The level curves of the function f(x,y) – 22 – 4y2 + 2 are o hyperbolas with asymptotes y=+(2). O parabolas elipses hyperbolas with asymptotes y=+(1) 2

The radian measure of the central angle 0 that intercepts an arc of length 18cm is 1.6 radians.

The radian measure of the central angle 0 that intercepts an arc of length 18cm can be found using the formula

S = rθ

Where s is the length of the arc, r is the radius of the circle, and θ is the central angle in radians. Rearranging this formula to solve for θ, we get:

θ = s/r

Plugging in the given values for s and r, we get:

θ = 18cm/11cm

Simplifying, we get:

θ = 1.63636... radians

Rounding to the nearest tenth, we get:

θ = 1.6 radians

Therefore, after we did the calculation, we know that the radian is 1.6 radians.

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The value of the error for Z, where x = 5.9 +/- 0.5 and y = 2.1 +/- 0.2, with one decimal place is 4.

To calculate the error in Z, we need to consider the uncertainties in both x and y. The error in Z can be determined by propagating the uncertainties using the formula for error propagation.

In this case, Z is given by the equation Z = x/y. To propagate the uncertainties, we use the formula for relative error:

ΔZ/Z = sqrt((Δx/x)^2 + (Δy/y)^2)

Given the uncertainties Δx = 0.5 and Δy = 0.2, and the values x = 5.9 and y = 2.1, we substitute these values into the formula:

ΔZ/Z = sqrt((0.5/5.9)^2 + (0.2/2.1)^2) = sqrt(0.0089 + 0.0181) ≈ 0.134

Multiplying this value by 100 to convert it to a percentage, we get approximately 13.4%. Rounding to one decimal place, the value of the error is 4.

Therefore, the value of the error for Z, with one decimal place, is 4.

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The probability that at least one customer arrives at the shop during a one-minute interval is 0.632.

Since the arrival of customers at a Starbucks shop can be modeled as a Poisson process with an average rate of 1/min, the probability of exactly k customers arriving in a one-minute interval is given by the Poisson probability mass function:

P(k arrivals) = (λ^k * e^(-λ)) / k!

where λ is the average rate of arrivals (in this case, 1/min), e is the mathematical constant e, and k! is the factorial of k.

To find the probability that at least one customer arrives during a one-minute interval, we can use the complement of the probability that zero customers arrive (i.e., the probability of at least one arrival is 1 minus the probability of zero arrivals).

Thus, the probability of at least one customer arriving during a one-minute interval is:

P(at least one arrival) = 1 - P(0 arrivals)

P(at least one arrival) = 1 - [(\(1^{0}\) * \(e^{-1}\)) / 0!] = 1 - \(e^{-1}\) = 0.632

Therefore, the probability that at least one customer arrives at the shop during a one-minute interval is 0.632.

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Rounding to 0 decimal places, the Estimated Ultimate Recovery (EUR) for this reservoir is approximately 5,988 MMscf.

To calculate the Estimated Ultimate Recovery (EUR) for the reservoir, we can use the Arps equation, which relates the cumulative production (Q) to time (t) for a declining reservoir:

Q = (b / Di) * ((t + Di)^(-b) - Di^(-b))

Given the following data:

Initial production rate (agi): 165 MMscf/day

Decline rate (Di): 0.09/yr

Hyperbolic exponent (b): 0.51

We want to find the EUR, which is the cumulative production at infinite time (t = ∞).

At infinite time, the Arps equation simplifies to:

EUR = (b / Di) * (Di^(-b))

Substituting the given values into the equation:

EUR = (0.51 / 0.09) * (0.09^(-0.51))

EUR ≈ 5.67 * (1.056)

EUR ≈ 5.98752 MMscf

Rounding to 0 decimal places, the Estimated Ultimate Recovery (EUR) for this reservoir is approximately 5,988 MMscf.

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Let's call:

a: number of adults

c: number of children

90 people visited a museum, then:

a + c = 90

Tickets to the museum cost $12 for each adult and $7 for each child and the museum collected $950, then:

12a + 7c = 950

Isolating c in the first equation:

c = 90 - a

Replacing it into the second equation:

12a + 7(90 - a) = 950

12a + 7(90) - 7a = 950

5a + 630 = 950

5a = 950 - 630

a = 320/5

a = 64

64 adults visited the museum

Answer:

D.

