Name the theorem or postulate that lets you immediately conclude

49, 36, 25, 16, 9, 4

============================================================

Explanation:

We always start with n = 1 when it comes to sequences and series problems.

Plug in n = 1 to get

\(a_n = (n-8)^2\\\\a_1 = (1-8)^2\\\\a_1 = (-7)^2\\\\a_1 = 49\\\\\)

The first term is 49, showing that the answer is choice C.

We can stop here, but I'll show how to do another one to help you get practice.  Plug in n = 2.

\(a_n = (n-8)^2\\\\a_2 = (2-8)^2\\\\a_2 = (-6)^2\\\\a_2 = 36\\\\\)

I'll let you compute the other terms.

Answer:

49,36,25,16,9,4

Step-by-step explanation:

First, eliminate anwser A since it's all negatives, and when squaring, negatives (without imaginary numbers) are impossible.

Foil out the equation:

a=(n-8)^2

a=(n-8)(n-8)

a=n^2-8n-8n+64

a=n^2-16n+64

Now find the values by substituting values n>=1:

49=1^2-16(1)+64

36=4-32+64

etc.

Answer:

Green = 18.84

Blue =24

Orange = 20

Total outer perimeter = 18.84 + 24 + 20 = 62.84

Answer:

18.84 m, 24m, 20m

Step-by-step explanation:

Green:

We need the radius of this circle, is can be calculated by 12 ÷ 2 = 6

2π6 / 2 = 37.68 / 2 = 18.84 m

Blue:

12 + 12 = 24 m

Orange:

10 + 10 = 20 m

Answer:

Option B is the correct answer

Step-by-step explanation:

\(3 \bigg( \frac{7}{5} x + 4 \bigg) - 2\bigg( \frac{3}{2} - \frac{5}{4}x \bigg) \\ \\ = \bigg( \frac{7 \times 3}{5} x + 4 \times 3\bigg) - \bigg( \frac{3 \times \cancel 2}{\cancel 2} - \frac{5 \times 2}{4}x \bigg)\\ \\ = \bigg( \frac{21}{5} x + 12\bigg) - \bigg( 3 - \frac{5 }{2}x \bigg)\\ \\ = \frac{21}{5} x + 12 - 3 + \frac{5 }{2}x \\ \\ \frac{21}{5} x + \frac{5 }{2}x + 9 \\ \\ = \frac{42 + 25}{10} x + 9 \\ \\ \huge \purple{ = \frac{67}{10} x + 9}\)

Answer:

B, 67/10x + 9

Step-by-step explanation:

Pls, choose me as brainliest!

after tht, lets zo.....om meet

A)  Different arrangements that can be formed by using all letters of the word DISTRIBUTION if the last letter must be ‘T’ is equal to 9! (factorial) = 362,880.Word problems can be tricky to solve, and they can take up a lot of time.

This is because it is often difficult to figure out what the problem is asking you to do. Once you understand the problem, you can then figure out the solution. For example, in the question above, we are being asked how many different arrangements can be formed by using all letters of the word DISTRIBUTION if the last letter must be ‘T’.To solve this problem, we must first identify how many letters are in the word DISTRIBUTION. There are 11 letters in the word. However, we are only concerned with the last letter, which must be ‘T’. Therefore, we must arrange the remaining 10 letters. Since we are not allowed to use the same letter twice, we can use the factorial formula to calculate the number of arrangements. 10! = 3,628,800. However, this includes all possible arrangements, including those that do not have ‘T’ as the last letter. Therefore, we must subtract the number of arrangements that do not have ‘T’ as the last letter. There are 10! arrangements that do not have ‘T’ as the last letter. Therefore, the number of arrangements that can be formed by using all letters of the word DISTRIBUTION if the last letter must be ‘T’ is equal to 9! (factorial) = 362,880. The number of different arrangements that can be formed by using all letters of the word DISTRIBUTION if the last letter must be ‘T’ is equal to 9! (factorial) = 362,880.

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Answer:

Step-by-step explanation:

a + 9 = 15

a = 15 - 9

a = 6

c + 9 = 16

     c = 16 - 9

     c = 7

d = c + 9

   = 7 + 9

  = 16

e = d + 15

  = 16 + 15

e = 31

P(selecting a boy) = total boy /total pupils = 16/31

Answer:

y = 3/4x + 45

Step-by-step explanation:

I just took the practice test and got it right

The line that is parallel to y = 3/4x + 7 and passes through (-12,36) is y = 3/4x + 43.

