$1500 at 4% for 5 years

show your work please.

Using the formula for the sum of an alternating harmonic series, the sum of the series is π/28. Rounded to four decimal places, the sum is approximately 0.1117.

The given series can be written as:

∑_{n=1}^∞ [(-1)^(n+1) / (7*(2n-1))] = ∑_{n=1}^∞ [(-1)^(n+1) / 7] * [1 / (2n-1)]

Recognizing that the series on the right-hand side is an alternating harmonic series, we can use the formula for the sum of an alternating harmonic series:

∑_{n=1}^∞ [(-1)^(n+1) / (2n-1)] = π/4

Multiplying both sides by 1/7, we get:

∑_{n=1}^∞ [(-1)^(n+1) / (7*(2n-1))] = π/28

Rounding to four decimal places, the sum of the series is approximately 0.1117.

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--The given question is incomplete, the complete question is given

" find the sum of the convergent series by using a well-known function. ∑_{n=1}^∞ [(-1)^(n+1) / (7*(2n-1))] round your answer to four decimal places."--

Answer:

Step-by-step explanation:

it is 2x

Answer:

(10, 800)

Step-by-step explanation

The point where it's coming from is where x = 10 and y = 800, so (10, 800).

Answer:

1. m = 1/3

2. m = -2.43

3. m = 1.2

4. m = -1/3

The estimated time for the 100th repetition of this job is approximately 111.11 minutes, assuming a learning curve of 90 percent.

To estimate the time for the 100th repetition of the job, we can use the concept of a learning curve. The learning curve assumes that as the number of repetitions increases, the time required decreases at a constant percentage rate. In this case, the learning curve is 90 percent.

To estimate the time for the 100th repetition, we can use the formula:

Estimated time for the 100th repetition = Time for the 50th repetition / (Learning curve)\(^log2\)(100/50)

Plugging in the given values:

Estimated time for the 100th repetition = 100 minutes / (0.90)\(^log2(100/50)\)

Simplifying the expression:

Estimated time for the 100th repetition ≈ 100 minutes / \((0.90)^1\)

Estimated time for the 100th repetition ≈ 100 minutes / 0.90

Estimated time for the 100th repetition ≈ 111.11 minutes

Therefore, the estimated time for the 100th repetition of this job is approximately 111.11 minutes.

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Answer:

33 people.

Inequality: \(150 + 1.50x \leq 200\)

Step-by-step explanation:

200 dollar budget.

-150 for a one-time fee.

50 dollars left over.

50 divided by 1.50 equals 33.333

It is impossible to have 0.333 of a person, so you round down because John cannot afford 34 people.

So the answer is 33.

Answer:

the second one i believe:)

Step-by-step explanation:

i literally just did this in algebra lol...hope this helps:))

Answer:

A

Step-by-step explanation:

The length and the width of the rectangle are 1cm and 8/3cm

The formula that is used to calculate the area of a rectangle is expressed with the equation;

A = lw

Given that the parameters are;

From the information given, we have that;

Length = 3w - 7

Substitute the values, we have;

40 = (3w - 7)w

expand the bracket

40 = 3w² - 7w

3w² - 7w - 40 = 0

3w² + 15w - 8w - 40 = 0

3w(w + 5) - 8(w + 5) = 0

w = 8/3 or - 5

Length = 3(8/3) - 7 = 1

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Answer:

  -2 and -18

Step-by-step explanation:

It is useful to consider the factors of 36:

  36 = (-1)(-36) = (-2)(-18) = (-3)(-12) = (-4)(-9) = (-6)(-6)

The sums of these factor pairs are -37, -20, -15, -13, -12.

The factor pair of interest is -2 and -18.

Here, we have been given damping ratio values for different period values. Our objective is to compare the correlation coefficient values of the three regression models and determine the best one.

We will do this by using Excel or Matlab's analysis tools. Here, we can clearly see that the damping ratio is non-linearly related to the period. In this case, we will fit a non-linear model which is capable of predicting the damping ratio for given period values. We will start by plotting a scatter plot of the given data. Based on the scatter plot, we can conclude that a non-linear model will be the best fit.  

From the given table, we will first plot a scatter plot for the given damping ratio values against their corresponding period values. This will help us visualize the relationship between the two variables and select the best regression model. Here, we can clearly see that the damping ratio is non-linearly related to the period. In this case, we will fit a non-linear model which is capable of predicting the damping ratio for given period values.

We will start by plotting a scatter plot of the given data.Based on the scatter plot, we can conclude that a non-linear model will be the best fit. The correlation coefficient values for the three regression models are as follows:Linear regression model: r = -0.9441Non-linear regression model: r = -0.9992Polynomial regression model: r = -0.9984 From the above values, we can conclude that the non-linear regression model has the highest correlation coefficient value and is the best fit for the given data. We can now use this model to predict the damping ratio for any given period values.

