The function f(x) = \frac{5}{(1 - 9 x)^2} is represented as a power series \displaystyle f(x) = \sum_{n=0}^\infty c_n x^n . Find the first few coefficients in the power series. c_0 = c_1 = c_2 = c_3 = c_4 = Find the radius of convergence R of the series.

Answer:

[tex]\frac{4}{15}[/tex]  (4/15)

Step-by-step explanation:

[tex]\frac{4}{6}=\frac{2}{3}[/tex]

[tex]\frac{2}{5}*\frac{2}{3};[/tex]

1- Multiply the numerators:

[tex]2*2=4[/tex]

2- Multiply the denominators:

[tex]5*3=15[/tex]

3- Thus:

[tex]\frac{2}{5}*\frac{2}{3}= \frac{4}{15}[/tex]

Hope this helps ;)

Answer:

7

Step-by-step explanation:

the answer I got was 7 hope this helped

The probability that all orders are fulfilled on a day chosen at random is approximately 1. Answer: 1.0000 (rounded off to at least four decimal places).

The quantities ordered by customers are independent continuous random variables, and they are uniformly distributed over the interval (0, 9).

The fresh food distributor only has the capacity to ship 477 kg of products daily, and the distributor receives orders from 100 customers daily.

The probability that all orders are fulfilled on a day chosen at random is given by;P(all orders fulfilled) = P(X1 + X2 + ... + X100 < 477)

where X is the quantity ordered by each customer. Since X is a continuous random variable, we can use the probability density function of a uniform distribution to calculate the probability density function of X as;f(x) = 1/9, 0 < x < 9

Hence, the probability that all orders are fulfilled on a day chosen at random is given by;

P(all orders fulfilled) = P(X1 + X2 + ... + X100 < 477)= P[(X1/9) + (X2/9) + ... + (X100/9) < (477/9)]= P[U < (53 + 1/3)], where U ~ Uniform(0, 1)

Now, using the central limit theorem, we can approximate the distribution of U by a normal distribution with mean μ = 1/2 and variance σ^2 = 1/12 such that;Z = (U - μ) / σ ~ N(0, 1)

Hence, P[U < (53 + 1/3)] = P[Z < (53 + 1/3 - μ) / σ]= P[Z < (53 + 1/3 - 1/2) / sqrt(1/12)]≈ P[Z < 9.6067]≈ 1

Thus, the probability that all orders are fulfilled on a day chosen at random is approximately 1. Answer: 1.0000 (rounded off to at least four decimal places).

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Answer:

True

Step-by-step explanation:

The wording of the question is a little tricky, but here's what I think.

If a function f(x) is not defined at a point c, then the function has a discontinuity at that point. In order for a function to be continuous on an interval, it must be defined and have no abrupt changes or jumps within that interval. Since f(x) is not defined at c, it violates the condition of continuity, and therefore f(x) cannot be continuous on any interval that includes c.

The given statement "If f(x) is not defined at c, then f(x) cannot be continuous on any interval." is false because it does not automatically mean that f(x) cannot be continuous on any interval.

Continuity of a function depends on the behavior of the function around the point of interest, rather than just the absence of a definition at a single point. A function can still be continuous on an interval except at the specific point where it is not defined.

For example, consider the function f(x) = 1/x. This function is not defined at x = 0, but it is continuous on any interval that does not include x = 0. This is because f(x) approaches positive or negative infinity as x approaches 0 from the left or right side, respectively, indicating that there is no abrupt jump or discontinuity.

In general, the continuity of a function is determined by its behavior around a point, including its limit as x approaches that point. The absence of a definition at a single point does not automatically imply that the function cannot be continuous on any interval.

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Answer:

24

Brainliest?

Answer:

nxbxbxxbznznxnxnxnxnxnxnxbxbbxbnxxnxnx

Step-by-step explanation:

xnncxbbxbxbxbxbxbx hahahahahahahahahahahah

Answer:

in right angled triangleBCD

BC=√{DC²-BC²)=√{10²-6²)=8

again in right angled triangle ABC

AB=√(BC²-AC²)

x=√(8²-7²)=3.87

The answer is x = 15.

