0 V12(-1)" V12(-1)" 1. Consider the series 3" (2n + 1) Note: this was changed from 13"(2n +1) (a) (3 marks) Use any test for convergence/ divergence to show that the series converges. 12-1)" (b) (2 marks) It is possible to show that the sum of the series Σ is , in other words, the series converges to the number . (You do NOT need to prove this, but it can be done somewhat easily using a Taylor series expansion of arctanx.) 263"(2n+1) Suppose you want to use a partial sum of this series to estimate the value of to an accuracy of within 0.0001. Would using the first 8 terms of the series be enough to ensure you get an accuracy of within 0.0001? (8 terms means the terms where = 0,1,2,3,...., 7.) Note: This was changed from "7 terms":

To find out how much the Guilderian trader must pay for the same 50 flop barrel of pickles, we need to calculate the cost per gulp and then multiply it by the number of gulps in the barrel.

Given that the Guilderian trader initially exchanged 25 gulps for the 50 flop barrel of pickles, we can determine the cost per gulp by dividing the total cost (50 flops) by the number of gulps (25).  Cost per gulp = 50 flops / 25 gulps = 2 flops/gulp . Since the gulp depreciates to 0.5 flops per gulp, the Guilderian trader must pay 0.5 flops per gulp for the same barrel of pickles.

Therefore, the Guilderian trader must pay 0.5 flops/gulp * 25 gulps = 12.5 flops for the 50 flop barrel of pickles. For the Florish trader, we need to calculate the cost per flop and then multiply it by the number of flops in the crate.

Given that the Florish trader initially exchanged 40 flops for the 20 gulp crate of apples, we can determine the cost per flop by dividing the total cost (40 flops) by the number of flops (20).

Cost per flop = 40 flops / 20 flops

= 2 flops/flop .

Therefore, the Florish trader must pay 2 flops per flop for the same crate of apples.

The Guilderian trader must pay 12.5 flops for the same 50 flop barrel of pickles, and the Florish trader must pay 2 flops for the same 20 gulp crate of apples.

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Answer:

The total hours of exercising is 2 hours and 15 minutes.

27 minutes is your total of him playing soccer. i got this by getting the minutes  from the total time, so 135 and I divided it by 5 and got 27 or you could even know that  1/5 of an hour is 12 and multiply that by 12 and 1/5 of 15 is 3 so it equals 27 minutes!

Answer:

28.8 minutes

Step-by-step explanation:

Total hours the student exercised = 2hours 15 minutes. = 2.4 hours.

Given that:

1/5 of this came from soccer, so we must find 1/5 of 2.4:

1/5 x 2.4  = 0.48 hours.

We can write this as minutes = 28.8 minutes.

So, the student plays soccer for 28.8 minutes.

hope this helps.

Good Luck

Please mark brainiest

Answer:

15+85+x =180

X=180-15-85

X=8O°

Step-by-step explanation:

The posterior probability associated  with sample  information  is of the integrated form.

We may modify our beliefs or probabilities in light of new knowledge according to the Bayes theorem, a key idea in probability theory and statistics.

Using Bayes' theorem we may determine the posterior probability by normalising the prior probability, which is our original belief or probability, and the likelihood, which is the likelihood of seeing the supplied data or sample.

The following formula is used to get the posterior probability:

Prior Probability = Likelihood x Prior Probability / Normalising Constant

The term "prior probability" refers to our previous knowledge or conviction about a situation or a theory, regardless of any new information. The likelihood displays the possibility of locating the provided data or sample in a certain circumstance.

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Answer:

75

Step-by-step explanation:

9 + 9 + 9 + 9 + 9 + 30 = 75

Good luck on your assignment!

The area of the triangle that she drew is given as follows:

315 square miles.

To calculate the area of a triangle, you can use the formula presented as follows:

Area = (1/2) x base x height

In which the parameters are given as follows:

From the figure, the parameter values for this problem are given as follows:

Hence the area is given as follows:

Area = 0.5 x 18 x 35

Area = 315 square miles.

