how many permutations of abcde are there in which the first character is abc and the last character is cde

Answer:

The list of these events from least likely to most likely is Blue-Blue -> Black-Blue -> Blue-Black -> Black-Black

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Possible outcomes:

Black - Black

Black - Blue

Blue - Black

Blue - Blue

Probability of each outcome:

Black-Black:

14 out of 20, and then 9 out of 12. So

\(P_{BkBk} = \frac{14}{20} \times {9}{12} = \frac{14*9}{20*12} = \frac{126}{240}\)

Black-Blue:

14 out of 20, then 3 out of 12. So

\(P_{BkBl} = \frac{14}{20} \times {3}{12} = \frac{14*3}{20*12} = \frac{42}{240}\)

Less likely than black-black.

Blue - Black:

6 out of 20, then 9 out of 12. SO

\(P_{BlBk} = \frac{6}{20} \times {9}{12} = \frac{6*9}{20*12} = \frac{54}{240}\)

More likely than black-blue, less likely than black-black.

Blue - Blue

6 out of 20, then 3 out of 12

\(P_{BlBl} = \frac{6}{20} \times {3}{12} = \frac{6*3}{20*12} = \frac{18}{240}\)

Least likely of the outcomes.

List these events from least likely to most likely:

The list of these events from least likely to most likely is Blue-Blue -> Black-Blue -> Blue-Black -> Black-Black

The 98% confidence interval for the average number of hours studying for the exam is approximately 6.61 to 7.99 hours. The correct option is d.

To calculate the 98% confidence interval for the average number of hours studied, we need to use the sample mean (7.3 hours), sample standard deviation (1.9 hours), sample size (41 students), and the appropriate Z-score for a 98% confidence level.

Step 1: Find the Z-score for a 98% confidence level.
Using a Z-table or calculator, the Z-score for a 98% confidence interval is approximately 2.33.

Step 2: Calculate the standard error.
Standard error (SE) = (sample standard deviation) / sqrt(sample size) = 1.9 / sqrt(41) ≈ 0.297

Step 3: Calculate the margin of error.
Margin of error (ME) = Z-score * standard error = 2.33 * 0.297 ≈ 0.692

Step 4: Calculate the confidence interval.
Lower limit = sample mean - margin of error = 7.3 - 0.692 ≈ 6.61
Upper limit = sample mean + margin of error = 7.3 + 0.692 ≈ 7.99

This means that we can be 98% confident that the true mean of hours studied for the entire class of 115 students lies within this range. The closest answer choice to these values is option D (6.11 and 8.49).

For more about confidence interval:

https://brainly.com/question/29680703

#SPJ11

Answer:

Step-by-step explanation:

Answer:

option a.

1/5 in my opinion.

Using proportions, it is found that the scale of the drawing is:

1 inch = 12 yards.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The scale is that 144 yards are represented by 12 inches, hence:

144/12 = 12

Then, 1 inch = 12 yards.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

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.

To know more about time-independent Schrödinger equation,visit:

https://brainly.com/question/31642338

#SPJ11

Answer:

442

Step-by-step explanation:

(Comment for the step-by-step explanation.)

Roads that are well-maintained, dry, and free from hazards are generally less likely to result in traction loss.

The likelihood of losing traction depends on various factors such as road conditions, weather, vehicle type, and driver behavior. However, in general, roads that are well-maintained, dry, and free from debris or hazards are less likely to result in traction loss. Additionally, roads with good grip surfaces, such as asphalt or concrete, tend to provide better traction compared to unpaved or slippery surfaces. It's important to drive cautiously and adapt to the specific conditions of the road to minimize the risk of losing traction.

To know more about traction,

https://brainly.com/question/5039394

#SPJ11

The calculated length of the segment EF is (c) 5

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

The trapezoid

The length of segment EF can be calculated using

EF = 1/2 * Sum of BC and AD

using the above as a guide, we have the following:

EF = 1/2 * (3.3 + 6.7)

Evaluate

EF = 5

Hence, the length of segment EF is (c) 5

Read more about midsegments at

https://brainly.com/question/7423948

#SPJ1

Answer:

m = 65

Step-by-step explanation:

Given

- 13 = \(\frac{m}{-5}\) ( multiply both sides by - 5 )

65 = m

Answer:

plz mark brainliest

Step-by-step explanation:

16/3 or 5 1/3

Answer:

\(u=\frac{16}{3}\)

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define

\(\frac{7}{6} =\frac{u+4}{8}\)

Step 2: Solve for u

Step 3: Check

Plug in u into the original equation to verify it's a solution.

Here we see that 7/6 does indeed equal 7/6.

∴ \(u=\frac{16}{3}\) is a solution of the equation.

