3. D 49° B mzB = ? 70° d = 18 C length of arc CD = length of are BD =​

The probability of no more than 8 heads given that at least one toss resulted in heads will be 511/512.

What is probability ?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

A coin has two possibility, either head or tail.

So, there will be 2 possible outcomes when a coin is tossed.

hence, Total no. of outcomes (T) =  2^9. = 512

  Now,  Probability of getting one tail = 1/2^9 = 1/512

and, Probability of getting at most 8 heads

       = 1 - Probability of getting one tail

       = 1 - 1/512

       = 511/512.

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Plugging in the value of w = 3.156 rad/s, we can calculate the maximum Displacement.

To find the positive angular frequency w that leads to maximum practical resonance, we can solve the given equation for steady-state response by setting the input force equal to the damping force.

The given equation represents a damped mass-spring system with an oscillating force. The equation of motion for this system can be written as:0.72x'' + 1.54x' + 8.7x = 3.3cos(wt)

To determine the angular frequency w that leads to maximum practical resonance, we need to find the value of w that results in the maximum amplitude of the steady-state response.

The steady-state solution for this equation can be expressed as:

x(t) = X*cos(wt - φ)

where X is the amplitude and φ is the phase angle.

To find the maximum displacement (maximum amplitude), we can take the derivative of the steady-state solution with respect to time and set it equal to zero:

dx(t)/dt = -Xwsin(wt - φ) = 0

This condition implies that sin(wt - φ) = 0, which means wt - φ must be an integer multiple of π.

Since we are interested in finding the maximum practical resonance, we want the amplitude to be as large as possible. This occurs when the angular frequency w is equal to the natural frequency of the system.

The natural frequency of the system can be calculated using the formula:

ωn = sqrt(k/m)where k is the spring constant and m is the mass.

Given that the mass is 0.7 kg and the spring constant is 8.7 N/m, we can calculate the natural frequency:

ωn = sqrt(8.7 / 0.7) ≈ 3.156 rad/s

Therefore, the positive angular frequency w that leads to maximum practical resonance is approximately 3.156 rad/s.

To calculate the maximum displacement (maximum amplitude) of the mass at practical resonance, we need to find the amplitude X. Given the steady-state equation: x(t) = X*cos(wt - φ)

We know that at practical resonance, the input force is equal to the damping force:3.3cos(wt) = 1.54x' + 8.7x

By solving this equation for the amplitude X, we can find the maximum displacement: X = (3.3 / sqrt((8.7 - w^2)^2 + (1.54 * w)^2))

Plugging in the value of w = 3.156 rad/s, we can calculate the maximum displacement.

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The maximum displacement is:x_max = 0.695 cos(-0.298) = 0.646 m (approx)

The steady-state solution for the given damped mass-spring system is of the form:

x(t) = A cos(wt - phi)

where A is the amplitude of oscillation, w is the angular frequency, and phi is the phase angle.

To find the angular frequency that leads to maximum practical resonance, we need to find the value of w that makes the amplitude A as large as possible. The amplitude A is given by:

A = F0 / sqrt((k - mw^2)^2 + (cw)^2)

where F0 is the amplitude of the oscillating force, k is the spring constant, m is the mass, and c is the damping coefficient.

To maximize A, we need to minimize the denominator of the above expression. We can write the denominator as:

(k - mw^2)^2 + (cw)^2 = k^2 - 2kmw^2 + m^2w^4 + c^2w^2

Taking the derivative of the above expression with respect to w and setting it to zero, we get:

-4kmw + 2m^2w^3 + 2cw = 0

Simplifying and solving for w, we get:

w = sqrt(k/m) / sqrt(2) = sqrt(8.7/0.7) / sqrt(2) = 3.16 rad/s (approx)

This is the value of w that leads to maximum practical resonance.

