What are the first 129 numbers of pie?

Answer:

131

Step-by-step explanation:

The n th term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₁₂ = 38 and a₈₅ = 257 , then

a₁ +11d = 38 → (1)

a₁ + 84d = 257 → (2)

Subtract (1) from (2) term by term

73d = 219 ( divide both sides by 73 )

d = 3

Substitute d = 3 into (1)

a₁ + 11(3) = 38

a₁ + 33 = 38 ( subtract 33 from both sides )

a₁ = 5

Thus

5 + 3(n - 1) = 395 ( subtract 5 from both sides )

3(n - 1) = 390 ( divide both sides by 3 )

n - 1 = 130 ( add 1 to both sides )

n = 131

Thus there are 131 terms in the sequence

Answer:

Step-by-step explanation: Square feet

The inequalities and their graphs are;

1)  -x - 5 ≤ -2 is represented by the third graph

2) 6 + x ≤ 3 is represented by the fourth graph

3) x - 4 < -7 is represented by the second graph

4) 2x > -6 is represented by the first graph

1) We are given the inequality;

-x - 5 ≤ -2

Rearranging gives us;

-x ≤ -2 + 5

- x ≤ 3

Divide both sides by -1 to get;

x ≥ -3

The graph must be a closed circle starting at -3 and pointing to the right.

It is the third graph in the link at the end of this answers.

2) We are given the inequality; 6 + x ≤ 3

Rearranging gives;

x ≤ -6 + 3

x ≤ -3

The graph must be a closed circle starting at -3 and pointing to the left. Thus, it is the fourth graph.

3) We are given the inequality; x - 4 < -7

Rearranging gives us;

x < -7 + 4

x < -3

The graph must be an open circle starting at -3 and pointing to the left.

Thus, it is the second graph.

4) We are given the Inequality; 2x > -6

Divide both sides by 2 to get;

x > -6/2

x > -3

It must be a graph with an open circle starting at -3 and then to the right.

Thus, it is the first graph as seen in the attached link

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The inventory turnover is 5 days and the number of days sales is  73 days if we assume 365 days a year.

The given data is as follows;

Cost of goods sold = $259,150

Average inventory = 51,830

a. Inventory turnover

Inventory turnover is calculated by dividing the cost of goods sold by the average inventory of the report.

Inventory turnover = (Cost of goods sold) / (Average inventory )

Inventory turnover = $259,150 / $51,830

Inventory turnover = 4.99 = 5

b. Number of days' sales in inventory

Assuming that 365 days in a year.

The number of days' sales in inventory is calculated by dividing the number of days in a year by the Inventory turnover

Number of days' sales = 365 days / (Inventory turnover)

Number of days' sales = 365 days / 4.999 = 73.015

Therefore we can conclude that the Inventory turnover is 5 and the Number of days' sales is 73 days.

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The frequencies of the first three allowed modes of vibration are 4.14 Hz, 8.29 Hz, and 12.43 Hz, respectively.

The given problem can be solved using the formula given below; f_n = (n*v)/(2L), where; f_n - frequency v - velocity of the wave L - length of the wire, n - mode number.

Part a: Given; Length of the wire, L = 1.75 m, Mass of the wire, m = 0.100 kg. Tension in the wire, T = 21.0 N`.

To find the frequency of the wire for the first three allowed modes of vibration, we need to calculate the velocity of the wave, v.

We can use the following formula to calculate the velocity of the wave; v = √(T/m), where; T - tension in the wire, m - mass of the wire.

Substituting the given values, v = √(21.0 N / 0.100 kg) = √(210) = 14.5 m/s.

The frequencies of the first three allowed modes of vibration can be found by substituting the values in the given formula.

For n = 1, `f_1 = (1*14.5)/(2*1.75) = 4.14 Hz.

For n = 2,`f_2 = (2*14.5)/(2*1.75) = 8.29 Hz

For n = 3,`f_3 = (3*14.5)/(2*1.75) = 12.43 Hz.

