Find mLJKL if mDKL = 80°
and mJKD=65º.

The difference in the cooking quality of cheddar cheese compared to that of fat-free cheddar cheese is Fat-free cheddar cheese does not melt as well as regular cheddar cheese.

Cheddar cheese's main source of protein is casein.

Cheddar cheese without fat does not melt as well as cheddar cheese with fat. When heated to a high temperature, fat-free cheddar cheese separates more readily than conventional cheddar cheese. Additionally, since fat-free cheese has more protein than conventional cheese, it will become difficult when heated. Regular cheese, on the other hand, would experience a stronger oiling off action, resulting in a glossier surface on the cooked cheese product.

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Answer: √3(cos(19pi/12) + isin(19pi/12))

Step-by-step explanation: I took the test.

Answer:

5,775 for the cost of parking tuition

Step-by-step explanation:

45% = 0.45

0.45(10,500)= 4,725

10,500 - 4,725 = 5,775 for the cost of parking tuition

Answer:

The square root of 37 is approximately 6.0827. To determine which two integers it lies between, we can find the integers that are closest to the square root of 37.

The integer that is smaller than 6.0827 is 6, and the integer that is larger than 6.0827 is 7.

Therefore, the square root of 37 is between the integers 6 and 7.

The given nth term is `an = 2n/(3^(2n))`. To find the limit of the sequence with the given nth term, we first convert the nth term to a fraction: `an = 2n/(3^(2n)) = 2n/(9^n)`.As `n` approaches infinity, the denominator `9^n` becomes extremely large, causing the fraction to approach zero. Therefore, the limit of the sequence is zero.

To find the limit of the sequence with the given nth term, we must first convert the nth term to a fraction. Therefore, we can write the nth term `an = 2n/(3^(2n))` as `an = 2n/(9^n)`.To understand the limiting behavior of the sequence as `n` approaches infinity, we need to observe how the values of `an` behave as `n` becomes larger and larger. We can create a table to observe the values of `an` as `n` increases:| `n` | `an` |1 | `2/9` |2 | `8/81` |3 | `16/729` |4 | `32/6561` |5 | `64/59049` |... | ... |We can see that as `n` increases, the values of `an` become progressively smaller. For example, `a5 = 64/59049` is much smaller than `a1 = 2/9`.As `n` approaches infinity, the denominator `9^n` becomes extremely large, causing the fraction to approach zero. Therefore, the limit of the sequence is zero: `lim_(n→∞) an = 0`.Conclusion: The limit of the sequence with the given nth term `an = 2n/(3^(2n))` is zero. As `n` approaches infinity, the values of `an` become progressively smaller, approaching zero.

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The limit of the sequence as n approaches infinity is infinity.

We have,

The given sequence is defined by the nth term formula: an = 2n³ / (2n).

To find the limit of this sequence as n approaches infinity, we want to determine the behavior of the sequence as n gets larger and larger.

First, let's simplify the expression for the nth term.

We notice that there is a common factor of 2n in both the numerator and the denominator.

By canceling out this common factor, we get:

an = n².

Now, as n approaches infinity, we consider the behavior of n².

When n becomes larger and larger, n² will also increase without bound.

In other words, the value of n² will keep growing indefinitely as n approaches infinity.

Therefore,

We can conclude that the limit of the sequence as n approaches infinity is infinity.

This means that the terms of the sequence will become arbitrarily large as n becomes larger and larger.

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The complete question.

Find the limit as n approaches infinity of the sequence defined by the nth term an = 2n³/ (2n).

24 different orders in which the movie buff can watch the movies.

Permutation refers to the arrangement of objects or elements in a specific order. In mathematics, a permutation is a specific ordering of a set of items.

The number of permutations of a set of n items taken r at a time is denoted by P(n, r) or nPr.

The formula for calculating permutations is:

P(n, r) = n! / (n - r)!,

where n is the total number of movies and r is the number of movies to be watched.

In this case, we have:

P(4, 3) = 4! / (4 - 3)!

Simplifying the expression, we get:

P(4, 3) = 4! / 1!

P(4, 3) = 4 x 3 x 2 x 1 / 1

P(4, 3) = 24

Therefore, there are 24 different orders in which the movie buff can watch the movies.

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Signal a) is not absolutely band-limited and so, its Nyquist sampling rate cannot be determined. Signal b) is absolutely band-limited with an absolute bandwidth of B Hz, and its Nyquist sampling rate is 2B.

Let x(l) be a band-limited signal with absolute bandwidth B Hz. For each of the signals below, we need to determine whether the signal is absolutely band-limited, and if so, express the Nyquist sampling rate for the signal in terms of B.

a) x(0) + x(t - 1)dx(t)dt:For this signal, let us apply the Fourier transform. The Fourier transform of the first term is 2πX(ω)δ(ω), and that of the second term is e^(-jω)X(ω).

Thus, X(ω) = 2πX(ω)δ(ω) + e^(-jω)X(ω)On rearranging this expression, we get: X(ω) = [1 / (1 - 2πδ(ω))]e^(-jω)Therefore, the signal is not absolutely band-limited because it has components at all frequencies.

Hence, the Nyquist sampling rate cannot be determined.b) x:For this signal, let us consider its Fourier transform. Its Fourier transform will be a scaled version of the Dirac comb function, centered at ω = 0, with a spacing of 2π. Hence, X(ω) = 2πBδ(ω).

The signal is absolutely band-limited with absolute bandwidth B Hz, and hence, the Nyquist sampling rate will be 2B. The Nyquist sampling rate is twice the absolute bandwidth, and so, the sampling rate for this signal will be 2B Hz.

Thus, the answer to the question is as follows:Signal a) is not absolutely band-limited and so, its Nyquist sampling rate cannot be determined. Signal b) is absolutely band-limited with an absolute bandwidth of B Hz, and its Nyquist sampling rate is 2B.

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Answer:

x = 63

Step-by-step explanation:

2x - 6 = 120

2x = 126

x = 63

Answer:

x=63

Step-by-step explanation:

You put 2x-6=120. So 120+6 is 126. You then divide 126 by to and get 63.

The calculated value of the length of the segment ST is 13.5

From the question, we have the following parameters that can be used in our computation:

The trapezoids

The length of the segment ST is then calculated as

XY/XW = ST/SR

substitute the known values in the above equation, so, we have the following representation

9/12 = ST/18

So, we have

ST = 18 * 9/12

Evaluate

ST = 13.5

Hence, the length of the segment ST is 13.5

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

22

Step-by-step explanation:

because if you divide 45 first it will be wrong so you must always first will the biggest number in your problem

Answer:22

Step-by-step explanation:

990/45

45 goes 2 times into 99 with 9 left over. Bring down the 0 and you have 90. 45 goes into 90 2 times evenly. So 22 is the answer,

Answer:

y = 3x + 1

Step-by-step explanation:

The equation for slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

(a) Probability that a randomly selected is 9.68%; (b) 29.12% will receive the tax break; (c) Minimum and the maximum starting salaries are 35,679.71 and 4,320.29. (d) 6.3% of the total number of students.

a) P(X>30,400) = P(Z>(30,400-20,000)/8,000)

                          = 1-P(Z<1.3)

                          = 0.0968

                         = 9.68%

b) P(X<15600) = P(Z<(15600-20000)/8000)

                        = 29.12%

c) Maximum of the starting salaries of the middle 95% is

                     (x - 20,000)/8,000 = 1,96

                                                  x  = 35,679.71

Minimum of the starting salaries of the middle 95% is

                      (x - 20,000)/8,000 = -1,96

                                                   x = 4,320.29

d) P(X>32,240) = 1-P(Z<(32,240-20,000)/8,000)

                         = 0.063

Therefore, the 189 represents 6.3% of the total number of students, means that the total number is 3,000.

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Since Line V and Line W are parallel, they must have the same slope.

This gives us that the equation for Line W looks like: y = 8x + b

We need to find b and we use that point (-1,-2) to find it.  Substitute (-1,-2) into x and y and you can solve for b:

    -2 = 8(-1) + b

    -2 = -8 + b

    -2 + 8 = -8 + 8 + b

     6 = b

Now you have b (AKA the y-intercept).

The final equation is y = 8x + b.

Answer:

3x^2=81

x²=81/3

x=√27=3√3

Step-by-step explanation:

3x²=81

With this we have to square root both sides to find the value of x.

\( \sqrt{3 {x}^{2} } = \sqrt{81} \)

So the x will cancel the square root sign so;

\(3x = \sqrt{81} \)

And now we have to find the square root of 81 which is 9, because when we multiply 9 by 9 we are going to be get 81 so the square of 9 is 81 and the square root of 81 is 9

So;

\(3x = 9\)

And then we divide both sides by 3 to find the value of x ;

\( \frac{3x}{3} = \frac{9}{3} \)

\(x = \frac{9}{3} \)

\(x = 3\)

The profit margin made by True Blue Vintage Toy Company is; 0.3 or 30%

A profit margin is defined as a profitability ratio that can tell you whether a company makes money. It highlights what portion of the company's sales have turned into profits or how many cents per dollar it generates per sale.

Now, the parameters given are;

Selling price = #40

Profit = $12

Thus;

Cost price = 40 - 12 = $28

Profit margin = (40 - 28)/40

= 0.3 or 30%

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Answer:

-3

Step-by-step explanation:

\(F(x)=-\,(-x)\\f(-3)=-(-(-3))\\f(-3)=-3\)

To graph the inequality:

We use the x and y-intercepts.

When x=0

We have the point: (0, 5.5)

When y=0

We have the point: (-1.83, 0)

We plot the points (0, 5.5) and (-1.83,0).

The points are joined using a broken line because of the inequality sign: >

The graph is shown below:

To determine which side is required, we use the origin test.

When x=0 and y=0

This means the side of the line containing (0,0) is where we need. (Shaded above)

Answer:

I just answered this obviously for a previous post.

Given:

44, 38, 21, 37, 48, 43, 28

To find the box-and-Visker plot representing the given data:

Let us write it in ascending order.

21, 28, 37, 38, 43, 44, 48.

The median of the given data is 38.

The median of the first three terms is 28.

The median of the last three terms is 44.

The lowest of the given data is 21.

The highest of the given data is 48.

Hence, the correct option c.

The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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The system needs to handle customer details, yacht information, port data, and support various business processes such as adding new customers, calculating the total length of stay, retrieving a list of yachts visiting their home port.

4.1. To add details of a new customer without specifying the yacht or ports, the system can have a customer table with attributes like name, nationality, email address, phone number, and ID number. Additionally, a charter table can store the start date and duration of the charter, associated with the customer ID. The SQL code would involve inserting a new record into the customer table and creating a charter record for the customer without specifying the yacht or ports initially.

4.2. To list the total length of stay for yachts in each port between given dates, the system would utilize the charter table, yacht table, and port table. By joining these tables and filtering based on the specified dates, the SQL code would calculate the sum of the durations of all charters for each yacht in each port, providing the total length of stay.

4.3. To get a list of yachts visiting their home port between given dates, the SQL code would involve joining the yacht and charter tables, filtering the records based on the specified dates, and retrieving the yacht name, date of arrival, and length of stay for each matching record.

4.4. To list the ports visited by a given customer, the system would use the customer table, charter table, and port table. By joining these tables and filtering based on the customer ID, the SQL code would retrieve the ports visited by the customer, along with the date of arrival and length of stay. The resulting list can be sorted by the date of arrival in ascending order.

4.5. To remove a yacht temporarily, the system can add a status attribute to the yacht table indicating availability. When a yacht is temporarily unavailable, its status would be updated. To get a list of unavailable yachts, the SQL code would query the yacht table and filter the records based on the unavailability status.

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Outline Business Scenario A yacht charter company requires a web-based system to manage aspects of its holiday charter business. There are a number of customers, each of whom may book a number of holiday charters, with each charter booked by an individual customer. A holiday charter may involve one yacht only, but each yacht may be involved in many holiday charters. A holiday charter may visit several ports and each port will be visited by many holiday charters. Most ports have several yachts based in them (although a few smaller ports have no yachts based in them) with each yacht based in just a single home port. Information to be held and manipulated include: • the name, nationality, email address, phone number and id number of each customer. • the name, type, model, home port, number of berths and cost of hire per day of each yacht. • the name, phone number, email address and number of docking places at each port. • the charter id, start date and duration of each charter, and the visit id, expected date of arrival and duration of stay at each port visited. Business processes to be supported include the ability to: • add details of a new customer together with the start date and duration of the charter they have booked, but without specifying the yacht to be used or the ports to be visited. • list the total length of stay, between two given dates, of yachts in the fleet in each port. • get a list of yachts (by name) visiting their home port between two given dates, together with the date of arrival and the length of the stay. • list the ports visited by a given customer together with the date of arrival and length of stay, ordered by date. • remove a yacht temporarily for a period of time (e.g., for servicing) and get a list of yachts that are not available. 4. Business Processes Showing the SQL code developed and clearly stating any assumptions made, briefly discuss your approach to implementing each of the given business processes. 4.1. Add details of a new customer .... 4.2. List the total length of stay .... 4.3. Get a list of yachts (by name) .... 4.4. List the ports visited by a given customer ..... 4.5. Remove a yacht temporarily ...

