Use the Law of Cosines to find the values of x°and y°. Round to the nearest tenth.

Answer:

its B

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Yes, it is possible for a plot of a partial expansion of f[x] to share ink with the plot of f[x] all the way from -[infinity] to + [infinity].

Explanation:

We can approximate f(x) as a Fourier series, as follows:

\($$f(x) = \sum_{n=0}^{\infty}a_n\cos\left(\frac{n\pi x}{L}\right)+\sum_{n=1}^{\infty}b_n\sin\left(\frac{n\pi x}{L}\right)$$\)

If f(x) is an odd function, the cosine terms are gone, and if f(x) is an even function, the sine terms are gone.

We can create an approximation for f(x) using only the first n terms of the Fourier series, as follows:

\($$f_n(x) = a_0 + \sum_{n=1}^{n}\left[a_n\cos\left(\frac{n\pi x}{L}\right)+b_n\sin\left(\frac{n\pi x}{L}\right)\right]$$\)

For any continuous function f(x), the Fourier series converges uniformly to f(x) on any finite interval, as given by the Weierstrass approximation theorem.

However, if f(x) is discontinuous, the Fourier series approximation does not converge uniformly.

Instead, it converges in the mean sense or the L2 sense. The L2 norm is defined as follows:

\($$\|f\|^2 = \int_{-L}^{L} |f(x)|^2 dx$$\)

Hence, it is possible for a plot of a partial expansion of f(x) to share ink with the plot of f(x) all the way from -[infinity] to + [infinity].

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Solution to given logarithmic equations and inequalities are;

x = 1

x = 9

x = 261

x = 10/3

x = 4

3x² - 2x - 1 = 0

x = 1 or x = -1/3

x = 13

x = 0

x = 0 or x = 5

1. 3x = log6 216

Using the definition of logarithm, we have:

\(6^{3x} = 216\)

\(6^{3x} = 6^3\)

3x = 3

x = 1

2. x - 4 = log3 243

Using the definition of logarithm, we have:

\(3^{x - 4} = 243\)

\(3^{x - 4} = 3^5\)

x - 4 = 5

x = 9

3. log4 (4x - 20) = 5

Using the definition of logarithm, we have:

4⁵ = 4x - 20

1024 = 4x - 20

4x = 1044

x = 261

4. log9 (3 - x) = log9(5x – 15)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

3 - x = 5x - 15

20 = 6x

x = 10/3

5. log81 (x + 20) = log81 (6x)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

x + 20 = 6x

20 = 5x

x = 4

6. log9 (3x²) = log9 (2x + 1)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

3x² = 2x + 1

3x² - 2x - 1 = 0

7. Using the quadratic formula, we have:

x = (-(-2) ± √((-2)² - 4(3)(-1))) / (2(3))

x = (2 ± √(16)) / 6

x = (2 ± 4) / 6

x = 1 or x = -1/3

8. log4(x - 1) = log4(12)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

x - 1 = 12

x = 13

9. log7(5 - x) = log7 (5)

Using the property of logarithms that states that if log a b = log a c, then b = c, we have:

5 - x = 5

x = 0

10. logx (5x) = 2

Using the definition of logarithm, we have:

x² = 5x

x² - 5x = 0

x(x - 5) = 0

x = 0 or x = 5

Note that x = 0 is not a valid solution, since log 0 is undefined. Therefore, the only solution is x = 5.

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Answer:

  1. A. contain a right angle

  1. B. opposite sides are parallel

  2. (c) 2 pairs of parallel sides

  3. (b) 2 sides of equal length

Step-by-step explanation:

Here you are asked to find patterns and to make use of the definitions of different geometric figures.

The figures in Circle A do not all have the same number of sides, or sides of the same length. However, they do all have at least one right angle.

The figures in Circle B are rectangles and parallelograms. The attributes listed in question 2 can be used here. They all have two pairs of parallel sides.

As we observed in question 1, rectangles and parallelograms share the feature of 2 pairs of parallel sides.

A kite may have 2 pairs of equal-length sides. While a square and a rhombus have 4 sides of equal length, that description is not true of rectangles and parallelograms in general.

Angles in a rectangle are all 90°, while those in a parallelogram may not be. The offered descriptions of angles do not apply to apply to both shapes.

An isosceles triangle has two sides equal length and two equal angles. An equilateral triangle is a special case of an isosceles triangle in which all three sides are equal, as are all three angles. The description that applies to both kinds of triangles is 2 sides of equal length.