Based on the given data and analysis, we have concluded that the non-linear regression model is the best fit for the given data. This model is capable of predicting the damping ratio for any given period values. The correlation coefficient value for this model is the highest among the three regression models considered.

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The scenario described here can be considered an experimental setup.

In this experiment, Kara is manipulating the independent variable, which is the presence or absence of ice cubes surrounding the smaller jars that hold the frogs. By placing ice cubes only in one set of jars and not in the other set, Kara is creating two different conditions: one with a cold environment (ice cubes surrounding the jar) and one without (no ice cubes surrounding the jar).

Kara's objective seems to be to observe the effect of the cold environment on the frogs, as she inserted a thermometer through a hole in the lid of each jar to monitor the temperature.

The setup allows for a comparison between the two groups of frogs: one group was exposed to the cold environment created by the ice cubes and the other group was exposed to a regular room temperature. By comparing the behavior, reactions, or physiological responses of the frogs in the two groups, Kara can draw conclusions about the potential impact of temperature on the frogs' well-being or behavior.

Therefore, this scenario represents an experimental study, as Kara is actively manipulating the independent variable and observing the effects on the dependent variable (the behavior or physiological response of the frogs) to draw conclusions.

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Answer:

\(x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}\)

Step-by-step explanation:

1) Move all terms to one side.

\(2x^{3} -x^{2} -3x-210=0\)

2) Factor \(2{x}^{3}-{x}^{2}-3x-210\) using Polynomial Division.

1 -  Factor the following.

\(2x^{3} -x^{2} -3x-210\)

2 -  First, find all factors of the constant term 210.

\(1,2,3,4,5,6,7,10,14,15,21,30,35,42,70,105,210\)

3) Try each factor above using the Remainder Theorem.

Substitute 1 into x. Since the result is not 0, x-1 is not a factor..

\(2*1^{3} -1^{2} -3*1-210=-212\)

Substitute -1 into x. Since the result is not 0, x+1 is not a factor..

\(2(-1)^{3} -(-1)^{2} -3*-1-210=-210\)

Substitute 2 into x. Since the result is not 0, x-2 is not a factor..

\(2*2^{3} -2^{2} -3*2-210=-204\)

Substitute -2 into x. Since the result is not 0, x+2 is not a factor..

\(2{(-2)}^{3}-{(-2)}^{2}-3\times -2-210 = -224\)

Substitute 3 into x. Since the result is not 0, x-3 is not a factor..

\(2\times {3}^{3}-{3}^{2}-3\times 3-210 = -174\)

Substitute -3 into x. Since the result is not 0, x+3 is not a factor..

\(2{(-3)}^{3}-{(-3)}^{2}-3\times -3-210 = -264\)

Substitute 5 into x. Since the result is 0, x-5 is a factor..

\(2\times {5}^{3}-{5}^{2}-3\times 5-210 =0\)

------------------------------------------------------------------------------------------

⇒ \(x-5\)

4)  Polynomial Division: Divide \(2{x}^{3}-{x}^{2}-3x-210\)  by \(x-5\).

                                               \(2x^{2}\)                       \(9x\)                      \(42\)

                                      -------------------------------------------------------------------------

\(x-5\)                               |    \(2x^{3}\)                          \(-x^{2}\)                     \(-3x\)     \(-210\)

                                           \(2x^{3}\)                             \(-10x^{2}\)

                                        -----------------------------------------------------------------------

                                                                             \(9x^{2}\)                \(-3x\)       \(-210\)

                                     --------------------------------------------------------------------------

                                                                          \(42x\)                              \(-210\)

                                                                         \(42x\)                               \(-210\)

                                      -------------------------------------------------------------------------

5)  Rewrite the expression using the above.

\(2x^2+9x+42\)

\((2x^2+9x+42)(x-5)=0\)

3) Solve for \(x.\)

\(x=5\)

4)  Use the Quadratic Formula.

1 - In general, given \(a{x}^{2}+bx+c=0\) , there exists two solutions where:

\(x=\frac{-b+\sqrt{b^{2} -4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}\)

2 -  In this case, \(a=2,b=9\) and \(c = 42.\)

\(x=\frac{-9+\sqrt{9^2*-4*2*42} }{2*2} ,\frac{-9-\sqrt{9^2-4*2*42} }{2*2}\)

3 - Simplify.

\(x=\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}\)

5) Collect all solutions from the previous steps.

\(x=5,\frac{-9+\sqrt{255}i }{4} ,\frac{-9-\sqrt{255}i }{4}\)

The sequence for just 49 flips in one case or 50 flips in the other case. This increases the probability of guessing correctly since you have a smaller set of options to consider.

To maximize the probability of guessing the correct sequence when flipping a coin 100 times in a sequence, you can ask the following yes/no question:

"Is the outcome of the 50th flip heads?"

