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

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.

Answer:

D over 24

Step-by-step explanation:

just had the same question

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.

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?

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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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.

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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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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Answer:

Following are the equation to this question:

Step-by-step explanation:

\(\to \frac{\sqrt{(.24)(.76)}}{60} + \frac{(.24)(.76)}{60}\\\\\to \frac{\sqrt{0.1824}}{60} + \frac{0.1824}{60}\\\\\to \frac{0.42708313}{60} + \frac{0.1824}{60}\\\\\to \frac{0.42708313+0.1824}{60} \\\\\to \frac{0.60948313}{60} \\\\\to 0.0101580522\)

Answer:

8

Step-by-step explanation:

x³; x = 2

2³ or 2 × 2 × 2 = 8

I hope this helps!

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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Answer:

Step-by-step explanatiobxbsbsx

xbsbxs sbsbx

bxbxb xx xgsgsywubxhshs bxhx ss

bx bx sh bxsh sxhssbxhs

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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Answer:

C

Step-by-step explanation:

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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Answer:

\(\sqrt[7]{(-4)^{2} }\)

Step-by-step explanation:

Answer:25%

Step-by-step explanation: lost 2 so divide 2 by the total number of 8

Answer:

4000 mg

Step-by-step explanation:

4grams · 1000 = 4000 milligrams

Answer:

4000 mg

Step-by-step explanation:

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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The y-intercept of the equation 2x - y = -3 is 3 and in ordered pair form is (0,3).

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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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:

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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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.

Answer:

x=b6+y

Step-by-step explanation:

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)

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

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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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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Answer:

I think option no B is the correct answer wer.