I
- Marissa is trying to lose some weight. So far she has lost 13 pounds. Her goal is
to lose 51 pounds. She is on a calorie counting plan that will allow her to lose
2 pounds a week. What is the minimum number of weeks she must follow her
plan before she hits her goal?

a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

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The standard normal distribution has a mean of 0 and a standard deviation of 1. M ≈ 30.935. The median of the distribution is also 25.

(a) To find M, we first need to convert the given values of mean and standard deviation to the standard normal distribution. This can be done by using the formula Z = (X - μ) / σ, where Z is the Z-score, X is the value of interest, μ is the mean, and σ is the standard deviation. In this case, we have X ~ N(25, 9). Substituting the values into the formula, we get Z = (X - 25) / 3. Now we need to find the Z-score that corresponds to the desired probability of 0.95. Using a standard normal distribution table or a calculator, we find that the Z-score corresponding to a cumulative probability of 0.95 is approximately 1.645. Setting Z equal to 1.645, we can solve for X: (X - 25) / 3 = 1.645. Solving for X, we get X ≈ 30.935. Therefore, M ≈ 30.935.

(b) The median is the value that divides the distribution into two equal halves. In a normal distribution, the median is equal to the mean. In this case, the mean is given as 25. Therefore, the median of the distribution is also 25.

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Answer: It is 4 Yards, 1 Foot, and 2 Inches.

Step-by-step explanation: You have to add 3 feet 7 inches, 2 feet 11 inches, and 6 feet 8 inches togather.

Answer:

To determine whether the given triangle is a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's label the sides of the triangle as follows:

side a = 40 inches

side b = 75 inches

side c = 85 inches (the longest side)

Now we can apply the Pythagorean theorem:

c^2 = a^2 + b^2

85^2 = 40^2 + 75^2

7225 = 1600 + 5625

7225 = 7225

Since the equation is true, we can conclude that the given triangle is a right triangle.

Answer: yes

Step-by-step explanation:

To test if this is a right triangle, let's test these side lengths with the Pythagorean Theorem.

a^2 + b^2 = c^2

c is the hypotenuse, the longest side of a right triangle.

a and b are the legs of the right triangle.

40²+75²=85²

1600+5625=7225

7225=722

In this question, we are asked to determine the truth-values of two statements involving sets A and B. For each statement, we need to determine if it is true or false. If it is false, we need to provide specific counterexamples by choosing appropriate sets A and B.

a. (A\B) ⊆ A

The statement (A\B) ⊆ A is true for any sets A and B. This is because the set difference (A\B) contains elements that are in A but not in B. Therefore, by definition, every element in (A\B) is also an element of A. There are no counterexamples to this statement.

b. A^c ⊆ (AUB)

The statement\(A^c\) ⊆ (AUB) is true for any sets A and B. This is because the complement of A, denoted as \(A^c\), contains all elements that are not in A.

On the other hand, the union of A and B, denoted as (AUB), contains all elements that are in A or in B or in both.

Since the complement of A contains all elements not in A, it includes all elements in B that are not in A as well.

Therefore, \(A^c\) ⊆ (AUB) holds true for any sets A and B. There are no counterexamples to this statement.

In conclusion, both statements are true for any sets A and B, and there are no counterexamples.

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P₂ = (-3, 10)

The midpoint, (a, b) = (-5, 3)

The starting point, P₁ = (x₁, y₁) = (-7, 4)

Let P₂ = (x₂, y₂)

The formulae for the coordinates of the midpoint are:

To solve for x₂, substitute a = -5, x₁ = -7 into the formula

To solve for y₂, substitute b = 3, y₁ = -4 into the formula

Therefore, P₂ = (-3, 10)

The answer is "no, the normal/large sample condition is not met." In order to carry out a t-test for a difference in means, several conditions must be met.

One of the most important conditions is the normal/large sample condition, which requires that the data come from a population that is approximately normally distributed or that the sample size is large enough to apply the Central Limit Theorem. If this condition is not met, a t-test may not be appropriate, and other methods may need to be used to make inferences about the population.

Other conditions that need to be met include the random condition, which requires that the data be collected using a random sampling method, and the independence condition, which requires that the observations be independent of each other. The 10% condition may also need to be met, which requires that the sample size be no more than 10% of the population size. If all of these conditions are met, then a t-test may be appropriate for making inferences about the population means.

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The decision for this test at a .05 level of significance is not enough information to make a decision the correct answer is (d).

To make a decision for a hypothesis test, we compare the obtained test statistic (in this case, z = 1.80) with the critical value(s) based on the chosen level of significance (in this case, α = 0.05).

