Let a_{n} be the sequence defined by a_{1}=1, a_{2}=8 , and a_{n}=a_{n-1}+2 \cdot a_{n-2} for n ≥ 3 . Prove that a_{n}=3 \cdot 2^{n-1}+2 \cdot(-1)^{n} for all n \in \

Answer:

16,625

Step-by-step explanation:

In order to increase R14 in a ratio of 16:19 you need to devide 14 by 16 then multiply by 19 then you will get 16,625

Answer:

The area of Polygon

W

WW is

49

4949 square units.

Step-by-step explanation: dk

Scale factors are used to enlarge or reduce the size of a shape

The area of polygon w is 49 square units

The area of polygon v is given as:

\(v =1\)

The scale factor of the sides of polygon v, that forms polygon w is given as:

\(k=7\)

The area of polygon w is then calculated as:

\(w =v\times k^2\)

So, we have:

\(w =1\times 7^2\)

Evaluate the exponents

\(w =1\times 49\)

Multiply 1 and 49

\(w =49\)

Hence, the area of polygon w is 49 square units

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Answer:

b 16.4 ft

Step-by-step explanation:

To solve this problem using a graphing calculator, we need to plug in the value of q (which is given as 7) into the equation y = 2 csc e, and then graph the resulting equation.

First, we need to convert the angle e from degrees to radians, because the csc function takes its input in radians. We can use the conversion formula:

radians = degrees x (π/180)

So for e = 2, we have:

e (in radians) = 2 x (π/180) = 0.0349 radians

Now we can plug this value into the equation y = 2 csc e:

y = 2 csc(0.0349) ≈ 103.8 feet

This tells us that the length of the rafters needed to make the roof is approximately 103.8 feet. However, the question asks us to round to the nearest tenth of a foot, so the answer is:

y ≈ 103.8 feet ≈ 103.8 rounded to the nearest tenth of a foot

Therefore, the length of the rafters needed to make the roof for q 7" is approximately 103.8 feet, rounded to the nearest tenth of a foot.

So the correct answer is (b) 16.4 feet.

Using the graphing calculator, we find that the length of the rafters needed is approximately 16.4 feet, Therefore, the correct answer is option B, 16.4 feet.

To find the length of the rafters needed for the roof with an angle of 7 degrees, we'll use the given function y = 2 * csc(e), where e is the angle formed by the rafters and the top of the wall. Here's a step-by-step explanation:

1. Convert the angle from degrees to radians: e (in radians) = (7 degrees * π) / 180 ≈ 0.1222 radians.

2. Calculate the cosecant  (csc) of the angle e: csc(0.1222) ≈ 8.185.

3. Plug the value of csc(e) into the function: y = 2 * 8.185 ≈ 16.37.
Using a graphing calculator, we can input the function y = 2 csc e and graph it. Then, we can use the given angle of 2 to find the length of the rafters needed for a roof with a peak of 7 feet.

4. Round the length to the nearest tenth of a foot: 16.37 ≈ 16.4 feet.
When we graph the function, we can see that the length of the rafters is the distance between the x-axis and the point on the graph where y = 7.
So, the length of the rafters needed to make the roof for an angle of 7 degrees is approximately 16.4 feet (Option b).

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Since x it is the distance from the boat not from you, and the boat is a 2-meter wide, the distance must be greater than 0, because if any value of x is less than 0 the root could not be used for representing a real function, it would be a complex function due to the negative result. The answer is all positive numbers.

Answer: I'm pretty sure it's D

[10 4 7]

[13 9 6]

Step-by-step explanation:

The volume of the rectangular prism is (b) 93.9 cubic centimeters

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

Dimension = 3 centimeters by 5 centimeters by 6.26 centimeters

The volume of the rectangular prism is calculated as

Volume = Length * width * height

So, we have

Volume = 3 * 5 * 6.26

Evaluate

Volume = 93.9

Hence, the volume in cubic centimeters is 93.9

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Question

Find the volume of the rectangular prism that is 3 centimeters by 5 centimeters by 6.26 centimeters

The volume of the rectangular prism 150 cubic centimeters cm3.

The formula for the volume of a rectangular prism is given as:

VOLUME OF RECTANGULAR PRISM = Length × Width × Height

Since no dimensions have been provided, let us assume the length is 10 cm, the width is 5 cm and the height is 3 cm.

The volume of the rectangular prism is given by the formula:

The volume of the rectangular prism = length × width × heigh

Substitute length as 10cm, width as cm), and height as 3cm into the formula to get:

The volume of the rectangular prism = 10 × 5 × 3 = 150 cubic centimeters cm3

Therefore, the volume of the rectangular prism is 150 cm3.