To find the steady-state solution at practical resonance, we can substitute w = 3.16 rad/s into the equation of motion:

0.7x'' + 1.54x' + 8.7x = 3.3 cos(3.16t)

The steady-state solution is of the form:

x(t) = A cos(3.16t - phi)

where A and phi can be determined by matching coefficients with the right-hand side of the above equation. We can write:

x(t) = Acos(3.16t - phi) = Re[Ae^(i(3.16t - phi))]

where Re denotes the real part of a complex number. The amplitude A can be found from:

A = F0 / sqrt((k - mw^2)^2 + (cw)^2) = 3.3 / sqrt((8.7 - 0.7(3.16)^2)^2 + (1.54(3.16))^2) = 0.695

The maximum displacement occurs when cos(3.16t - phi) = 1, which happens at t = 0. Therefore, the maximum displacement is:

x_max = A cos(-phi) = 0.695 cos(-phi)

The phase angle phi can be found from:

tan(phi) = cw / (k - mw^2) = 1.54 / (8.7 - 0.7(3.16)^2) = 0.308

phi = atan(0.308) = 0.298 rad

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The average score of all students, calculated by taking a weighted average based on the number of students in each group, is 38. The overall performance is slightly below the group averages.

The average score of students in the first, second, and third groups are 39, 32, and 43, respectively. There are 24 students in the first group, 26 students in the second group, and 27 students in the third group.

To find the average score of all students, we need to take a weighted average of the scores in each group, with the number of students in each group as the weights.

Here's how to do it: First, we calculate the total number of students:24 + 26 + 27 = 77. Then, we calculate the total score across all students: 39*24 + 32*26 + 43*27 = 936 + 832 + 1161 = 2929

Finally, we divide the total score by the total number of students to get the average score:2929/77 = 38. The average score of all students is 38.

This means that the overall performance of all the students is slightly below the average of the scores in each group.

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If x < y, then all of the following are true except - x < -y.

What is inequality?

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

A statement that demonstrates the connection between two (or more) phrases containing one of the following five signs:,, >,, is known as an inequality. An inequality can be true or untrue, just like an equation. The statement "34 - 12 > 5 + 2" is accurate. A false statement is made when 1 + 3 6 - 2.

The value remains the same after addition, multiplication, and division.

However, if you reverse the sign, the inequality direction in this instance will be >; otherwise, that is not true.

For example,

2 < 3

-2 < -3 is not true.

Because -2 is greater than -3.

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Answer:

6/3

Step-by-step explanation:

I think bhjukjkfiffo

Answer:

-5/3

Step-by-step explanation:

rise/run you go down 5 and over 3

The correct option that represents the electric field is:

Option D: E = 4πε₀Q(x² + y² + z²)^(3/2)x^ + y^ + z^

The electric field is given by the formula:

E = -∇V

where:

∇ is the del operator, which in Cartesian coordinates is represented as:

∇ = (∂/∂x)x^ + (∂/∂y)y^ + (∂/∂z)z^

Taking the negative gradient of V gives us:

E = -∇V = -[(∂V/∂x)x^ + (∂V/∂y)y^ + (∂V/∂z)z^]

First, let's calculate the partial derivatives of V with respect to x, y, and z:

(∂V/∂x) = (∂/∂x)[4πε₀(Q/√(x² + y² + z²))]

= -4πε₀(Qx/√(x² + y² + z²)³)

(∂V/∂y) = (∂/∂y) [4πε₀(Q/√(x² + y² + z²))]

= -4πε₀(Qy/√(x² + y² + z²)³)

(∂V/∂z) = (∂/∂z) [4πε₀(Q/√(x² + y² + z²))]

= -4πε₀(Qz/√(x² + y² + z²)³)

Now, substituting these derivatives into the expression for E:

E = -[(-4πε₀(Qx/√(x² + y² + z²)³))x^ + (-4πε₀(Qy/√(x² + y² + z²)³))y^ + (-4πε₀(Qz/√(x² + y² + z²)³))z^]

Simplifying, we have:

E = 4πε₀Q(x/√(x² + y² + z²)³)x^ + 4πε₀Q(y/√(x² + y² + z²)³)y^ + 4πε₀Q(z/√(x² + y² + z²)³) z^

Therefore, the correct option is:

(d) E = 4πε₀Q(x² + y² + z²)^(3/2)x^ + y^ + z^

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Jeff does not have any money left.

Jeff originally had $20. He spent 18 1/8 of his money on lunch and 25 2/5 of his money at the movies. To find out how much money Jeff has left, we need to subtract the amount he spent from the original amount.

First, we need to convert the fractions to decimals so we can easily subtract them from the original amount. 18 1/8 = 18.125 25 2/5 = 25.4

Now we can subtract these amounts from the original amount: $20 - $18.125 - $25.4 = -$23.525

Since Jeff cannot have a negative amount of money, this means that he does not have enough money to cover the cost of both lunch and the movies. Therefore, Jeff does not have any money left.

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Option D (9) is not a probability and is not a possible answer choice for a probability question.

To find the probability of the intersection of events A and B (denoted as P(A ∩ B)), we need to know how many elements are in both A and B. Since there are 2 repeated elements between the events, this means that there are a total of 7 - 2 = 5 distinct elements between them.

Therefore, P(A ∩ B) = 5/7.

Note that none of the answer choices provided match this result exactly. Option A is the closest with a probability of 4/7, but this is the probability of A alone, not the intersection of A and B. Option B (2/7) is the probability of B alone and option C (5/7) is the probability of either A or B occurring, not the intersection.

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Given information: The marginal profit of a certain commodity is

P(q)=100−2q

when q units are produced. When 10 units are produced, the profit is $700.

To find: Profit function P(q)Formula used:

Profit = Total Revenue - Total Cost

Total Revenue = Selling Price x Quantity.

Total Cost = Fixed Cost + Variable Cost

x Quantity Profit function can be defined as the difference between total revenue and total cost. Since we have the marginal profit function

P(q) = 100 - 2q,

we can find the total profit function by integrating this marginal profit function.

So,

∫P(q)dq = ∫(100 - 2q)dq=100q - q²/2 + C

Where C is the constant of integration.

To find the constant of integration, we can use the given information that when 10 units are produced, the profit is $700. Therefore, using the profit formula,

Profit = Total Revenue - Total Cost700 = SP - TC

We are not given the selling price and fixed cost, but we can find the variable cost using the marginal profit function.

When q = 10, P(q) = 100 - 2(10) = 80Therefore, the variable cost of producing

10 units = 700/80 = $8.75

Now, we can use the variable cost and marginal profit function to find the fixed cost.

Fixed Cost + Variable Cost

x 10 = 1000-8.75 x 10 = 1000 - 87.5 = $912.5

Now we can substitute the value of C in the total profit function obtained above.

100q - q²/2 + 912.5 = P(q)

the profit function

P(q) is given by:

P(q) = 100q - q²/2 + 912.5

Thus, the required answer is more than 100 words.

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Answer:

  see attached

Step-by-step explanation:

You want a graph of the function F(x) = 2x² -5.

A graphing calculator can help a lot when you want the graph of a function. This one is an x² function with a vertical translation of -5 and a vertical stretch by a factor of 2.

It is often useful to consider points ±1 or ±2 either side of the vertex, and the vertex itself.

The graph is attached.

The recursive rule for the number of acres at the beginning of the nth day in a forest fire that grows by 20% each day and is battled by firefighters who can put out 15 acres per day is given by: A(n) = 1.2 * A(n-1) - 15, where A(n) represents the number of acres at the beginning of the nth day. Using this rule, we can calculate that there are 89.6 acres burning at the beginning of the 8th day.