15 or 20.33 are the possible values of the x.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

We know that sin(x+37)°=cos(90°-(x+37)°) and cos(2x+8)°=sin(90°-(2x+8)°)

So we have sin(x+37)°=cos(2x+8)° becomes sin(x+37)°=sin(82°-2x)

For the above equation to be true, either of the following must hold:

x+37 = 82 - 2x (since the sin function is periodic)

x+37 = 180 - (82-2x)

Solving the first equation for x gives:

3x = 45

x = 15

Solving the second equation for x gives:

3x = 61

x = 20.33 (rounded to two decimal places)

Therefore, the possible values of x are 15 or 20.33 (rounded to two decimal places).

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Ancient Egyptian way of computation, division was performed using a method called "repeated subtraction." (a) 26 ÷ 20 = 1 remainder 6.

(b) 55 ÷ 6 = 9 remainder 19.

(c) 71 21 ÷ = 50 remainder 29.

(d) 25 18 ÷ = 7.

(e) 52 ÷ 68 = 0 remainder 52.

(f) 13 36 ÷ = 0 remainder -23.

In the ancient Egyptian way of computation, division was performed using a method called "repeated subtraction." Here's how it would be applied to the given divisions:

(a) 26 ÷ 20:

To divide 26 by 20, we repeatedly subtract 20 from 26 until we cannot subtract anymore. The number of times we subtract is the quotient.

26 - 20 = 6

6 - 20 = -14 (cannot subtract anymore)

Therefore, 26 ÷ 20 = 1 remainder 6.

(b) 55 ÷ 6:

Using the same method, we repeatedly subtract 6 from 55 until we cannot subtract anymore.

55 - 6 = 49

49 - 6 = 43

43 - 6 = 37

37 - 6 = 31

31 - 6 = 25

25 - 6 = 19 (cannot subtract anymore)

Therefore, 55 ÷ 6 = 9 remainder 19.

(c) 71 21 ÷:

To divide 71 21 by a number, we first convert it to a whole number by multiplying the fraction part by the denominator.

71 21 = 71 + (21/100) = 71 + 21/100

Now, we can perform division using repeated subtraction.

71 - 21 = 50

50 - 21 = 29 (cannot subtract anymore)

Therefore, 71 21 ÷ = 50 remainder 29.

(d) 25 18 ÷:

Similar to the previous case, we convert 25 18 to a whole number.

25 18 = 25 + (18/100) = 25 + 18/100

Performing division:

25 - 18 = 7

Therefore, 25 18 ÷ = 7.

(e) 52 ÷ 68:

Since 52 is smaller than 68, the quotient is 0.

Therefore, 52 ÷ 68 = 0 remainder 52.

(f) 13 36 ÷:

Converting to a whole number:

13 36 = 13 + (36/100) = 13 + 36/100

Performing division:

13 - 36 = -23 (cannot subtract anymore)

Therefore, 13 36 ÷ = 0 remainder -23.

Please note that the ancient Egyptian method of division is not as efficient as modern division methods and may not produce exact decimal results.

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Answer:

6/9

Step-by-step explanation:

The correct statement regarding r squared is:

r squared equals 0.4268 meaning that Years of Experience explains 42.68 percent of the variability in Salary.

Part A: The correct null and alternate hypotheses are:

H₀: β₁=0;

H₁: β₁≠0.

Part B: The correct p-value for the test in Q1 is 1.74e-13.

Part C: The fitted regression model from this output in Q1 is:

E(Salary) = 31.8387 + 2.8205 x Years of Experience.

Part D: The correct statement regarding r squared is:

r squared equals 0.4268 meaning that Years of Experience explains 42.68 percent of the variability in Salary.

