Define a sequence a,, so that ao = 2, a₁ = 3, and a₁ = 6an-1-8an-2. (a) Write a generating function for (a) in the form of a rational function. That is, find a rational function f such that f(x) = 0 anx".

Answer:

D

Step-by-step explanation:

Answer:

no picture

Step-by-step explanation:

For  the quadratic function f(x) = x^2 - 5x + 6, the values of the coefficients and constant are:

a = 1
b = -5
c = 6.

To identify the coefficients and constant in the quadratic function f(x) = x^2 - 5x + 6, let's examine the standard form of a quadratic equation:

f(x) = ax^2 + bx + c

Comparing this with the given quadratic function, we can determine the values of the coefficients and constant:

a = 1 (coefficient of x^2 term)
b = -5 (coefficient of x term)
c = 6 (constant term)

Therefore, for the quadratic function f(x) = x^2 - 5x + 6, the values of the coefficients and constant are:

a = 1
b = -5
c = 6.

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Answer:

8/10 or 4/5 as a fraction. the percentage is 80%

Step-by-step explanation:

The correct answer is option d) 9x² + 12xy + 4y². To simplify the expression (3x + 2y)² using the square of a binomial formula, we need to apply the formula (a + b)² = a² + 2ab + b². In this case, a = 3x and b = 2y.

Using the formula, we have:

(3x + 2y)² = (3x)² + 2(3x)(2y) + (2y)²

= 9x² + 12xy + 4y²

So the simplified form of (3x + 2y)² is 9x² + 12xy + 4y².

Now let's analyze the given options:

a) 9x² + 4y²: This option is incorrect because it is missing the term 12xy.

b) 9x² + 5xy + 4y²: This option is also incorrect because it contains an additional term, 5xy, which is not present in the simplified expression.

c) 9x² + 6xy + 4y²: This option is incorrect because it also contains an additional term, 6xy, which is not present in the simplified expression.

d) 9x² + 12xy + 4y²: This option is correct because it matches the simplified form we obtained using the square of a binomial formula.

Therefore, the correct answer is option d) 9x² + 12xy + 4y².

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Answer:

2.True

3. HGK

4. 17°

hope it helps

Answer:

√89

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(9 - 1)² + [-6 - (-1)]²

√(8)² + (-5)²

√64 + 25

√89

The probability distribution of X is as follows:P(X = x) = 0 for x < 1P(X = x) = 0 for 1 ≤ x < 10.5P(X = x) = 1 for 10.5 ≤ x < 31P(X = x) = 0 for x ≥ 31.

Given function: f(x)={0x<10.51≤x<313≤xTo verify that the given function is a cumulative distribution function, we have to check the following conditions:1. f(x) is non-negative for all x.2. f(x) is continuous from the right for all x.3. f(x) is a non-decreasing function for all x.4. lim{x → -∞} f(x) = 0 and lim{x → ∞} f(x) = 1. Now, let's verify these conditions one by one.1. f(x) is non-negative for all x. This condition is satisfied, as the given function f(x) is defined only for x ≥ 1, and is non-negative for all x in this domain. Therefore, f(x) is non-negative for all x.2. f(x) is continuous from the right for all x. This condition is also satisfied, as the given function f(x) is defined piecewise as a continuous function for all x. Therefore, f(x) is continuous from the right for all x.3. f(x) is a non-decreasing function for all x. This condition is satisfied, as the given function f(x) is non-decreasing for all x in its domain.4. lim{x → -∞} f(x) = 0 and lim{x → ∞} f(x) = 1.

Using the definition of f(x) for x < 10, we have f(x) = 0 for x < 10. Therefore, lim{x → -∞} f(x) = 0. Using the definition of f(x) for x ≥ 31, we have f(x) = 1 for x ≥ 31. Therefore, lim{x → ∞} f(x) = 1. Hence, all four conditions are satisfied. Therefore, the given function is a cumulative distribution function. To find the probabilities of the intervals, we use the formula: P(a ≤ X ≤ b) = F(b) - F(a)where P(a ≤ X ≤ b) is the probability that X lies between a and b, and F(x) is the cumulative distribution function of X. Furthermore, the probability of the interval (a, b] is: P(a < X ≤ b) = F(b) - F(a)Therefore, the probabilities of the intervals are: P(1 < X ≤ 10.5) = F(10.5) - F(1) = 0 - 0 = 0P(10.5 < X ≤ 31) = F(31) - F(10.5) = 1 - 0 = 1P(X > 31) = F(∞) - F(31) = 1 - 1 = 0Therefore, we have: P(1 < X ≤ 10.5) = 0P(10.5 < X ≤ 31) = 1P(X > 31) = 0

Hence, the probability distribution of X is as follows: P(X = x) = 0 for x < 1P(X = x) = 0 for 1 ≤ x < 10.5P(X = x) = 1 for 10.5 ≤ x < 31P(X = x) = 0 for x ≥ 31. Therefore, the given function is a cumulative distribution function, and the probability distribution of X is as above.

