(1/4)x-(1/6)y=5, and (4/5)x+(3/8)y=1
Please help

The solutions to each trigonometric equation are:

Case 6: x = 50.768° (0.282π) or x = 129.232° (0.718π) or x = 230.768° (1.282π) or x = 309.232° (1.718π)

Case 9: x = 41.810° (0.232π) or x = 138.190° (0.768π) or x = 199.471° (1.108π) or x = 340.529° (1.892π)

Case 11: x = 208.164° (1.156π) or x = 331.836° (1.844π)

In this problem we find four cases of quadratic-like trigonometric equations, whose solutions must be found by means of algebra properties and trigonometric formulas. Now we proceed to solve for each case:

Case 6

cos² x + 3 / 5 = 1

cos² x = 2 / 5

cos x = ± √(2 / 5)

x = 50.768° (0.282π) or x = 129.232° (0.718π) or x = 230.768° (1.282π) or x = 309.232° (1.718π)

Case 9

9 · sin² x - 3 · sin x - 2 = 0

sin x = 2 / 3 or sin x = - 1 / 3

x = 41.810° (0.232π) or x = 138.190° (0.768π) or x = 199.471° (1.108π) or x = 340.529° (1.892π)

Case 11

sin² x - 8 · sin x - 4 = 0

sin x = - 0.472

x = 208.164° (1.156π) or x = 331.836° (1.844π)

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Answer:

The missing value is \(14\).

Step-by-step explanation:

Divide the known denominator by its numerator.

\(4\div2=2\)

Now multiply the quotient by the other numerator (\(7\)).

\(2×7=14\)

or

First, find the factor by which the numerators have been multiplied.

\(2x=7→x=3.5\)

Now, do the same for the denominators.

\(4(3.5)=14\)

It would be closest rounded to about 30.25/30.26. Would be better to know the radius rather than the circumference.

4. f(x,y) is homogeneous of degree 2.

5. a) f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1

4. Show that f(x,y)=\(x^2\)y is homogeneous, and find its degree of homogeneity:

A function is said to be homogeneous of degree k, if it satisfies the condition:

f(tx,ty) = \(t^k\)f(x,y)

We have f(x,y) = \(x^2\)y. Let’s check if it satisfies the above condition:

f(tx,ty) = \((tx)^2(ty) = t^3x^2y = t^2(x^2y\)) = \(t^2\)f(x,y)

Hence f(x,y) is homogeneous of degree 2.

5. Which of the following functions f(x,y) are homothetic? Explain.

(a) f(x,y)=\((xy)^2\)+1

(b) f(x,y)=\(x^2+y^3\)

Let us first understand the meaning of homothetic transformation.

A homothetic transformation is a non-rigid transformation of the Euclidean plane that preserves the direction of the straight lines but not their length. It stretches or shrinks the plane by a constant factor called the dilation.

Let’s now find out whether the given functions are homothetic or not.

(a) f(x,y)=\((xy)^2\)+1

In order to check if f(x,y) is homothetic or not, we need to check if the function satisfies the following condition:

f(x,y) = g(h(x,y))

where g is a strictly monotonic function and h is a homogeneous function with degree 1

We have

f(x,y) = \((xy)^2\)+1

Let’s assume g(x) = x - 1, then g(x+1) = x

Similarly, let’s assume h(x,y) = (xy), then h(tx,ty) = \(t^2\)h(x,y)

Now, we have

g(h(x,y)) = h(x,y) - 1 = (xy) - 1

Thus f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1

(b) f(x,y)=\(x^2+y^3\)

We can’t write this function in the form f(x,y) = g(h(x,y)) where h(x,y) is a homogeneous function with degree 1. Hence this function is not homothetic.

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The statement says that you've triggered the Penalty APR so that it has now increased to 28.99%. What action triggered this? You failed to pay the minimum payment by the due date.

You failed to make the minimum payment by the due date. This is an action that can result in a message that "you've triggered the Penalty APR so that it has now climbed to 28.99%."

