Which of the following is a solution of (x - 5)(x + 7) = 3x + 21
0
45
8
5

The best-case space complexity of A* search is O(bd), where b is the branching factor and d is the maximum depth of the search tree.

A* search is a popular algorithm for finding the shortest path in a graph or tree.

The space complexity of A* search refers to the amount of memory required by the algorithm to perform the search. In the best-case scenario, A* search only expands nodes that are on the optimal path and never expands any redundant nodes.

In this scenario, the maximum amount of memory required by the algorithm is proportional to the maximum depth of the tree, d, and the branching factor, b, which is the average number of children per node in the tree. Thus, the best-case space complexity of A* search is O(bd).

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Answer:

i think it might be number 1

Step-by-step explanation:

Answer:

51

Step-by-step explanation:

2*5=10

3*10=30

11*1=11

10+30+11

51

Answer:

She has $51

Step-by-step explanation:

You would do 10*3 = 30 since she has 3 tens. Then you would do 5*2 = 10 since she has 2 fives. And then you would do 11*1 = 11 since she has 11 ones. Then after you do that you would add all of them together so you would do 30+10+11 = $51

Answer:

2 = x (by the symmetric property) and x = y, so y = 2 by the transitive property.

Answer:

It would be the last one

Step-by-step explanation:

The required area of the triangle ABC is 67.30.

Given that,
AB = 14 ft, BC = 10 ft, and ∠ABC = 74
The area of triangle ABC to the nearest tenth is to be determined.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.

Here,
AB = 14 ft, BC = 10 ft, and ∠ABC = 74
The area of triangle ABC to the nearest tenth,
Area of the triangle = 1/2 bc sin75
                              = 1 / 2 * 14 * 10 * sin 75
                              = 67.3

Thus, the required area of the triangle ABC is 67.3.

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The probability of all 3 selected were rated excellent is 1/114 and the probability of one from each category was selected, is 7/114.

In the given question,

In a certain department, 5 employees received excellent ratings, 14 received good ratings, and 1 received a marginal rating.

So total number of employees = 5+14+1 = 20

If 3 employees in this department are randomly selected to complete a form for an internal study of the firm, then we have to find the probability that the following occurs.

The following occurs given below:

(a) We have to find the probability of all 3 selected were rated excellent.

5 employees who got excellent rating. So the selection of 3 employees from 5 employees who got excellent rating is:

selection of 3 employees from 5 employees = \(^5C_{3}\)

Using, \(^nC_{r}=\frac{n!}{r!(n-r)!}\)

selection of 3 employees from 5 employees = \(\frac{5!}{3!(5-3)!}\)

selection of 3 employees from 5 employees = \(\frac{5!}{3!2!}\)

selection of 3 employees from 5 employees = \(\frac{5\times4\times3!}{3!\times2\times1}\)

selection of 3 employees from 5 employees = 5×2

selection of 3 employees from 5 employees = 10

Selection of 3 employees from 20 employees= \(^{20}C_{3}\) = 1140

Probability of 3 employees who got excellent rating

P(E) = 10/1140

P(E) = 1/114

(b) We have to find the probability of one from each category was selected.

One candidate selected from excellent category = \(^5C_{1}\) = 5

One candidate selected from marginal category = \(^1C_{1}\) = 1

One candidate selected from good category = \(^{14}C_{1}\) = 14

Selection of 3 employees from 20 employees= \(^{20}C_{3}\) = 1140

The probabilty of one from each category = (5*1*14)/1140

The probabilty of one from each category = 70/1140

The probabilty of one from each category = 7/117

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Answer:

D

Step-by-step explanation:

First, we know that we're trying to disprove the following statement. Two interesting lines that form two pairs of vertical angles, one is acute and one is obtuse.

Now let's go through the answer choices.

A: The lines are parallel and not intersecting, so this does not work.

B: The lines are intersecting, but we can clearly see one set of acute angles and one set of obtuse

C: These look like right angles but we don't know for sure.They could be 89 and 91 Is there a better choice?