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Answer:

7 cm

Step-by-step explanation:

10 mm = 1cm

All you need to do is add 10mm + 6cm.

10mm = 1cm

So, 6cm + 1cm.

Therefore, it equals to 7cm.

Answer:

471.2 cm cubed

Step-by-step explanation:

The formula for the volume of a cylinder is:

π*radius squared*height

The diameter is the distance across the circle.

10 mm is the same as 1 cm

The radius is half of the diameter.

1/2=.5

Radius=.5 cm

Height=6 cm

Plug the numbers in.

.5 squared is .25

π*(.25)(6 cm)

Volume=4.71

Rounded to the nearest tenth:

Volume=4.7 cm cubed

Answer:

69 minutes? i don't know haha

Step-by-step explanation:

The symbolic argument ~p -> q is valid.

To determine the validity of the argument ~p -> q using a truth table, we need to consider all possible combinations of truth values for p and q and evaluate the truth value of the implication ~p -> q.

The symbolic form of the argument is ~p -> q, which can also be written as ¬p → q.

A truth table for this argument would have columns for p, ~p, q, and ~p -> q.

Let's construct the truth table:

|   p      |  ~p    |   q      |  ~p -> q |

| True  | False | True  |   True    |

| True  | False | False |   False   |

| False | True  | True  |   True    |

| False | True  | False |   True    |

In the truth table, we consider all possible combinations of true (T) and false (F) for p and q. For ~p, we negate the value of p.

For the implication ~p -> q, it is true (T) if either ~p is false (F) or q is true (T). In all other cases, it is false (F).

Looking at the truth table, we can see that in all rows where ~p -> q is true (T), the corresponding conclusion q is true (T). Therefore, the argument ~p -> q is valid because whenever ~p is true (F), the conclusion q is also true (T).

In summary, the symbolic argument ~p -> q is valid.

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The square root of -i that graphs in the second quadrant,

⇒ z = (1/2)((√(2))(cos(135°) + i sin(135°))

To find the square root of -i,

we can start by writing -i in polar form.

⇒ i = 1(cos(270°) + i sin(270°))

Now, we can find the square root by taking the square root of the magnitude and dividing the angle by 2.

⇒ √(-i) = √(1)  [cos(270°/2) + i sin(270°/2)]

⇒ [tex](1)^{(1/2)}[/tex]  [cos(135°) + i sin(135°)]

⇒ (1/2)(√(2)) [cos(135°) + i sin(135°)]

⇒ (1/2)(√(2)) (-√(2)/2 + i(√(2))/2)

⇒ -1/2 + ((√t(2)/2)i

Therefore,

The square root of -i that graphs in the second quadrant in the form of

z = r(cosθ + i sinθ)

Hence,

z = (1/2)((√(2))(cos(135°) + i sin(135°)).

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Answer:

(-2,2)

Step-by-step explanation:

Hi,

4x + 5y = 2

-2x + 2y = 8

To solve using elimination, we can multiply the second equation by 2 to try and get rid of the x. So...

4x + 5y = 2

-4x + 4y = 16

Now, add...

9y = 18

Divide by 9...

y = 2

Now, let's solve for x...

4x + 5(2) = 2

4x + 10 = 2

4x = -8

x = -2

Your solution is, (-2,2)

I hope this helps :)

There is not sufficient evidence to conclude that the proportion of union members differs from 13.7% at the 0.01 level of significance.

To determine if there is sufficient evidence to conclude that the proportion of union members differs from 13.7%, we can perform a hypothesis test using the given sample data.

Let's define the hypotheses:

Null Hypothesis (H0): The proportion of union members is equal to 13.7%.

Alternative Hypothesis (H1): The proportion of union members differs from 13.7%.

We can set up the test using the z-test for proportions. The test statistic is calculated as:

z = (p(cap) - p) / √(p × (1 - p) / n)

where p(cap) is the sample proportion, p is the hypothesized proportion, and n is the sample size.

Given that the sample size is 200 and 30 workers belonged to a union, the sample proportion is p(cap) = 30/200 = 0.15.

The hypothesized proportion is p = 0.137.

Let's calculate the test statistic:

z = (0.15 - 0.137) / √(0.137 × (1 - 0.137) / 200)

z ≈ 1.073

To determine if there is sufficient evidence to conclude that the proportion differs from 13.7%, we compare the test statistic to the critical value.