2√3

To simplify the given radical expression √363 - 3√27, follow these steps:

Step 1: Find the prime factorization of the numbers inside the radicals.
- 363 = 3 × 121
- 27 = 3 × 3 × 3

Step 2: Simplify the square roots.
- √363 = √(3 × 121) = √(3 × 11²) = 11√3
- 3√27 = 3 × √(3 × 3 × 3) = 3 × 3√3 = 9√3

Step 3: Combine the terms with the same radicals.
- 11√3 - 9√3

Step 4: Simplify by combining the coefficients.
- (11 - 9)√3 = 2√3

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Answer: C. Is true 7/8>-0.78

Answer:

R = 3

Step-by-step explanation:

8595 / 24 = 358.125

24 * 358 = 8568

8595 - 8592 = 3

The committee can best catalog the data so it can be used to make meaningful changes by using a database management system (DBMS).

A database management system (DBMS) is a system that enables users to create, read, update, and delete data in a database. The DBMS is a tool that handles all data-related tasks. Organizations employ a DBMS to keep data organized and easy to access and manage.

DBMS provides a set of computerized tools for managing all types of data. A DBMS allows end-users to extract and analyze data from a database.

The committee can use a database management system to ensure that data is organized and easily retrievable. They can employ a DBMS to streamline data entry and report production for high-quality output.

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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:

12% of 88 is 10.56

Answer:

10.56

Step-by-step explanation:

Answer:

$6.19

Step-by-step explanation:

We have 3 meals and 1 ice cream at 20.46

Take away the 1 ice cream to get 20.46-1.89=18.57

18.57 is the cost of 3 meals so divide it by 3 to get

18.57/3 = 6.19

Answer:

6.19 per meal

Step-by-step explanation:

20.46-1.89

18.57/3

6.19+ tax

Answer:

d. d<2/3 or g>2

Step-by-step explanation: I got it right on the test!

Answer:

0.5

Step-by-step explanation:

0.5=0.42 then the answer is 0.5

The area of the region enclosed by the curves: Y = 3X and Y = 6X² is

1/8 sq. unit.

Linear equation are those in which power is 1 or maximum degree is 1. For example: x + y = 3 here the maximum degree is 1.

Quadratics equation are those in which power is 2 or maximum degree is 2. For example: X² + 6X + 3 = 0. here the maximum degree is 2.

Here, we have given two equation:

Y = 3X

Y = 6X²

To find the limit we will equate the both equation:

3X = 6X²

6X² - 3X = 0

3X ( 2X - 1 ) = 0

here we get two values of X, X = 0 and X = 1/2

so, Lower limit = 0 and Upper limit = 1/2.

Area = \(\int\limits^ \frac{1}{2} _0 {(3x - 6x^{2} ) } \, dx\)

Area = ( 3/2 ( x ⁸ )  - 2 ( x³ ) )          --- Limit from: 0 to 1/2

Area = (3/2 ( 1/2 ² ) - 2 ( 1/2 ³) ) - ( 3/2 ( 0² ) - 2 ( 0³) )

Area = 3/8 - 1/4 - 0 + 0

Area = 1/8 sq. unit

Hence,

The area of the region enclosed by the curves: Y = 3X and Y = 6X² is

1/8 sq. unit. For graph See the attached image.

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Step-by-step explanation:

180-(90° +32°)

180- 122= 58

triangle =180°

180° - (58° +58°)

180° - 116°= 64°

Answer:

x=64

Step-by-step explanation:

∠A = 180-(90°+32°)

=> ∠A=180-122= 58

Angle sum property in Triangle=180°

=> x = 180° - (58°+58°)

=> x = 180° - 116°= 64°

Answer:

145) A

146) C

147) B

148) D

Answer:

Step-by-step explanation:

The law of large numbers states that as the number of trials (or bets) increases, the average outcome of those trials will converge to the expected value. In this case, the expected value of a $1 bet on red is $0.947, which means that over many bets, the average payoff will be very close to $0.947.

However, it's important to note that the law of large numbers doesn't guarantee that any individual bet will have a particular outcome. Each bet is still subject to the random chance of the ball landing in a particular slot. So while the overall outcome of many bets will tend towards the expected value, any individual bet could result in a win or a loss.

Changing the bet to black would not improve the odds of winning, as the probabilities of red and black are equal. However, it would change the expected value of the bet to $0, since a $1 bet on black would have the same payout and probability as a $1 bet on red.