24x + 18y ≤ 225

x + y ≥ 10

Step-by-step explanation:

"He wants to frame no fewer than 10"

x + y ≥ 10

"and he can spend a maximum of $225. Large frames cost $24, and medium frames cost $18."

24x + 18y ≤ 225

Answer:

D.

24x + 18y ≤ 225

x + y ≥ 10

Answer: D.

24x + 18y ≤ 225

x + y ≥ 10

Step-by-step explanation: "He wants to frame no fewer than 10"

x + y ≥ 10

"and he can spend a maximum of $225. Large frames cost $24, and medium frames cost $18."

24x + 18y ≤ 225

Answer: D.

24x + 18y ≤ 225

x + y ≥ 10

The probability of selecting an independent and then a republican is 0.235 x 0.375 = 0.088.

The probability of selecting an independent and then a republican can be calculated using the formula for the probability of two independent events happening in succession. The formula is P(A and B) = P(A) x P(B)

Since there are 7 democrats, 6 republicans, and 4 independents in the discussion group, the probability of selecting an independent is 4/17, or 0.235. The probability of selecting a republican, given that an independent has already been selected, is 6/16, or 0.375.

Therefore, the probability of selecting an independent and then a republican is 0.235 x 0.375 = 0.088.

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Answer:

1:3

n=3

Step-by-step explanation:

1 hour = 60 minutes

20:60

20÷20=1

60÷20=3

1:3

Given:

The dimensions of the square photo are 12'' × 12''.

The frame is 2 inches wider than the photo in both length and width.

To find:

The perimeter of the frame.

Solution:

We have,

Length of the photo = 12 inches

Width of the photo = 12 inches

The frame is 2 inches wider than the photo in both length and width. So,

Length of the frame = 12+2 inches

                                 = 14 inches

Width of the frame  = 12 inches

                                = 14 inches

The perimeter of a square is:

\(P=4a\)

Where, a is the side length.

Now, the perimeter of the square frame with side 14 inches is:

\(P=4(14)\)

\(P=56\)

Therefore, the perimeter of the square frame is 56 inches, Hence, option A is correct.

If it takes 48 days for patch to cover entire lake, then it will take (a) 47 days to cover the half of lake.

The patch of Lilypad doubles in size every day, so, we use the exponential growth to represent its size.

Let the initial size of patch be = "P" and

Let the final size of the patch (when it covers the entire lake) be = "L",

So, we have , L = 2⁴⁸ × P,

We have to find out how long it takes for patch to cover half of lake.

Let the size of patch at that point be = "H", where "H" is half the size of L,

Which is written as : H = L/2 = 2⁴⁷ × P,          ...equation(1)

Let the number of days to cover half lake be = "d",

So, we write equation to solve for the number of days it takes for the patch to reach size "H",

⇒ H = \(2^{d}\) × P,

Substituting the value of "H" from equation(1),

We get,

⇒ 2⁴⁷ × P = \(2^{d}\) × P,

Simplifying further,

We get,

⇒ 2⁴⁷ = \(2^{d}\),

Since, the base is same, we can equate the power,

We get,

⇒ d = 47,

Therefore, it takes 47 days for the patch to cover half the lake, Correct option is (a).

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The given question is incomplete, the complete question is

In a lake, there is a patch of Lilypad. Every day, the patch doubles in size, if it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half the lake?

(a) 47 days

(b) 24 days

(c) 12 days

(d) 36 days

The table representing the relationship between hours of lawn care and the amount of money the company charges is:

8 $220

10 $275

12 $330

14 $385.

Equations are mathematical expressions with two algebraic expressions flanking the equals (=) symbol on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS (left hand side equals right hand side) is the most widely accepted theorem.

Let x be the charge of lawn care for 1 hour.

Given, charge for 4 hours of lawn care =$110

So, x= Amount charged/ Hours of lawn care

x=110/4

x=27.5

Now, the company charges $27.5 for 1 hour of lawn care.

So now we can find the amount charged by the company for

"y" no. of hours by using the equation. x × y = z

Here x, y and z are variables, where x is the charge of lawn care for 1 hour. y is the number of hours of lawn care and z is the total amount

charged by the company.

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Multiply the original dimensions by the scale:

8 x 3.5 = 28

6 x 3.5 = 21

New dimensions:  length = 28, width = 21

The equation Y=-3x-1 represents a linear relationship between x and y, and can be used to model real-world situations such as distance vs. time or cost vs. quantity.