At a significance level of 0.01, the critical value for a two-tailed test is approximately ±2.576 (obtained from a standard normal distribution table).

Since |1.073| < 2.576, the test statistic does not fall in the rejection region. Therefore, we fail to reject the null hypothesis.

Conclusion: Based on the given sample data, there is not sufficient evidence to conclude that the proportion of union members differs from 13.7% at the 0.01 level of significance.

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Answer:

5

Step-by-step explanation:

3x-7=8

x=5

Answer:

If 100km enables consumption of 6lts

what about 42lts

42/6 multiply by 100km

42/6*100= 700km

The car will consume 42lts in 700 km.

Thank you.

Step-by-step explanation:

Answer:

The answer and work are in the pdf

Step-by-step explanation:

Answer: A. The majority of the math scores are greater than the median of the science scores

Step-by-step explanation:

I took the test!

The mass of the wire is given by the integral [tex]\int[0, R] k\sqrt{(1 + (-x/\sqrt{(9 - x^2}))^2}[/tex] dx, and the centre of mass is given by [tex]\int[0, R] x(k\sqrt{1 + (-x/\sqrt{9 - x^2})^2}[/tex] dx divided by the mass.

Find the mass and centre of mass of the wire?

To find the mass and center of mass of the wire, we need to integrate the linear density function along the curve of the wire.

The linear density function is given as a constant k, which means the mass per unit length is constant.

To find the mass of the wire, we integrate the linear density function over the length of the wire. The length of the semicircle can be found using the arc length formula:

[tex]s = \int[0, R] \sqrt{(1 + (dy/dx)^2} dx[/tex]

In this case, the equation of the semicircle is x² + y² = 9, so y = √(9 - x²). Taking the derivative with respect to x, we have dy/dx = -x/√(9 - x²).

Substituting this into the arc length formula, we have:

s = ∫[0, R] √(1 + (-x/√(9 - x²))²) dx

To find the centre of mass, we need to find the weighted average of the x-coordinate of the wire. The weight function is the linear density function, which is a constant k.

Therefore, the mass of the wire is given by the integral [tex]\int[0, R] k\sqrt{(1 + (-x/\sqrt{(9 - x^2}))^2}[/tex] dx, and the center of mass is given by [tex]\int[0, R] x(k\sqrt{1 + (-x/\sqrt{9 - x^2})^2}[/tex] dx divided by the mass.

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Answer:

Q' = (1, -5)

R' = (3, 1)

S' = (0, 0)

T' = (-2, -3)

Step-by-step explanation:

Look at the numbers of the current vertices and then change the signs of the y-coordinates around. For example, the original Q-coordinate was (1,5) so I changed the 5 to a -5 to reflect across the axis. Changing the y-coordinate sign reflects across the x-axis, while changing the x-coordinate sign reflects across the y-axis.

The solution of the differential equation is 1 = c₁v₁ + c₂v₂ and 5 = c₁v₁ + c₂v₂

We are given a system of two differential equations:

x₁' = – 5x₁ + 0x₂

x₂' = – 16x₁ + 3x₂

To solve this system, we can use several methods, such as substitution or matrix methods. In this explanation, we will use the substitution method.

We can write the given system of differential equations in matrix form as follows:

X' = AX

where X is the column vector [x₁, x₂], X' is the derivative of X, and A is the coefficient matrix:

A = [–5 0]

[–16 3]

To find the eigenvalues λ and eigenvectors v, we solve the characteristic equation:

|A - λI| = 0

where I is the identity matrix. Solving this equation will give us the eigenvalues and eigenvectors.

A - λI = [–5-λ 0]

[–16 3-λ]

Setting the determinant of A - λI to zero, we get:

(–5-λ)(3-λ) - (0)(–16) = 0

Simplifying, we have:

(λ + 5)(λ - 3) = 0

Solving this equation, we find two eigenvalues:

λ₁ = -5

λ₂ = 3

For each eigenvalue, we need to find its corresponding eigenvector. For λ₁ = -5, we solve the system of equations:

(A - (-5)I)v₁ = 0

Substituting the values of A and λ₁, we have:

[0 0] v₁ = 0

[–16 8]

Simplifying the equation, we get:

0v₁ + 0v₂ = 0

-16v₁ + 8v₂ = 0

From the first equation, we can see that v₁ can take any value. Let's choose v₁ = 1 for simplicity. Substituting this value into the second equation, we get:

-16(1) + 8v₂ = 0

-16 + 8v₂ = 0

8v₂ = 16

v₂ = 2

So, for λ₁ = -5, the corresponding eigenvector is v₁ = [1, 2].