If two strains have a transversal which paperwork alternative ve interior angles which are congruent, then the two strains are parallel. If strains have a transversal which forms corresponding angles which might be congruent, then the two lines are parallel.

explanation,

parallel line should be equal distance from equal interval between each point.

slope = 3/4

y-intercept = 7

For the lines to be parallel their slope must be equal.

y intercept of the second line is 36

therefore new line parallel to y = 3/4x + 7 is

y = 3/4x + 7 + 36

y = 3/4x + 43

The graph follows a straight line equation shows a straight line graph.

           slope(m)=tan∅=y axis/x axis.

Straight line graphs show a linear relationship between the x and y values.

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Answer:

for store a 260 + 20 times x and then store b 140 + 30 times x

Step-by-step explanation:

Answer:

80 lemons

Step-by-step explanation:

Let x represent the amount of lemons that were on the tree.

We can use this to set up an equation:

\(40\%x=32\)

Note that percentages can also be written as that number over 100.

\(\frac{40}{100}x=32\)

Simplify the fraction.

\(\frac{2}{5}x=32\)

Multiply both sides by 5

\(2x=160\)

Divide both sides by 2

\(x=80\)

There were 80 lemons on the tree before he picked the lemons.

Answer:

Step-by-step explanation:

Just got in online image to simple explanation. Now it is your turn to fill out your answer.

For 1) through 10) you got to approximately by looking at the image.

Answer: 1. right 2. obtuse 3. acute 4. acute 5. obtuse 6. straight 7. obtuse 8. acute 9. obtuse 10. acute 11. obtuse 12. acute 13. acute 14. obtuse 15. right 16. acute 17. obtuse 18. straight 19. acute 20. acute

Answer:

86868600 for C and 416.88 for the D

Answer:

12.57

Step-by-step explanation:

We need to find of area of a circle and the formula for that is pie * radius ^2.

Pie * 2 squared = 12.57 rounded to the nearest hundredth

Answer:

Polynomial product A:

(4x2 – 4x)(x2 – 4) Polynomial product B:

(x2 + x – 2)(4x2 – 8x)

They are trying to determine if the products of the two polynomials are the same. But they disagree about how to solve this problem.

1. Complete the table to summarize each student's conjecture about how to solve the problem. (2 points: 1 point for each row of the chart)

Classmate Conjecture

Emily: says they should just check one method

Zach: says that they should check all three bc there could be multiple answers

Evaluating the Conjectures

Who do you think is correct? (1 point)

If they do all of the methods correctly, they should get the same answer for all of them.

Analyzing the Data

Table Method:

2. Use the table to find the products of the two polynomials. Write your answer in descending order. (4 points: 2 points for each product)

A) (4x2 – 4x)(x2 – 4)

         4x2        –4x

x2      4x^4     –4x^3

–4     -16x^2     16x

4x^4 - 4x^3 - 16x^2 + 16x

B) (x2 + x – 2)(4x2 – 8x)

              x^2           x            -2

4x^2       4x^4      4x^3       -8x^2

-8x       -8x^3       -8x^2       16x

4x^4 - 4x^3 - 8x^2 - 8x^3 - 8x^2 +16x

combine like terms

4x^4 - 4x^3 - 16x^2 + 16x

3. Are the two products the same when you multiply them with the table method? (1 point)

yes

Multiplying Using the Distributive Property:

4. Multiply the two polynomials using the distributive property. (4 points: 2 points for each product)

5. Are the two products the same when you multiply them horizontally? (1 point)

yes

Making a Decision:

8. Who was right, Emily or Zach? Are the products the same with the three different methods of multiplication? (1 point)

Emily was correct. the products are the same no matter what method.

9. Which of these three methods is your preferred method for multiplying polynomials? Why? (1 point)

personally, i like the distributive property, but do whichever one you like.

The final series solution can be written as: y(x) = a₀x⁰ + a₁x¹ + a₂x² + ...

To find the series solution for the given differential equation:

Step 1: Assume a power series solution of the form:

y(x) = ∑[n=0 to ∞] aₙxⁿ

where aₙ represents the coefficients to be determined.

Step 2: Differentiate y(x) with respect to x to find y'(x) and y''(x):

y'(x) = ∑[n=0 to ∞] aₙn xⁿ⁻¹

y''(x) = ∑[n=0 to ∞] aₙn(n-1)xⁿ⁻²

Step 3: Substitute y(x), y'(x), and y''(x) into the given differential equation:

(x² + 2)∑[n=0 to ∞] aₙn(n-1)xⁿ⁻² + 3x∑[n=0 to ∞] aₙn xⁿ⁻¹ - ∑[n=0 to ∞] aₙxⁿ = 0

Step 4: Simplify the equation:

∑[n=0 to ∞] aₙn(n-1)xⁿ + 2∑[n=0 to ∞] aₙn(n-1)xⁿ⁻² + 3∑[n=0 to ∞] aₙn xⁿ + 3∑[n=0 to ∞] aₙn xⁿ⁻² - ∑[n=0 to ∞] aₙxⁿ = 0

Step 5: Rearrange the terms:

∑[n=0 to ∞] (aₙn(n-1)xⁿ + 2aₙn(n-1)xⁿ⁻² + 3aₙn xⁿ + 3aₙn xⁿ⁻² - aₙxⁿ) = 0

Step 6: Group the terms with the same power of x:

(a₀(0(0-1)x⁰ + 2(0(0-1)x⁻²) + 3a₀x⁰) + a₁(1(1-1)x¹ + 2(1(1-1)x⁻¹) + 3a₁x¹) + a₂(2(2-1)x² + 2(2(2-1)x⁰) + 3a₂x²) + ... = 0

Step 7: Simplify the expressions:

(3a₀ + a₁ + 2a₂)x⁰ + (2a₀ + 3a₁ + 4a₂)x¹ + (6a₁ + 6a₂)x² + ... = 0

Step 8: Equate the coefficients of xⁿ to zero for each term:

3a₀ + a₁ + 2a₂ = 0 (n = 0)

2a₀ + 3a₁ + 4a₂ = 0 (n = 1)

6a₁ + 6a₂ = 0 (n = 2)

...

Step 9: Solve the system of equations:

From the first equation: a₁ = -3a₀ - 2a₂

Substitute a₁ into the second equation:

2a₀ + 3(-3a₀ - 2a₂) + 4a₂ = 0

2a₀ - 9a₀ -

6a₂ + 4a₂ = 0

-7a₀ - 2a₂ = 0

7a₀ + 2a₂ = 0 (equation 3)

From the third equation:

6(-3a₀ - 2a₂) + 6a₂ = 0

-18a₀ - 12a₂ + 6a₂ = 0

-18a₀ - 6a₂ = 0

-3a₀ - a₂ = 0 (equation 4)

Solve equations 3 and 4 simultaneously to find the values of a₀ and a₂.

Step 10: Once you have the values of a₀ and a₂, substitute them back into the equation for a₁ to find its value.

Step 11: The final series solution can be written as:

y(x) = a₀x⁰ + a₁x¹ + a₂x² + ...

where the coefficients a₀, a₁, a₂, ... are determined from the above calculations.

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The break-even point is when the cost of buying ski equipment ($400) is equal to the cost of renting and buying lift tickets for 20 days ($1200).

In order to find the break-even point, we need to compare the cost of buying ski equipment to the cost of renting the equipment and buying lift tickets. The cost of buying ski equipment is $400, while the cost of renting the equipment and buying lift tickets is $60 per day plus $35 for the lift ticket, for a total of $95 per day. If we divide the cost of buying ski equipment ($400) by the cost of renting and buying lift tickets ($95), we get 4.21. This means that it would take 4.21 days to break even on the cost of buying the equipment. To make this easier to understand, we can round up to 5 days, which means it would take 5 days of skiing for the cost of buying the equipment to equal the cost of renting and buying lift tickets. Therefore, the break-even point is after 5 days of skiing.

400/95

=4.21

rounded up to 5 days.

