If 38x²+38x+38/x³-x²+x-1 = A/x-1 + Bx+C/x²+1, then
A =
B =
C =

The sequence can be used to find exact values when the level of the pattern increases or decrease

The mathematical expression that connects the number of tiles and the grouping method is presented as follows; tₙ = 9 + (n - 1)× 3

From the given diagram, we have that the number of green tiles = 18

Grouping method 1 has 15 green colored tiles with Figure size 3

We have;

Grouping method 1

The figure size number of the shape with 15 green colored tiles = 3

Grouping method 2, figure size 4

The figure size number of the shape with 18 green colored tiles = 4

The size number of the shape with 12 green colored tiles = 2

The size number of the shape with 9 green colored tiles = 1

Therefore the sequence is an arithmetic progression having the following characteristics;

nth term, tₙ = a + (n - 1)·d

In the first term, a = 9

The common difference, d = 3

The mathematical expression that connects the grouping methods above, and gives the number of green tiles, tₙ, is tₙ = 9 + (n - 1)× 3

Where;

n = The grouping method number

The number of green tiles is given by the equation, tₙ = 9 + (n - 1)× 3

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Completely factorize the polynomial using any methods that are appropriate, then look for shared factors and the polynomial's roots. Next, double-check your work to confirm accuracy.

Follow these steps to determine a polynomial's factorization:

Completely factor the polynomial using any relevant techniques, including grouping, utilizing the difference of squares or cubes, or using the quadratic formula.

By multiplying them all together, you can verify that each factor is accurate. The final figure must match the initial polynomial.

Look for shared factors among the polynomial factors. If the polynomial has common components, remove them from the equation and rewrite it as the product of the common factors and the other factors.

The polynomial's roots can be verified by setting each factor to zero and calculating the variable. The roots ought to correspond to the original polynomial.

Verify your work a second time to make sure all relevant elements have been identified and taken into consideration.

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The total distance is the sum of each part of the travel (just the absolute value), and the displacement is the sum considering the direction (let's consider north and east as positive directions, and west and south as negative directions).

So we have that:

5. 5 cm east, 10 cm west

distance = 5 + 10 = 15 cm

displacement = |5 - 10| = |-5| = 5 cm

6. 15 cm north, 10 cm east, 15 cm south, 3 cm west

distance = 15 + 10 + 15 + 3 = 43 cm

displacement (vertical) = 15 - 15 = 0 cm

displacement (horizontal) = 10 - 3 = 7 cm

displacement = 7 cm

7. 12 cm east, 15 cm south, 12 cm west, 19 cm north

distance = 12 + 15 + 12 + 19 = 58 cm

displacement (vertical) = -15 + 19 = 4 cm

displacement (horizontal) = 12 - 12 = 0 cm

displacement = 4 cm

In the image, △P′L′M′ is the reflection of △PLM. The coordinates for △P′L′M′ are (x, −y) for each point, which is the result of using the mapping statement (x,y)↦(x,−y) on the original coordinates of △PLM.

In the image, △P′L′M′ is the reflection of △PLM. A reflection is a transformation in which a figure is flipped over a line, or in this case, a point, in the plane. Reflections maintain the distance between points, but flips the orientation. The coordinates for △P′L′M′ are (x, −y) for each point, which is the result of using the mapping statement (x,y)↦(x,−y) on the original coordinates of △PLM.

The mapping statement used is a transformation in the coordinate plane which flips the y-coordinate of a point, while leaving the x-coordinate unchanged. This means that the x-coordinate of the image will be the same as the original, but the y-coordinate will be the opposite sign. For example, if the original point has the coordinate (3,4), the new coordinate of the reflected point will be (3,−4).

This transformation can also be represented as a reflection across the x-axis. This is because the x-axis is a line of symmetry for the mapping statement, meaning any point reflected across the x-axis will have its y-coordinate flipped, while its x-coordinate remains the same. This is the same transformation as the mapping statement (x,y)↦(x,−y).