The equation Y=-3x-1 represents a straight line on a coordinate plane. The "slope-intercept" form of the equation is y=mx+b, where m is the slope and b is the y-intercept.

In this case, the slope is -3 and the y-intercept is -1. This means that the line goes downwards at a rate of 3 units for every 1 unit to the right, and intersects the y-axis at -1.

To find the solution to this equation, you would need to have a specific value for either x or y.

If you were given a value for x, you could plug it into the equation to find the corresponding value for y. If you were given a value for y, you could solve for x by rearranging the equation.

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The data in a table indicate the exponential function f(x) = 3(2)x.The formula for an exponential function is: y = abx, where y and x are variables .

A mathematical function using the following formula is an exponential function: f (x) = an x. where x is a variable and an is a fixed amount known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base. If your function has the formula y = a b x, where and are constants, a 0 and b > 0 and b 1, then it must be exponential. Your functions in quadratic equations were always to the second power. The exponent of exponential functions is a variable.

given

From the table, at point (0, 3):

3 = ab°  , a = 3

At point (2, 12):

12 = ab²

12 = 3b²

b² = 4

b = 2

f(x) = 3(2)ˣ

The data in a table indicate the exponential function f(x) = 3(2)x.

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Paco was able to sell a total of 1,582 gallons more in March than he was able to in February.

Paco was able to sell 4,510 gallons of gas in February and then a further 6,092 gallons in March.

The amount that he sold in March that was more than what he sold in February was:

= Amount sold in March - Amount sold in January

= 6,092 - 4,510

= 1,582 more gallons

In conclusion, Parco sold 1,582 gallons more in March than in February.

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The product of the expression is 2x⁶ + 23x³ + 63

First, we should note that algebraic expressions are described as expressions that are composed of coefficients, terms, constants, variables and factors.

These algebraic expressions are also made up of mathematical operations, such as;

From the information given, we have that;

2x3 +9 and x3 +7?

Then,

(2x³ + 9)(x³ + 7)

expand the bracket

2x⁶ + 14x³ + 9x³ + 63

add like terms

2x⁶ + 23x³ + 63

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The angle of impact for the bullet hitting the wall, assuming it approaches along the major axis, is approximately 41.19 degrees.

To determine the angle of impact for a bullet hitting a wall, we need additional information such as the shape of the bullet and the direction of its motion. The dimensions you provided, minor axis = 12 mm and major axis = 13 mm, suggest that you are referring to an elliptical shape.

If we assume that the bullet is approaching the wall along the major axis, we can calculate the angle of impact using trigonometry. Let's denote the angle of impact as θ.

Since the minor axis is perpendicular to the major axis in an ellipse, the tangent of the angle of impact can be calculated as the ratio of the minor axis to the major axis:

tan(θ) = (minor axis) / (major axis) = 12 / 13

Taking the inverse tangent (arctan) of both sides, we can find the angle θ:

θ = arctan(12 / 13)

Using a calculator or trigonometric table, we find that θ ≈ 41.19 degrees.

Therefore, the angle of impact for the bullet hitting the wall, assuming it approaches along the major axis, is approximately 41.19 degrees.

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The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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The probability that a die will land on an even number at least once when rolled twice is 3/4.

To find the probability that a die will land on an even number at least once when rolled twice, we can use complementary probability.

Step 1: Identify the complementary event.
The complementary event to landing on an even number at least once is that the die lands on odd numbers both times.

Step 2: Calculate the probability of the complementary event.
There are 3 odd numbers (1, 3, and 5) on a standard 6-sided die. So, the probability of landing on an odd number in one roll is 3/6 or 1/2.
For two rolls, the probability of landing on odd numbers both times is (1/2) * (1/2) = 1/4.

Step 3: Calculate the probability of the original event using complementary probability.
The probability of landing on an even number at least once is 1 - the probability of the complementary event,

which is 1 - 1/4 = 3/4.

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The correct answer is (a) yes; the equilateral triangle tessellates the plane.

A tessellation is a tiling of the plane using one or more geometric shapes without any gaps or overlaps. For a regular polygon to tessellate the plane, the sum of its interior angles must be a multiple of 360 degrees.

For an equilateral triangle, each angle measures 60 degrees, so the sum of the angles in a triangle is 180 degrees. Therefore, the sum of the interior angles in a tessellation of equilateral triangles must be a multiple of 180 degrees.