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Answer:

see below

Step-by-step explanation:

3y = -9

Divide each side by 3

3y/3 = -9/3

y = -3

(a) To calculate the area surrounding the swimming pool, we need to consider the width of the cement around all sides of the pool. Since the cement has a uniform width of 4m on all sides, we need to add 4m to the length and width of the pool.

The length of the pool with the surrounding cement is 10m + 2(4m) = 10m + 8m = 18m.

The width of the pool with the surrounding cement is 5m + 2(4m) = 5m + 8m = 13m.

The area surrounding the swimming pool is the difference between the area of the larger rectangle (with the cement) and the area of the pool itself.

Area surrounding pool = Area of larger rectangle - Area of pool

= (18m) x (13m) - (10m) x (5m)

= 234m² - 50m²

= 184m².

(b) The cost to install the cement is determined by multiplying the area surrounding the pool by the cost per square meter, which is $50.

Cost to install cement = Area surrounding pool × Cost per square meter

= 184m² × $50/m²

= $9,200.

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The correct answer is: B. The function has no local maximums and has local minimums at approximately x = 5.8 and x = 28.8 (rounded to the nearest tenth).

To determine the location of the local extrema (maxima and minima) of the function f(x) = -0.697x^3 + 16642x^2 - 102407x + 650015, we need to find the critical points where the derivative of the function is equal to zero or does not exist. First, let's find the derivative of f(x) with respect to x: f'(x) = -2.091x^2 + 33284x - 102407. To find the critical points, we set f'(x) = 0 and solve for x: -2.091x^2 + 33284x - 102407 = 0. Using the quadratic formula, we can solve for x: x = (-b ± √(b^2 - 4ac)) / (2a). Plugging in the values a = -2.091, b = 33284, and c = -102407, we can calculate the values of x: x ≈ 5.779 or x ≈ 28.755. These are the potential locations of the local extrema.

To determine whether these points are maxima or minima, we can analyze the concavity of the function. Taking the second derivative, we have: f''(x) = -4.182x + 33284. Setting f''(x) = 0 and solving for x: -4.182x + 33284 = 0; x ≈ 7963.28. Since the second derivative is negative for x < 7963.28, we can conclude that x ≈ 5.779 corresponds to a local maximum, and x ≈ 28.755 corresponds to a local minimum. Therefore, the correct answer is: B. The function has no local maximums and has local minimums at approximately x = 5.8 and x = 28.8 (rounded to the nearest tenth).

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Answer:

x=7

Step-by-step explanation:

Using parallel lines, cut off by a transversal, we can do this (see image):

Using the image, we can say that 94 = c = a= f, and 13x-5 = b = d =g

Since angles on a straight line add to 180, we can say that

13x-5+94 = 180

13x + 89 = 180

subtract 89 from both sides

13x = 91

x = 7

Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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The factorisation of xm - 2pq + xq - 2pm is (m + q)(x - 2p).

Factorization is the process of breaking down an expression or number into its constituent parts, such that the product of these parts equals the original expression or number.

With respect to our question above, we can begin by grouping the first two terms and the last two terms together:

xm - 2pq + xq - 2pm

= x(m + q) - 2p(q - m)

Now we can see that we have a common factor of (q - m):

= x(m + q) - 2p(q - m)

= x(m + q) - 2p(q - m)

= (m + q)(x - 2p)

So the factorization of xm - 2pq + xq - 2pm is (m + q)(x - 2p).

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Answer:

f(x)=x−4x2−3x−28 f ( x ) = x - 4 x 2 - 3 x - 2 8 .

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given function:

Find f(x) when x = -2

Answer:

The answer is p = 2.

Step-by-step explanation:

1) Divide both sides by 9.

\(p - 4 = - \frac{18}{9} \)

2) Simplify 18/9 to 2.

\(p - 4 = - 2\)

3) Add 4 to both sides.

\(p = - 2 + 4\)

4) Simplify -2 + 4 to 2.

\(p = 2\)

Therefor, the answer is p = 2.

