for each sequence find the first 4 terms and 10th term 2n squared

To approximate the base length of a regular square pyramid with a given volume and height, we can use the formula for the volume of a pyramid and rearrange it to solve for the base length.

The volume of a pyramid is given by the formula V = (1/3) * base area * height. In the case of a regular square pyramid, the base is a square, so the base area is equal to the length of one side squared. Let's denote the base length as 'l'.

Given that the volume of the pyramid is 2400 cm^3 and the height is 18 cm, we can substitute these values into the formula:

2400 = (1/3) * l^2 * 18

To solve for the base length, we can rearrange the equation:

l^2 = (2400 * 3) / 18

l^2 = 400

Taking the square root of both sides, we get:

l = √400

l = 20 cm

Therefore, the approximate base length of the pyramid is 20 cm.

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Answer:

-41

Step-by-step explanation:

f(x) = 4x + 3 and g(x) = -2x + 5

g(f(5) ) =

First find f(5) = 4(5)+3 = 20+3 = 23

Then find g(23) = -2(23) +5 = -46+5 = -41

The option that best explains how to minimize response bias is E. carefully word and field-test survey questions.

Response bias describes a number of variables that may cause someone to give a false or inaccurate answer to a question. This kind of bias is especially common in self-report questions, like those found on surveys and in structured interviews.

Response bias is a term that encompasses a wide range of participant tendencies to give false or inaccurate answers to questions. In research involving participant self-report, such as structured interviews or surveys, these biases are pervasive.

In conclusion, the correct option is E.

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The translation in y = (x + 3)² is of 3 units to the left. The correct option is the last one.

For a general function y = f(x), we define a horizontal translation of N units as:

g(x) = f(x + N)

Here the original function is y = x² and the translated one is:

y = (x + 3)²

So we just added 3 on the argument, so this is a shift of 3 units to the left, the correct option is the last one.

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The graph of line a and line b is shown in the image attached below. The lines do not intersect each other.

To check if both lines intersect, we need to graph the system of equations. First, use the points given to write out the equations.

Line a:

Slope (m) = change in y / change in x = 6 - 4 / 8 - 0 = 2/8

m = 1/4

Find the y-intercept (b) by substituting m = 1/4, x = 0 and y = 4 into y = mx + b:

4 = 1/4(0) + b

b = 4

The equation of line a is: y = 1/4x + 4.

Line b:

Slope (m) = change in y / change in x = 1 - (-2) / 8 - 0

m = 3/8

Find the y-intercept (b) by substituting m = 3/8, x = 0 and y = -2 into y = mx + b:

-2 = 3/8(0) + b

b = -2

The equation of line b is: y = 3/8x - 2.

Both lines are graphed in the image attached below. Line a is the red line and line b is the red line. They do not intersect at any point.

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SSA  is not congruent rule of triangle.

What is SSS congruence postulate ?

A type of triangle congruence rule called Side-Side-Side (SSS) asserts that two triangles are congruent if their three sides are equal to their respective three sides of another triangle. When the dimensions of the matching sides and angles of two or more triangles match, the triangles are said to be congruent.

In order for two triangles to be congruent, their sides (S) and angles (A) must match. SAS, ASA, SSS, and RHS are the requirements for the triangle's congruence. The congruency of a triangle is not determined by SSA.

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We have a sample of 28 data points. The sample mean is 30.0 and the sample standard deviation is 2.40. The confidence level required is 98%. Then, we calculate α by:

The confidence interval for the population mean, given the sample mean μ and the sample standard deviation σ, can be calculated as:

Where n is the sample size, and Z is the z-score for 1 - α/2. Using the known values:

Where (from tables):

Finally, the interval at 98% confidence level is:

Answer:

If f(x)=x^3, evaluate f(x+h)-f(x)÷h, Where h* 0. Use your result to find the derivative of f(x) with respect to x. Differentiate with respect to x (x²-3x+5)(2x-7) .Find with respect to x the derivative of sinx ÷1– cosx​

Step-by-step explanation:

We are given f(x) = x^3. We need to find the value of (f(x+h) - f(x))/h.

f(x+h) = (x+h)^3 = x^3 + 3x^2h + 3xh^2 + h^3

Therefore, (f(x+h) - f(x))/h = [x^3 + 3x^2h + 3xh^2 + h^3 - x^3]/h

= 3x^2 + 3xh + h^2

Taking the limit of the above expression as h approaches 0, we get:

lim(h→0) [(f(x+h) - f(x))/h] = 3x^2

Therefore, the derivative of f(x) = x^3 with respect to x is 3x^2.

