since the year 2000, the law no longer permits people to indicate multiple racial identities to the u.s. census but must select just one.

To find a second solution, y2(x), for the given differential equation y" + 2y' + y = 0 using the reduction of order or the formula y2 = y1(x)∫e^(-∫P(x)dx)y1^2(x)dx, we will substitute the given solution y1(x) = xe^(-x) into the formula.

The second solution is y2(x) = e^(-2x) (Option C).

To explain the solution, let's start by substituting y1(x) = xe^(-x) into the formula for y2(x):

y2(x) = xe^(-x) ∫e^(-∫(2x)dx)(xe^(-x))^2dx

Simplifying the expression, we have:

y2(x) = xe^(-x) ∫e^(-2x)(x^2e^(-2x))dx

Integrating the expression inside the integral, we get:

y2(x) = xe^(-x) ∫(x^2e^(-4x))dx

Integrating this expression, we find:

y2(x) = xe^(-x) (-1/4) * (x^2e^(-4x) - 2∫xe^(-4x)dx)

Simplifying further, we have:

y2(x) = xe^(-x) (-1/4) * (x^2e^(-4x) - 2(-1/4)e^(-4x))

Finally, simplifying the expression, we obtain:

y2(x) = xe^(-x) (1/4) * (x^2e^(-4x) + (1/2)e^(-4x))

This can be further simplified as:

y2(x) = (1/4) * x^3e^(-5x) + (1/8) * xe^(-5x)

Therefore, the second solution is y2(x) = e^(-2x) (Option C).

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Triangle ABD is congruent to triangle BCD

Congruent triangles are triangles with thesame corresponding sides and also with thesame corresponding angles.

To show that triangle ABD is congruent to triangle BCD

It has been shown that line AD is equal to line DC

i.e AD = DC

angle BMA = BMC = 90°

Therefore AB = BC

And line BD is common to both triangles

Therefore ;

AB = BC

AD = DC

Therefore we can say that triangles ABD is congruent to triangle BCD.

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Answer:20 ft

Step-by-step explanation:

Answer:

A complementary angle are angles that add up to 90 degrees.  For example, a 30 degree angle and a 60 degree angle are complementary angles because 30+60=90

Step-by-step explanation:

Answer:

Complementary angles are angles that add to a total of 90 degrees. An example of complementary angles are 44 and 46 degrees, because they sum to 90! Hope this helps you out!

Answer:

y>2/3+3

Step-by-step explanation:

We know that the rise is two and run is three, 2/3. Then the blue shaded are would stand for y>. And the y-intercept is 3.

The image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin is (-24, -8).

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

To find the image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin, we can use the following formula:

(x', y') = (kx, ky)

where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the image after dilation, k is the scale factor, and (0, 0) is the center of dilation.

Substituting the values given in the problem, we get:

(x', y') = (4*(-6), 4*(-2))

Simplifying,

(x', y') = (-24, -8)

Therefore,

The image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin is (-24, -8).

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Answer:

1. 8.5 inches

2. 20 inches

Step-by-step explanation:

1. Total area of the shelve = (4b x 3b)

864 = 12

      = 12

=  

   = 72

b =

  = 8.486 inches

b = 8.5 inches

2. Bernard wish to cover an area of 4800 square inches.

Then,

Area = length x width

4800 = 4b x 3b

         = 12

=

   = 400

b =

   = 20 inches

The value of b should be 20 inches.

Answer:

9.3 ft

Step-by-step explanation:

Answer:

x₂ = - 3

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to \(\frac{5}{6}\)

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (9, 9) and (x₂, y₂ ) = (x₂, - 1)

m = \(\frac{-1-9}{x_{2}-9 }\) , that is

\(\frac{-10}{x_{2}-9 }\) = \(\frac{5}{6}\) ( cross- multiply )

5(x₂ - 9) = - 60 ( divide both sides by 5 )

x₂ - 9 = - 12 ( add 9 to both sides )

x₂ = - 3

The mass of the original sample of phosphorus-32 was approximately 717.7 grams.

To solve this problem, we can use the radioactive decay formula:

A = Ao * 2^(-t/h)

Where:

A = resulting amount after time t

Ao = initial amount (at t=0)

t = time

h = half-life of the substance

In this case, we are given that the half-life of phosphorus-32 is 14.28 days. We want to find the initial mass, represented by Ao.