Explanation: The output shows a multiple linear regression model:

Salary=β0+β1x

Years of Experience + ϵ.β0 is the intercept and represents the expected mean salary for an individual with 0 years of experience.

β1 is the slope and represents the expected change in salary due to one year increase in experience.

ϵ is the error term (deviation from the expected salary).

The correct null and alternate hypotheses are:

H₀: β₁=0 (there is no linear relationship between salary and years of experience).

H₁: β₁≠0 (there is a linear relationship between salary and years of experience).

The correct p-value for the test in Q1 is 1.74e-13, which is much smaller than the significance level of 0.05.

Thus, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that there is a linear relationship between salary and years of experience.

The fitted regression model from this output in Q1 is:

E(Salary) = 31.8387 + 2.8205 x Years of Experience.

The coefficient of determination, or R-squared, is a statistical measure that shows how well the regression model fits the observed data.

It is the proportion of the variance in the dependent variable that is explained by the independent variable(s).

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Answer:

12

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√[4 - (-8)]² + (10 - 10)²

√(12)² + (0)²

√144 + 0

√144

=12

The solution to the system of inequalities is the region above the x-axis and to the right of the line y = 1, shaded in green.

Given system of inequalities is: x - 2y ≤ 3 ...(1)3x + 4y ≥ 12 ...(2)x ≥ 0 ...(3)y ≥ 1 ...(4)

We graph the lines x - 2y = 3 and 3x + 4y = 12 and shade the appropriate regions.

Let's start with the line x - 2y = 3.

We rewrite this as y = (1/2)x - 3/2 and plot the line as shown below: graph{(1/2)x - 3/2 [-10, 10, -5, 5]}

Now we determine which side of the line we want to shade.

Since the inequality is of the form ≤, we shade below the line y = (1/2)x - 3/2 (including the line itself) as shown below: graph {(1/2)x - 3/2 [-10, 10, -5, 5](-10,-5)--(10,0)}

Next, we graph the line 3x + 4y = 12. We rewrite this as y = (-3/4)x + 3 and plot the line as shown below: graph{(-3/4)x + 3 [-10, 10, -5, 5]}

We determine which side of the line we want to shade. Since the inequality is of the form ≥, we shade above the line y = (-3/4)x + 3 (including the line itself) as shown below: graph{(-3/4)x + 3 [-10, 10, -5, 5](-10,4)--(10,0)}

Finally, we shade the region that satisfies x ≥ 0 and y ≥ 1.

This is the region above the x-axis and to the right of the line y = 1 as shown below: graph{(-3/4)x + 3 [-10, 10, -5, 5](-10,4)--(10,0)(0,1)--(10,1)[above]}

The shaded region is the region that satisfies all three inequalities.

Thus, the solution to the system of inequalities is the region above the x-axis and to the right of the line y = 1, shaded in green.

We graph the lines x - 2y = 3 and 3x + 4y = 12 and shade the appropriate regions.

Let's start with the line x - 2y = 3. We rewrite this as y = (1/2)x - 3/2 and plot the line.

Now we determine which side of the line we want to shade. Since the inequality is of the form ≤, we shade below the line y = (1/2)x - 3/2 (including the line itself).

Next, we graph the line 3x + 4y = 12. We rewrite this as y = (-3/4)x + 3 and plot the line. We determine which side of the line we want to shade.

Since the inequality is of the form ≥, we shade above the line y = (-3/4)x + 3 (including the line itself).

Finally, we shade the region that satisfies x ≥ 0 and y ≥ 1.

This is the region above the x-axis and to the right of the line y = 1. The shaded region is the region that satisfies all three inequalities.

Thus, the solution to the system of inequalities is the region above the x-axis and to the right of the line y = 1, shaded in green.

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Answer:

FGH DEJ .................

Answer:

22cm

Step-by-step explanation:

Length of arc = [tex]\frac{theta}{360}[/tex] * 2[tex]\pi[/tex]r

                      = [tex]\frac{45}{360}[/tex] * 2 * [tex]\frac{22}{7}[/tex] * 28

                      = 22 cm

The most probable values for X and Y are X = 11.75 and Y = 1.1, respectively.