Explanation: To determine the recursive rule for the number of acres at the beginning of the nth day, we need to consider the given information. The forest fire initially covers 60 acres and grows by 20% each day. This means that the number of acres at the beginning of the next day (n+1) is 1.2 times the number of acres at the beginning of the current day (n). However, the firefighters are able to put out 15 acres of fire per day.

Therefore, to calculate A(n), we start with the initial number of acres, which is 60, and apply the recursive rule. A(n) = 1.2 * A(n-1) - 15. This formula takes into account the growth of the fire by 20% and the reduction of 15 acres due to the firefighters' efforts. By substituting the values, we can calculate the number of acres at the beginning of each day.

To find the number of acres burning at the 8th day, we substitute n = 8 into the recursive rule. A(8) = 1.2 * A(7) - 15. We need to determine A(7) first by substituting n = 7, and so on, until we reach the initial value A(1) = 60. Once we have calculated A(8), we can determine that there are 89.6 acres burning at the beginning of the 8th day

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Under the given translation, the point B(2, 4) is translated to B'(-2, 1), and the point C(1, -4) is translated to C'(-3, -7).

To find the coordinates of B' and C' after the translation, we need to determine the change in x and y coordinates for each point.
For point B, the x-coordinate changes by -2 and the y-coordinate changes by -3. Therefore, the coordinates of B' are (-2 + 2, 4 + (-3)), which simplifies to (-2, 1).
Similarly, for point C, the x-coordinate changes by -2  and the y-coordinate changes by -3. Thus, the coordinates of C' are (1 + (-2), -4 + (-3)), which simplifies to (-3, -7).
In conclusion, the coordinates of B' are (-2, 1) and the coordinates of C' are (-3, -7) under the given translation.

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Computation of the cross product (a ⨯ b) of the given vectors a = i - 9j + k and b = 8i + j + k, gives -10i + 7j + 73k.

To compute the cross product (a ⨯ b) of the given vectors a = i - 9j + k and b = 8i + j + k, follow these steps:
1. Write the cross product formula:
a ⨯ b = (\(a_{2}b_{3} -a_{3} b_{2}\))i - (\(a_{1} b_{3}- a_{3} b_{1}\))j + (\(a_{1} b_{2}- a_{2} b_{1}\))k
2. Plug in the values from the given vectors:
a ⨯ b = ((-9)(1) - (1)(1))i - ((1)(1) - (1)(8))j + ((1)(1) - (-9)(8))k
3. Simplify:
a ⨯ b = (-9 - 1)i - (1 - 8)j + (1 + 72)k
a ⨯ b = -10i + 7j + 73k
So, the cross product of the given vectors is -10i + 7j + 73k.

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Answer:

No solution

Step-by-step explanation:

The given lines on the graph are parallel . So they will never intersect each other. Therefore they have no solution.

Answer:

184in

Step-by-step explanation:

Since the scale for the statue is 3 inches to 100 feet, we can say 3:100 as a ratio.

To find approximately 305 feet you must divide 305 by 100.

100 can go into 300 evenly 3 times. Since the ratio is 3:100 you should multiply how many times the 100ft fit into the 300ft and the 3in (3 x 3) which is about 9in.

One way we can do this is to divide the hight of the Statue by the model height:

305ft 20in = 15.25ft 1in or 184in (12in per foot).

And so for every inch of the model, it represents 15.25 feet.

For 305 it would be

Answer:

If I'm not mistaking, they want you to find the number in the middle that's between X and Z.

That number would be 3.

Hope this helps a bit! :)

Answer:

y would be at 3

Step-by-step explanation:

I hope this helps!

Step-by-step explanation:

First you subtract five on both sides. Now we're left with C=6

If  a deadly disease infected the hummingbird population, what would most likely happen to the plants option (b) They would become endangered

If a deadly disease infected the hummingbird population, it would most likely lead to a decrease in the pollination of plants that rely on hummingbirds for pollination. Without the hummingbirds to transfer pollen between flowers, these plants would have a reduced rate of successful pollination, which would result in a decrease in their ability to reproduce.