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(a) s(t) = -e-t - 60t + 100

(b) s(t) = -20ln(t+2) + 20t + 20 + 20ln(2),

a. Given that the acceleration, initial velocity, and initial position of the object are a(t) = e-t, v(0) = 60, s(0) = 40, we have to find the position and velocity of the object.For that, we can find the velocity by integrating the acceleration equation.v(t) = integral of a(t) dtv(t) = integral of e-t dtv(t) = -e-t + Cv(0) = 60, so Cv = 60 and v(t) = -e-t + 60Now, we can find the position by integrating the velocity equation.s(t) = integral of v(t) dts(t) = integral of (-e-t + 60) dts(t) = -e-t - 60t + C'Now s(0) = 40, so we have40 = -e0 - 60(0) + C'C' = 100Therefore, s(t) = -e-t - 60t + 100, which is the position of the object.b. Given that the acceleration, initial velocity, and initial position of the object are a(t) = 20/(t+2)2, v(0) = 20, s(0) = 10, we have to find the position and velocity of the object.For that, we can find the velocity by integrating the acceleration equation.v(t) = integral of a(t) dtt+2 in the denominator of the acceleration equation suggests that we use u-substitution.u = t+2, du = dtSo the integral becomesv(t) = integral of (20/u2) duv(t) = -20/u + Cv(0) = 20, so Cv = 20 andv(t) = -20/(t+2) + 20Now, we can find the position by integrating the velocity equation.s(t) = integral of v(t) dts(t) = integral of (-20/(t+2) + 20) dts(t) = -20ln(t+2) + 20t + C'Now s(0) = 10, so we have10 = -20ln(2) + 20(0) + C'C' = 20 + 20ln(2)Therefore, s(t) = -20ln(t+2) + 20t + 20 + 20ln(2), which is the position of the object.

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Answer:

Hey there!

15x-43+8x+18=90

23x-25=90

23x=115

x=5

RSQ=15(5)-43, or 32

TSQ=8x+18, or 58

Let me know if this helps :)

Answer:

yes the corresponding angles are congruent...

it can be wrong

Substitute \(y=4+5\sqrt x\) and \(dy=\frac5{2\sqrt x}\,dx\). Then the integral is

\(\displaystyle \int \frac5{\sqrt x (4+5\sqrt x)^2} \, dx = 2 \int \frac{1}{(4+5\sqrtx)^2} \frac{5}{2\sqrt x} \, dx = 2 \int y^{-2} \, dy\)

By the power rule,

\(\displaystyle \int y^{-2} \, dy = -y^{-1} + C\)

so that

\(\displaystyle \int \frac5{\sqrt x (4+5\sqrt x)^2} \, dx = \boxed{-\frac2{4+5\sqrt x} + C}\)

Answer:

Divide 1/3

Step-by-step explanation:

To get rid of the 1/3 fraction on x, we want to multiply by 3 or divide by 1/3

Answer:

divide by 1/3

Step-by-step explanation:

Statistical Process Control (SPC) is a methodology used to monitor, control, and improve processes by analyzing data and applying statistical techniques. Control charts are a key tool in SPC.

It involves the collection and analysis of data from a process to understand and control its variability. The goal of SPC is to ensure that a process operates within specified limits and remains stable over time, leading to consistent and predictable outcomes.

Control charts are a key tool in SPC. They provide a visual representation of process data over time and help to distinguish between common cause variation (inherent to the process) and special cause variation (resulting from specific factors).

Control charts display process measurements, such as sample means or individual measurements, plotted against time or the sequence of data collection.

Control charts typically include three lines: a centerline, an upper control limit (UCL), and a lower control limit (LCL). The centerline represents the process mean, while the control limits are calculated based on the process variability.

These control limits act as thresholds, indicating when the process is operating within acceptable limits or when it has deviated from its usual behavior.

By monitoring the data points on the control chart, process operators can identify patterns, trends, or unusual observations that may signal special causes of variation. When special causes are detected, actions can be taken to investigate and eliminate them, thereby improving process performance and reducing variability.

The use of SPC and control charts provides several benefits, including early detection of process issues, reduction of defects and waste, improved process stability, and the ability to make data-driven decisions for process improvement.

By focusing on understanding and controlling variability, organizations can achieve higher process quality, efficiency, and customer satisfaction.

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Answer:

a. fill in 8out of the 10 rows of the grid. Then subtract 3/10ths of the squares that are filled in

b. 70/100 x 8/10 = 14/25 kg

c. 0.7 x 0.8 = 0.56 kg

d. less, by 0.24 kg

I hoped this helped! :)

Answer:

Y-intercept :(0,2)

X-intercept: (2,0)

Step-by-step explanation:

Between 20 and 40 units per hour, the long-run average cost curve exhibits constant returns to scale. The statement that indicates between 20 and 40 units per hour, the long-run average cost curve exhibits constant returns to scale. This is option B.

