What is 14 + 6 =
+11

The solution of the second-order differential equation y'' - y' = 0 with the given initial conditions y(-1) = 2 and y'(-1) = -2 is y(x) = 2e^x - 4e^-x.

To find a solution to the second-order differential equation y'' - y' = 0, we first solve the characteristic equation by assuming a solution of the form y(x) = e^(rx). Plugging this into the differential equation, we get r^2e^(rx) - re^(rx) = 0. Factoring out e^(rx), we have e^(rx)(r^2 - r) = 0. This gives us two possible values for r: r = 0 and r = 1.

For r = 0, the corresponding solution is y₁(x) = c₁, where c₁ is a constant.

For r = 1, the corresponding solution is y₂(x) = c₂e^x, where c₂ is a constant.

To find the particular solution that satisfies the given initial conditions, we substitute the values of x = -1, y(-1) = 2, and y'(-1) = -2 into the general solution. This gives us the equations 2 = c₁ and -2 = c₂e^-1. Solving for c₁ and c₂, we find c₁ = 2 and c₂ = -2e.

Therefore, the solution to the second-order differential equation with the given initial conditions is y(x) = 2e^x - 4e^-x.

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The posterior probability mass function of X is given below:0.4 * 0.0183 = 0.00732.0.6 * 0.0513 = 0.03078. Posterior Probability Mass Function of X: ____0.00732 if A = 1.0.____0.03078 if A = 1.5.

Explanation: The probability mass function for Poisson distribution is given by: P(X = x) = (e^-λ * λ^x) / x!Where,λ is the mean. The given prior probability mass function of A is P (A = 1.0) = 0.4P(A = 1.5) = 0.6.

Thus, the mean is either A = 1.0 or A = 1.5.

Now, let X be the number of defects on a roll of tape. Using the law of total probability, the probability mass function of X is P (X = x) = P (X = x, A = 1.0) + P (X = x, A = 1.5)

Using Bayes' theorem, the posterior probability mass function is given by: P (A = 1.0 | X = 4) = P (X = 4 | A = 1.0) * P (A = 1.0) / P (X = 4) P (A = 1.5 | X = 4) = P (X = 4 | A = 1.5) * P (A = 1.5) / P (X = 4)

Now, we need to calculate P (X = 4 | A = 1.0) and P (X = 4 | A = 1.5) using the Poisson distribution.

P (X = 4 | A = 1.0) = (e^-1 * 1^4) / 4! = 0.0183.P(X = 4 | A = 1.5) = (e^-1.5 * 1.5^4) / 4! = 0.0513.

Now, we need to calculate the value of the denominator,

P (X = 4). P (X = 4) = P (X = 4, A = 1.0) + P (X = 4, A = 1.5) = P (X = 4 | A = 1.0) * P (A = 1.0) + P (X = 4 | A = 1.5) * P (A = 1.5)

Put the values: P (X = 4) = (0.0183 * 0.4) + (0.0513 * 0.6) = 0.0342.

Put the values in the above posterior probability mass function equations,

we get: P (A = 1.0 | X = 4) = 0.00732 and P (A = 1.5 | X = 4) = 0.03078.

Therefore, the posterior probability mass function of X is:0.00732 if A = 1.0.0.03078 if A = 1.5.

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To construct a proof of the conclusion "-(∀x) (S(x) ∧ P(x))" from the given premises "-(3x) (P(x) ∧ M(x))" and "(3x) (M(x) ∧ S(x))," we can use a proof by contradiction.

We will assume the negation of the conclusion and derive a contradiction. Here's the proof:

Therefore, we have derived a contradiction, which allows us to conclude that the negation of the assumption is false. Thus, we can conclude:

-(∀x) (S(x) ∧ P(x))

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Answer:

angel a is 65 degrees

Step-by-step explanation:

40+2x+10=180

40-40+2x+10-10=180-40-10

2x=130

x=65

checking:

65 + 10 + 40 = 75 + 40 = 115

115+65=180

180=180

Answer:  x = 10

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°.