Answer:

p =2

Step-by-step explanation:

9(p-4) =-18

9p-36=-18

9p = -18 +36

9p = 18

divide both side by 9

p =2

The solution of the given linear system of equations is x = 2, y = 1 and z = 2.

Given that the linear system of equations is

2x + 4y + 2z = 16-2x - 3y + z = -52x + 2y - 3z = -3

To solve the system of equations by Cramer's rule method, arrange them in the form of Ax = B as below:

A = [2, 4, 2; -2, -3, 1; 2, 2, -3], x = [x, y, z] and B = [16, -5, -3]

To find the inverse of the coefficient matrix A⁻¹, first, find the determinant of A as below:

|A| = 2[-3 - 2] - 4[-2 + 2] + 2[-8 + 1] = -12

The determinant is non-zero, hence A is invertible

A⁻¹ = 1/|A| [adj A]

where adj A is the transpose of the cofactor matrix [C] of A:

adj A = [C]T

So, we find [C] by replacing each element of A with its cofactor and taking its transpose matrix as below:

C = [5, 2, 6; 2, -2, 2; -4, -4, -4]

Then [C]T = [5, 2, -4; 2, -2, -4; 6, 2, -4]So, A⁻¹ = 1/|A| [adj A] = 1/(-12) [5, 2, -4; 2, -2, -4; 6, 2, -4] = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2]

To solve the system of equations, we have x = A⁻¹B as below:

x = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2][16; -5; -3] = [2; 1; 2]

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Given

France won more gold medals than Italy and Italy won more gold medals than Korea.

total number of gold medals won by these three countries is three consecutive integers whose sum is 33

Find

number of gold numbers won by each.

Explanation

Let smaller number be x

so , three consecutive numbers are x , x + 1 , x + 2

according to the question ,

so , x = 10

x + 1 = 10 + 1 = 11

x + 2 = 10 + 2 = 12

Final Answer

Therefore ,

the number of golds won by korea = 10

the number of golds won by Italy = 11

the number of golds won by France = 12

The three computations covered by the reliability factor table are sample size, index of reliability, and index of precision. Sample size deals with the size of the sample being used in order to achieve a desirable level of reliability.

Index of reliability is used to measure the consistency of results achieved over multiple trials. It does this by calculating the total number of items that contribute significantly to the final result. Finally, the index of precision measures the effect size of the sample, which is determined by comparing the results from the sample with the expected results.

The sample size computation gives the researcher an idea of the number of items that should be included in a sample in order to get the most reliable results. This is done by taking into account a number of factors including the variability of the population, the type of measurements used, and the desired level of accuracy.

The index of reliability is commonly calculated by finding the ratio of the number of items contributing significantly to the total result to the total number of items in the sample. This ratio is then multiplied by 100 in order to get a final score.

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The rate at which the circumference is growing when the water covers 50 ft is found to be at  0.019 ft/s.

The formula for the area of a circle is shown as  :

A = πr^2

where A = area

π = 3.142

r = radius

We will differentiate with respect to time, :

dA/dt = 2πrn xdr/dt

we have that dA/dt = 3 ft²/s

3 = 2π(25) x dr/dt

we calculate for  dr/dt,

dr/dt = 3/(50π) =  0.019 ft/s

In conclusion, if a person is making an ice rink by pouring water out of a hose. If water is spreading in a circular shape and the area covered by water grows with the rate of 3 ft?/sec, the rate at which the circumference is growing when the water covers 50 ft is found to be at  0.019 ft/s.

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The complementary event of rolling a die and getting a number less than three is that the six-sided die is rolled and the outcome is greater than three. Where P = n < 3  is the event and its complement is P' = n > 3.

The sample space of all outcomes that are not the event in question is the complement of an event. The inverse of "a flipped coin lands on heads" is "a flipped coin lands on tails."

If the chance of drawing a red marble from a bag is 26%, the chance of the complement (picking a non-red marble ) is 74%.

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Answer:

greater than

Step-by-step explanation:

6,938 is greater than 6,822 by 116

Answer:

c

Step-by-step explanation:

Answer: 339.29ft^3

Step-by-step explanation:

The formula for a cylinder is πr^2h

In your scenario, r=8 and h=3 so put those into the equation -

π8^2(3) and just solve!