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Step-by-step explanation:

Interior angles of a 5-gon    sum to   ( 5-2)(180 = 540 degrees

smallest angle =x

largest angle = x + 4d    

          where d is the arithmetic sequence common difference

x + 4d     -x     =  44    shows d = 11

then    x    + x+d    + x+2d   + x+3d   + x + 4d = 540

      5x + 10d = 540      we know d = 11

       5x + 10(11) = 540

         5x = 430

           x = smallest angle = 86 degrees

The smallest interior angle of the pentagon is 86 degrees. This was found by setting up an equation involving the common difference "d" in the arithmetic sequence of angles and solving for "x."

Let's denote the five interior angles of the pentagon as follows:

Let the smallest angle be "x" degrees.

The other four angles form an arithmetic sequence, so we can represent them as x + d, x + 2d, x + 3d, and x + 4d, where "d" is the common difference between the angles.

Now, we know that the difference between the largest angle and the smallest angle is $44^\circ$. Therefore, we can write the equation:

(x + 4d) - x = $44^\circ$

Simplify and solve for "d":

4d = $44^\circ$

Now, divide both sides by 4 to find the value of "d":

d = $44^\circ / 4 = $11^\circ

Now that we know the common difference "d" is $11^\circ", we can find the smallest angle "x" by using the equation for the sum of angles in a pentagon, which is 540 degrees:

x + (x + d) + (x + 2d) + (x + 3d) + (x + 4d) = 540

Simplify and solve for "x":

5x + 10d = 540

5x + 10($11^\circ) = 540

5x + $110 = 540

Now, subtract $110 from both sides:

5x = 540 - $110

5x = $430

Finally, divide by 5 to find the smallest angle "x":

x = $430 / 5 = $86

So, the smallest angle of the pentagon is $86 degrees.

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The cost of each small charcuterie boards is $6 and one medium charcuterie boards is $7.

A mathematical statement known as an equation is made up of two expressions joined together by an equal sign. It is a formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Let small charcuterie boards = c

Let medium charcuterie boards = m

Therefore, the equation will be:

10c + 12m = 144

5c + 9m = 93

Multiply equation i by 5

Multiply equation ii by 10

50c + 60m = 720

50c + 90m = 930

Subtract

30m = 210

m = 210/30

m = 7

Therefore, 5c + 9m = 93

5c + 9(7) = 93

5c + 63 =93

5c = 93 - 63

5c = 30

Divide both sides by 5

c =  30 / 5

c = 6

Therefore, based on the information the cost of each small charcuterie boards is $6 and one medium charcuterie board is $7.

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77 is the sum of their integers  squares .

What in math is an integer?

Let the numbers be ( n - 1 ), n , ( n + 1 )

according to question

  ( n - 1 ) (n) ( n + 1 ) = 8( n + n - 1 + n + 1 )

  n( n² - 1 ) = 8(3n)

   ( n² - 1 ) = 24

    n²= 25

    n = 5

since n is positive integer n = 5

thus required numbers are 4,5,6

4² + 5² + 6² = 77

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Answer:

\(m=\frac{-1}{2}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (-4, 0)

Point (0, -2)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m. Rate of change is the same as slope.

Answer:

1. B. The bag of candy produced last Monday is different from the standard bag.

2. A. The bag of candy produced last Monday are like the standard bag.

3. B. The bag of candy produced last Monday is different from the standard bag.

Step-by-step explanation:

Given - A company that makes hard candy have a standard bag of hard candy with 150 pieces. The hard candy has three distinct colors red, white and orange and equal proportion of each candy is present in the standard bag. The manager wants to know whether the bags produced last Monday were similar to the standard bag. To test this, they plan to choose a random bag from the batch and compare it with the standard bag. You will have to answer questions below to assist the manager in comparing the two bags.

To find - 1. What is the alternate hypothesis for this exercise?

