show all work please!
Use any method to determine whether the series converges. 00 k2 «Σ a. 5* Σ. 2+(-1)* b b 5k k=1
Answers
we can only say that the series ∑a_k^2 converges, but we cannot determine the convergence of the series ∑(-1)^k b_k.
Let's evaluate the two series separately:
First, for the series ∑a_k^2, we note that a_k^2 is always non-negative. Therefore, we can use the comparison test and compare it to the p-series ∑1/k^2, which we know converges:
```
0 ≤ a_k^2 ≤ 1/k^2
```
Since ∑1/k^2 converges, so does ∑a_k^2 by the comparison test.
Next, for the series ∑(-1)^k b_k, we note that the terms alternate in sign. Therefore, we can use the alternating series test to check for convergence. The alternating series test states that if a series ∑(-1)^k b_k converges, then b_k must satisfy the following conditions:
1. b_k ≥ 0 for all k
2. b_k is a non-increasing sequence (i.e., b_k ≥ b_{k+1} for all k)
3. lim_{k→∞} b_k = 0
We can see that condition 1 is not satisfied for the given series, as b_k = 2 for all even values of k and b_k = -1 for all odd values of k. Therefore, the alternating series test does not apply to this series.
In conclusion, we can only say that the series ∑a_k^2 converges, but we cannot determine the convergence of the series ∑(-1)^k b_k.
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Related Questions
Evaluate x³ for x = 2.
06
02
08
Answers
Answer:
8
Step-by-step explanation:
x³; x = 2
2³ or 2 × 2 × 2 = 8
I hope this helps!
A six-sided die is rolled. (Enter your probabilities as fractions.) (a) What is the probability that a 3 will result? 9/24 (b) What is the probability that a 10 will result? 0 (c) What is the probability that an even number will result?
Answers
Answer: 50%
Step-by-step explanation:
For an even # to result, the fraction would be 3/6 or 1/2 which would become 0.5 or 50%.
(a) The probability of rolling a 3 is 1/6.
(b) The probability of rolling a 10 is 0 since a standard six-sided die only has numbers from 1 to 6.
(c) The probability of rolling an even number is 3/6 or 1/2. This is because there are three even numbers (2, 4, and 6) out of the six possible outcomes.
(a) The probability of rolling a 3 on a six-sided die is 1/6. There are 6 possible outcomes when rolling a die, and only 1 of those outcomes is a 3.
(b) The probability of rolling a 10 on a six-sided die is 0. There are no possible outcomes when rolling a die that will result in a 10.
(c) The probability of rolling an even number on a six-sided die is 1/2. There are 3 possible outcomes when rolling a die that will result in an even number: 2, 4, and 6.
Here are the answers in mathematical notation:
(a) P(3) = 1/6
(b) P(10) = 0
(c) P(even) = 1/2
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Powers of products and quotients (integer exponents)
Answers
Answer:
C
Step-by-step explanation:
What is the y-intercept of 2x y =- 3?
Answers
The y-intercept of the equation 2x - y = -3 is 3 and in ordered pair form is (0,3).
What is the y-intercept of the given equation?The slope-intercept formula is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation in the question
2x - y = -3
First, we solve form for y and reorder in slope intercept form.
2x - y = -3
Subtract 2x from both sides
2x - 2x- y = -3 - 2x
- y = -3 - 2x
Divide each term by -1
y = 3 + 2x
Reorder in slope intercept form
y = 2x + 3
To find the y-intercept, replace x with zero and solve for y
y = 2(0) + 3
y = 3
Therefore, the y-intercept is 3.
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The nullspace of nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors.
A. True
B. False
Answers
The given statement, "The nullspace of a nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors" is False.
Explanation: Null space is a linear algebra term used to refer to the set of all vectors that are mapped to the null vector. The solution of Ax=0 is also referred to as the null space or kernel of A. Since the matrix is of size 4x4 and non-zero, it must have at least one non-zero eigenvalue. Any non-zero vector multiplied by this non-zero eigenvalue will result in a non-zero vector, even if it is in the nullspace of the matrix. Because of this, a non-zero 4 x 4 matrix's nullspace can have four or fewer linearly independent vectors.
Hence, the statement "The nullspace of a nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors" is false.
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on january 1, year 1, billy co signed a three-year lease for office space. the lease required monthly rent of $8,000 for the first year, $8,100 fo rhte second year
Answers
If on january 1, year 1, billy co signed a three-year lease for office space The amortization expense on this leasehold improvement that Billy should record for Year 2 is: $1,000.