(2x + 3) + (5x + 17) + 90 = 180

2x + 3 + 5x + 17 + 90 = 180

7x + 110 = 180

7x = 70

x = 10

Answer:

i dont know im not that smart ask someone else dude

Step-by-step explanation:

Answer:

1.2

Step-by-step explanation:

There are 2 lines in the middle of the circle. Im guessing by you saying "The line in the middle" You must mean the radius your trying to find the diameter so, the radius is half of the diameter so to find the diameter you do the radius x 2 in this case 3/5x2 equals 1.2 :)

I Hope this helps!!

Answer:

26 per week

Step-by-step explanation:

The average amount Rebecca pays for electricity based on the given data is $124.60.

To calculate the average, we add up the amounts she paid in each month and then divide by the total number of months. In this case, the sum of her payments is $135 + $129 + $99 + $120 + $140 = $623. Dividing this sum by the total number of months (5), we get an average of $623 / 5 = $124.60. Calculating the average helps us determine the typical amount Rebecca pays for electricity based on the given data. It provides an overall picture of her average expenses in the specified period.

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Answer:

20

Step-by-step explanation:

Answer:

5 gallons

Step-by-step explanation:

3/4 + 6/8 + 20/8 + 1

6/8 + 6/8 + 20/8 + 8/8

40/8 = 5 gallons

Answer: 6

Step-by-step explanation:

Answer: y=6

Step-by-step explanation:

Answer:

Finding the equation using the two points is: y=3x-8

The slope is: m=3

The slope and y-intercept is: 3, (0,-8)

Step-by-step explanation:

I put all of these answers because i was basically fully confused by the wording of this question.. Sorry.

Answer:

235.5 cubic feet

Step-by-step explanation:

The volume v of a circular cylinder whose base radius is r and height h is given as

v = πr^2h

where π is 22/7 or 3.14

Given that the radius is five feet and the height  is three feet

the volume v = 3.14 *5^2 * 3

= 235.5 cubic feet

The volume of the oblique circular cylinder is 235.5 cubic feet

To determine the angle of the ramp, we can use trigonometry and calculate the inverse tangent (arctan) of the ratio of the height to the length of the ramp.

Given a ramp length of 2.5 meters and a height of 30 centimeters (0.3 meters), the angle of the ramp is approximately 6.87 degrees. The angle of the ramp can be found using the formula: angle = arctan(height/length). By substituting the values, we get angle = arctan(0.3/2.5).

Using a calculator or math software to evaluate the arctan of this ratio, we find that the angle is approximately 6.87 degrees. This means that the ramp has a relatively gentle incline, indicating a low slope or gradient. Knowing the angle of the ramp can be useful in various applications, such as construction, accessibility planning, or determining the safety of the slope for specific purposes.

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The value of N₂(h), for the following data gives an approximation to the integral M = [tex]\int\limits^1_0 {f(x)} \, dx[/tex]  N₁(h)= 2.2341 N₁(h/2) = 2.0282 is 0.8754. So, none of the options are correct.

Given that N₁(h)= 2.2341 and N₁(h/2) = 2.0282.

Applying Richardson's extrapolation method, we can find the value of the definite integral M using the formula,

M = N₁(h) + k₂h² + k₄h⁴ + ...

Therefore, we have to find the value of N₂(h).

Here, h = 1 - 0 = 1.

N₂(h) can be obtained by the formula,

[tex]N_2(h) = \frac{(2^2 * N_1(h/2)) - N_1(h)}{2^2 - 1}[/tex] , Substituting the data values we get,

[tex]N_2(h) =\frac{(2^2 * 2.0282) - 2.2341}{2^2 - 1}[/tex]

[tex]N_2(h)= \frac{8.1128 - 2.2341}{3}[/tex]

[tex]N_2(h)=\frac{2.6263 }{3}[/tex]

[tex]N_2(h)=0.8754333 = 0.8754[/tex]

Therefore, none of the option is correct.