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Answer:

Step-by-step explanation:

Correct choice is C

Answer:

117

Step-by-step explanation:

Given expression:

\(72 \div 8 + 4y^3\)

To evaluate the expression when y = 3, substitute y = 3 into the expression and solve using the order of operations (PEDMAS).

Substitute y = 3 into the expression:

\(\implies 72 \div 8 + 4(3)^3\)

Carry out the exponent:

\(\implies 72 \div 8 + 4\cdot 27\)

Carry out the division and multiplication:

\(\implies 9 + 108\)

Carry out the addition:

\(\implies 117\)

Answer:

2 solutions: x= -1 x= \(\frac{1}{2}\)

Step-by-step explanation:

You could solve this 2 ways, either by factoring or using the quadratic formula.

Factoring:

Use the formula: \(a^2-b^2=(a-b)(a+b)\)

(4x+1-3)(3x+1+3)=0

(4x-2)(4x+4)=0

No we can factor out a 2 and a 4:

2(2x-1)4(x+1)=0

Divide both sides by 2x4:

(2x-1)(x+1)=0

Now set both equal to 0:

2x-1=0

x+1=0

x=\(\frac{1}{2}\)

x=-1

For quadratic formula:

Use the formula: \((a+b)^2=a^2+2ab+b^2\)

First expand the expression:

\(16x^2+8x-8=0\)

Divide both sides by 2:

\(2x^2+x-1=0\)

Now we can plug it in:

a=2

b=1

c=-1

\(x=\frac{-1+\sqrt{1^{2} -4(2)(-1)} }{4}\)

\(x=\frac{-1+\sqrt{9} }{4}\)

\(x=\frac{-1+3}{4}\)

Now solve for each solution:

\(x=\frac{-1+3}{4} \\\\x=\frac{-1-3}{4} \\\\x=\frac{1}{2}\\x=-1\)

Either way you get the same answer, hope this helps! :)

The correct answer is option (C) median.

The median will help Emily to find the number that appears in the middle of the 25 numbers that are arranged in ascending order.

The mean, median, and mode are the three most commonly used measures of central tendency for populations that do not have much data, that is, they do not need to be grouped.

The mean, also known as average, is the value obtained by dividing the sum of a cluster of numbers by the number of them.

When arranging the numbers from least to largest, the median sits exactly in the middle of the values that are above. The median is a set that is a value that is in the middle of the other values.

The number that appears most frequently in a set of numbers is called the mode.

So, The median will help Emily to find the number that appears in the middle of the 25 numbers that are arranged in ascending order.

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In order to restore general equilibrium, price adjustments are undertaken. In the short run, prices increase, and when expectations rise above actual inflation, prices continue to climb until they do. answer is option (d). price level.

The term "aggregate demand" in macroeconomics refers to the overall demand for locally produced commodities, including capital goods, consumer products, and services. Aggregate demand is calculated as the total of spending by consumers, corporate and governmental investment spending, and net imports and exports.

The overall demand of final products and services in an economy at any particular time is known as aggregate demand, often referred to as domestic final demand. Effective demand is a frequent word for it, however occasionally this phrase is used to distinguish between two things. This is the demand for a nation's gross domestic product.

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A perfect square is a number obtaining by squaring a whole number

A perfect square can be defined as a number that is being expressed as the product of an integer by itself.

It is also seen as the second exponent of an integer.

In determining the perfect of a number, when you multiply an integer which could be a “whole” number, positive, zero or negative) by itself, the product of the multiplication is termed a square number, or a perfect square.

Perfect square is also described as a number made by squaring a whole number.

Some perfect squares in mathematics are;

Number 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 139, 144, etc

Hence, a perfect square is described as a number that is the product of an integer with itself.

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Answer: In the picture, I showed my work to explain why the answer is four. Just plug in the given values and solve for the unknown.

Step-by-step explanation:

The number of months for the given principal, amount and rate of interest is 4 months.

Given that, an interest rate of 2.4% compounded monthly.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest =

\(A=P(1+\frac{r}{100} )^t\)

Here, using compound interest formula

\(5500=5000(1+\frac{2.4}{100} )^t\)

⇒ \(\frac{5500}{5000}=(1.024)^t\)

⇒ \(1.1=(1.024)^t\)

Take the logarithm of both sides of the equation to remove the variable from the exponent.

Exact Form:

t=ln(1.1)/ln(1.024)

Decimal Form:

t=4.01872421…

Therefore, the number of months for the given principal, amount and rate of interest is 4 months.