How to find the amortization expense?Since we were told that the new overhead lighting fixtures is the amount of $2,000 now let determine the Amortization expense using this formula
Amortization expense = New overhead lighting fixtures / 2 years
Let plug in the formula
Amortization expense = $2,000 /2
Amortization expense = $1,000
Therefore the Amortization expense is the amount of $1,000.
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The complete question:
On January 1 , Year 1, Billy Co. signed a three year lease for office space. The lease required monthly rent of 8,000 for the first year. 8,100 for the second year and 8,200 for the 3rd year. Billy has the option to renew the lease for a fourth year at 8,300 per month. On January 1, Year 2, Billy permanently installed new overhead lighting fixtures at a cost of $2,000. How much amortization expense on this leasehold improvement should Billy record for Year 2?
What is the average of −18.75 and 200.25?
90.75
100.125
109.5
181.5
Answers
I need help what’s the answer?
Answers
Answer:
Step-by-step explanatiobxbsbsx
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use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. y = x , x = 4y; about x = 17
Answers
The volume generated by rotating the region bounded by the curves y = x and x = 4y about the axis x = 17 can be found using the method of cylindrical shells.
To start, let's consider a vertical strip in the region, parallel to the y-axis, with a width dy. As we rotate this strip around the axis x = 17, it creates a cylindrical shell. The radius of each shell is given by the distance between the axis of rotation (x = 17) and the curve y = x or y = x/4, depending on the region. The height of each shell is given by the difference between the curves y = x and y = x/4.
We can express the radius as r = 17 - y and the height as h = x - x/4 = 3x/4. The circumference of each cylindrical shell is given by 2πr, and the volume of each shell is given by 2πrhdy. Integrating the volumes of all the shells over the appropriate range of y will give us the total volume.
By setting up and evaluating the integral, we can find the volume generated by rotating the region about the axis x = 17 using the method of cylindrical shells.
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There are 6 white socks, 3 blue socks, and 1 black sock in a basket. One sock is randomly picked and replaced. Then another sock is picked. What is the probability of getting a blue sock then a black sock?
Answers
The probability of getting a blue sock then a black sock is 3/100 or 0.03.
The probability of picking a blue sock on the first draw is 3/10 (since there are 3 blue socks out of a total of 10 socks).
Calculate the probability of picking a blue sock first.
There are 3 blue socks out of a total of 10 socks (6 white + 3 blue + 1 black), so the probability of picking a blue sock first is 3/10.
Since the sock is replaced, the total number of socks remains the same. Calculate the probability of picking a black sock second.
There is 1 black sock out of a total of 10 socks, so the probability of picking a black sock second is 1/10.
Multiply the probabilities together.
The probability of both events happening in sequence is (3/10) * (1/10) = 3/100.
So, the probability of getting a blue sock then a black sock is 3/100.
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calculate the solar flux density (also known as the solar constant) for mercury using the following information: solar luminosity = 3.865 x 10^26 w distance of mercury from the sun = 5.791 x 10^10 m
Answers
Therefore, the solar flux density for mercury after the calculation is 9.12 x 10⁻³ W/m².
The solar flux density also referred to as the solar constant is the total amount of energy derived from the sun per unit area per given unit of time. It is considered to be equal to solar luminosity divided by the surface area of a given sphere that has a radius equivalent to the distance between the respective planet from the sun.
using the formula for finding the solar flux density,
solar flux density = solar luminosity /(4 x π x distance between mercury and the sun)
solar flux density = 3.865 x \(10^{26}\) /(4 x π x ( 5.791 x \(10^{10}\)))
solar flux density = 9.12 x 10⁻³ W/m²
Therefore, the solar flux density for mercury after the calculation is 9.12 x 10⁻³ W/m².
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A customer has the option of paying for a kitchen knife set in 6 or 8 monthly installments. Either way, she will pay a total of d dollars. How many dollars less per month will she pay if she chooses 8 monthly installments instead of 6? A) d/14 B) d/24 C) d/2 D) d/48
I NEED
SERIOUS HELP TO OTHER QUESTIONS AS WELL
Answers
Answer:
D over 24
Step-by-step explanation:
just had the same question
Janice and her cousin Linda are a little competitive about the relative merits of their home towns. One contest they had was to determine who had more rainy days. They found weather records on the internet and each of them randomly selected 60 days from the past 5 years. Janice found that there had been measurable rainfall on 17 of the 60 days she selected for Asheville, and Linda found that there had been measurable rainfall on 12 of the 60 days she selected for Lincoln. They intend to perform a test of significance on their data, using the hypotheses When calculating the test statistic, what expression would they use to estimate the standard deviation of the sampling distribution of the difference in proportions,
Answers
Answer:
Following are the equation to this question:
Step-by-step explanation:
\(\to \frac{\sqrt{(.24)(.76)}}{60} + \frac{(.24)(.76)}{60}\\\\\to \frac{\sqrt{0.1824}}{60} + \frac{0.1824}{60}\\\\\to \frac{0.42708313}{60} + \frac{0.1824}{60}\\\\\to \frac{0.42708313+0.1824}{60} \\\\\to \frac{0.60948313}{60} \\\\\to 0.0101580522\)
estimate the change in the advertising budget necessary to maintain a monthly profit of $93,500 if the insurance company hires 5 new sales associates.