D: These are clearly right angles. Which are nto acute and obtuse. This is the right angles

Answer:

The main cause of deforestation is agriculture (poorly planned infrastructure is emerging as a big threat too) and the main cause of forest degradation is illegal logging. In 2019, the tropics lost close to 30 soccer fields' worth of trees every single minute

Answer: The answer to this question is 163.123

Answer:

A I think this will help

Step-by-step explanation:

I just take the test 5 days ago

The ratio of the volume of the cone to the volume of the cylinder is 1:2, or 1/2, meaning the volume of the cone is one-half of the volume of the cylinder. This is because the cone and the cylinder have the same height and base.

The formula for the volume of a cylinder is \(V = \pi r^2h,\) where V is the volume, r is the radius, and h is the height.

Let's assume that the cone and cylinder have a radius of 'r' and a height of 'h'.

The volume of the cylinder is given by \(= \pi r^2h.\)

The volume of the cone is given by V_cone = \((1/3)\pi r^2h.\)

Since the cone and cylinder have the same base and height, their radius and height are the same.

Therefore, we can simplify the volumes as V_cylinder = \(\pi r^2h\) and V_cone = \((1/3)\pi r^2h.\)

The ratio of the volume of the cone to the volume of the cylinder is then:

V_cone/V_cylinder = \(((1/3)\pi r^2h) / (\pi r^2h) = (1/3) / 1 = 1/3\)

So, the volume of the cone is one-third of the volume of the cylinder.

Alternatively, we can write this as the ratio of the volume of the cone to the volume of the cylinder being 1:2, since the volume of the cylinder is twice the volume of the cone.

Therefore,The ratio of the volume of the cone to the volume of the cylinder is 1:2, or 1/2, meaning the volume of the cone is one-half of the volume of the cylinder. This is because the cone and the cylinder have the same height and base.

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To calculate the amplitude of the electric field in the LIGO beam, we divide the power of 100 kW by the area of a square centimeter.

(a) The amplitude of the electric field in the LIGO beam can be calculated using the formula:

Amplitude of electric field = √(Power / Area)

Converting the power of 100 kW to 100,000 W and the area of a square centimeter to square meters:

Amplitude of electric field = √(100,000 / 0.0001) = √(10^9) = 10^4 V/m

Therefore, the amplitude of the electric field in the LIGO beam is 10,000 V/m.

(b) The phase shift caused by a gravitational wave temporarily lengthening one arm by 10^-18 m can be estimated using the formula:

Phase shift = (2π * d) / λ

Where d is the change in arm length and λ is the wavelength of the laser. In this case, the effective arm length is 1120 km, which is equivalent to 1.12 x 10^6 m, and the laser wavelength is 1064 nm, or\(1.064 x 10^-6 m.\)

Phase shift =\((2π * 10^-18) / (1.064 x 10^-6) = 2π * 10^-12 radians\)

Therefore, the estimated phase shift caused by the gravitational wave is approximately\(6.28 x 10^-12\) radians.

(c) Using Eq. (35.7), the sensitivity of the photodetector can be estimated by relating the minimal electric field strength required to detect a gravitational wave to the phase shift:

Minimal electric field strength = (λ * Amplitude of electric field) / (4π * d)

Substituting the values obtained:

Minimal electric field strength = \((1.064 x 10^-6 * 10^4) / (4π * 10^-12)\)

Simplifying the equation:

Minimal electric field strength = 8.49 x \(10^7\) V/m

Therefore, the estimated sensitivity of the photodetector is approximately 8.49 x \(10^7\) V/m, indicating the minimal electric field strength needed to detect a gravitational wave.

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The differential equation for the total volume of alcohol in the tank is dV/dt = (0.9 - V/200) * 0.1, and the time it takes to reach 20% alcohol concentration is found by solving the equation V(t) = 40.

To find the differential equation for the total volume of alcohol in the tank, we start by noting that the rate of change of alcohol volume is equal to the rate at which vodka is pumped in minus the rate at which the mixture is drained.