A charge APR is a charge that can be applied if you don't pay your bills on time. It may be set up so that future transactions may be subject to a penalty APR that is higher than the card's standard rate.

If the minimum payment was not made by the due date, Penalty APR would be applied.

But if the card also has a penalty APR and you trigger it, you will likely lose that promotional offer. Federal consumer protections that limit penalty APRs don't apply to small-business credit cards. That means issuers can be more punitive, such as applying penalty APRs sooner than 60 days after not making payments.

Therefore,

The statement says that you've triggered the Penalty APR so that it has now increased to 28.99%. What action triggered this? You failed to pay the minimum payment by the due date.

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The probability of randomly selecting a red, then a free marble from a bag of 5 red, 8 green, and 3 marbles

a)  0.1563

b) 0.1667

Since we are  given with bag of  5 red, 8 green, and 3 marbles. so, r=5, g=8 and b=  3. For the first  case, we replace the first  marble before drawing the second,  the total number of marble =  5 + 8 + 3 = 16. So, the probability of drawing a red marble at the 1st attempt is: 5/16. Then, the first marble is replaced back into the bag before making the second draw. Probability of drawing green marbles at the second draw is: 8/16= 1/2, Therefore the probability of selecting a red, then a green marble is: 5/16 * 1/2 = 5/32 =0.1563

For the second case , we do not replace the first marble, the probability of drawing a red marble at the 1st draw is:5/16 . Since we don't replace the balls  so the number of marbles remaining in the bag is: 16-1 =15 ,the probability of drawing green marbles at the second draw is: 8/15, therefore the combined probability of selecting a red, then a green marble is: 5/16 * 8/15  =0.1667

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Answer:

b. line j or MT

Step-by-step explanation:

as the plane contains the points Q, N, P, R, T also the lines connecting only these points are in the plane, and are not intersecting the plane.

only M is outside of the plane, and so (only) the connecting line MT intersects the plane (at point T).

by the way, the question means the line RQ and not RO, as there is no point O in the graphic.

To find the Fourier transform of y(t), we can apply the properties of the Fourier transform and use the definition of the unit step function u(t).

The given function y(t) can be expressed as the sum of three shifted unit step functions: u(t+2), -2u(t), and u(t-2). Applying the time-shifting property of the Fourier transform, we can obtain the individual transforms of each term. The Fourier transform of u(t+2) is e^(-jω2)e^(jωt)/jω, where ω represents the angular frequency.

The Fourier transform of -2u(t) is -2πδ(ω), where δ(ω) is the Dirac delta function. The Fourier transform of u(t-2) is e^(-jω2)e^(-jωt)/jω. Using the linearity property of the Fourier transform, the overall transform of y(t) is the sum of the transforms of each term.

Therefore, the Fourier transform of y(t) is e^(-jω2)e^(jωt)/jω - 2πδ(ω) + e^(-jω2)e^(-jωt)/jω.

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The Taylor polynomials P1, P2, P3, and P4 centered at a0 for f(x) are given as:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

We will apply the Taylor's theorem formula, which is supplied as follows, to determine the Taylor polynomials P1, P2, P3, and P4 centred at a0 for f(x) in the given question:f'(a)(x-a)/1 = f(x) = f(a) + f'(a)! + f''(a)(x-a)²/2! + ... + fⁿ(a)(x-a)ⁿ/n!We have f(0) = 1f'(0) = 0f''(0) = -1f'''(0) = 0f4(0) = 1 for f(x) = cos(x) at x = 0.We can get the following polynomial expressions by using these values in the Taylor's theorem formula:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!Consequently, the Taylor polynomials P1, P2, P3, and P4 for f(x) are provided as follows:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

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Yes, because rounding the cost of each pencil topper up to the nearest dollar gives $4, and $4(4)=$16.