By asking about the specific outcome of the 50th flip, you effectively divide the sequence into two equal halves. If the answer to your question is "yes," it tells you the result of the 50th flip. You can then focus on guessing the sequence for the first half, which consists of the first 49 flips. If the answer is "no," it means the outcome of the 50th flip is tails, and you can concentrate on guessing the sequence for the second half, which includes flips 51 to 100.

By narrowing down your focus to one half of the sequence, you effectively reduce the number of possibilities you need to consider. Instead of guessing the entire 100-flip sequence, you now have to guess the sequence for just 49 flips in one case or 50 flips in the other case. This increases the probability of guessing correctly since you have a smaller set of options to consider.

Keep in mind that this approach assumes that the coin flips are independent and random. However, if there are any biases or patterns in the coin flips, this strategy may not be as effective.

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Answer: 7 weeks

Step-by-step explanation:

16X + 127 = 239

16X = 239 - 127

16X = 112

X = 112/16

X = 7

Answer:

Im so sorry if this doesn't help

Step-by-step explanation:

Volume = length * width * height

           = 8 1/2  * 5 1/4  *  4

           =  17/2  * 21/4    * 4

            = 1428 / 8

             =357/2

          = 178  1/2  inches cube

Answer:

(-5, -3)

Step-by-step explanation:

Divide by 2

Answer:

48. 192

Step-by-step explanation:

In order to get from 3/4 to 3/16, one way would be to divide by 4. Another way is to multiply 3/4 by 1/4.

You can test whether multiplying by 4 works by multiplying 3/4 by 4 and 3 by 4.

When 3/4 is multiplied by 4, it would equal 12/3 which will simplify to 3. This can be done again with 3*4=12.

So the answer would be 12*4 = 48 and 48*4 = 192.

Given:

Nick, Jim and June share money in the ratio 5:5:3.

In total Nick and June received £88.

To find:

The amount received by Jim.

Solution:

Let Nick, Jim and June received 5x, 5x and 3x respectively.

In total Nick and June received £88.

\(5x+3x=88\)

\(8x=88\)

\(x=\dfrac{88}{8}\)

\(x=11\)

Now, the amount received by Jim is

\(\text{Jim get}=5x\)

            \(=5(11)\)

            \(=55\)

Therefore, the amount received by Jim is £55.

Answer:

c

Step-by-step explanation:

Answer:

315 chairs

Step-by-step explanation:

This question can instill your quick calculation skills which can be very useful when it comes to event planning.

1 row of chairs = 15 chairs

21 rows of chairs = 15 x 21

= 315 chairs.

Answer:True Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The prefix "kilo-" in the metric system means one thousand. Therefore, one kilometer equals 1000 meters.

The metric system is a decimal-based system that uses prefixes to denote multiples and submultiples of units. In this system, the prefix "kilo-" represents a factor of one thousand, which is equivalent to 10^3. For instance, one kilogram is equal to one thousand grams, and one kilometer is equal to one thousand meters. Similarly, other prefixes like "centi-" (one hundredth), "milli-" (one thousandth), and "mega-" (one million) are used in the metric system to denote different multiples and submultiples of units.

In conclusion, the prefix "kilo-" in the metric system represents a factor of one thousand. Therefore, when we use this prefix with the unit of length "meter," we get "kilometer," which is equal to 1000 meters.

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Answer:

f(-3) = 18

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 2x²

Step 2: Evaluate

Answer:

√

30

Step-by-step explanation: Simply multiply

√

2

and

√

15

=

√

30

[Caution: If it were -2 and -15, this type of multiplication would not be correct.]

Answer:

3x²(x - 2)(x + 5)

Step-by-step explanation:

Step 1: Factor GCF

3x²(x² + 3x - 10)

Step 2: Factor Quadratic

3x²(x - 2)(x + 5)

Answer:

3x^2(x - 2)(x + 5).

Step-by-step explanation:

3x^4 = 3 * x * x * x * x

9x^3 = 3 * 3 * x * x * x

-30x^2 = -1 * 2 * 3 * 5 * x * x

All three terms have a 3 and two x's.

3 * x * x (x * x + 3 * x - 2 * 5) = 3x^2(x^2 + 3x - 10)

x^2 + 3x - 10 = x^2 + 5x - 2x - 10 = (x - 2)(x + 5)

So, 3x^2(x - 2)(x + 5)

Hope this helps!

Question:

Find the area of the composite figure round to the nearest tenth

Answer:

Step-by-step explanation:

(25 x 12) + (10 x 6)

round it 360 >>>>> 360 it is the same

Answer:

360

Step-by-step explanation:

Split the given figure up into two different rectangles. One of these rectangles will have the dimensions (12 and 25), while the other will have the dimensions (6 and 10)  Find the area of each rectangle using the general formula                (\(length * width = area\)), then add the two areas up to find the total area of the figure.

12 * 25

= 300

6 * 10

= 60

300 + 60

= 360

Answer:

the answer is x=2 and y=2

Step-by-step explanation:

-3y=16+5x

-y=(16+5x)3