The rate at which vodka is pumped in is\(0.1 m^3\) per second, and since the fluid is thoroughly mixed, the concentration of alcohol is V(t)/200, where V(t) is the volume of alcohol in the tank at time t. The rate at which the mixture is drained is also\(0.1 m^3\)per second. Therefore, the differential equation can be written as dV/dt = 0.1 - 0.1V/200.

To find the time it takes for the alcohol concentration to reach 20%, we solve the differential equation from part (a) with the initial condition V(0) = 0. The solution to the differential equation is V(t) = 20 - 20e^(-t/200), where t is the time in seconds. Setting V(t) = 40, we can solve for t to find the time it takes to reach 20% alcohol concentration after pumping has started.

To completely solve the differential equation ray" - 2xy + 2y = x^2, we can use the method of variation of parameters. The general solution is y(x) = C1y1(x) + C2y2(x) + y3(x), where y1(x) and y2(x) are linearly independent solutions of the homogeneous equation ray" - 2xy + 2y = 0, and y3(x) is a particular solution of the non-homogeneous equation.

The solution can be expressed in terms of the Airy functions.

To find a second order homogeneous linear differential equation with the general solution Atan(x) + Bx, we differentiate the given solution twice and substitute it into the standard form of the differential equation, obtaining a quadratic equation in the coefficients A and B. Solving this equation gives the desired homogeneous equation.

The minimum value of the damping constant can be found by considering the critical damping condition, where the mass neither oscillates nor overshoots after hitting a bump. The damping constant is given by c = 2√(km), where k is the spring constant and m is the mass. Plugging in the given values, we can calculate the minimum damping constant.

If the shocks are worn and have 90% of the damping constant from part (a), the resulting motion of the car after being compressed and released can be described by a damped oscillation equation.

The motion can be analyzed using the equation mx'' + cx' + kx = 0, where m is the mass, c is the damping constant, and k is the spring constant. The solution will depend on the specific values of m, c, and k.

The Laplace transform of the given differential equation can be found using the properties of the Laplace transform. Solving the resulting algebraic equation for the Laplace transform of u(t), and then taking the inverse Laplace transform, will give the solution for u(t) in terms of the given input function sin(t-θ) and initial conditions u(0) and u'(0).

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1. The elasticity of demand= -38.46%, 2. percentage change in price= 292.86% The elasticity of demand is 0.1319.

The elasticity of demand measures the responsiveness of the quantity demanded to changes in price. In this case, the demand is relatively inelastic because the elasticity of demand is less than 1. This means that a change in price will result in a proportionately smaller change in quantity demanded.

To calculate the elasticity of demand, we can use the formula:
Elasticity of Demand = (Percentage Change in Quantity Demanded) / (Percentage Change in Price)
First, let's find the percentage change in quantity demanded:
Change in Quantity Demanded = 8 - 13 = -5
Percentage Change in Quantity Demanded = (Change in Quantity Demanded / Initial Quantity Demanded) * 100
                               = (-5 / 13) * 100
                               = -38.46%

Next, let's find the percentage change in price:
Change in Price = $5.50 - $1.40 = $4.10
Percentage Change in Price = (Change in Price / Initial Price) * 100
                        = ($4.10 / $1.40) * 100
                        = 292.86%
Now, we can calculate the elasticity of demand:
Elasticity of Demand = (Percentage Change in Quantity Demanded) / (Percentage Change in Price)
                   = (-38.46% / 292.86%)
                   = -0.1319
Ignoring the negative sign, the elasticity of demand is 0.1319.

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Solving for v in the given equation is performed by making v the equation's

subject.

The statement that describes where the error was made is option;

v can be solved for from the  given expression as follows;

\(\displaystyle k = \mathbf{\frac{1}{2} \cdot m \cdot v^2}\)

\(\displaystyle k \div m = \mathbf{\left(\frac{1}{2} \cdot m \cdot v^2 \right) \div m}\)

\(\displaystyle \frac{k}{m} \times 2 = \left( \frac{1}{2} \cdot v^2 \right) \times 2\)

\(\displaystyle \frac{2 \cdot k}{m}= \mathbf{v^2}\)

Taking the square root of both sides of the equation gives;

\(\pm \sqrt{\displaystyle \frac{2 \cdot k}{m}} = \mathbf{\sqrt{v^2}}\)

Therefore;

\(\displaystyle \pm \sqrt{\frac{2 \cdot k}{m} } = v\)

Therefore, the error was made in the step, \(\displaystyle \pm \frac{2 \cdot \sqrt{k} }{m} = \sqrt{v^2}\) , which is by

applying the square root property was applied to only some of the

variables on the left hand side of the equation, rather than the combined

expression on the left hand side of the equation.

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Answer:

The square root property should have been applied to both complete sides of the equation instead of to select variables.

or D

Step-by-step explanation:

I found the answer and just gave it to u straight up and I got it correct

Step-by-step explanation:

3 x p        three times p

 + 21        plus twent -one

    = 42          is forty two

3p + 21 = 42

The integral evaluates to 0 because I = sin(2t) v - 2[v cos(2t)] dt = sin(2t) v - 2(1/2)v sin(2t) = sin(2t) v - v sin(2t) = 0. For all x values, this indicates that the CDF of X is zero.

Integrating the probability density function (PDF) of a random variable X over the interval (-, x) is necessary in order to determine the cumulative distribution function (CDF).

We have the integral in this instance:

We can integrate this expression with respect to x to find the CDF; however, it is essential to note that you have used both t and x as variables in the expression. I = [0, x] sin(2t) (cos t)3 e(-t) dt To be clear, I will make the assumption that the proper expression is:

Now, let's evaluate this integral: I = [0, x] sin(2t) (cos t)3 e(-t) dt

We can use integration by parts to continue with the integration. I = [0, x] sin(2t) (cos t)3 e(-t) dt Let's clarify:

Using integration by parts, we have: u = sin(2t) => du = 2cos(2t) dt dv = (cos t)3 e(-t) dt => v = (cos t)3 e(-t) dt

I = [sin(2t) ∫(cos t)³ e^(- αt) dt] - ∫[∫(cos t)³ e^(- αt) dt] 2cos(2t) dt

= sin(2t) v - 2∫[v cos(2t)] dt

Presently, we should assess the leftover fundamental:

[v cos(2t)] dt Once more employing integration by parts, we have:

Substituting back into the integral: u = v, du = dv, dv = cos(2t), dt = (1/2)sin(2t), and so on.

[v cos(2t)] dt = (1/2)v sin(2t) When we incorporate this result into the original expression for I, we obtain:

The integral evaluates to 0 because I = sin(2t) v - 2[v cos(2t)] dt = sin(2t) v - 2(1/2)v sin(2t) = sin(2t) v - v sin(2t) = 0. For all x values, this indicates that the CDF of X is zero.

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The given statement "harold laswell constructed a(n) linear model of communication." is true because Harold Laswell constructed a linear model of communication.

The model suggests that the sender encodes a message, which is then transmitted through a channel to the receiver, who decodes the message.

The model emphasizes the importance of the message, the channel, and the audience, and it assumes that the communication process is successful if the message is accurately received and understood by the receiver.

The linear model of communication is considered one of the earliest and simplest models of communication. While it has been criticized for oversimplifying the communication process and ignoring the role of feedback and context, it remains a useful framework for understanding basic communication processes.

Many other communication models have been developed since then, including more complex models that incorporate feedback, noise, and other factors.

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Based on the information given in the question, it is not clear whether the city locations are sampled uniformly at random from all the locations in the U.S. In order for a sampling method to be considered uniformly random, each possible location would have an equal chance of being chosen. Without additional information about how the locations were chosen, it is difficult to determine if the sample is truly random and uniform.