Similarly, for λ₂ = 3, we solve the system of equations:

(A - 3I)v₂ = 0

Substituting the values of A and λ₂, we have:

[-8 0] v₂ = 0

[–16 0]

Simplifying the equation, we get:

-8v₁ + 0v₂ = 0

-16v₁ + 0v₂ = 0

From the first equation, we can see that v₁ can take any value. Let's choose v₁ = 1 for simplicity. Substituting this value into the second equation, we get:

-16(1) + 0v₂ = 0

-16 = 0

This equation has no solution. However, this means that v₂ can take any value. Let's choose v₂ = 1 for simplicity.

So, for λ₂ = 3, the corresponding eigenvector is v₂ = [1, 1].

The general solution of the system of differential equations can be expressed as:

X(t) = c₁e(λ₁t)v₁ + c₂e(λ₂t)v₂

where c₁ and c₂ are constants that need to be determined.

We are given the initial conditions x₁(0) = 1 and x₂(0) = 5. Substituting these values into the general solution, we get two equations:

x₁(0) = c₁e(λ₁(0))v₁ + c₂e(λ₂(0))v₂

x₂(0) = c₁e(λ₁(0))v₁ + c₂e(λ₂(0))v₂

Simplifying, we have:

1 = c₁v₁ + c₂v₂

5 = c₁v₁ + c₂v₂

Solving this system of equations, we can find the values of c₁ and c₂.

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Answer:

6a

Step-by-step explanation:

Answer:

6a

Step-by-step explanation:

3a+2a+a= 6a

6-4-2=0

6a+0=6a

Answer:

B

Step-by-step explanation:

Its dominant because its brown hair.

Answer:

the answer is the cheese soup has a good change of being picked but not as good as the chicken soup there would so 3:2 to 2. so if they picked the cheese soup the first time then there is not a good change of the cheese souo to be picked again i hope that helps if not let me know

Answer:

A rectangle

Step-by-step explanation:

A square can be a rectangle but a rectangle can't always be a square.

Answer:

Distancia restante = 1,3 kilómetroslp

Step-by-step explanation:

Dados los siguientes datos;

Distancia total = 4,5 km

Distancia recorrida = 3200 metros a kilómetros = 3200/1000 = 3,2 km

Para encontrar la distancia restante para cubrir la longitud requerida;

Distancia total = distancia recorrida + distancia a la izquierda

4.5 = 3.2 + distancia a la izquierda

Distancia a la izquierda = 4.5 - 3.2 Distancia restante = 1,3 kilómetros

The proportion of weeks in which the waste disposal facility is overloaded is approximately 0.4920.  No, this is not an acceptable level because it is not unusual for the system to be overloaded.

To solve this problem, we need to find the proportion of weeks in which the waste disposal facility is overloaded, given that the weights of the samples of 4712 households are normally distributed with a mean of 26.97 lb and a standard deviation of 12.29 lb.

Let's denote X as the random variable representing the mean weight of the samples of 4712 households in a week. We want to find P(X > 27.22).

To calculate this probability, we can use the standard normal distribution. First, we need to standardize the random variable X using the z-score formula:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation.

Substituting the given values:

z = (27.22 - 26.97) / 12.29

z ≈ 0.0203

Next, we can use a standard normal distribution table or a calculator to find the proportion of weeks in which the waste disposal facility is overloaded:

P(X > 27.22) = P(Z > 0.0203)

Looking up the z-score 0.0203 in the standard normal distribution table, we find that the corresponding proportion is approximately 0.4920.

Therefore, the proportion of weeks in which the waste disposal facility is overloaded is approximately 0.4920. This means that it is not unusual for the system to be overloaded.

So the correct answer is:

No, this is not an acceptable level because it is not unusual for the system to be overloaded.

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Answer:

144

Step-by-step explanation:

24 books at 6 points each would be 24 x 6 which equals 144

Answer:

They'll have 144 points if they read 24 books.

Step-by-step explanation:

6 x 24 = 144

Answer:

Step-by-step explanation:

1 pound = 16 ounces

35 pounds = 560 ounces + 24 ounce = 584ounces

35 pounds,24ounces = 16 ounces

Main Answer: The numerical value of y(2.0) rounded off to three figures is 1.279.

Supporting Explanation:

The student solved the initial-value problem and found that y(2.0) = 1.27977. The question asks to round off the value to three figures. Therefore, we have to keep only the first three digits after the decimal point, which are 279. The next digit after 9 is 7, which means we have to round up the last digit. Thus, the rounded off value of y(2.0) is 1.279.

The initial-value problem is a differential equation that has an initial condition given for a specific value of the independent variable. In this case, the initial condition is y(1) = 2. The solution of the initial-value problem gives the value of y for other values of x. Here, we are required to find the value of y for x = 2.0.

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