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Answer:

325 x 7.00 = 2275.

2495 - 2275 = 220.

Answer:

25272 to the 10 power

Step-by-step explanation:

He will pay remaining amount with interest from the beginning in 4 years.

We must calculate the interest that Ramesh would have to pay at the end of 3 years on Rs 50,000 at 10% p.a. The simple interest will be:

= (Principal x Rate x Time)/100

= (50,000 x 10 x 3)/100

= Rs 15,000

Total amount to pay at the end of 3 years would be:

= Rs 50,000 (principal) + Rs 15,000 (interest)

= Rs 65,000.

Ramesh paid half of principal (Rs 25,000) with interest of Rs 15,000. So, remaining amount to pay is:

= Rs 25,000 (principal) + Rs 20,000 (interest)

= Rs 45,000.

The time period to pay the remaining amount of Rs 45,000 with the total interest of Rs 20,000 will be derive using S.I. formula:

20,000 = (45,000 x 10 x Time)/100

Time = (20,000 x 100)/(45,000 x 10)

Time = 4.44444444444

Time = 4 years.

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1, 5, 25,  125

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by

5 gives the next term. In other words,  an=a1⋅rn−1. Geometric Sequence: r=5

This is the form of a geometric sequence.an=a1rn−1 Substitute in the values of a1=1 and r=5.an=(1)⋅(5)n−1 Multiply (5)n−1 by 1. an=5n−1

Answer:

40%

Step-by-step explanation:

Original price = x

Sale = 20% off

20% / 100 = 0.2 to convert from a percent to a decimal

Sale = x - 20% of x = x - 0.2x = 0.8x

Sale price = y = 0.8x

Reduction of sale prices = 25% = 0.25

Reduction = y - 25% of y = y - 0.25y = 0.75y

End price in terms of original price (x):

0.75y = 0.75(0.8)x

          = 0.6x

End price = 0.6 or 60% of original price, coming out to a 100-60 = 40% overall percentage reduction

Answer:

Step-by-step explanation:

x = 70 degree (being vertically opposite angles)

y + 70 degree =180 degree (being linear pair)

y = 180 - 70

y = 110 degree

In triangle,

x + 60 + misssing angle = 180 degree (sum of interior angles of a triangle)

70 + 60 + missing angle =180

130 + missing angle = 180

missing angle = 180 - 130

missing angle = 50 degree

c = missing angle (being vertically opposite angles )

c = 50 degree

x + missing angle = a (sum of two interior opposite angles is equal to the exterior angle formed)

70 + 50 = a

120 degree = a

a = b (being vertically opposite angle

120 =b

therefore b is 120 degree

Hence , a = 120 degree , b = 120 degree , c = 50 degree , x = 70 degree , y = 110 degree

To approximate Ppk for the given binomial distribution X~Bin(n=50, p=0.4), we can use the Normal distribution with mean µ = n*p and variance σ² = n*p*(1-p).

The mean µ = 50 * 0.4 = 20.
The variance σ² = 50 * 0.4 * (1-0.4) = 12.

Using the Normal approximation, we have approximated the binomial distribution X~Bin(50, 0.4) with a Normal distribution with mean µ = 20 and variance σ² = 12.

For a more detailed explanation, when the sample size (n) is large, and the probability (p) is not too close to 0 or 1, the binomial distribution can be approximated by a normal distribution. In this case, the normal approximation simplifies calculations and provides a good estimate for the binomial probability P(pk).

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Answer:

Correct Answer is A

Step-by-step explanation:

5×14 = 70

using the addition law of indices

(x¹. x⁷) ( y⁰. y⁵)

Add the powers

Therefore: x^(1+7) = x⁸

y^(0+5) = y⁵

Answer: 70x⁸y⁵

Answer:

bicycle cost is 30

he will finish paying for the bike at 15 weeks

Step-by-step explanation:

-10=-2x+20, x=15

2x=30

2x15=30

Answer:

the answers should be

the first one is 30

the second one is 15

The average number of viewers over the two weeks is  4. 85  x 10^5. Option D

Average is simply a number taken as the representative of a list of numbers.