Answer:

28x + 12

Step-by-step explanation:

4(7x + 3) = 4 times 7x +4 times 3 = 28x +12

Answer: when you expand the expression you get 21x+12
simplified- 21x+12, there's no other way to simplify it

Step-by-step explanation:

For 7 dozens cookies 3 1/2 cups needed.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

For 3 dozen cookies = 1 1/2 cups = 3/2 cups

For 1 dozen cookies = 3/2 * 1/3 = 1/2 cups needed

So, for 7 dozen cookies = 1/2 * 7

                                       = 3 1/2 cups needed

Hence, for 7 dozens cookies 3 1/2 cups needed.

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The four basic measurements that serve as the foundation for other units of measure are length, mass, time, and temperature.

Length is a measure of distance between two points, typically measured in meters (m) within the International System of Units (SI). Mass is the amount of matter in an object, measured in kilograms (kg) in the SI system. Time refers to the duration or interval between events and is measured in seconds (s) within the SI system.

Lastly, temperature is a measure of the average kinetic energy of particles in a substance, represented in degrees Celsius (°C) or Kelvin (K) in the SI system.

All other units of measure are defined and compared to these four basic measurements. For instance, speed is derived from the combination of length and time (e.g., meters per second). Similarly, force is derived from mass and acceleration, which itself is derived from the change in velocity over time (e.g., newtons).

The combination and comparison of these fundamental measurements enable scientists, engineers, and other professionals to quantify and analyze various phenomena in the physical world.

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PLEASE GIVE ME BRAINLIEST! :)

Answer:

17.3

Step-by-step explanation:

Using the Pythagorean theorem, we can solve for the length of the ladder.a² + b² = c²Where a is the height of the building (22 feet), b is the distance between the building and the bottom of the ladder, and c is the length of the ladder (which we are trying to find).Plugging in the given values, we get:22² + b² = 28²

484 + b² = 784

b² = 300

b = √300

b ≈ 17.3Therefore, the bottom of the ladder is about 17.3 feet from the bottom of the building.

The answers to each part is mentioned above.

Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.

Equation for tank {1} -

y = 175 - 25x

Equation for tank {2} -

y = 200 - 30x

For the solution we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5

and

y = 200 - 150

y = 50

For the same amount of water we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5 hours

In tank (1), there is : 175 - 25 x 5 = 50 gallons

In tank (2), there is : 200 - 30 x 5 = 50 gallons

Therefore, the answers to each part is mentioned above.

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There would be 3 linear coefficients (one for each original variable), 3 quadratic coefficients (one for each squared original variable), and 4 interaction coefficients (one for each unique combination of two original variables).

If there are 3 original predictor variables, and we want to create a quadratic regression model, we would need to include the square terms of each of the original variables, as well as the interaction terms between the variables.

This would result in a total of 10 coefficients, including the intercept term.

Specifically, there would be 3 linear coefficients (one for each original variable), 3 quadratic coefficients (one for each squared original variable), and 4 interaction coefficients (one for each unique combination of two original variables).

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The percentage or the Probability is only 2.5%

Probability is a number that reflects the chance or likelihood that a particular event will occur. This is arrived based on the central limit theorem that sample mean follows a normal distribution for large samples randomly drawn.

Given that on the average, hotel guests who take elevators weigh about 150 pounds with an SD of about 35 pounds.

An engineer is designing a large elevator for a convention hotel, to lift 50 such people.

Maximum capacity = 4 tons =8000 pounds

= 160 pounds/man

If average of 50 people exceeds 160 pounds then it would be overloaded.

Mean of the sample follows a normal with mean = 150 and std error = 35/√50-1 = 5

Required probability

= P(x>160)

= P(Z ? 2)

= 0.0250

Probability is only 2.5%

This is arrived based on the central limit theorem that sample mean follows a normal distribution for large samples randomly drawn.

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Answer:

Step-by-step explanation:

Q = F(K,L) = 3K+2L.