The digits {1,2,...,5} are randomly arranged in a row so total 5 ordered elements are in the sample space.

The digits {1,2,...,5} are randomly arranged in a row.

We have determine how many ordered elements are in the sample space.

The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.

So, we use the combination formula

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

Total digits are 5. So,

Sample space = \(^5C_{1}\)

Sample space = \(\frac{5!}{1!(5-1)!}\)

Sample space = \(\frac{5!}{1!4!}\)

Sample space = \(\frac{5\times 4!}{1\times 4!}\)

Sample space = 5

To learn more about sample space link is here

brainly.com/question/30206035

#SPJ4

Answer:

i think it's 51 because if you add 106 and 23 together it's 129 then 180-129= 51

Step-by-step explanation:

Answer: hahaha

Step-by-step explanation: ill answer some

Answer:

Do you have an actual question? If you do, I can help, but if you don't, you probably shouldn't ask inapplicable questions on this website.

Nice username though c:

The total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

In the given power system depicted in Figure 1, there are three units that are always running. Each unit has specific characteristics regarding their minimum power output (Pmin), maximum power output (Pmax), and incremental cost (Ci). Let's discuss the characteristics of each unit and calculate the total cost of power generation for a given load demand.

Unit 1:

Pmin = 200 MW

Pmax = 500 MW

Ci = $50/MWh

Unit 2:

Pmin = 150 MW

Pmax = 400 MW

Ci = $40/MWh

Unit 3:

Pmin = 100 MW

Pmax = 300 MW

Ci = $30/MWh

To calculate the total cost of power generation for a given load demand, we need to determine the optimal power output for each unit. We start by considering the units with the lowest incremental cost first.

Suppose the load demand is D MW. We allocate the load demand to the units as follows:

Step 1: Check if Unit 1 can meet the load demand within its power range. If yes, allocate the load demand to Unit 1 and calculate the cost:

Cost1 = Ci * P1, where P1 is the power output of Unit 1.

Step 2: If there is still remaining load demand, allocate it to Unit 2:

Cost2 = Ci * P2, where P2 is the power output of Unit 2.

Step 3: If there is still remaining load demand, allocate it to Unit 3:

Cost3 = Ci * P3, where P3 is the power output of Unit 3.

Finally, the total cost of power generation, Cost_total, is the sum of Cost1, Cost2, and Cost3:

Cost_total = Cost1 + Cost2 + Cost3

To find the optimal power output for each unit, we consider the load demand and compare it to the minimum and maximum power output limits for each unit. The power allocation is based on meeting the load demand while minimizing the overall cost of power generation.

In summary, given the characteristics of the three units in the power system (Pmin, Pmax, and Ci), the total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

Learn more about demand here

https://brainly.com/question/14274996

#SPJ11

The main criticism of differential opportunity theory is that it overlooks the fact that most delinquents become law-abiding adults (option c).

Differential opportunity theory, developed by Richard Cloward and Lloyd Ohlin, focuses on how individuals in disadvantaged communities may turn to criminal activities as a result of limited legitimate opportunities for success.

However, critics argue that the theory fails to account for the fact that many individuals who engage in delinquency during their youth go on to become law-abiding adults.

This criticism highlights the idea that delinquent behavior is not necessarily a lifelong pattern and that individuals can change their behavior and adopt prosocial lifestyles as they mature.

While differential opportunity theory provides insights into the relationship between limited opportunities and delinquency, it does not fully address the complexities of individual development and the potential for desistance from criminal behavior.

Critics suggest that factors such as personal growth, social support, rehabilitation programs, and the influence of life events play a significant role in individuals transitioning from delinquency to law-abiding adulthood.

To know more about  law-abiding adults refer here:

https://brainly.com/question/28317923

#SPJ11

Answer:

$120.67

Step-by-step explanation:

1. 55+29.99+27.79 = 112.78

2. 7% of 112.78 is 7.89

Answer:

The profit equation is modeled by the equation:

f(x) = -x^2 - 2*x + 3

The first thing that you can notice, is that the leading coefficient is negative, then the arms of the quadratic function will go downwards. This implies that the maximum of this function will be in the vertex.

For a quadratic equation

a*x^2 + b*x + c

the vertex is at:

x = -b/2a

In our case, the vertex is at:

x = +2/(-2) = -1

we evaluate our function in this value:

f(-1) = -(-1)^2 - 2*(-1) + 3 = -1 + 2 + 3 = 4

So x = -1 means that he must decrease the price by one unit, and the highest profit by toy will be 4.