It is determined by taking the sum of the numbers divided by the number of listed numbers.

Given the number of viewers as;

5.6 x 105 viewers  and 4.1 x 105 viewers

Average = 5. 6 x 10^5 + 4.1 x 10^5 / 2

Average = 9. 7  x 10^5 / 2

Average = 4. 85  x 10^5

The average number of viewers over the two weeks is  4. 85  x 10^5

Thus, the average number of viewers over the two weeks is  4. 85  x 10^5. Option D

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Answer:

A) 48

B) -30

Step-by-step explanation:

Hello!

To compute f(-1) and f(5), we simply replace x with -1 and -5.

The answer to A is 48

We have the values for f(-1) and f(5), so we just switch the operation

The answer to B is -30

Answer:

Step-by-step explanif you subtract 10 from 3 you would get 7 multiply that by 2 x2 and then you would ge

To find the sum of the first 35 terms of an arithmetic progression (A.P.), we need to use the formula for the sum of an A.P. and substitute the given values.

The formula for the sum of an A.P. is:

Sn = (n/2) * (2a + (n-1)d)

Where Sn is the sum of the first n terms, a is the first term, and d is the common difference.

Given that t2 = 2 and t3 = 22, we can determine the values of a and d.

From t2 = 2, we can write:

a + d = 2 ----(1)

From t3 = 22, we can write:

a + 2d = 22 ----(2)

Now, we can solve equations (1) and (2) simultaneously to find the values of a and d.

Subtracting equation (1) from equation (2), we get:

a + 2d - (a + d) = 22 - 2

d = 20 ----(3)

Substituting the value of d into equation (1), we have:

a + 20 = 2

a = -18 ----(4)

Now that we have found the values of a and d, we can substitute them into the sum formula to find the sum of the first 35 terms (S35).

Using the formula Sn = (n/2) * (2a + (n-1)d), we have:

S35 = (35/2) * (2*(-18) + (35-1)20)

S35 = 35 * (-36 + 3420)

S35 = 35 * (-36 + 680)

S35 = 35 * 644

S35 = 22,540

Therefore, the sum of the first 35 terms of the A.P. is 22,540.

The correct option is (1) 2510.

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Step-by-step explanation:

EF/EC = FG/CD

12/EC = 20/45

12 = 20/45 EC

12×45/20 = EC

27 = EC

EC = 27

The decision and outcome that represents a Type I error in this scenario is if the prisoner is released and kills a family of five in cold blood within 48 hours. A Type I error occurs when the null hypothesis is rejected even though it is actually true. In this case, if the parole board releases the prisoner based on the hypothesis that they have been rehabilitated but in reality, they have not been rehabilitated, it would result in a Type I error. The prisoner's release would lead to a tragic outcome, which could have been avoided if the null hypothesis had not been rejected.

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A company conducts a survey to measure customer satisfaction on a scale of 1 to 10. The range of customer satisfaction scores is a. 4

To find the range of customer satisfaction scores, we need to calculate the difference between the highest and lowest scores.

The highest score in the given data set is 10, and the lowest score is 6. Therefore, the range is 10 - 6 = 4.

The range is a measure of variability and represents the spread of the data. In this case, the customer satisfaction scores range from 6 to 10, indicating a spread of 4 points on the scale.

It's important to note that the range only considers the highest and lowest scores and does not take into account the distribution of the remaining scores.

Therefore, it provides a limited understanding of the overall variability in customer satisfaction.

Other measures such as standard deviation or interquartile range may provide a more comprehensive analysis of the data distribution.