In microeconomics, the long-run average cost (LRAC) is a method of showing the average expense per unit for a given level of production input. It is the cost of producing goods per unit using a specified number of inputs, such as labor and capital.

Long-run average cost is the average cost per unit of production after the company has adapted its production scale fully. As a result, the term "long-run" denotes a period in which all of the firm's inputs are variable.

The cost structure's shape is represented by the long-run average cost curve. The curve is determined by dividing the cost of producing goods by the number of goods produced. It aids in identifying the production rate at which a firm may generate the most output at the lowest cost.The long-run average cost curve depicts how the average cost of production varies with scale.

The curve might be downward-sloping, indicating economies of scale, flat, implying constant returns to scale, or upward-sloping, indicating diseconomies of scale, based on the company's production methods.

Hence, the answer is B.

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The 90% confidence interval for the mean number of pounds of trash per person per week in the city is estimated to be between 33.863 and 35.537 pounds.

CI = X± Z * (σ/√n),

where CI is the confidence interval, X is the sample mean, Z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Step 1: Calculate the z-score for a 90% confidence level.

The confidence level is 90%, which means there is a 10% chance that the true mean falls outside the interval. To find the z-score corresponding to this confidence level, we can use a standard normal distribution table or a calculator. The z-score for a 90% confidence level is approximately 1.645.

Step 2: Calculate the confidence interval.

Given data:

Sample mean X = 34.7 pounds

Population standard deviation (σ) = 8.2 pounds

Sample size (n) = 173 residents

Substituting the values into the formula, we have:

CI = 34.7 ± 1.645 * (8.2/√173)

Calculating the values within the parentheses first:

8.2/√173 ≈ 0.623

Then, multiplying the z-score and the calculated value:

1.645 * 0.623 ≈ 1.025

Finally, calculating the lower and upper bounds of the confidence interval:

Lower bound = 34.7 - 1.025 ≈ 33.675

Upper bound = 34.7 + 1.025 ≈ 35.725

Rounded to 3 decimal places, the 90% confidence interval for the mean number of pounds of trash per person per week is estimated to be between 33.863 and 35.537 pounds.

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Ordered pair{(−6,−1),(−8,4),(−5,4),(3,−9)} from the given set of ordered pairs represents the function.

As given in the question,

Given set of ordered pairs following is the one which represents the function :

In the given set of ordered pair for input value 3 there are two outputs 3 and -4 , therefore it is not a function.

In the given set of ordered pair for input value -5 there are two outputs 7 and 8 , therefore it is not a function.

In the given set of ordered pair each input has unique single output. Therefore it is a function.

In the given set of ordered pair for input value -1 there are two outputs 0 and -4 , therefore it is not a function.

Therefore, ordered pair{(−6,−1),(−8,4),(−5,4),(3,−9)}  from the given set of ordered pairs represents the function.

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lower limit of the 99% interval = 3.7265

Upper limit of the 99% interval = 6.1535

What do you mean  by standard deviation?

The standard deviation is a quantity that reveals the degree of variation (such as spread, dispersion, and spread) from the mean.

Number of students, n = 11

Averange time , mean , μ = 4.94

Standard deviation , \(s_{x}\) = 1.27

Significance level , α = 1 -= 0.99 = 0.01

Degree of freedom for t-distribution , d.f. = n - 1 = 11 - 1 = 10

Critical value = \(t_{\alpha /2,d.f\) = \(t_{0.005,10}\) = 3.169

Margin of error ,E = \(t_{\alpha /2,d.f\) × \(\frac{s_{x} }{\sqrt{n} }\) = 3.169  ×\(\frac{1.27}{\sqrt{11} }\) = 3.169 × 0.38292 = 1.21347

Limits of 99% confidence intervals are given by:

a) Lower limit = μ - E = 4.94 - 1.21347 = 3.7265

b) Upper limit = μ + E = 4.94 + 1.21347 = 6.1535

Therefore, lower limit of the 99% interval = 3.7265

Upper limit of the 99% interval = 6.1535

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