Answers
The change in the advertising budget necessary to maintain a monthly profit of $93,500 if the insurance company hires 5 new sales associates is estimated to be an increase of $2,308.
To estimate the change in advertising budget necessary to maintain a monthly profit of $93,500 with the addition of 5 new sales associates, we need to consider the potential impact of these new hires on the company's revenue and expenses.
Assuming that each new sales associate is expected to generate $10,000 in revenue per month, the total increase in revenue would be $50,000 (5 sales associates x $10,000).
However, there may also be additional expenses associated with the new hires, such as salaries and benefits. Let's assume that the total cost of adding 5 new sales associates is $30,000 per month.
Therefore, the net increase in monthly profit due to the new hires would be $20,000 ($50,000 in revenue - $30,000 in expenses).
To maintain a monthly profit of $93,500, the company would need to increase its advertising budget by an amount that would generate an additional $20,000 in profit. Assuming that the company's profit margin on its products is 20%, this would require an additional $100,000 in revenue per month ($20,000 / 0.20).
Based on the historical data and market conditions, the company could estimate the additional advertising budget required to generate this amount of revenue.
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How do you write an equation in slope-intercept form of the line that is perpendicular to a graph?.
Answers
The original slope's reciprocal will be the opposite of the perpendicular slope. To determine the intercept, b, enter the supplied point and the new slope into the slope-intercept form (y = mx + b). Rewrite the following equation in standard form: ax + by = c.
The values of the slope and y-intercept provide details on the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.
Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 6x + 2, is 6.
The slope is m and the y-intercept is b in the equation y=mx+b in slope-intercept form. Some equations can also be rewritten so that they resemble slope-intercept form. For instance, y=x can be written as y=1x+0, resulting in a slope and y-intercept of 1 and 0, respectively.
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PLEASE HELP QUICK!!!!!!!!
Question 3
Solve the division equation using the fraction model.
A fraction strip partitioned into two equal parts, each part is partitioned into three equal parts. One of those parts is shaded. Below is the equation one half divided by three equals blank.
A. one sixth
B. 5
C. three sixths
D. 6
Answers
Answer:
I think option no B is the correct answer wer.
find the value of k for which the equation 3x square-6x+k=0 has district real root
Answers
Explanation:
show that β=3α, by calculating the infinitesimal change in volume dv of a cube with sides of length l when the temperature changes by dt.
Answers
To show that β=3α, where β represents the volumetric thermal expansion coefficient and α represents the linear thermal expansion coefficient, we can calculate the infinitesimal change in volume (dv) of a cube with sides of length l when the temperature changes by dt.
The linear thermal expansion coefficient α is defined as the fractional change in length per unit change in temperature. Similarly, the volumetric thermal expansion coefficient β is defined as the fractional change in volume per unit change in temperature.
Let's consider a cube with sides of length l. The initial volume of the cube is \(V = l^3\). Now, when the temperature changes by dt, the sides of the cube will also change. Let dl be the infinitesimal change in length due to the temperature change.
The infinitesimal change in volume, dv, can be calculated using the formula for differential calculus:
\(\[dv = \frac{{\partial V}}{{\partial l}} dl = \frac{{dV}}{{dl}} dl\]\)
Since \(V = l^3,\) we can differentiate both sides of the equation with respect to l:
\(\[dV = 3l^2 dl\]\)
Substituting this back into the previous equation, we get:
\(\[dv = 3l^2 dl\]\)
Now, we can express dl in terms of dt using the linear thermal expansion coefficient α:
\(\[dl = \alpha l dt\]\)
Substituting this into the equation for dv, we have:
\(\[dv = 3l^2 \alpha l dt = 3\alpha l^3 dt\]\)
Comparing this with the definition of β (fractional change in volume per unit change in temperature), we find that:
\(\[\beta = \frac{{dv}}{{V dt}} = \frac{{3\alpha l^3 dt}}{{l^3 dt}} = 3\alpha\]\)
Therefore, we have shown that β = 3α, indicating that the volumetric thermal expansion coefficient is three times the linear thermal expansion coefficient for a cube.
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A large plane cruises at 530 miles per hour. What is the ratio, Unit Rate, and Rate?
Answers
Answer:
For this example they are all the same thing.