After approximately 57 days, 55 g of phosphorus-32 remain unchanged. Let's plug these values into the equation:

55 = Ao * 2^(-57/14.28)

To solve for Ao, we can isolate it by dividing both sides of the equation by 2^(-57/14.28):

55 / 2^(-57/14.28) = Ao

Using a calculator to evaluate 2^(-57/14.28), we find that it is approximately 0.07666.

Therefore, the initial mass, Ao, is:

Ao = 55 / 0.07666 ≈ 717.7 g

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5! permutation of the letters abcdefgh contains strings ab, de, and gh.

The number of permutations of 'n' objects taken 'r' at a time is determined by the following formula:

P(n,r)=n! / (n−r)!

We can also find permutation using the Selection and Formation Method:

For example:

1. Number of ways to arrange the letter SANOJ:

here number of alphabets are 5, and we have to arrange all the letter so using permutation formula:

P(5, 5 ) = 5! / (5-5)!

P(5, 5 ) = 5!                : 0! = 1

without using the formula we can simply write 5! as the answer.

Here, we have given the word, " abcdefgh "

and we have to make those arrangements in which ab, de, and gh come together:

so now, we will count ab, de, and gh as a single word.

now, we will have 5 different words/alphabet:

1 → ab

2 → c

3 → de

4 → f

5 → gh

Number of ways to arrange all the 5 words/alphabet: 5!

Hence,

5! permutation of the letters abcdefgh contains strings ab, de, and gh.

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Answer:

The probability of winning the bet is approximately 0.4238, or about 42.38%.

Step-by-step explanation:

We can solve this problem using the normal approximation to the binomial distribution. Let X be the number of heads in 100 tosses of a fair coin. Then X follows a binomial distribution with n = 100 and p = 0.5. The mean of X is µ = np = 100 × 0.5 = 50, and the standard deviation of X is σ = sqrt(np(1-p)) = sqrt(100 × 0.5 × 0.5) = 5.

Now, we want to calculate the probability that |X - 50| ≥ 4. This is equivalent to calculating the probability that |(X - 50)/5| ≥ 4/5, which is the probability that a standard normal variable Z = (X - 50)/5 is less than -4/5 or greater than 4/5. Using a standard normal distribution table or a calculator, we can find:

P(Z ≤ -4/5) ≈ 0.2119

P(Z ≥ 4/5) ≈ 0.2119

Therefore, the probability of winning the bet is:

P(|X - 50| ≥ 4) = P(|(X - 50)/5| ≥ 4/5)

≈ P(Z ≤ -4/5 or Z ≥ 4/5)

≈ P(Z ≤ -4/5) + P(Z ≥ 4/5)

≈ 0.2119 + 0.2119

≈ 0.4238

So the probability of winning the bet is approximately 0.4238, or about 42.38%.

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Answer:

Q

Step-by-step explanation:

Answer: Q, it's the only horizontal line

Answer:

30

Step-by-step explanation:

Answer:

Oh thats easy its $30

Step-by-step explanation:

so for 2 icecreams it costs $6

so if u divide them it would become 1 icecream for $3 so

10 times 3 will be $30

The value of f(0) in the function f(x) is -6

The coordinates are given as:

(-2, 0), (-1, 0), (1, 0), and (3, 0), and (0, -6)

To calculate f(0), we determine the function value when x =0

From the coordinate points, we have:

Point (0, -6)

This means that:

f(0) = -6

Hence, the value of f(0) is -6

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Answer:

Step-by-step explanation:

-2,1 or 3 only

The Laplace transform of the given function is,

L{f(t)} = (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

Given function is f(t) = {8 12 1 Jo, 0 ≤ t < 3/2, 3/2 ≤ t < 2, 2 ≤ t < ∞ respectively.

We have to find Laplace transform of the given function.

For first interval 0 ≤ t < 3/2,

f(t) = 8u(t) - 8u(t-3/2)

For second interval 3/2 ≤ t < 2,

f(t) = 12u(t-3/2) - 12u(t-2)

For third interval 2 ≤ t < ∞,

f(t) = Jo(u(t-2))

Hence, we can write the Laplace transform of the given function as,

L{f(t)} = L{8u(t) - 8u(t-3/2)} + L{12u(t-3/2) - 12u(t-2)} + L{Jo(u(t-2))}

Where, L is Laplace transform.