For a one-sample z test, if the obtained test statistic falls in the rejection region (i.e., beyond the critical value(s)), we reject the null hypothesis. Otherwise, if the obtained test statistic does not fall in the rejection region, we fail to reject the null hypothesis.

Without knowing the critical value(s) corresponding to a significance level of 0.05 and the directionality of the test (one-tailed or two-tailed), we cannot determine the decision for this test. Therefore, the correct answer is (d) There is not enough information to make a decision.

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The expected value for the given binomial distribution is approximately 0.91648.

To calculate the expected value for a binomial distribution, you need to multiply each possible value by its corresponding probability and then sum them up. Let's calculate the expected value using the provided probabilities: Successes Probability

0 1024/3125

1 256/625

2 128/625

3 32/625

4 4/625

5 1/3125

Expected Value (μ) = (0 * (1024/3125)) + (1 * (256/625)) + (2 * (128/625)) + (3 * (32/625)) + (4 * (4/625)) + (5 * (1/3125)). Expected Value (μ) = 0 + 0.4096 + 0.32768 + 0.1536 + 0.0256 + 0.00032. Expected Value (μ) = 0.91648. Therefore, the expected value for the given binomial distribution is approximately 0.91648.

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The schedule for the number of hours worked by employees at Waterloo Park is represented by the functions b(x), t(x), r(x), and s(x) for Bill, Ted, Rufus, and Socrates, respectively, on a given day x.

In the schedule, the function b(x) represents the number of hours worked by Bill on a given day x. Similarly, the function t(x) represents the number of hours worked by Ted, the function r(x) represents the number of hours worked by Rufus, and the function s(x) represents the number of hours worked by Socrates on the same given day x.

By using these functions, you can determine the specific number of hours each employee worked on any given day. For example, if you have a value for x, you can substitute it into the functions to find the corresponding number of hours worked by each employee.

It's important to note that the functions b(x), t(x), r(x), and s(x) are specific to Waterloo Park and the employees mentioned. The given schedule provides a way to track the hours worked by each employee on different days. By utilizing these functions, you can analyze and calculate the hours worked by each employee effectively.

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The distance of 42.5 km correct to 3 significant figures has an error interval of 42.0 km to 43.0 km.

What is error interval?

The accuracy thresholds that apply when a number has been rounded or shortened are known as error intervals. In other words, they represent the range of values that a number may have taken had it not been rounded off or truncated.

If the distance is measured as 42.5 km correct to 3 significant figures, this means that the last digit is uncertain and could be off by up to 0.5.

To determine the error interval for this statement, consider the range of possible values that could result from the uncertainty in the measurement.

Since the last significant digit is in the ones place, the error interval is ±0.5 km.

Therefore, the error interval is 42.0 km to 43.0 km.

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Answer: 35000

I hope this helps :) Can I get brainiest ?

The amount of cherries bought by the Harrison is 62.5 pounds.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

The amount of cherries bought by the Harrison should be more than the cherries bought by the Liam which is 5/8. Thus, The amount of cherries bought by the Harrison is more than the 5/8 or 62.5 pounds of cherries percent.

The cherries bought by the Liam is 5/8 pounds

The cherries bought by the Harrison is more than the Liam.

As in the problem the number of cherries bought Harrison (let) should be more than the cherries bought by the Liam (let ). Therefore,

H > L

As we know that the number of cherries bought by the Liam is 5/8 pounds. Keep the value of  in the above equation, we get,

H > 5/8

This equation can be rewritten in the percentile form as,

h > (5/8) * 100 %

h > (5/2) * 25 %

h > 62.5 %

Hence, The amount of cherries bought by the Harrison is more than 5/8 pounds or 62.5 pounds of cherries percent.

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Answer:

 its a geometric sequence where each term is 3 times the previous term.

Step-by-step explanation:

{2,6,18,54,162,486,1458...}

Answer:

what do you mean by find all the zeros and multiplicities, you have me confused on that part, if you explain that part a little more then I might be able to help you out a little bit M8

To determine whether the series ∑(n=1 to infinity) 7n/n is convergent or divergent, we can apply the ratio test. The ratio test helps us determine the convergence or divergence of a series by examining the limit of the ratio of consecutive terms.

In this case, let's calculate the ratio of consecutive terms using the formula for the ratio test:

lim(n→∞) |(7(n+1)/(n+1))/((7n/n)|

Simplifying the expression, we get:

lim(n→∞) |7(n+1)/n|

As n approaches infinity, the limit evaluates to:

lim(n→∞) |7(n+1)/n| = 7

Since the limit is a finite positive value (7), which is less than 1, the ratio test tells us that the series is convergent.

However, you mentioned identifying an (term) in the series, and it seems there may be an incomplete part of the question. Please provide additional information or clarification about identifying an term in the series so that I can provide a more specific answer.