Since the measure of the interior angle of an equilateral triangle is 60 degrees, we can tile the plane with equilateral triangles meeting at each vertex. At each vertex, the sum of the interior angles of the three triangles is 180 degrees, so the tessellation meets the requirement that the sum of the interior angles is a multiple of 360 degrees.

Therefore, the answer is (a) yes; the equilateral triangle tessellates the plane.

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Answer:

73,205 vinyls

Step-by-step explanation:

To calculate the number of vinyls sold we need to calculate the compounded increase. To do this we simply raise the number of times that the initial value increases by the number of difference in years from the start to the current year. Then we multiply this number by the initial number of vinyl records. Since there are 4 years between 2012 and 2016, the formula would be the following...

50,000 * \(1.1^{4}\) = x

50,000 * 1.4641 = x

73,205 = x

Finally, we can see that there will be a total of 73,205 vinyls in 2016

Answer:

1. -10

2. -11

Step-by-step explanation:

Answer:

linear

hope this was helpful

The set of all pure and mixed strategy Nash Equilibria of the given two-person game is {(U, D), (D, U), (1/3, 2/3), (2/3, 1/3)}.

The given two-person game is shown in the given table below.Player 2Player 1UDUD2,20,00,20,4The given two-person game has two pure strategy Nash equilibria, (U, D) and (D, U).Mixed strategy Nash EquilibriaIn this game, if player 1 selects U with a probability of q, then the expected payoff of player 2 will be: U = 2q + 0 (1 - q) = 2q where 1 - q is the probability of selecting D.

Similarly, if player 1 selects D with a probability of q, then the expected payoff of player 2 will be: D = 0q + 4 (1 - q) = 4 - 4q where 1 - q is the probability of selecting U.

Similarly, if player 2 selects U with a probability of p, then the expected payoff of player 1 will be: U = 2p + 0 (1 - p) = 2p where 1 - p is the probability of selecting D.

Similarly, if player 2 selects D with a probability of p, then the expected payoff of player 1 will be: D = 0p + 2 (1 - p) = 2 - 2p where 1 - p is the probability of selecting U.

If player 1 mixes his strategies, then the best response of player 2 can be obtained as: U = 2q and D = 4 - 4q.

Similarly, if player 2 mixes his strategies, then the best response of player 1 can be obtained as: U = 2p and D = 2 - 2pThe following table can be drawn for the best response of each player.

Best Responses Player 2 Player 1 U D U D BR21 1 2 2 BR12 1/2 1/2 2 0.

By solving the above best responses, the set of all pure and mixed strategy Nash equilibria can be obtained.

SolutionThe pure strategy Nash equilibria are (U, D) and (D, U).Now we will find the mixed strategy Nash equilibria of the given two-person game by solving the best response correspondences of each player.

The set of all pure and mixed strategy Nash equilibria of the given two-person game is {(U, D), (D, U), (1/3, 2/3), (2/3, 1/3)}.

The given two-person game has been given in the table shown below.Player 2Player 1UDUD2,20,00,20,4The two-person game given above can have a pure strategy Nash Equilibrium and mixed strategy Nash Equilibrium, which can be found by plotting the best response correspondences of each player.

The Nash equilibrium can be defined as a state where no player can increase its payoff by changing its strategy given the other player's strategy.The mixed Nash equilibrium can be solved by considering the probability with which each player is playing each of its strategies.

The expected payoff of the player is calculated by multiplying the payoff of each outcome with its probability and then adding up all the values of each outcome after multiplication. Each player tries to choose the strategy that maximizes its expected payoff given the strategy of the other player.

The best response of each player can be plotted on a graph. If the best response of each player coincides, then it is a Nash Equilibrium.

The set of all pure and mixed strategy Nash Equilibria of the given two-person game is {(U, D), (D, U), (1/3, 2/3), (2/3, 1/3)}. The Nash equilibrium can be defined as a state where no player can increase its payoff by changing its strategy given the other player's strategy. The best response of each player can be plotted on a graph. If the best response of each player coincides, then it is a Nash Equilibrium.

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Answer:

\(x=5.24\tan 41^{\circ}\)

Step-by-step explanation:

\(\tan 41^{\circ}=\frac{x}{5.24} \\ \\ x=5.24\tan 41^{\circ}\)

Answer:

16 ft

Step-by-step explanation:

height of pyramid = (3×512)/(½×24×8)

= 1536/96

= 16 ft