Next, we need to differentiate (x^2-3x+5)(2x-7) with respect to x.

Using the product rule, we get:

d/dx [(x^2-3x+5)(2x-7)] = (2x-7)(2x-3) + (x^2-3x+5)(2)

Simplifying, we get:

d/dx [(x^2-3x+5)(2x-7)] = 4x^2 - 20x + 11

Therefore, the derivative of (x^2-3x+5)(2x-7) with respect to x is 4x^2 - 20x + 11.

Finally, we need to find the derivative of sin(x)/(1-cos(x)) with respect to x.

Using the quotient rule, we get:

d/dx [sin(x)/(1-cos(x))] = [(1-cos(x))cos(x) - sin(x)(sin(x))]/(1-cos(x))^2

Simplifying, we get:

d/dx [sin(x)/(1-cos(x))] = cosec(x/2)^2

Therefore, the derivative of sin(x)/(1-cos(x)) with respect to x is cosec(x/2)^2.

I hope this helps

Answer:

32.75

Step-by-step explanation:

If you divide 131 by 4 (131/4), then you should get the answer 32.75, so if you need to round it, round it to 31, and if you do not need to round it, then it will be 32.75

When a hexagon is rotated 60° counterclockwise, it is carried onto itself.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Rotation is the rotation of a figure about a given point.

The exterior angles of a regular hexagon measures 60 degrees each, hence:

When a hexagon is rotated 60° counterclockwise, it is carried onto itself.

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Severe hand or wrist pain due to inflammation of the tendons is commonly referred to as tendinitis.

Tendinitis is a condition characterized by inflammation or irritation of the tendons, which are the fibrous tissues that connect muscles to bones. It commonly occurs in the hand and wrist area, leading to pain, swelling, and discomfort. Tendinitis can be caused by repetitive motions, overuse of the hand or wrist, injury, or certain medical conditions.

The inflammation of the tendons can result in severe pain in the affected hand or wrist, making it difficult to perform everyday activities that involve gripping or moving the hand. The pain may worsen with movement or after prolonged use of the hand. Rest, ice, immobilization, and anti-inflammatory medications are often recommended for managing tendinitis symptoms.

It is important to note that while tendinitis is a common cause of hand and wrist pain, there could be other underlying conditions or injuries that may require further evaluation and medical intervention. Consulting a healthcare professional for an accurate diagnosis and appropriate treatment is recommended for individuals experiencing severe hand or wrist pain.

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Answer:

0

x

Step-by-step explanation:

Answer:

  16

Step-by-step explanation:

Age problems can be solved by expressing the given relationships in math terms, then solving the resulting equation(s). Let J represent Judy's age now. Then Adami's age now is J/2. Six years ago, the relationship was ...

  (J -6) = 5(J/2 -6)

  J -6 = 2.5J -30

  24 = 1.5J

  16 = J

Judy is now 16 years old.

__

Additional comment

Adami is 8 now. 6 years ago, Judy was 10 and Adami was 2.

Here is an alternate approach. Let 'a' represent Adami's age 6 years ago. The relationship at present is ...

  2(a+6) = 5a +6

  6 = 3a . . . . . . . . . simplify, subtract 2a+6

  2 = a   ⇒   5a+6 = 16

Answer:

y = 9/4

Step-by-step explanation:

Step 1: Write equation

3(4y - 7) = 6

Step 2: Solve for y

Step 3: Check

Plug in y to verify it's a solution.

3(4(9/4) - 7) = 6

3(9 - 7) = 6

3(2) = 6

6 = 6

Answer:

40 shirts

Step-by-step explanation:

if half of her shirts are short sleeved, then double that amount is the total shirts

Based on this, we can conclude that an increase in price will result in a decrease in total revenue, since the increase in price will be offset by a larger decrease in quantity demanded

To find the elasticity of demand, we need to calculate the derivative of q with respect to p multiplied by the ratio of p to q.

Taking the derivative of the demand function with respect to p, we get:

q + 100 = -p/q

Multiplying both sides by p/q, we get:

p/q * q + 100p/q = -p

Simplifying, we get:

p/q = -100/(q^2 - p)

When p = $200, we can substitute this value into the equation to get:

200/q = -100/(q^2 - 200)

Solving for q, we get:

q = 50

So at a price of $200, the quantity demanded is 50 units. To find the elasticity, we need to calculate:

E = (dq/dp) * (p/q)

Taking the derivative of the demand function with respect to p, we get:

dq/dp = -1/q^2

Substituting p = $200 and q = 50, we get:

dq/dp = -1/2500

Substituting into the formula for elasticity, we get:

E = (-1/2500) \(\times\) (200/50) = -0.16

Since the elasticity is negative, we know that demand is inversely related to price, meaning that as the price increases, the quantity demanded will decrease.

Since the elasticity is greater than 1 in absolute value, we know that demand is elastic, meaning that a change in price will result in a relatively larger change in quantity demanded.

Based on this, we can conclude that an increase in price will result in a decrease in total revenue, since the increase in price will be offset by a larger decrease in quantity demanded.

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The answer is unknown number of inches for the long sides is 14.

Let's solve this problem step by step. We know that the short sides of the rectangle are 2 inches. Let's denote the unknown number of inches for the long sides as 'x'. According to the problem, the long sides are three less than this unknown number, so the length of the long sides can be expressed as 'x - 3'.

The area of a rectangle is given by the formula A = length × width. In this case, the area is given as 22 square inches, and the width (short side) is 2 inches. We can now set up the equation:

22 = 2 × (x - 3)

Simplifying the equation, we have:

22 = 2x - 6

Adding 6 to both sides, we get:

28 = 2x

Dividing both sides by 2, we find:

x = 14

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The probability is 99.87 that the sample proportion will be greater than 0.74.

      z = (x - μ)/σ

μ = E(X)

σ = √V(X)

n = 400 ; p = 0.8

Thus,

μ = E(X) = np = 400 x 0.8 = 320

σ = √V(X) = √np(1 - p) = √(400 x 0.8 x 0.2) = 8

The probability that given sample proportion would be greater than 0.74.

= 74% of the 400

= 0.74 x 400 = 296

Thus, p -value when  x = 296

z = (x - μ)/σ

x = (296  - 320)/8

z = -3

p value = 0.0013

probability = 0.13

Thus,  greater than 0.74.

1 - 0.0013 = 0.9987

Thus, the probability is 99.87 that the sample proportion will be greater than 0.74.

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Answer:

https://brainly.com/question/19363018

Step-by-step explanation:

Try ur hardest and Brianly is not the best way to get awnsers quizlet is :) You welcome

ps. look it up thats the best way (:

The correct option is b) Label.

In a chart, each data point, bar, slice, and so on has a unique label. This label is used to identify and differentiate the different elements within the chart. It provides a clear and concise description of what each element represents.

For example, in a bar chart that shows the sales of different products, each bar would have a label indicating the specific product it represents. This allows the viewer to easily understand which product corresponds to each bar.

The label is crucial in making the chart understandable and meaningful. Without it, the chart would be confusing and difficult to interpret. It helps to provide context and clarity to the data being presented.

While color, size, and position can also be used to distinguish between elements in a chart, they do not provide the same level of specificity as a label. Color, for instance, may be used to represent different categories, but it does not provide specific information about each individual element.

In summary, the unique label assigned to each data point, bar, slice, or other element in a chart is what helps identify and differentiate them. It provides a clear description of what each element represents, making the chart more understandable and meaningful.

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The value of a/b is  \(\sqrt{6}\) / 2

The area of mathematics known as mensuration is concerned with measuring geometric shapes and their various characteristics, such as length, volume, shape, surface area, lateral surface area, etc. In fundamental mathematics, learn about mensuration.

Measurement of agricultural fields, floor areas required for purchase/selling transactions. Measurement of volumes required for packaging milk, liquids, solid edible food items. Measurements of surface areas required for estimation of painting houses, buildings, etc.

According to the question:-

Side of an equilateral triangle equals a/3.

Therefore, the equilateral triangle's area is equal to (1/2)(a/3)2 sqrt (3) / 2 = a2 [sqrt (3)/ 36].

Hexagonal side equals b / 6.

The area is thus 6 (1/2) (b/6)^2 sqrt (3) / 2 

= b^2 [ 3 sqrt (3) / 72] = b^2 [sqrt (3) / 24]

So

sqrt (3) / 36 a2 = sqrt (3) / 24 b2

So

A2 / B2 = [Sqrt(3)/24] / [Sqrt(3)/36]

a^2 / b^2 = [ 36 / 24 ]

a^2/ b^2 = 3/2

A/ B = Sqrt(3) / Sqrt(2)

=Sqrt(6) / 2

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Answer:

53 degrees

Step-by-step explanation:

ACB seems to be a right angle so since ACD is 37 degrees:

DCB+37=90

DCB=53

Answer:53 degrees

Step-by-step explanation:

90-37= 53

The Power series representation of f(x) = \(x^8tan^-^1x^3\) is \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}\)

The Maclaurin series expansion method can be used to get the power series of such functions if the function has a composite part, such as the multiplication or quotient form.

An infinite series in mathematics known as a "power series" can be compared to a polynomial with an infinite number of terms.

The Maclaurin series will be used in this instance to expand the function:

\(tan^-^1x\) = \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^2^n^+^1}{2n+1}\)

and for    \(tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{(x^3)^2^n^+^1}{2n+1}\)

=>  \(tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}\)  -------(i)

and f(x) = \(x^8tan^-^1x^3\)

now we need to multiply \(x^8\) in the above equation to get the power series expansion of f(x)

\(x^8tan^-^1x^3\) = \(x^8\) \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}\)

=> \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3^+^8}{2n+1}\)

=>  \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}\)

so the expansion of f(x) = \(x^8tan^-^1x^3\) is \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}\)

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Answer:

0.3

Step-by-step explanation

d is the feet so you would grab your calculator and do v35/4 and that would come out to (rounded to the nearest tenth) 1.4  and for the other one you would do the same thing but replace "35" with 23 and that would give you (rounded to the nearest tenth) 1.1, so what is the distance between this two? 0.3

If a triangle side is created, the outside angle that results is equal to the product of the two opposite internal angles.

Given:

Using Exterior Angle Property

36x+ 2 = 18x -2 + 76

36x+ 2= 18x + 74

36x- 18x = 72

18x = 72

x= 4

So, <HTL = 36(4)+ 2= 144+2= 146 degree.

Now, Using Similarity

x/ 48 = 12/ 12

x= 48

and, Using Exterior Angle Property

7x+ 7 = 5x+ 3+ 4x- 26

7x+ 7= 9x - 23

-2x = -30

x= 15

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Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

A number's  root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as  or as 3 x 3.

Here,

If an equation have 2 roots , it means it is a quadratic function

If D=0, a quadratic function has two roots that are equal.

D (discriminant) = 0

=>b24ac=0 is required for a polynomial function to have equal roots.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

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It is possible to break a clock into 7 pieces so that the sums of the numbers in each piece are consecutive numbers.

To achieve a set of consecutive sums, we can divide the clock numbers into different groups. Here's one possible arrangement:

1. Group the numbers into three pieces: {12, 1, 11, 2}, {10, 3, 9}, and {4, 8, 5, 7, 6}.

2. Calculate the sums of each group: 12+1+11+2=26, 10+3+9=22, and 4+8+5+7+6=30.

3. Verify that the sums are consecutive: 22, 26, 30.

By splitting the clock into these particular groupings, we obtain consecutive sums for each group.

This arrangement meets the given conditions, where each piece has at least two numbers, and no number is damaged or split into separate digits.

Therefore, it is possible to break a clock into 7 pieces so that the sums of the numbers in each piece form a sequence of consecutive numbers.

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Answer:

I think the answer is 10 or −2(x-6)

Step-by-step explanation:

The range of the function g(x) is [300, ∞)

In this question, we have been given that we have deposited $300 into a savings account that earns interest annually.

The function g(x) = 300(1.04)^x used to find the amount of money in the savings account, g(x), after x years.

We need to find the range of the function.

Since a savings account earns interest annually, x can have take values from 0 to infinity.

For x = 0 year,

g(0) = 300(1.04)^0

g = 300 * 1

g = 300

For x tends to ∞, the value of function would be ∞

Therefore, the range of the function g(x) is [300, ∞)

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