To solve the system of equations using the tabular or matrix method, we first convert the given equations into matrix form. We create a coefficient matrix A by arranging the coefficients of the variables X and Y, and a constant vector B by placing the constants on the other side of the equations.

To solve the system of equations using the tabular method or matrix method, we'll first write the equations in matrix form. Let's define the coefficient matrix A and the constant vector B:

A = | 1 2 |

| 2 -3 |

| 2 -1 |

B = | 10.5 |

| 5.5 |

| 10.0 |

Now, we can solve the system of equations by finding the inverse of matrix A and multiplying it with vector B:

[tex]A^{(-1)[/tex] = | 1.5 1 |

| 0.4 0.2 |

X = [tex]A^{(-1)[/tex] * B

Multiplying [tex]A^{(-1)[/tex] with B, we get:

X = | 1.5 1 | * | 10.5 | = | 11.75 |

| 0.4 0.2 | | 5.5 | | 1.1 |

Therefore, the most probable values for X and Y are X = 11.75 and Y = 1.1, respectively.

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Answer:

181 feet

Step-by-step explanation:

From the the diagram attached ,

Sinθ = a/b..................... Equation 1

Where θ = angle to the horizontal, a = Height of the tower, b = length of the wire.

make b the subject of the equation

b = a/sinθ................. Equation 2

Given: a = 128 feet, θ = 45°

Substitute these values into equation 2

b = 128/sin45°

b = 128/0.7071

b = 181 feet

b = 181 feet

In Hausdorff-space "X", if A and B are disjoint "compact-subspaces", then there is disjoint "open-sets" U and V such that A is contained in U and B is contained in V, this is because by Hausdorff-Property, the existence of disjoint open neighborhoods for any two "distinct-points".

To prove the existence of disjoint "open-sets" U and V with A⊂U and B⊂V, where A and B are "compact-subspaces" of "Hausdorff-space" X,

Step (1) : A and B are disjoint compact-subspaces, we use Hausdorff property to find "open-sets" Uₐ and [tex]U_{b}[/tex] such that "A⊂Uₐ" and "B⊂[tex]U_{b}[/tex]", and "Uₐ∩[tex]U_{b}[/tex] = ∅". This can be done for every pair of points in A and B, respectively, because X is Hausdorff.

Step (2) : We consider, set U = ⋃ Uₐ, where "union" is taken over all of Uₐ for each-point in A. U is = union of "open-sets", hence open.

Step (3) : We consider set V = ⋃ [tex]U_{b}[/tex], where union is taken over for all [tex]U_{b}[/tex] for "every-point" in B. V is also a union of open-sets and so, open.

Step (4) : We claim that U and V are disjoint. Suppose there exists a point x in U∩V. Then x must be in Uₐ for some point a in A and also in [tex]U_{b}[/tex] for some point b in B. Since A and B are disjoint, a and b are different points. However, this contradicts the fact that Uₐ and [tex]U_{b}[/tex] are disjoint open sets.

Therefore, U and V are disjoint open sets with A⊂U and B⊂V.

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The given question is incomplete, the complete question is

Let A and B be disjoint compact subspaces of a Hausdorff space X. Show that there exist disjoint open sets U and V, with A⊂U and B⊂V.

Answer:

40,000

Step by step explanation:

842,963

840,000

40,000

The values of c₁ and c₂ that satisfy the initial values u(0) = 60 and u'(0) = 56 are:

c₁ = 148 / (3e²)

c₂ = (20 - 148/9)e⁴

The given solution, u(t) = c₁e² + c₂e⁻⁴, indeed satisfies the given ordinary differential equation (ODE) u"(t) + u'(t) - 12u(t) = 0. To find the values of c₁ and c₂ such that the solution satisfies the initial values u(0) = 60 and u'(0) = 56, we substitute these values into the solution.