              2. What is the null hypothesis for this exercise?

              3. After performing the necessary calculations, the chi-square value of the test is 6.7. The cut-off/critical value of chi-square test is 5.991 (for 5% chance).  What is your conclusion about the bags based on this result?

Proof -

1.

The alternate hypothesis is - B. The bag of candy produced last Monday is different from the standard bag.

2.

The null hypothesis is - A. The bag of candy produced last Monday are like the standard bag.

3.

The conclusion is - B. The bag of candy produced last Monday is different from the standard bag.

A) The new values for the mean and standard deviation, after adding 3 points to every score, would be a mean of 53 and a standard deviation of 10. B) The new values for the mean and standard deviation, after multiplying every score by 2, would be a mean of 100 and a standard deviation of 20.

A) Adding 3 points to every score in the population would result in a shift of the entire distribution. The new mean would be the original mean plus 3, so the new mean would be 50 + 3 = 53. The standard deviation would remain the same since it measures the spread of the data relative to the mean. Therefore, the new standard deviation would still be 10.

B) Multiplying every score in the population by 2 would affect both the mean and the standard deviation. The new mean would be the original mean multiplied by 2, so the new mean would be 50 * 2 = 100. The new standard deviation would also be multiplied by 2 since it measures the spread of the data relative to the mean. Therefore, the new standard deviation would be 10 * 2 = 20.

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Answer:  20%

Step-by-step explanation:

if 500 = 100kg

          = 10kg

     50 = 10kg

%Profit = S.P/B.P *100

%Profit = 60/50 *100

%Profit = 120%

%Profit = 120% -100% = 20%

Answer:

False.

Step-by-step explanation:

The statement "1:24,000" is not an example of a verbal statement. It is a numerical ratio or scale commonly used in cartography and map scales. Verbal statements typically involve spoken or written language rather than numerical representations. :)

We can conclude after answering the provided question that As a result, inequality the correct answer is: x > 0 and x < 38

In mathematics, an inequality is a non-equal connection that exists between expressions or values. As a result, imbalance relates to inequality. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two points are not equal, the not equal sign is commonly used (). Different inequalities, no matter how small or large, are utilized to calculate contrast values. Many simple inequalities can be solved by modifying its two sides until only the variables remain. But a few factors contribute to inequality: Negative values are divided or added on both sides. Trade off the left and right.

Mrs. A always grills more onions than peppers, so the number of onions grilled (38) must be greater than the number of peppers grilled (38). (x). As a result, the inequality can be used to represent this relationship:

38 > x

Mrs. A also grills some of each, so the total number of peppers grilled (x) must be greater than zero. As a result, the inequality can be used to represent this relationship:

x > 0

The inequity pair that represents the number of peppers, x, she could have grilled on Sunday is:

x > 0 and 38 > x

This can also be expressed as:

0 < x < 38

As a result, the answer is:

x > 0 and x < 38

As a result, the correct answer is:

x > 0 and x < 38

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In the 1st quadrant:

sin x > 0, cos x > 0, tan x > 0

In the 2nd quadrant

sin x > 0, cos x < 0, tan x < 0

In the 3rd quadrant

tan x > 0, sin x < 0, cos x < 0

In the 4th quadrant

cos x > 0, sin x < 0, tan x < 0

In the first one

tan is > 0 and sin < 0

Then the angle should be in the 3rd quadrant

The answer is Angle C

In the second one

tan > 0 and cos > 0

Then the angle should be in the 1st quadrant

The answer is Angle A

In the third one

sin > 0 and cos < 0

Then the angle should be in the 2nd quadrant

The answer is Angle B

In the fourth one

tan > 0 and sin > 0

Then the angle should be in the 1st quadrant

The answer is Angle A

In the last one

tan < 0 and cos > 0

Then the angle should be in the 4th quadrant

The answer is Angle D

The surface area can be obtained by integrating the square root of the sum of the squares of the partial derivatives of f(x, y) with respect to x and y over the region r.