Answer:

Part A

The rational equation that can be used to determine how long it would take Lara to clean the tank alone is; 6/9 + 6/x = 1

Part B

It would take Lara 18 hours to clean the tank if she works by herself

Step-by-step explanation:

Part A

The time it takes Kevin to clean an aquarium tank alone = 9 hours

The time it takes Kevin and Lara to clean the tank together = 6 hours

Let '1/x' represent Lara's cleaning rate, we have;

The time it would take Lara to clean 1 tank alone = 1/(1/x) = x

Kevin's cleaning rate, y = 1/9 tank per hour

The number of tanks, z =  tank

The total time it takes both of them to clean the tank, t = 6 hours

Therefore, we get;

t × y + t × 1/x = z

When t = 6, y = 1/9, and z = 1, we get;

6 × (1/9) + 6·(1/x) = 1

Therefore, the rational equation that can be used to determine how long it would take Lara to clean the tank if she work by herself, '1/x', is given as follows;

6/9 + 6·(1/x) = 1

6/9 + 6/x = 1

Part B

Solving the rational equation gives;

1/x = (1 - 6/9)/6 = 1/18

∴ 1/x = 1/18)

∴ x = 18

The time it would take Lara to clean the tank if she worked by herself, x = 18 hours

Answer:

-5x+(- 15 ) = 20

x=-7

Step by Step

-5x+(-15)= 20 becomes

-5-15=20 add 15 tp (15 and 20)

-5x=35 ( divide by 51

x=-7

Answer:

x=32

Step-by-step explanation:

sum of interior angles of a triangle = 180

add up all angles and equate to 180

(4x-13)+(x+18)+15=180

5x=160

x=160/5=32

x+18  =   32+18    = 50

4x-13  =  4x32-13 = 128-13 = 115

add up all to check whether ans = 180;  15+50+115=180

step 1 solve for x step 2 after getting the value of x ,substitute and get the value of angles

Answer:

To fine the surface area is to add all the area of the faces

Answer: 50

Step-by-step explanation: Common factor of 150 and 350 = 1, 2, 5, 5. Highest common factor of 150 and 350 = 2 × 5 × 5 = 50.

Answer:

yes!

Step-by-step explanation:

When we make inferences about the difference of two independent population proportions, we assume that it is a random sample, and the number of successes and failures are at least 15 in each group.

Two independent proportions tests involve comparing the proportions of two unrelated datasets.

For these two datasets to be regarded as an independent population, the following must be true or assumed to be true

Hence, the above highlights are the assumptions of two independent population proportions.

To learn more about independent populations from the given link

https://brainly.com/question/23989150

#SPJ4

Answer:

3.25 miles

Step-by-step explanation:

Combine the total laps by doing 6 + 7 to get 13. Then, multiple 13 by 0.25 to get your sum of 3.25 miles.

=======================================================

Explanation:

For any equilateral triangle, the interior angle is 60 degrees (we consider this equiangular as well).

Equilateral triangles tesselate the plane because the interior angle 60 degrees is a factor of 360. We're able to tile these triangles so that there are no gaps or overlaps, and we can cover the plane. Think of it like tiling a wall. So we rule out choice B.

Combining 6 equilateral triangles together forms a regular hexagon, so we can rule out choice A as well (I'm assuming your teacher meant to say "regular" in front of "hexagon"; as some non-regular hexagons do not tessellate).

As I mentioned with the wall tiling example, squares also tesselate the plane. Simply look at any floor tile or wall tile for a real world application. Another application is any xy grid. The 90 degree interior angle is a factor of 360. Therefore, we rule out choice D.

-----------------------

In the previous section, we ruled out choices A, B, and D.

So the only thing left are octagons. The interior angle is 180(n-2)/n = 180(8-2)/8 = 135 degrees which is not a factor of 360. Note how 360/135 = 2.667 approximately which isn't a whole number.

So if we tried to glue octagons together such that there are no gaps or overlaps, then we'll find that it's impossible to do.

If you wanted octagons to be part of a tessellation, then you would need to involve squares as well. Otherwise there will be gaps.

This is why octagons do not tesselate the plane.

Answer:

a=1 is the answer

Step-by-step explanation:

let

p(x)=x³-2ax²+16

put x= -2

p(-2)=(-2)³-2a(-2)²+16

p(-2)=-8+16-8a

p(-2)=8-8a

as (x+2) is a factor of p(x) then p(x) is equal to zero

8-8a=0

8=8a

a=1

i hope this will help you

Answer:

ii) 1

Step-by-step explanation:

Let p(x) = \(x^3-2ax^2+16\)

Given that x+2 = 0

Then => x = -2

Putting this in p(x)

p(-2) = \((-2)^3-2a(-2)^2+16\)

By remainder theorem , Remainder will be zero

0 = -8-8a+16

0 = -8a+8

-8a = -8

Dividing both sides by -8

=> a = 1