First, let's find u(0) by substituting t = 0 into the solution:

u(0) = c₁e² + c₂e⁻⁴

Since u(0) = 60, we have:

60 = c₁e² + c₂e⁻⁴    (Equation 2)

Next, let's find u'(0) by differentiating the solution with respect to t and substituting t = 0:

u'(t) = 2c₁e² - 4c₂e⁻⁴

u'(0) = 2c₁e² - 4c₂e⁻⁴

Since u'(0) = 56, we have:

56 = 2c₁e² - 4c₂e⁻⁴    (Equation 3)

Now we have a system of two equations (Equations 2 and 3) with two unknowns (c₁ and c₂). We can solve this system to find the values of c₁ and c₂.

To do that, let's first divide Equation 3 by 2:

28 = c₁e² - 2c₂e⁻⁴

Next, let's multiply Equation 2 by 2:

120 = 2c₁e² + 2c₂e⁻⁴

Adding the two equations, we get:

148 = 3c₁e²

Dividing both sides by 3e², we find:

c₁ = 148 / (3e²)

Substituting this value of c₁ back into Equation 2, we can solve for c₂:

60 = (148 / (3e²))e² + c₂e⁻⁴

60 = 148/3 + c₂e⁻⁴

60 - 148/3 = c₂e⁻⁴

20 - 148/9 = c₂e⁻⁴

c₂ = (20 - 148/9)e⁴

Therefore, the values of c₁ and c₂ that satisfy the initial values u(0) = 60 and u'(0) = 56 are:

c₁ = 148 / (3e²)

c₂ = (20 - 148/9)e⁴

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Answer:

17cm

Step-by-step explanation:

The two equal sides are 14cm long so 45 - 14 - 14 = 17

Answer:

b

Step-by-step explanation:

oi did the quiz f. 6373737

Answer:

-6

Step-by-step explanation:

Step One: The goal is to isolate the x. So first, we would do 4-22, which is -18. The equation is: 3x=-18.

Step Two: Lastly, we need to divide by three to completely isolate the x. This is -6.

Answer:

78

Step-by-step explanation:

Answer:

1440 and 144 on edg 2020-2021

Step-by-step explanation:

Answer:

y=10

Step-by-step explanation:

[tex]\frac{4}{100}[/tex]=[tex]\frac{y}{250}[/tex]

cross-multiply, 4*250=100y

isolate the variable and solve for y, 1000=100y

divide 100 on both sides, 10=y

Answer:

[tex]\frac{b^2 - 4ac}{4a^2}[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required:

Complete step 6

At step 5, we have:

[tex](x + \frac{b}{2a})^2 = \frac{b^2}{4a^2} - \frac{4ac}{4a^2}[/tex]

Take LCM

[tex](x + \frac{b}{2a})^2 = \frac{b^2 - 4ac}{4a^2}[/tex]

Take square roots of both sides to get step 6

[tex]x + \frac{b}{2a} = \±\sqrt{\frac{b^2 - 4ac}{4a^2}}[/tex]

Hence, the missing radicand is: [tex]\frac{b^2 - 4ac}{4a^2}[/tex]

Answer:

2.28871.0005^14

Step-by-step explanation:

Answer:

i got 8067661468.26  

Step-by-step explanation:

Answer:

Given -

In a certain chemical, the ratio of zinc to copper is 4 to 13.

The chemical contains 546 grams of copper.

Prove  -

How many grams of zinc does it chemical contain.

Answer

suppose that scalar multiple of the  zinc and copper be y .

As given

In a certain chemical, the ratio of zinc to copper is 4 to 13.

The chemical contains 546 grams of copper.

Than equation is

13y = 546

13y = 546

y = 42

Zinc contain in the certain chemical = 4y

                                             = 4 42

                                             = 168 grams

Therefore 168 grams of zinc contain in a certain chemical .Step-by-step explanation:

The answer is A, 3.9a + b

Step-by-step explanation:

youre welcome