Let's calculate each Laplace transform stepwise,

1. L{8u(t) - 8u(t-3/2)}L{8u(t)} = 8/L{u(t)}L{u(t)}

= 1/sL{u(t-3/2)}

= e^{-3s/2}/s

Therefore,

L{8u(t) - 8u(t-3/2)} = 8[1/s - e^{-3s/2}/s]

2. L{12u(t-3/2) - 12u(t-2)}L{12u(t-3/2)}

= 12e^{-3s/2}/sL{12u(t-2)}

= 12e^{-2s}/s

Therefore,

L{12u(t-3/2) - 12u(t-2)} = 12[e^{-3s/2}/s - e^{-2s}/s]

3. L{Jo(u(t-2))}L{Jo(u(t-2))} = ∫_{0}^{∞}δ(t-2)e^{-st}dtL{Jo(u(t-2))}

= e^{-2s}

Hence, the Laplace transform of the given function is,

L{f(t)} = 8[1/s - e^{-3s/2}/s] + 12[e^{-3s/2}/s - e^{-2s}/s] + e^{-2s}

= (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

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Answer:

How though?

Step-by-step explanation:

Answer:

hey, good afternoon!

Step-by-step explanation:

here is an example: the cost of a pizza is 7.50 and you can add a topping for 0.65 cents. find the cost of the pizza with 6 toppings

y=mx+b

the x stands for the toppings and y is the cost. the rate is 0.65 cents and the orginal amount of money is b. so the equation would look like this:

y= .65x+7.50. x=6

y = 65(6)+7.50

    =3.9+ 7.50= $11.50(answer)

the m is the rate of change in this question is 0.65 cents

b is initial/ fixed/ value once again in this qeustion it 7.50$  

hope this helps. have a great day!

Step-by-step explanation:

\( \frac{x}{10} = 7\)

x = 7 ×10

x = 70

Answer:

X=70

Step-by-step explanation:

We know from the equation that you can take X and divide it by 10 to get 7. So we just have to reverse this process:

what's 7 * 10?

70

X=70

Answer:

V = 1469.52 cm^3

Step-by-step explanation:

cylinder volume = base area * height

                           = ( pi * R^2) * h

                           = pi * 6^2 * 13 = 1469.52 cm^3  (ANS)

this will provide you the answer

Answer:

14 students

Step-by-step explanation:

The ratio of students to teachers is 2:3.  That can be written as a conversion factor:  (2 students)/(3 teachers)

If there are 21 teachers, there would be

  (21 teachers)*(2 students)/(3 teachers) = 14 students

The number of combination 6-letter words using five vowels in alphabetical order,

5*4*3*2*1*21=2520

Permutation and combination are methods for representing a collection of objects by selecting them from a set and forming subsets. It specifies the various ways to arrange a specific set of data. Permutations are when we select data or objects from a specific group, whereas combinations are the order in which they are represented.

The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used.

We have five vowels: a, i, e,0, and u.

make the 6-letter word using five vowels in alphabetical order,

5*4*3*2*1*21=2520

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Answer:

The second one/B

Step-by-step explanation:

The first constraint is a linear equation that relates the variables x1, x2, and x3, and the second constraint is an inequality constraint involving x1 and x2The given problem is a linear programming problem in its primal form.

The objective is to maximize the expression z = 7x1 - 5x2 - 2x3, subject to two constraints.. The goal is to find the values of x1, x2, and x3 that maximize the objective function while satisfying the given constraints.

In the primal problem, the objective is to maximize the expression z, which is a linear combination of the decision variables x1, x2, and x3. The coefficients 7, -5, and -2 represent the weights assigned to each variable in the objective function. The constraints represent the relationships and limitations imposed on the variables. The first constraint is an equality constraint, which means that the left-hand side of the equation must equal the right-hand side. The second constraint is an inequality constraint, indicating that the value of the expression 2x1 + x2 must be less than or equal to a certain value.

To solve this linear programming problem, various optimization techniques such as the simplex method or interior point methods can be applied. These methods iteratively adjust the values of the decision variables to find the optimal solution that maximizes the objective function while satisfying the given constraints. By solving the primal problem, the values of x1, x2, and x3 can be determined, leading to the maximum value of the objective function z.

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Answer:

12

Step-by-step explanation: