Suppose a tim horton's manager claims the standard deviation of wait times at their drive through is 3 minutes. a recent sample of 28 customers reveals a sample standard deviation wait time of 3.75 minutes. test whether or not the manger's goal was achieved using a 5% level of significance. calculate the appropriate test statistic (round to 2 decimal places as needed) enter each critical value (round to 3 decimal places as needed) enter the smaller critical value here: enter the larger critical value here: determine the appropriate p-value (round to 3 decimal places as needed) which of the following is your conclusion based on the information above?
Do not reject the null hypothesis. There is insufficient evidence to support the Manager's claim.
Reject the null hypothesis. There is sufficient evidence to support the Manager's claim.
Do not reject the null hypothesis. There is sufficient evidence to reject the Manager's claim.
Reject the null hypothesis. There is sufficient evidence to reject the Manager's claim.
Reject the null hypothesis. There is insufficient evidence to reject the Manager's claim.
Do not reject the null hypothesis. There is insufficient evidence to reject the Manager's claim.

To find the value of z for a 95% confidence level, we can use a z-score table or a calculator. The z-score corresponding to a 95% confidence level is 1.96.

To determine the sample size, we can use the formula:

n = (z^2 * s^2) / E^2

where:
n = sample size
z = z-score (1.96 for 95% confidence level)
s = estimated standard deviation (3 cards)
E = margin of error (1 card)

Plugging in the values, we get:

n = (1.96^2 * 3^2) / 1^2
n = 34.56

We need to round up to the nearest whole number, so the sample size should be 35 people. This means that if we randomly select 35 employees and calculate their average number of credit cards, we can be 95% confident that the true average number of credit cards per employee is within 1 card of our sample mean.
To determine the required sample size for your survey with a 95% confidence level and a margin of error of 1 point, you'll need to use the sample size formula and find the appropriate z-value.

The sample size formula is: n = (z^2 * σ^2) / E^2

Where:
- n is the sample size
- z is the z-value corresponding to the desired confidence level (95% in this case)
- σ is the estimated standard deviation of the population (3 credit cards per employee)
- E is the margin of error (1 point)

For a 95% confidence level, the z-value is approximately 1.96. You can find this value using a z-table or an online calculator.

Now, plug the values into the formula:

n = (1.96^2 * 3^2) / 1^2
n = (3.8416 * 9) / 1
n ≈ 34.5744

Since you cannot survey a fraction of a person, round up to the nearest whole number. Therefore, you should survey approximately 35 people to achieve a 95% confidence level with a margin of error of 1 point for the average number of credit cards per employee.

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Answer:

coefficient

Step-by-step explanation:

the 4 is the coefficient

The shape of the data of the line plot is best described by the option

A line plot is a graphical display of data as check marks showing the frequency of a data point above a number line.

The description of the line plot can be presented as follows;

The number of dota above the points marked 10, 11, 14, 16, and 17 = One dot each

The number of dots above the point marked 13 = Two dots

The number of dots above the points marked 12, and 15 = Four dots each

The above description of the line plot indicates;

The mode of the dataset are 12 and 15, therefore;

The option that best describes the shape of the data, is therefore;

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Sleeping is more important than the having full stomach when it comes to doing well on an exam

Based on the contour diagram, it seems that the percentage a student earns on an exam (l) is affected by both x and y. In other words, the more hours a student sleeps (x), the higher their percentage in the exam tends to be. Similarly, the fuller a student's stomach is (y), the higher their percentage in the exam tends to be.
It's important to note that the impact of x and y on l isn't necessarily equal. For example, if a student sleeps for 10hours (x=10) and has a full stomach (y=10), their percentage in the exam appears to be close to 100%. However, if they only sleep for 5 hours (x=5) and have a full stomach (y=10), their percentage in the exam appears to be closer to 70%. This suggests that sleeping is more important than having a full stomach when it comes to doing well on an exam.
Overall, this function seems to demonstrate that the amount a student sleeps and their level of hunger can impact their performance on an exam. However, it's important to note that this is just one function and may not apply to every student or every exam.

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The expression  x²-6x+9 is equal to the expression (x-3)², option A is correct.

The given expression is x²-6x+9

x is the variable in the expression

Plus and minus are the operators

We have to factor the expression

x²-6x+9

x²-3x-3x+9

x(x-3)-3(x-3)

(x-3)(x-3)

x²-6x+9 is equal to (x-3)²

(x-3)²

Hence, the expression  x²-6x+9 is equal to the expression (x-3)², option A is correct.

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The curvature is zero at the origin, but f(x) is not twice continuously differentiable function at x = 0, because f''(x) does not exist at x = 0. Therefore, the statement is not necessarily true.

An inflection point is a point on a curve where the sign of the curvature changes. At an inflection point, the curvature may be zero, but it may also be undefined.  Moreover, even if the curvature is defined and equal to zero at an inflection point, it does not necessarily imply that the function is twice continuously differentiable at that point.

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Answer: Number Question #1 - To find the volume generated by rotating the region bounded by y=e^(−x^2), y=0, x=0, and x=1 about the y-axis using the method of cylindrical shells, we can integrate the volume of each cylindrical shell. The radius of each shell will be x, and the height will be e^(−x^2).

Thus, the volume is given by:

V = ∫[0,1] 2πxe^(−x^2) dx

Using u-substitution with u=−x^2 and du/dx=−2x, we can rewrite this integral as:

V = ∫[0,−1] −πe^udu

Evaluating the integral, we get:

V = π/2(e^0 − e^(−1)) ≈ 0.436

Therefore, the volume generated by rotating the region about the y-axis is approximately 0.436 cubic units.

Number Question #2 - To find the volume of the solid obtained by rotating the region bounded by y=sqrt(x−1), y=0, x=5 about the line y=5, we can again use the method of cylindrical shells. In this case, the radius of each shell will be 5−y, and the height will be x−1.

Thus, the volume is given by:

V = ∫[0,4] 2π(5−y)(x−1)dy dx

Integrating with respect to y first, we get:

V = ∫[1,5] π(x−1)(5−y)^2 dx

Expanding and simplifying, we get:

V = 2π/3 [(5x−x^2−13)∣[1,5]]

Evaluating the integral, we get:

V = (32π/3)

Therefore, the volume of the solid obtained by rotating the region about y=5 is (32π/3) cubic units.

Number Question #3 - To find the volume of the solid obtained by rotating the region enclosed by the graphs of y=x^2, y=8−x^2, and to the right of x=1.5 about the y-axis using the method of cylindrical shells, we can integrate the volume of each cylindrical shell. The radius of each shell will be x, and the height will be (8−x^2)−x^2=8−2x^2.

Thus, the volume is given by:

V = ∫[1.5,2] 2πx(8−2x^2)dx

Integrating, we get:

V = (32π/3) − (9π/2)

Therefore, the volume of the solid obtained by rotating the region about the y-axis is (32π/3) − (9π/2) cubic units.

Answer: 5

Step-by-step explanation: The center of the circle will be (–3, 6), and the radius, which is the distance from (–3,6), will be 5. The standard form of a circle is given below: (x – h)2 + (y – k)2 = r2, where the center is located at (h, k) and r is the length of the radius. In this case, h will be –3, k will be 6, and r will be 5.

The final matrix product has dimensions 10x1.

To multiply a chain of matrices with given dimensions, we need to follow the associative property of matrix multiplication and multiply the matrices in a certain order.

Given the dimensions 10x3, 3x5, 5x10, 10x12, and 12x1, we need to multiply them in the order of (10x3) x (3x5) x (5x10) x (10x12) x (12x1).

Step 1: Multiply the first two matrices, (10x3) and (3x5), to get a resulting matrix of dimension (10x5).

Step 2: Multiply the resulting matrix from step 1, which is (10x5), with the next matrix, (5x10), to get a new matrix of dimension (10x10).

Step 3: Multiply the resulting matrix from step 2, which is (10x10), with the next matrix, (10x12), to get a new matrix of dimension (10x12).

Step 4: Multiply the resulting matrix from step 3, which is (10x12), with the last matrix, (12x1), to get a final matrix of dimension (10x1).

Therefore, the final answer obtained by multiplying the chain of matrices in the given order is a matrix of dimension (10x1).

The steps performed in the multiplication of the chain of matrices with dimensions 10x3, 3x5, 5x10, 10x12, and 12x1 are as follows:
(10x3) x (3x5) = (10x5)
(10x5) x (5x10) = (10x10)
(10x10) x (10x12) = (10x12)
(10x12) x (12x1) = (10x1)

To multiply a chain of matrices efficiently, you should follow the Matrix Chain Multiplication algorithm, which determines the optimal parenthesization to minimize the number of scalar multiplications. For your matrices with dimensions 10x3, 3x5, 5x10, 10x12, and 12x1, here's the best way to multiply them:

1. Start by finding the optimal parenthesization:
  - Multiply the 10x3 and 3x5 matrices first, resulting in a 10x5 matrix.
  - Then, multiply the 5x10 and 10x12 matrices, resulting in a 5x12 matrix.
  - Finally, multiply the 10x5 and 5x12 matrices, and then the resulting 10x12 matrix with the 12x1 matrix.

2. Perform the multiplications:
  - A = 10x3 * 3x5 = 10x5
  - B = 5x10 * 10x12 = 5x12
  - C = A * B = 10x5 * 5x12 = 10x12
  - D = C * 12x1 = 10x12 * 12x1 = 10x1

By following this approach, you minimize the total number of scalar multiplications, resulting in a more efficient calculation. The final matrix product has dimensions 10x1.

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Answer: x = 2√381

Step-by-step explanation:

Call A the dotted line.

Using the Pythagorean theorem, we find that [tex]A^{2} + 16^{2}[/tex] [tex]= 22^{2}[/tex]

Simplifying gives:

[tex]A = \sqrt{16^2 + 22^2}\\A = \sqrt{740}\\A = 2\sqrt{185}[/tex]

Now we move to the other triangle we can call the sides: a, the dotted side, b the height, and x, the hypotenuse.

[tex]a = 2\sqrt{185}[/tex]

and

[tex]b = 44-16 = 28[/tex]

So,

[tex](2\sqrt{185})^{2} + 28^2 = x^2\\x = \sqrt{(2\sqrt{185})^2 +28^2 }\\x = \sqrt{740+784}\\x= \sqrt{1524}\\x= 2\sqrt{381}[/tex]

At the perpendicular bisector of any line

XY and the bisector of any angle XYZ, the correct option is A. The locus of points equidistant from lines XY and YZ.

Angle bisector is a locus or set of points that bisects an angle and is equidistant from two intersecting math that create an angle

The perpendicular bisector is a set of points that bisects a line generated by Linking two points and are equidistant from two points.

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The probability that an arrival does not have to wait before service is 0.7 (Option B).

To calculate the probability that an arrival does not have to wait before service, we need to use the Poisson and exponential distributions.

First, we can calculate the average number of arrivals per hour:

60 minutes / 10 minutes per arrival = 6 arrivals per hour

Next, we can use the exponential distribution to calculate the probability that a phone call is less than or equal to 10 minutes (the time between arrivals):

P(call length ≤ 10 minutes) = 1 - e^(-10/3) ≈ 0.957

This means that there is a 95.7% chance that a phone call will end before the next arrival.

Finally, we can use the Poisson distribution to calculate the probability that there are no arrivals in the 10-minute window between the end of a phone call and the next arrival:

P(no arrivals in 10 minutes) = e^(-6) ≈ 0.002

So the probability that an arrival does not have to wait before service is:

P(no wait) = P(call length ≤ 10 minutes) * P(no arrivals in 10 minutes)

P(no wait) = 0.957 * 0.002

P(no wait) ≈ 0.002

Therefore, the answer is A) 0.3.

We're given that arrivals at a telephone booth follow a Poisson distribution with an average time of 10 minutes between arrivals, and the length of a phone call is exponentially distributed with a mean of 3 minutes. We need to find the probability that an arrival does not have to wait before service.

Step 1: Calculate the arrival rate (λ) and service rate (μ)
The average time between arrivals is 10 minutes, so the arrival rate λ is 1/10 arrivals per minute.
The average length of a phone call is 3 minutes, so the service rate μ is 1/3 calls per minute.

Step 2: Calculate the traffic intensity (ρ)
The traffic intensity ρ is the ratio of the arrival rate to the service rate.
ρ = λ/μ = (1/10) / (1/3) = 3/10 = 0.3

Step 3: Calculate the probability that an arrival does not have to wait (P_0)
For an M/M/1 queue (Poisson arrivals and exponential service times with a single server), the probability that an arrival does not have to wait before service is given by P_0 = 1 - ρ.
P_0 = 1 - 0.3 = 0.7

So, the probability that an arrival does not have to wait before service is 0.7 (Option B).

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The equation of the parabola in standard form is f(x) = -(x - 3)² + 25

the vertex of the parabola is given as (3, 25), we know that the equation of the parabola can be written in vertex form as:

f(x) = a(x - 3)² + 25

where a is a constant that determines the shape of the parabola.

The point (6, 16) lies on the parabola

so we can substitute x = 6 and y = 16 into the equation above to find 'a'.

16 = a(6 - 3)² + 25

-9 = 9a

Dividing both sides by 9, we get:

a = -1

Now we know that the equation of the parabola is:

f(x) = -(x - 3)² + 25

Hence, the equation of the parabola in standard form is f(x) = -(x - 3)² + 25

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The missing values are:

1. 0.16667

2. 0.16667

3. 0.16667

4. 0.16667

5. 0.6667

6. 0.5

7. 0.5

We have a spinner having 6 sections.

1. Probability (getting e)

= 1/6

= 0.16667

2.  Probability (getting D)

= 1/6

= 0.16667

3.  Probability (getting vowel)

= 2/6

=1/3

= 0.16667

4.  Probability (getting C)

= 1/6

= 0.16667

5.  Probability (getting consonant)

= 4/6

= 2/3

= 0.6667

6.  Probability (getting Capital letter)

= 3/6

= 0.5

7.  Probability (getting lowercase letter)

= 3/6

= 0.5

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According to the information, Samuel can stain the deck in 4 hours, and Julio can do it three times faster, in 4/3 hours or 1 hour and 20 minutes.

Let's assume that Samuel can stain the deck in x hours. Then, Julio can do the same job in x/3 hours (since he is three times faster).

Working together, they can stain the deck in 3 hours. Using the concept of work, we can set up the following equation:

1/x + 1/(x/3) = 1/3

Simplifying this equation by finding a common denominator, we get:

3/(3x) + x/(3x) = 1/3

Combining like terms, we get:

4x/(3x) = 1/3

Cross-multiplying, we get:

12x = 3x

Solving for x, we get:

x = 4

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The amount of milk Hasina need to steam cannot be calculated with the given information

From the question, we have the following parameters that can be used in our computation:

Size = 12 fl oz

Mix type = steams milk to mix with hot tea

The available parameters is not enough to determine the ratio

Assuming that we have

Ratio of steam to hot tea is 1 : 2

Then the steam would be:

Steam = 12/2

Simplify

Steam = 6 oz

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The number -3/11 on the number line is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Number = -3/11

To represent -3/11 on a number line, we use the following steps

Using the above as a guide

The number line is added as an attachment

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Answer:

I'm not sure if this what your looking for as an answer, but I hope it helped!

The function h(x) is given as the power series:

=h(x) = x³ + (x⁴/3) + (x⁵/5) + (x⁶/7) + (x⁷/9) + ...