The question should be:

The following data gives an approximation to the integral M =  [tex]\int\limits^1_0 {f(x)} \, dx[/tex]  N₁(h)= 2.2341 N₁(h/2) = 2.0282. Assume M = N₁(h) + k₂h² + k₄h⁴ + ... then, N₂(h) =

a. 2.01333

b. 1.95956

c. 0.95957

d. 2.23405

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y=-2x^2-8x-4

-2x^2-8x=4

divide by negative 2

x^2+4x=-2

complete the square

(x+2)^2=-2+4

(x+2)^2=2

x+2=±[tex]\sqrt{2}[/tex]

x=-2±[tex]\sqrt{2}[/tex]

nearest hundreths,

x=-0.59

x=-3.41

Answer:

i think its c hope it helps

Step-by-step explanation:

Answer:

Alternate exterior angles

Step-by-step explanation:

If they shared a vertex, they would be vertical angles, but since they are on different lines, and alternate sides, the dark blue (alternate exterior angles) answer is correct.

Answer:

horizontal

vertical

diagonal

Step-by-step explanation:

I guess I only know those.hope it helps you

The level of confidence that can be attributed to the interval estimate is approximately 97%. This means that we can be 97% confident that the true average amount of money spent by Australian students on subscription-based entertainment platforms falls within the range of $32,468 to $37,224.

To determine the level of confidence for the interval estimate, we need to consider the t-distribution and the degrees of freedom associated with the sample size.

Since the sample size is 48, the degrees of freedom would be 48 - 1 = 47. Using a t-distribution table or calculator, we can find that with 47 degrees of freedom, a confidence level of approximately 97% corresponds to a t-value of 2.682.

Since the interval estimate is not explicitly provided, we can assume it to be the range between $32,468 and $37,224.

We have that the t-value is associated with a two-tailed test, the level of confidence for this interval estimate is approximately 97%.

Therefore, we can attribute a confidence level of 97% to this interval estimate, indicating that we can be 97% confident that the true average amount of money spent by Australian students on subscription-based entertainment platforms falls within the given range.

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There is a strong negative linear relationship between x and y, and almost all of the variation in y can be explained by the variation in x.

The correlation coefficient is -0.961 and the proportion of the variation in y that can be explained by the variation in the values of x is 92.3%.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient between x and y is -0.961, which indicates a strong negative linear relationship between the two variables.

The coefficient of determination (r²) measures the proportion of the variation in y that can be explained by the variation in the values of x. In this case, the value of r² is 0.923, or 92.3%. This means that 92.3% of the variability in y can be explained by the variability in x. Therefore, there is a strong negative linear relationship between x and y, and almost all of the variation in y can be explained by the variation in x.

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Answer:

226.19 inches

Step-by-step explanation:

Answer:

600 cm²

Step-by-step explanation:

The shaded area (A) is calculated as

A = area of square - ( area of 3 unshaded triangles )

area of square = 40 × 40 = 1600 cm²

area of lower right triangle = [tex]\frac{1}{2}[/tex] × 20 × 40 = 10 × 40 = 400 cm²

area of upper left triangle = [tex]\frac{1}{2}[/tex] × 40 × 20 = 20 × 20 = 400 cm²

area of lower left triangle = [tex]\frac{1}{2}[/tex] × 20 × 20 = 10 × 20 = 200 cm²

Then

A = 1600 - (400 + 400 + 200 ) = 1600 - 1000 = 600 cm²

Answer:

22

Step-by-step explanation:

according to your question

Answer:

1. If D= whole numbers then the answer is B.0 if it is integers the answer is A.-10

2. The answer is D. That number is an irrational number.

Step-by-step explanation:

Im pretty sure that #1 is B.0, but since there are no labels and i haven't done this in a while, I wasn't quite sure. Sorry.

Answer: √113 or 10.63

Step-by-step explanation: the exact answer is √113, or 10.63 if you're looking for the decimal form

Step-by-step explanation:

Let the distance between two points A = (-4,7) and B = (4,0).

Here, x1 = -4 , y1 = 7

x2 = 4 , y2 = 0

Use the distance formula to find out the distance between two points are:

AB = √[(x2-x1)²+(y2-y1)²]

= √[{4-(-4)}²+(0-7)²]

= √[(4+4)²+(-7)²]

= √[(8)² + (-7)²]

= √[(8*8)+(-7*-7)]

= √[64+49]

= √[113] ⇛10.630 units approximately.