However, it is unlikely that the plants would die within hours or become endangered immediately, nor would they need to migrate. The effect of the loss of hummingbird pollinators on the plants would depend on the specific plant species, their pollination requirements, and the availability of alternative pollinators. Some plants may be more adaptable to using alternative pollinators, while others may suffer more severe consequences. It is also possible that the loss of hummingbirds could lead to a decline in the populations of other animals that depend on the plants, creating a ripple effect in the ecosystem.

Therefore, the correct option is (d) They would become endangered

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Answer:

-29

Step-by-step explanation:

-3(10)+1

-30+1

-29

Answer:

The cost price was $48

Step-by-step explanation:

60-20%=48

hope it helps :)

Answer:

50

Step-by-step explanation:

60-x*100=20

6000-100x=20x

6000=20x+100x

6000= 120x

x= 6000/120

x= 50

The general solution of the system is given by x(t) = c_1 * v_1 * e^(λ_1 * t) + c_2 * v_2 * e^(λ_2 * t), where c_1 and c_2 are constants. Thus, the general solution of the given system is x(t) = c_1 * (6 1) * e^(12.32 * t) + c_2 * (-2 3) * e^(-2.32 * t).

The given system can be represented as x' = Ax, where A is the coefficient matrix (-1 -6 6 11). To find the eigenvalues and eigenvectors, we solve the characteristic equation det(A - λI) = 0, where I is the identity matrix.

Setting up the characteristic equation, we have:

det((-1-λ) -6; 6 (11-λ)) = 0,

(λ+1)(λ-11) - 36 = 0,

λ^2 - 10λ - 47 = 0.

Solving this quadratic equation, we find the eigenvalues λ_1 ≈ 12.32 and λ_2 ≈ -2.32.

Next, we find the corresponding eigenvectors by solving (A - λI)v = 0 for each eigenvalue. For λ_1 ≈ 12.32, we get the eigenvector v_1 = (6 1). For λ_2 ≈ -2.32, we get the eigenvector v_2 = (-2 3).

The general solution of the system is given by x(t) = c_1 * v_1 * e^(λ_1 * t) + c_2 * v_2 * e^(λ_2 * t), where c_1 and c_2 are constants. Thus, the general solution of the given system is x(t) = c_1 * (6 1) * e^(12.32 * t) + c_2 * (-2 3) * e^(-2.32 * t).

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Answer:

For $10.50, you can buy 1 pound of shrimp

Step-by-step explanation:

We know that "c" is the total cost and "p" is the number of pounds of shrimp. The number 10.50 is considered to rate for every pound of shrimp because, if we replace "p" with 1 pound, we will get the answer of $10.50. Thus, it costs $10.50 for every pound of shrimp.

Answer:

48

Step-by-step explanation:

if its not right sorry

Answer:

Rs. 924000.

Step-by-step explanation:

Cost of  house = 765000

Additional money spent on it = 115000

Total cost incurred by Ravi = 765000 + 115000 = 880000

Gain  = 5% of total cost

gain in Rs = 5/100 * 880000 = Rs. 44000

Total selling price of house = total cost incurred + profit = 880000+ 44000

Total selling price of house = Rs. 924000

Thus, Ravi got  Rs. 924000.

Answer:

It should be C. AAS

Step-by-step explanation:

There are symbols on the triangle indicating a shared right triangle, congruent angles, and a shared congruent side.

Hope this helps :)

Answer:

Yes, AAS

Step-by-step explanation:

Answer: $2400

Step-by-step explanation:

Given

Interest earned is $450

The rate of interest is R=7.5%

Time period T=2.5 years

Simple Interest is given by

\(S.I.=\dfrac{P\times R\timesT}{100}\quad [\text{P=Principal}]\)

Substitute values

\(450=\dfrac{P\times 7.5\times2.5}{100}\\\\P=\dfrac{450\times 100}{7.5\times 2.5}=\$2400\)