Part A: To determine the interval of convergence, we use the ratio test:

lim(n→∞) |(x^(n+4))/(2(n+2)+1) * (2n+1)/(x^n+3)| = lim(n→∞) |x|^2/2 = |x|^2/2

The ratio test tells us that the series converges if |x|²/2 < 1 and diverges if |x|²/2 > 1. Therefore, the interval of convergence is -√2 < x < √2.

Part B: To find h′(−1), we differentiate the power series term by term:

h′(x) = 3x² + 4x³/3 + 5x⁴/5 + 6x⁵/7 + 7x⁶/9 + ...

h′(−1) = 3(−1)² + 4(−1)³/3 + 5(−1)⁴/5 + 6(−1)⁵/7 + 7(−1)⁶/9 + ...

= 3 − 4/3 + 1/5 − 6/7 + 1/9 − ...

= ∑(n=0 to ∞) (−1)^n * (2n+3)/(2n+1)

We can use the alternating series test to show that the series converges. The terms decrease in absolute value, and the limit of the terms approaches zero. Therefore, h′(−1) converges.

The relationship between the radius of convergence and interval of convergence of h(x) and h′(x) is that the radius of convergence of h′(x) is the same as that of h(x), but the interval of convergence may be different due to the behavior at the endpoints.

Part C: To determine if h(x²) has any points of inflection, we differentiate twice:

h(x²) = (x²)³ + ((x²)⁴/3) + ((x²)⁵/5) + ((x²)⁶/7) + ((x²)⁷/9) + ...

h′(x) = 3x⁴ + 4x⁵/3 + 5x⁶/5 + 6x⁷/7 + 7x⁸/9 + ...

h″(x) = 12x³ + 20x⁴/3 + 30x⁵/5 + 42x⁶/7 + 56x⁷/9 + ...

We can see that h″(x) is always positive, so h(x²) does not have any points of inflection.

When we compare functions we see that Jack and Jill have the smaller slopes

Jack's function: d = 0.05t

Slope (m1) = 0.05

Y-intercept (b1) = 0

Jill's function: d = 0.04t + 0.5

Slope (m2) = 0.04

Y-intercept (b2) = 0.5

Linear parent function: d = t

Slope (m0) = 1

Y-intercept (b0) = 0

When we compare functions we see that Jack and Jill have the smaller slopes

B. Given that they have smaller slopes this tells us that the pace with which they are running is smaller than that of the parent function

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Answer:{2,2,3,3}

Step-by-step explanation:

six by six is 36 and 2 times three would give you six

Answer:

(2,2,3,3)

Step-by-step explanation:

If a square pyramid is sliced in a way that the plane cuts in a direction perpendicular to the base but doesn't pass through the vertex, the resulting cross-section will be a trapezoid.

This trapezoid will have one pair of parallel sides and one pair of non-parallel sides.

To understand why the resulting cross-section is a trapezoid, imagine a square pyramid standing on its base. Now, imagine slicing the pyramid horizontally, parallel to the base. The resulting cross-section would be a square.

However, if we change the direction of the slice to be perpendicular to the base, but not passing through the vertex, the resulting cross-section will not be a square. Instead, it will be a trapezoid, with one set of parallel sides corresponding to the base of the pyramid, and the other set of sides corresponding to the slice that was made.

This type of cross-section is commonly seen in architectural and engineering designs, where different shapes need to be created by slicing or intersecting 3D shapes. Understanding the resulting cross-section of different slicing techniques is essential to ensure the proper fit and function of the final product.

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The probabilities of the possible outcomes obtained from tossing a fair coin two times are;

(a) Pr(0 heads) = 1/4

(b) Pr(1 head) = 1/2

(c) Pr(2 heads) = 1/4

The probability of an event is the ratio of the number of required outcome to the number of possible outcomes.

The equiprobable sample space of tossing a fair coin two times is; {HH, HT, TH, TT}, where;

H = Heads

T = Tails

The sample space indicates that there are 4 possible outcomes

(a) The possibility of getting 0 heads, is to get TT, therefore, the probability of getting zero heads, Pr(0 heads) = TT = 1/4

(b) The possibility of getting 1 head is to get. HT or TH, therefore;

The probability of getting 1 head, Pr(1 heads) = 2/4 = 1/2

(c) The number of possibility of getting 2 heads, is to get HH = 1

Therefore, the probability of getting 2 heads, Pr(2 heads) = 1/4

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Answer: Not sure which one you need my guess would be RADIANS

Step-by-step explanation:

For COS THETA RADIANS = 1.9

For COS THETA DEGREES = 111.7

Sorry if its wrong

Answer:

a. The interior angles of Parallelogram B (Pipe B) are 30°, 150°, 150°, and 30°. Angle x measures 60° because the 120° angle and angle x are supplementary angles.

c. Correct answers, in order: 360, 360, 150, supplementary, 30, complementary, 60

The best day to sell both stocks is Day 2, since the total value of both stocks is highest on that day, option C is correct.

On Day 1, the total value of the 30 shares of Metropolis stock is:

30 shares x $17.95 per share = $538.50

And the total value of the 55 shares of Suburbia stock is:

55 shares x $5.63 per share = $309.65

So the total value of both stocks on Day 1 is:

$538.50 + $309.65 = $848.15

On Day 2, the total value of the shares of Metropolis stock is:

30 shares x $18.28 per share = $548.40

And the total value of the shares of Suburbia stock is:

55 shares x $5.88 per share = $323.40

The total value of both stocks on Day 2 is: $871.8

for Day 3, total value of both stocks on Day 3 is $$821.40

Therefore, we can see that the best day to sell both stocks is Day 2, since the total value of both stocks is highest on that day:

$871.80 - $848.15 = $23.65

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The probability that two batteries used sequentially will remaining greater than 4 years is about 6.95%.

The time to failure of a single rechargeable battery is exponentially distributed with a median of three years. which means that the opportunity that a single battery will ultimate more than 4 years is given via:

P(X > 4) = e^(-4/3) ≈ 0.2636

Wherein X is the time to failure of a single battery.

Assuming that the two batteries are used sequentially and independently, the chance that each batteries will remaining more than four years is given by means of the made from their man or woman probabilities:

P(X1 > 4 and X2 > 4) = P(X1 > 4) * P(X2 > 4)

For the reason that two batteries are used successionally, the probability of the alternate battery lasting further than 4 times is analogous to the chance of the first battery lasting redundant than 4 years

P(X1 > 4 and X2 > 4) = P(X > 4)^2 ≈ 0.0695

Consequently, the probability that two batteries used sequentially will remaining greater than 4 years is about 0.0695 or 6.95%.

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The length of the arc BC is given as follows:

Arc BC = 10π units.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The radius in this problem is of 10 units, hence the length of the whole circumference is of:

C = 20π units.

The entire circumference is of 360º, hence arc BC is half the circumference, and it's length is given as follows:

Arc BC = 10π units.

The problem asks for the length of arc BC.

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The perimeter of the equlateral triangle is 42 units

The dimensions of the triangle are given as

x + 8, y + 4 and 4x - y​

The side lengths of an equilateral triangle are equal

So, we have

x + 8 = y + 4

4x - y​  = y + 4

When evaluated, we have

x = 6 and y = 10

So, we have

Perimeter = 3 * (y + 4)

This gives

Perimeter = 3 * (10 + 4)

Evaluate

Perimeter = 42

Hence, the perimeter is 42 units

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The common difference is 6, and the sum of the first 20 terms for the arithmetic sequence 1120.

U2 = 5

U3 = 11

Finding the common difference (d)

U3 - U2

= 11 - 5

= 6

Finding the first term (U1):

U1 = U2 - (2 - 1) × d

= 5 - (2 - 1) × 6

= 5 - 6

= -1

Finding the sum of the first 20 terms:

Sn = n/2 × (2U1 + (n - 1)d)

Sn = 20/2 × (2 × -1 + (20 - 1) × 6)

= 10 × (-2 + 19 × 6)

= 10 × (-2 + 114)

= 10 × 112

= 1120

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