The probability of winning the top prize in the Pennsylvania Cash 5 lottery is: (43! / (5! * 38!)) / (43! / (5! * 38!)) = 1/C(43,5) = 1/69,096.

Probability is a measure of how likely an event is to occur. In the case of the Pennsylvania Cash 5 lottery, we can use probability to determine the chances of winning the top prize.

To win the top prize in the Pennsylvania Cash 5 lottery, a player must select the correct five different numbers between 1 and 43 (in any order). To calculate the probability of this happening, we use the formula: probability = (number of favorable outcomes) / (number of total outcomes).

The number of favorable outcomes is the number of ways that the five correct numbers can be selected from the 43 available numbers. Since the order of the numbers does not matter, this is known as a combination, and the formula for finding the number of combinations is: C(n,r) = n! / (r! * (n-r)!), where n is the total number of options (43) and r is the number of options to choose (5). This simplifies to 43! / (5! * 38!).

The number of total outcomes is the number of ways that any five numbers can be selected from the 43 available numbers, which is also a combination and can be calculated using the same formula: C(43,5) = 43! / (5! * 38!).

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Answer:

2√ 3

Step-by-step explanation:

since the roots are the same yoy can just subtract 4 and 2 and get the answer

The equilibrium price is $0 and the equilibrium quantity is 5 units.

To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied and solve for the equilibrium values.

Setting Q_d = Q_s, we can equate the equations for demand and supply:

-2Q - 2Q_d = -5 + 3Q_s

Since we know that Q_d = Q_s, we can substitute Q_s for Q_d:

-2Q - 2Q_s = -5 + 3Q_s

Now, let's solve for Q_s:

-2Q - 2Q_s = -5 + 3Q_s

Combine like terms:

-2Q - 2Q_s = 3Q_s - 5

Add 2Q_s to both sides:

-2Q = 5Q_s - 5

Add 2Q to both sides:

5Q_s - 2Q = 5

Factor out Q_s:

Q_s(5 - 2) = 5

Q_s(3) = 5

Q_s = 5/3

Now that we have the value for Q_s, we can substitute it back into either the demand or supply equation to find the equilibrium price. Let's use the supply equation:

P = -5 + 3Q_s

P = -5 + 3(5/3)

P = -5 + 5

P = 0

Therefore, the equilibrium price is $0 and the equilibrium quantity is 5 units.

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Answer:

25 ft

Step-by-step explanation:

based on the graph on the width of the porch with the greatest area is 25

A. To save for her payout annuity with an ordinary annuity set up thirty years before her retirement, Holly Krech must make a monthly payment of $175.97.

B. If she sets up the ordinary annuity twenty years before her retirement, Holly Krech must make a monthly payment of $432.00.

To calculate the monthly payment for an ordinary annuity set up thirty years before retirement, we can use the formula for the present value of an ordinary annuity. Given the deposit amount of $218,437.048 and the total amount received from the annuity of $432,000, and solving for the monthly payment, we find that Holly must make a monthly payment of $175.97.

For an ordinary annuity set up twenty years before retirement, we use the same formula for present value. With the deposit amount and total amount received unchanged, we solve for the monthly payment, which comes out to be $432.00.

It's important to note that the monthly payment increases when the annuity is set up closer to the retirement date. This is due to the shorter time period available for saving, resulting in a higher required contribution to reach the desired payout amount.

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Answer:

the number is 33 and 35 respectively

Step-by-step explanation:

The computation is shown below:

Let us assume X and X + 2 are the two consecutive odd integers

Now the equation is

(X ÷ 3) = ((X + 2) ÷ 7) + 6

(X ÷ 3) = (X + 2 + 6 × 7) ÷ 7

(X ÷ 3) = (X + 2 + 42) ÷ 7

(X ÷ 3) =  (X + 44) ÷ 7

Now do the cross multiplication

7X  = 3(X + 44)

7X = 3X + 132

4X = 132

X = 33

And, X + 2 = 33 + 2 = 35

hence, the number is 33 and 35 respectively

In probability theory, the binomial probability distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials with two possible outcomes: success and failure.