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Answer:

4 6/7

Step-by-step explanation:

(Not really sure you should go with whatever answer you're sure of)

or 4 1/6

Answer:

B. 4 2/3

it's right, I took this last year.

The given statement "If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients give rise to the horizontal asymptote." is true.

Given information

The given information is " If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients give rise to the horizontal asymptote. "

We know that for a rational function having the same degree of the numerator and the denominator the horizontal asymptotes is equal to the ratio of leading coefficients of the numerator to that of the denominator.

Thus, the given statement is true.

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The domain of the function shown in the graph is the one in option A:

6 ≤ k ≤ 11

The domain of a function y = f(x) is the set of the inputs of the function. To identify the domain in a graph, we need to look at the horizontal axis (also called the x-axis).

On the graph we can see that it starts at x = 6 with a closed dot, and it ends at x = 11 also with a closed dot.

That means that these values belong to the domain, so we can write the domain as follows:

Domain = 6 ≤ k ≤ 11

(notice that the variable in the horizontal axis is k).

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The ladder demanded for Hill 2 must be no less than 108.27 meters high.

In order to find the necessary height of the ladder for Hill 1, we can employ an equation-based method:

height = tan(60 degrees) * 50 meters

height = 28.87 meters

From this calculation, it follows that a ladder is required that is at least 28.87 meters tall in order to climb Hill 1.

For Hill 2, using the same technique, we ascertain the required minimum ladder height:

tan(75 degrees) =height / 40 meters

height = tan(75 degrees) * 40 meters

height = 108.27 meters

Consequently, the ladder demanded for Hill 2 must be no less than 108.27 meters high.

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Answer: (b)

x g(x)

1 -16

2 -12

3 -8

If g(x) is 4*f(x), then we can find g(x) by multiplying 4 by x-5

g(x) = 4(x-5)

= 4x-20

Now we can plug in 1,2, and 3 for x to see which table makes sense.

g(1) = 4(1) - 20

= -16

g(2) = 4(2) - 20

= -12

g(3) = 4(3) - 20

= -8

hope this helps

Answer:

x g(x)

1 -16

2 -12

3 -8

Step-by-step explanation:

Answer:

Help me

Step-by-step explanation:

Answer:

3r^6

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

For the CDF of a continuous real function, the answers are as follows:

(i) P(X = Y) = 0 because P(X ≤ Y) > 0 and P(X < Y) > 0 and both are strictly positive

(ii) P(exist i < j with Xi = Xj) = 0 which is a contradiction.

(i) Suppose the CDF F is a continuous real function and note that this does not imply F is differentiable. Assume for simplicity that F(0) = 0 and F(1) = 1 (this does not change the major statements below but makes the proof a bit cleaner). If X, Y are independent F-distributed RVs, then for any n in N, we have; P(X ≤ Y) = P(X ≤ Y, Y ≤ X) = P(X ≤ Y|Y ≤ X) P(Y ≤ X) = P(Y ≤ X|X ≤ Y) P(X ≤ Y) = P(X ≤ Y|X ≤ Y) P(X ≤ Y) = P(X = Y). Hence, P(X = Y) = P(X ≤ Y)P(Y ≤ X) = P(X ≤ Y)P(X ≤ Y) = P²(X ≤ Y).Since F is continuous, P(X ≤ Y) = P(X < Y) = P(X ≤ Y) - P(X = Y). Therefore, P(X = Y) = 0 because P(X ≤ Y) > 0 and P(X < Y) > 0 and both are strictly positive.

(ii) Conclude that P(X = Y) = 0 (remember that you cannot assume F has a density). As for the sample case, we show that P(exist i < j with Xi = Xj) = 0. Suppose, for the purpose of contradiction, that we have X1, . . . , Xn in F such that P(exist i < j with Xi = Xj) > 0. Then, there must be some distinct i < j such that Xi = Xj. Without loss of generality, we may assume i = 1 and j = 2. Then, the probability that this event occurs is; P(X1 = X2, X3 ≠ X1, . . . , Xn ≠ X1) = P(X2 ≤ X1, X3 ≠ X1, . . . , Xn ≠ X1) + P(X1 < X2, X3 ≠ X1, . . . , Xn ≠ X1)Since Xi are independent F-distributed RVs and P(X = Y) = 0, it follows that the probability of the first term in the sum above is zero. Therefore, P(exist i < j with Xi = Xj) = 0 which is a contradiction.

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Answer:

Using x=5, then x exponent 2 = 5 exponent2 =5 x5 = 25 1 exponent5=1x1x1x1x1=1 5 exponent 1 = 5 my sister said the answer is 162 you could try that