Answer:

The common factor is 2b

Step-by-step explanation:

By factorization, we can determine the common factor by finding a number or variable which when multiplied by other numbers maintains a specific pattern.

For the question above, when 2b is multiplied by 4b² we arrive at 8b². Similarly when 2b is multiplied by 5 we have 10b, hence 2b is the common factor of both 8b³ and 10b.

\(2b \times 5 = 10b \\ 2b \times {4b}^{2} = 8 {b}^{3} \)

it may be permissible to proceed with a hypothesis test even if the assumption of random participant selection is violated, under the conditions of known and accounted for non-random selection or random assignment to treatment groups

Random participant selection is an important assumption in hypothesis testing, as it helps ensure the generalizability of the results to the target population. However, in some situations, it may be impractical or impossible to achieve perfect random selection. In such cases, there are a few conditions under which it may still be permissible to proceed with a hypothesis test despite the violation of this assumption:

Non-random selection is known and accounted for: If the non-random selection process is well-documented and understood, researchers can adjust their analysis or statistical methods to account for potential biases introduced by the non-random selection.

Random assignment to treatment groups: Even if participants are not randomly selected, random assignment to different treatment groups can help mitigate the impact of non-random selection. By randomly assigning participants to treatment groups, the effects of non-random selection are distributed evenly across the groups, allowing for valid comparisons and hypothesis testing.

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The rigid motion that verifies the congruence of two triangles using the Side-Angle-Side (SAS) criterion is the combination of a translation and a rotation.

To establish congruence between two triangles using the SAS criterion, we need to show that the triangles have two corresponding sides and the included angle equal in measure. This can be achieved through a specific rigid motion, which preserves the shape and size of the triangles.

The first step in the rigid motion is a translation. Translation involves moving the entire triangle along a straight line without altering its shape or size. By sliding one triangle along the plane, we can place the corresponding sides of the two triangles in the same position.

The second step is a rotation. A rotation is a transformation that turns the triangle around a fixed point, called the center of rotation. By rotating one triangle around its center, we can align the corresponding angles of the two triangles. By combining the translation and rotation, we ensure that the sides and the included angle of the two triangles match, verifying their congruence using the SAS criterion.

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Answer:

divide each number by negative 3

Step-by-step explanation:

-3y=-2x-9

y=2/3+3

Answer:

if im correct, x = 64

Step-by-step explanation:

since a triangle's angles must sum to 180°, i subtracted 52 from 180 which gave me 128. then, i divided 128 in two so that it could equal to both of the sides of the triangle.  128/2 = 64

Answer:

the answer is 15x+3=3(5x+1)

The latest time for pickup, found by converting the 150 minutes maximum time provided by the school, from minutes to hours is about 5:45 pm

Minutes can be converted into hours by dividing the number of minutes by 60, which is the number of minutes in an hour.

The time that school ends = 3:15 pm

The latest time for pick up after school care = 150 minutes after school ends

Therefore, the latest time for pick up after school care = 3:15 pm + 150 minutes

60 minutes = 1 hour

150 minutes = (1/60) × 150 = 2.5

The latest for pick up = 3:15 pm + 2.5 hours = 5:45 pm

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Answer:

75

Step-by-step explanation:

9 + 9 + 9 + 9 + 9 + 30 = 75

Good luck on your assignment!

It should be noted that the value on the blank on the equation will be -2.

The equation given is:

2(4x+1) + 8 = 4(2x+1) + 8 - x

Simplifying the left-hand side:

8x + 2 + 8 = 8x + 4 + 8 - x

Simplifying the right-hand side:

8x + 4 + 8 - _ = 8x + 12 - x

Combining like terms on both sides:

8x + 10 = 8x + 12 - x

Subtracting 8x from both sides:

10 = 12 - x

x = 10 - 12

x = -2

The value will be -2 to make the equations equal.

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Answer:

2%

Step-by-step explanation:

Answer:

Step-by-step explanation:

B

The form of a system of inequalities that would allow you to solve for the number of each type of animal that can be won is 10x + 6y = 12.

Given:

A carnival has a game where players can win stuffed animals. the rules allow for players to win no more than 10 small animals, no more than 6 large animals, and no more than 12 total animals.

x be the number of small animals and y be the number of large animals

The number of small animals = 10x

Number of large animals = 6y

The equation:

= 10x + 6y = 12.

Therefore the form of a system of inequalities that would allow you to solve for the number of each type of animal that can be won is 10x + 6y = 12.

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