The binomial probability distribution can be used to model many real-world situations, such as the success or failure of an experiment or event.

The expression LaTeX: \binom{n}{k} in the equation for binomial probabilities represents the number of ways to choose k items from a set of n items. It is read as "n choose k" and is formally known as the binomial coefficient.

The formula for the binomial coefficient is:

LaTeX: \binom{n}{k} = \frac{n!}{k!(n-k)!}

where n is the total number of items, k is the number of items being chosen, and ! denotes the factorial function (i.e., the product of all positive integers up to a given number).

The binomial coefficient is important in the binomial probability distribution because it represents the number of possible ways to get exactly k successes in n trials. By multiplying this by the probability of getting k successes on any one trial (i.e., p^k) and the probability of getting n-k failures on any one trial (i.e., (1-p)^(n-k)), we get the probability of getting exactly k successes in n trials. This is the basic formula for the binomial probability distribution.

In summary, the binomial coefficient LaTeX: \binom{n}{k} represents the number of ways to choose k items from a set of n items, and is the key factor in the formula for the binomial probability distribution.

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The population scenario of Dhaka City is characterized by rapid urbanization, high population density, and significant population growth.

1. The population scenario of Dhaka City is characterized by rapid urbanization, high population density, and significant population growth. These factors have led to numerous challenges, including increased traffic congestion, inadequate infrastructure, and strain on public services. The city's population is growing at a rapid pace, resulting in overcrowding, housing shortages, and environmental concerns.

2. To mitigate the present traffic jam situation in Dhaka City, a restructuring of the population can be pursued through various strategies. One approach is to promote decentralization by developing satellite towns or encouraging businesses and industries to establish themselves in other regions. This would help reduce the concentration of population and economic activities in the city center. Additionally, improving public transportation systems, including expanding the metro rail network, introducing dedicated bus lanes, and enhancing cycling and pedestrian infrastructure, can provide viable alternatives to private vehicles. Encouraging telecommuting and flexible work arrangements can also help reduce the number of daily commuters. Moreover, urban planning should focus on creating mixed-use neighborhoods with residential, commercial, and recreational spaces to minimize the need for long-distance travel.

By implementing these measures, the population of Dhaka City can be restructured in a way that reduces the strain on transportation systems, alleviates traffic congestion, and creates a more sustainable and livable urban environment.

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The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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a) Decision tree for Lardy plc including all relevant data on the diagram is given below:

b) To calculate expected values as appropriate and recommend a course of action for Lardy plc with the reasons, we need to create a decision tree.

Expected value is calculated by multiplying each outcome by its probability and adding them together.

Hence, the expected value at each node of the tree is calculated and represented in the diagram below.

It is assumed that the probability of not being able to deliver the semi-conductors on time without sub-contracting the work to Blarney pic is 20% and the probability of delivering the semi-conductors on time with Blarney pic is 100%.

So, based on the decision tree, the expected value of sub-contracting is £64,000 and the expected value of producing the semi-conductors on their own is £70,000.

Thus, Lardy plc should sub-contract the work to Blarney pic with expected values being the decision criteria.

Because the expected value of sub-contracting is less than the expected value of producing the semi-conductors on their own, it makes more financial sense to sub-contract the work.

c) Macher and Mowery (2003) estimate that there is a learning rate of 85% in the semiconductor industry.

A learning curve refers to the rate at which learning occurs during a process or activity.

It demonstrates how the time required to complete a task decreases as the number of times the task is done increases.

The learning curve shows the relationship between the cost of production and the volume of goods manufactured.

As the production volume of semiconductors increases, the cost of production per unit decreases due to increased learning by the production workers, which leads to increased productivity.

Macher and Mowery (2003) estimated an 85% learning rate for the semiconductor industry, which implies that the production cost of semiconductors will decline by 15% each time the cumulative production volume doubles.

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