of another set. For example, {1, 2} is a subset of {1, 2, 3, 4}.

Universal Set: The universal set is the set of all elements under consideration. It is usually denoted by U.

Disjoint Set: Two sets are disjoint if they have no common elements. For example, {1, 2} and {3, 4} are disjoint sets.

Equal Set: Two sets are equal if they have exactly the same elements.

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The sinusoidal function of the form y = A·sin(k·x) + C that matches the function in the graph is; y = 4·sin((π/5)·x) - 1

A sinusoidal function is a periodic function based on the sine or cosine functions.

The form of the function is y = A·sin(k·x)

The peak and trough of the graph are; (-7.5, 3), (-2.5, -5)

The amplitude of the function is therefore; A = (3 - (-5))/2 = 4

The vertical shift of the function is; C = (3 + (-5))/2 = -1

The period of the graph (Number of input x-values required to complete a cycle) = 2.5 - (-7.5) = 10 = 2·π/k

Therefore; k = 2·π/10 = π/5

The horizontal shift can be found as follows;

When x = 0, y = -1, therefore;

-1 = 4 × sin(π/5 × (0 - θ)) - 1

arcsin(0/4) = π/5 × (- θ)

θ = 0

The sinusoidal function is therefore;

y = 4·sin((π/5)·x) - 1

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The sine equation for the object's height is given as follows:

d = -5sin(0.24t).

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The amplitude for this problem is of 5 inches, hence:

A = 5.

The period is of 1.5 seconds, hence the coefficient B is given as follows:

2π/B = 1.5

B = 1.5/2π

B = 0.24.

The function starts moving down, hence it is negative, so:

d = -5sin(0.24t).

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Answer:

Step-by-step explanation:

T+4 = -7

T = -7 -4

T = -11