Because the temperature is greater, the relative humidity of the atmosphere is higher.

Water vapor is also measured by relative humidity (RH), which is stated as a percentage but RELATIVE to the air's temperature. In plenty of other terms, it is a comparison between the quantity of water vapor that is really present in the air and the maximum amount water vapor that is possible for the air at the current temperature.

By deducting the temperature just on wet-bulb thermometer from of the temperature just on dry-bulb thermometers and utilizing a relative humidity chart, one may determine the relative humidity.

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Answer:

C

Step-by-step explanation:

hope this helps :)

For a storage bin of rectangular prism and volume of prism, 10x³ + 9x² + 2x, then the linear expressions can represent possible dimensions of the bin is x( 2x + 1)(5x+2).

The volume of a rectangular prism is also called the capacity that it can hold or the space occupied by it. The formula used to calculate the volume of a rectangular prism is written as Volume (V) = height of the prism × width × length--(1). It is represented in cubic units such as cm³, m³etc. We have a storage bin in the shape of a rectangular prism.

Volume of prism, V = 10x³ + 9x² + 2x.

We have to determine the linear expression which represent possible dimensions of bin.

Now, Volume expression is V = 10x³ + 9x² + 2x.

Using factorization, for determining dimensions,

= x( 10x² + 9x + 2) ( taken out x )

Using the the middle term splitting in Quadratic form,

= x( 10x² + 5x + 4x + 2)

= x( 5x( 2x + 1) + 2( 2x + 1)) ( making pairs and factorize)

V = x( 2x + 1)(5x+2)

from equation (1), height of the prism × width × length that is dimensions = x( 2x + 1)(5x+2). Hence, requird expression is x ( 2x + 1)(5x+2).

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Answer:

25！=1*2*3*4*5*6*...23*24*25

26= 2*13

28=2*14or 4*7

36=2*18or 3*12 or 4*9

56=7*8

All products above are inside 25! So they are all factors of 25!

But 58=2*29 and 29 is not inside 25! so it's not a factor of 25!

Step-by-step explanation:

hope it helped

Answer:

n=25

Step-by-step explanation:

Let n be the greatest possible integer Jo could be thinking of. We know n<100 and n=8k-1=7l-3 for some positive integers k and l. From this, we see that 7l=8k+2=2(4k+1), so $7l$ is a multiple of 14. List some multiples of 14, in decreasing order: 112, 98, 84, 70, .... Since n<100, 112 is too large, but 98 works: \($7k=98\Rightarrow n=98-3=95=8(12)-1$\). Thus,\($n=\boxed{95}$\).

Hope this helped! :)

The distance between successive fourth roots of the complex number √3/2 - 1/2i on the unit circle is 5π/24 units.

To find the distance between successive fourth roots of a complex number on the unit circle, we can use the concept of the angle between the roots. Let's proceed step by step:

The given complex number is √3/2 - 1/2i. This complex number lies on the unit circle because its magnitude is equal to 1.

1. Convert the given complex number to trigonometric form:

  √3/2 - 1/2i = cos(θ) + i*sin(θ)

  By comparing the real and imaginary parts, we can determine the angle θ:

  cos(θ) = √3/2

  sin(θ) = -1/2

  Using the unit circle, we can find that θ = 5π/6 (or 150 degrees). This angle represents the position of the given complex number on the unit circle.

2. Find the angle between successive fourth roots:

  Since we are interested in the fourth roots, we divide the angle θ by 4:

  θ/4 = (5π/6) / 4 = 5π/24

  This angle represents the angular distance between two successive fourth roots on the unit circle.

3. Calculate the distance between the two points:

  To find the distance, we multiply the angular distance by the radius of the unit circle (which is 1):

  Distance = (5π/24) * 1 = 5π/24

  Therefore, the distance between successive fourth roots of the complex number √3/2 - 1/2i on the unit circle is 5π/24 units.

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