To find the surface area, we need to calculate the square root of the sum of the squares of the partial derivatives of f(x, y) with respect to x and y. In this case,

√(1 + (∂f/∂x)^2 + (∂f/∂y)^2) becomes √(1 + 16x^2 + 4y^2).

Then, we integrate this expression over the region r, which is the disk of radius 3 centered at the origin.

Using polar coordinates, we can rewrite the integral as

∫∫r √(1 + 16r^2 cos^2 θ + 4r^2 sin^2 θ) r dr dθ, where 0 ≤ r ≤ 3 and 0 ≤ θ ≤ 2π. By evaluating this integral, we can determine the area of the given surface.

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Answer:

The answer is

\( \huge - \frac{6}{11} \\ \)

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\ \)

From the question we have

\(m = \frac{8 - 2}{ - 6 - 5} = \frac{6}{ - 11} = - \frac{6}{11} \\ \)

We have the final answer as

\( - \frac{6}{11} \\ \)

Hope this helps you

The most appropriate choice for distance will be given by

Veronica has not calculate the number of animals seen per kilometer, she has arranged only on the basis of animals seen.

What is distance?

Distance is how much ground travelled by an object during its motion.

Here,

For River Edge

Number of animals seen = 8

Length of hike =  3 km

Number of Animals seen per km = 8/3

                                                      =2.66

For Wooden Marsh

Number of animals seen = 24

Length of hike =  8 km

Number of Animals seen per km = 24/8

                                                       =3

For Canyon Creek

Number of animals seen = 35

Length of hike =  15 km

Number of Animals seen per km = 35/15

                                                      =2.33

So from least to greatest it will be

Canyon Creek, River Edge, Marshy Land

Veronica has not calculate the number of animals seen per kilometer, she has arranged only on the basis of animals seen. That was her mistake.

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Answer:

B

Step-by-step explanation:

The value of the x would be 25.723 cm.

What is the area of the circle?

For any circle, if 'r' is the radius of the circle then the area of the circle would be

      Area = π×r²

Where π = 3.14 (or) π = 22/7.

And the diagonal of the square with side 'a' is √2*a.

Given:

The square is inscribed into a circle.

The length of the side of the square is 'x' cm.

and the area of the circle is 56 cm².

            Area of circle = π.r²

                56 = 22/7×r²

                r² = 57 * 7/22

                r² = 18.1363

Taking square root on both sides, we get

                  r = 4.25

Now as the square is inscribed into a circle, then the radius will be half the diagonal of the square.

                Diagonal = 2 × r

                 √2x =  36.27

                    x = 36.27/√2

                    x = 25.723 cm

Hence, the value of the x would be  25.723 cm.

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The solution to the given differential equation is:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]\)

To solve the given differential equation

\(x^3y'''\ -\ 6y\ =\ 0,\)

we can use the method of power series. Let's assume a power series solution of the form

\(y(x)\ =\ \sum_{n=0}^{\infty} a_nx^n.\)

Differentiating y(x) with respect to x gives:

\(\[y'(x)\ =\ \sum_{n=0}^{\infty} n a_n x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+1) a_{n+1} x^n\]\)

Differentiating again gives:

\(\[y''(x)\ =\ \sum_{n=0}^{\infty} (n+1)na_{n+1}x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+2)(n+1)a_{n+2}x^n\]\)

Differentiating one more time gives:

\(\[y'''(x)\ =\ \sum_{n=0}^{\infty} (n+2)(n+1)na_{n+2}x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^n\]\)

Substituting these expressions into the differential equation, we have:

\(\[x^3 \sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^n - 6 \sum_{n=0}^{\infty} a_n x^n\ =\ 0\]\)

Rearranging the terms and combining like powers of x, we get:

\(\[\sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^{n+3} - 6 \sum_{n=0}^{\infty} a_n x^n\ =\ 0\]\)

Now, let's equate the coefficients of like powers of x to zero:

For n=0:

\(\[(3)(2)(1)a_3 - 6a_0 = 0 \implies 6a_3 - 6a_0 = 0 \implies a_3 = a_0\]\)

For n=1:

\(\[(4)(3)(2)a_4 - 6a_1 = 0 \implies 24a_4 - 6a_1 = 0 \implies a_4 = \frac{1}{4}a_1\]\)

\(For \: n\geq 2:

\[(n+3)(n+2)(n+1)a_{n+3} - 6a_n = 0 \implies a_{n+3} = \frac{6a_n}{(n+3)(n+2)(n+1)}\]

\)

Now we can write the solution as:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{6a_{n-2}}{n(n-1)(n-2)}x^{n+3}\]

\)

Simplifying the series, we get:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_

1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]

\)

Therefore, the solution to the given differential equation is:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]\)

where a₀ and a₁ are arbitrary constants to be determined based on the initial conditions or boundary conditions given in the problem.

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Answer:

Step-by-step explanation:

From the figure attached,

ΔABC has been dilated to form another triangle ΔA'B'C'.

Therefore, ΔA'B'C' is the image triangle of preimage ΔABC.

Coordinates of preimage ΔABC are,

A(3, 3), B(2, 0) and C(5, 2)

Coordinates of ΔA'B'C',

A'(6, 6), B'(0, 4) and C'(10, 4)

Since, dilation of a triangle is a similarity transformation which produces the  similar image of the preimage.

Rule for the dilation is,

(x, y) → (kx, ky)

Here, k = scale factor of dilation

By this rule,

A(3, 3) → A'(6, 6)

          → A'(2×3, 2×3)

Scale factor = 2

Therefore, "Triangle (ABC) is dilated by a scale factor 2 about the origin to form triangle (A'B'C') ".

Answer:

1) degree: 5 / number of terms: 4

2) degree: 4 / number of terms: 3

3) degree: -1 / number of terms: 2

4) degree: 8 / number of terms: 2

5) degree: 2 / number of terms: 3

6) degree: 3 / number of terms: 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alice paid $25 for her pair of jeans, and Jeff paid $4 for the steaks.

Let's calculate the final amount paid by Alice and Jeff for their purchases.

Alice:

Jeff:

So, Alice paid $25 for her pair of jeans, and Jeff paid $4 for the steaks.

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Answer:

-1/3x

Step-by-step explanation:

the slope formula is y divided by x. it goes down 1 unit and right 3 units. so

-1 divided by 3 is -\(\frac{1}{3}\)

From the given graph, f (  - 2 ) can be found to be - 3 .

When given a function such as f ( - 2 ), the meaning is that you need to find the value on the y - axis that corresponds to the value on the x - axis which in this case is - 2.

Going by the given graph, the value that corresponds to - 2 on the graph, would be the value of - 3 which is shown on the horizontal line that originates from - 3 and extends leftwards.

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Answer:

1.25 lawns/per hour

Step-by-step explanation:

The probability that a person arriving to use the machine will find it idle is 1/3 or 0.3333. Option a is correct.

Use the concept of an M/M/1 queue to calculate the probability, which models a single-server queue with exponential interarrival times and exponential service times.

In this case, the interarrival time follows an exponential distribution with a rate parameter of λ = 5 persons per hour (or 1/12 persons per minute). The service time (copying time) also follows an exponential distribution with a rate parameter of μ = 1/8 persons per minute (since each person uses the machine for an average of 8 minutes).

In an M/M/1 queue, the probability that the system is idle (no person is being served) can be calculated as:

P_idle = ρ⁰ × (1 - ρ), where ρ is the traffic intensity, defined as the ratio of the arrival rate to the service rate. In this case, ρ = λ/μ.

Plugging in the values, we have:

ρ = (1/12) / (1/8) = 2/3

P_idle = (2/3)⁰ × (1 - 2/3) = 1/3

Therefore, the probability is 1/3 or approximately 0.3333.

Thus, option (A) is the correct answer.

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