The function’s equation written in factored form and in vertex form are respectively;

f(x) = 2x(x - 4)

f(x) = 2(x - 2)² - 8

The factored form of a quadratic function is;

f(x) = a(x - p)(x - q)

where:

p and q are the x-intercepts

a is a constant

Now, we are given x-intercepts as; (0, 0) and (4, 0)

Thus;

f(x) = a(x - 0)(x - 4)

f(x) = ax(x - 4)

To find a, substitute the given vertex (2, -8) into the equation and solve for a:

2a(2 - 4) = -8

-4a = -8

a = 2

Thus;

f(x) = 2x(x - 4)

The vertex form of a quadratic equation is;

f(x) = a(x - h)² + k

where:

(h, k) is the vertex

a is constant

Since vertex is (2, -8), then we have;

f(x) = a(x - 2)² - 8

Put the coordinate (0, 0) to find a;

0 = a(0 - 2)² - 8

4a = 8

a = 2

Thus;

f(x) = 2(x - 2)² - 8

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The random variable X represents the number of rooms in a randomly chosen owner-occupied housing unit in a certain city. The distribution for the units is given with the respective probabilities.

The provided distribution shows the probabilities associated with specific values of X. However, the probabilities for the values 8, 9, and 10 are missing. In order to fully describe the probability distribution, the probabilities for all possible values of X should be provided.

The random variable X represents the number of rooms in the housing units, and each value of X has an associated probability. For example, the probability of X=3 is 0.06, the probability of X=6 is 0.26, and the probability of X=7 is 0.4. These probabilities indicate the likelihood of encountering housing units with a specific number of rooms.

To fully analyze the probability distribution, the missing probabilities for the values 8, 9, and 10 need to be provided. Once all the probabilities are known, one can calculate various statistical measures such as the expected value (mean), variance, and standard deviation to gain a better understanding of the distribution and the number of rooms in the owner-occupied housing units in the city.

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Answer:

738%

Step-by-step explanation:

The length of the propoi tunnel is determined to be equal to 9945.9066 square feet using the cosine rules.

The cosines rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Using the cosine rule:

AB² = AC² + BC² - 2(AC)(BC)cosC

AB² = (4500ft)² + (6800ft)² - 2(4500)(6800)cos122°

AB² = 66,490,000ft² - 61,200,000ft²cos122°

AB² = 66,490,000ft² + 32,431,058.9712ft²

AB² = 98,921,058.9712ft²

AB = √(98,921,058.9712ft²) {take square root of both sides}

AB = 9945.9066ft

Therefore, the length of the proposed tunnel is determined to be equal to 9945.9066 square feet using the cosine rules.

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3 (hight) × 8 (base) = 24

24 ÷ 2 = 12 (area of triangle)

12 × 2 = 24 (because there are 2 triangles)

5 × 7 = 35 (because length times width)

35 × 2 = 70 (because there are 2 rectangles)

8 × 7 = 56 (because of the base)

24 + 12 + 24 + 35 + 70 + 56 = 221

The probability that a flight between New York City and Chicago is less than 135 minutes is 0.6667, or approximately 0.67. This means there is a 67% chance that a randomly selected flight will take less than 135 minutes.

In the given problem, we are told that the time to fly between the two cities follows a uniform distribution, with a minimum of 120 minutes and a maximum of 150 minutes. In a uniform distribution, the probability of an event within a certain range is proportional to the length of that range. Therefore, to find the probability of a flight being less than 135 minutes, we need to calculate the length of the range from 120 to 135 minutes and divide it by the length of the entire distribution, which is 150 - 120 = 30 minutes.

The length of the range from 120 to 135 minutes is 135 - 120 = 15 minutes. Dividing this by the length of the entire distribution gives us 15/30 = 0.5, or 50%. However, since the distribution is continuous and the probability of exactly 135 minutes is zero (as the distribution is uniform), the probability of a flight being less than 135 minutes is slightly greater than 0.5. Thus, the correct answer is approximately 0.67.

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Answer:

Step-by-step explanation:

it is 2x