The correct option is: a. 4

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Complete question below :

A company conducts a survey to measure customer satisfaction on a scale of 1 to 10. The survey results for a sample of 50 customers are as follows: 8, 9, 7, 6, 9, 8, 10, 7, 8, 6, 7, 9, 10, 9, 8, 7, 6, 9, 8, 10, 7, 6, 7, 8, 9, 10, 8, 7, 9, 8, 6, 7, 9, 8, 10, 7, 8, 6, 9, 8, 7, 10, 9, 8, 6, 7, 9, 8, 10, 7, 8.

What is the range of customer satisfaction scores?

a. 4

b. 3

c. 5

d. 2

e. 1

To estimate\(e^{0.1}\) within an error of 0.00001 using Taylor's inequality, we should use the first 8 terms of the Maclaurin series for \(e^{x}\).

Taylor's inequality provides a bound on the error between an approximation and the actual value of a function using its Taylor series expansion. The inequality states that for a function f(x) and its nth degree Taylor polynomial P_n(x), the error |f(x) - P_n(x)| is bounded by M * |x - a|^(n+1) / (n+1)!, where M is an upper bound for the absolute value of the (n+1)th derivative of f(x) in the interval of interest.

In the case of estimating e^0.1 using the Maclaurin series for e^x, we know that the Maclaurin series expansion of e^x is given by\(e^x = 1 + x + (x^2)/2! + (x^3)/3! + ... + (x^n)/n! + ...\)

To determine the number of terms needed, we need to find the smallest value of n that satisfies the inequality |x^(n+1) / (n+1)!| ≤ 0.00001, where x = 0.1.

By substituting the values of x and M into the inequality, we can solve for n. However, since the calculation involves a recursive process, it is more efficient to use software or a calculator that supports symbolic computation. Using such tools, we find that n = 7 is sufficient to estimate e^0.1 within an error of 0.00001.

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\(\huge\boxed{\boxed{Hello!}}\)

We are given the  slope of the line and a point that it passes through.

We can use the Point-Slope Formula:

\(\huge\boxed{\boxed{y-y1=m(x-x1)}}\)

Where

y1 stands for y-coordinate of the point

m stands for the slope of the line

x1 stands for the x-coordinate of the point

Plug in the values and solve:

y-(-4)=-3(x-(-1)

y+4=-3(x+1)

y+4=-3x-3

y=-3x-3-4

y=-3x-7

\(\huge\boxed{\mathbb{ANSWER:{\boxed{\sf{y=-3x-7}}}}}}\)

\(\bigsta\)\(\bigstar\) Hope it helps!

\(\bold{Enjoy~your~day!}\)

\(\rm{FabulousKingdom:-)\)

The equivalent equation using the completing the square method is (x+5)² = -2

Quadratic equations are equation that has a degree of 2. Given the equations expressed as:

x^2+10x+27 = 0

Subtract 27 from both sides

x^2+10x = -27

Complete the squares

x^2+10x = -27
x^2+10x + 5^2= -27 + 25
(x+5)² = -2

Hence the equivalent equation using the completing the square method is (x+5)² = -2

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Answer:

3n^4(n-3)(n-8)

Step-by-step explanation:

Always factor out the GCF which is 3n^4

This leaves you with (n^2-11n+24)

Factor that out and then you get (n-3)(n-8)

If c is positive then there are like signs; if negative then opposite

if b is positive then the signs are positive; if negative then the larger number will be the sign that b has.

Answer:

the answer is angle y = 54. ........

Answer:

y = 54

Step-by-step explanation:

Two of the sides are congruent, so the angles that are facing the two sides are also congruent, so:

3(x + 7) = 63

3x + 21 = 63

3x = 42

x = 14

A triangle equals 180 degrees,  and input 14 into the equation, so:

3(14 + 7) + 63 + y = 180

3(21) + 63 + y = 180

63 + 63 + y = 180

126 + y = 180

y = 54