530:1 or 530 mph
Step-by-step explanation:
A unit rate is when the denominator is 1. In this case, the denominator is already 1 hour.
Use the image to answer the question.
A rectangular prism net has a length of 6 inches, width of 3 inches, and a height of 2 inches.
Use the net to find the surface area of this rectangular prism.
A.
36 square cm
B.
72 square cm
C.
66 square cm
D.
60 square cm
Answers
Answer:
To find the surface area of the rectangular prism, we need to add up the areas of all six faces.
From the net, we can see that there are two rectangles with dimensions 6 x 3 (the top and bottom faces), two rectangles with dimensions 2 x 3 (the left and right faces), and two rectangles with dimensions 6 x 2 (the front and back faces).
The area of each rectangle is given by the formula A = lw, where l is the length and w is the width.
So, the surface area of the rectangular prism is:
2(6 x 3) + 2(2 x 3) + 2(6 x 2)
= 2(18) + 2(6) + 2(12)
= 36 + 12 + 24
= 72
Therefore, the surface area of the rectangular prism is 72 square inches.
could you help me with this
Answers
Answer: 40
Step-by-step explanation:
All you have to do is divide it. However, the actual answer is 40.5, but I'm sure that they round it.
Answer:
There would be 40
Step-by-step explanation:
The Steelers have won 6 out of their 8
Super Bowl games. What percent of their
Super Bowl games did they not win?
Please help me!
Answers
Answer:25%
Step-by-step explanation: lost 2 so divide 2 by the total number of 8
Please help me answer I need one now
Answers
Answer:
\(\sqrt[7]{(-4)^{2} }\)
Step-by-step explanation:
A piece of equipment has two components, A and B. The equipment will fail if either component A or B fails. If the system Has a probability of failure =.003, and A has a reliability of 998 , what is the reliability of B ?
Answers
The reliability of component B in the equipment system can be calculated based on the given information that the probability of system failure is 0.003 and component A has a reliability of 0.998.
The reliability of a system is the probability that it will function without failure over a specified period. In this case, the system will fail if either component A or B fails. Let's denote the reliability of component B as R(B). The probability of system failure is equal to the complement of the reliability, so we have:
Probability of failure = 1 - R(B) = 0.003.Given that the reliability of component A is 0.998, we know that the system will only fail if both components A and B fail simultaneously. Since the system failure probability is very low (0.003), we can assume that the probability of both components failing together is negligible.
Probability of failure = Probability of failure of A * Probability of failure of B. Since the probability of failure of A is negligible compared to the system failure probability, we can simplify the equation as: 1 - R(B) ≈ 0.003. Solving for R(B), we find: R(B) ≈ 1 - 0.003 = 0.997
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How do you find the Constant of Proportionality in a graph, table or in ordered pairs?
a.divide x by x
b.divide x by y
c.divide y by x
d.divide y by k
Answers
The constant of proportionality in a graph, table or ordered pairs is divide y by x
Ising a graph, the constant of proportionality is the constant value of the ratio obtained from two proportional quantities.
How to obtain a constant of proportionality?
The constant of proportionality is the slope of the graph of a straight line.
The slope of a graph of a straight line is determined by:
Slope = rise /run or increase in y/increase in x or decrease in y/decrease in x
In conclusion, rise in y/run in x determines the constant of proportionality.
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can someone please help me with this page? it would be very greatly appreciated! thanks!
Answers
Answer:
x=b6+y
Step-by-step explanation:
Ali's tyre pressure gauge shows a reading which is 8% lower than the actual pressure.
What is the actual pressure of Ali's tyres when the gauge shows 33.58?
Answers
8% is 0.08
If 33.58 is .08 lower than the actual, just add the two decimals together.
33.58 + 0.08 = 33.66
Find value of x.
A. 110
B. 47
C. 68
D. 112
Answers
Answer:
B
Step-by-step explanation:
The sum of the inner angles of a quadrilateral is 360 degrees
135 + 110 + 68 + x = 360
313 + x = 360
x = 47 degrees
Answer:
47
Step-by-step explanation:
whole thing is 360 degrees
68 + 110 + 135 = 313
360 - 313 = 47
x looks small too (if you had to guess in a multiple choice question)
Convert 4g into mg please- i'll give you 10 points
Answers
Answer:
4000 mg
Step-by-step explanation:
4grams · 1000 = 4000 milligrams
Answer:
4000 mg
Step-by-step explanation:
3x + 5y=32 2x + 3y=23 solve by elimintaion method
Answers
Answer:
x=19, y=-5
Step-by-step explanation:
Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.
Point Form:
(19, -5)
Equation Form:
x=19, y=-5
Hope this helps.