Answer:

1. 20 pounds

2. $11

Step-by-step explanation:

To set this up, you have to use a system of equations. It would look like this, where  is pounds and  is total cost:

UPS:

FedEx:

In order to solve a system of equations you must either a.) graph it, or b.) set them equal to each other.

If you graph it, the answer is where the two lines intersect.

If you set them equal to each other, solve it.

I will set them equal to each other in this:

The first step in a problem like this, where there's the same variable on both sides, is to subtract the smaller variable from both sides. In this case, it is  . That would turn the equation into:

After that, you must solve it like a regular two-step equation.

Start by subtracting 5 from both sides:

Now, you must divide both sides by .

That would give us:

This means that in order for the prices to be the same, the package must be 20 pounds.

Now in order to find the total cost, you must plug 20 into one of the equations. It doesn't matter which, since they both equal the same. I will plug it into the FedEx equation:

Now you can just use a calculator and solve that or do it by hand. Multiply 0.30 by 20, to get 6, then add 5, which equals 11.

You should get: .

This means that the total cost, when the costs are the same for both FedEx and UPS, is $11.

The probability that when he enters the restaurant today it will be at least 5 minutes until he is served is  0.2676 and probability that average time until he is served in eight randomly selected visits is 0.0409.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation can be calculated as the square root of variance.

Given that mean μ = 4.2 , standard deviation σ = 1.3

1. P(X >= 5) = P((X - μ)/σ >

                    = (5 - 4.2) /1.3

                    = P(Z ≥ 0.6154)

                    = 1 - P(Z < 0.6154)

                    = 1 - 0.7324

                    = 0.2676

The required probability is 0.2676.

2.Given that n = 8 then  \(\bar x\) = σ/\(\sqrt{(n)\)  = 1.3/√(8) = 0.4596

P(x-bar ≥ 5) = P((\(\bar x\) - μ)/σx-bar ≥ (5 - 4.2)/0.4596)

                        = P(Z ≥ 1.7406)

                        = 1 - P(Z < 1.7406)

                        = 1 - 0.9591

                        = 0.0409

The required probability is 0.0409.

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a) the value of the integral 1.664. b) the coefficient of x4 is (3/1280). c) the value of the integral  2.14 d) the percentage error in the approximation is -28.67%.

a) To evaluate the integral exactly, we make a substitution in the form of ax = sin 0 where a = (1/2).

Substitute x = (sin θ)/2, dx = (cos θ)/2 dθ, and 1 - 4x² = cos² θ in the integral to get it in terms of θ.

∫5√(1-4x²)dx = ∫(5/2) cos²θ dθApply the identity cos²θ = (1 + cos 2θ)/2 to simplify the integrand as shown.∫(5/2) cos²θ dθ = (5/4)∫(1 + cos2θ) dθ = (5/4)θ + (5/8)sin 2θ

Evaluate the above expression from 0 to π/2 to get the value of the integral.

(5/4)θ + (5/8)sin 2θ = (5/4) π/2 + (5/8) sin π = 1.664

b) The integrand is f(x) = 5√(1-4x²).We can write it as shown below, using the binomial series. f(x) = 5(1 - 4x²)^(1/2) = 5∑_(n=0)^∞〖(1/2)_n (2n)!/n! (1/16)^n x^(2n) 〗

The above expression is the Maclaurin Series expansion of f(x) as required.In the expansion, the coefficient of x4 is (1/2)_2 (2.4)/(2!) (1/16)^2 = (3/1280)

c) Integrating each term of the expansion, we obtain the following expression.(5/4)θ + (5/8)sin 2θ = (5/4) π/2 + (5/8) sin π = 1.664

We approximate the value of the integral using the first three terms of the series expansion, and then add the values of the integrated terms.

The terms up to x4 are included in this calculation. I=5[1+(1/2) (-4x²) +(1/2)_2 (-4x²)²]I=5[1-2x²+3x^4/4] = (5/4) (π/2 + (5/16)π²) ≈ 2.14

d) The percentage error in the approximation is given by:%Error = [(Exact value - Approximation value)/ Exact value] x 100Substitute the appropriate values to calculate.%Error = [(1.664 - 2.14)/1.664] x 100 = -28.67% (correct to 3 significant figures)Thus, the percentage error in the approximation is -28.67%.

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Answer: Hello there!

There are 3 ways Ruth can go from high school to the library, and 5 ways she can go from the library to her home.

The number of possible combinations is equal to the product between the options of each event (where the events are going from high school to the library and going from library to her house):

\(3\times5 = 15\)

Then there are 15 different routes that Ruth can take from high school to her home, where she makes a stop at the library.