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Answer: 13+6=21

Step-by-step explanation:

The distance that you have walked around the perfectly circular lake can be determined using the formula for the circumference of a circle, which is C = πd, where C is the circumference

(1 point), π is pi, and d is the diameter.

In this case, the diameter is 500 m, so the circumference of the lake is C = π(500 m) = 1570.8 m. To determine the distance that you have walked, you can use the formula for arc length, which is L = θ/360∘ × C, where L is the arc length, θ is the central angle, and C is the circumference. In this case, θ is 800∘ and C is 1570.8 m, so the distance that you have walked is L = (800∘/360∘) × 1570.8 m = 3489.78 m. Rounded to two decimal places, the distance that you have walked is 3489.78 m, or 3.49 km. Therefore, the answer is 3.49 km.

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Answer:

cant see it clearly

Step-by-step explanation:

bc it's to far

Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).

Answer:

Step-by-step explanation:

The points on a circle can be determines by the equation of a circle

The point (-11,2) is not on the circle

How to determine the position of the point

The equation of a circle is represented as:

Where:

Center = (a,b)

Radius = r

The radius of the circle is 5, and the center is (-7,4).

So, we have:

The point is given as:

(x,y) = (-11,2)

So, we have:

Evaluate the exponents

Evaluate the sum

The above equation is not true.

Hence, the point (-11,2) is not on the circle

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Answer:

Step-by-step explanation:

Answer:

S=2t

or

T=1/2 S

n=6

Answer:

Solution given:

The coefficient of x^2=60

we have,

\((a+x)^n=C(n,0)a^n+C(n,1)a^(n-1)x+C(n,2)a^(n-2)x^2+C(n,3)a^(n-3)x^3....C(n,r)a^(n-r)x^r+C(n,n)x^n\)

we get x² in 3rd term,so

3rd term of  (1+2x)^n is C(n,2)*1^n-2)(2x)^2=C(n,2)4x²

since 1^n is 1.

we have a coefficient of x^2 is 60, so

C(n,2)4=60

C(n,2)=60/4

\(\frac{n!}{(n-2)!*2!}\)=15

\(\frac{n(n-1)(n-2)!}{(n-2)!*2!}\)=15

n(n-1)=15*2

n^2-n=30

n^2-n-30=0

doing middle term factorization

n^2-6x+5x-30=0

n(n-6)+5(n-6)=0

(n-6)(n+5)=0

either n-6=0

n=6

or,

n+5=0

n=-5 since n>0

so neglected.

So the value of n is 6.

Step-by-step explanation:

The value of n is 6.

Since the expression is (1 + 2x)ⁿ, it is a binomial expression.

The general term is ⁿCₓ(1)ⁿ⁻ˣ(2x)ˣ = [ⁿCₓ(2)ˣ]xˣ

Now, for the term in x², xˣ = x². ⇒ x = 2

So, the coefficient of x² is [ⁿC₂(2)²] = 4ⁿC₂

Since the coefficient of x² is 60, we have that

4[ⁿC₂] = 60

Dividing through by 4, we have

ⁿC₂ = 15

n(n - 1)/2! = 15

n(n - 1) = 15 × 2

n(n - 1) = 30

Simplifying

n² - n - 30 = 0

n² + 5n - 6n - 30 = 0

Factorizing, we have

n(n + 5) - 6(n + 5) = 0

(n + 5)(n - 6) = 0

n + 5 = 0 or n - 6 = 0

n = -5 or n = 6

since n > 0, n = 6.

So, the value of n is 6.

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Answer:

Step-by-step explanation:

Aaahhhhh!!! Ja haw has b ha HA n zzz's

The joint pdf of u and v  is f(u, v) = Beta(u/v; α, β) * Beta(v; αβ, γ) * (1/v)

If x follows a beta distribution with parameters α and β, and y follows a beta distribution with parameters αβ and γ, and x and y are independent random variables, the joint probability density function (pdf) of u and v can be determined.

To find the joint pdf of u and v, we can use the transformation method. Let u = xy and v = y. We can find the inverse transformation as x = u/v and y = v.

Next, we compute the Jacobian of the transformation:

J = ∂(x, y) / ∂(u, v) = ∂x/∂u * ∂y/∂v = (1/v) * 1

The joint pdf of u and v is given by:

f(u, v) = f(x(u, v), y(u, v)) * |J|

Since x and y are independent, their individual pdfs can be multiplied:

f(u, v) = f(x(u, v)) * f(y(u, v)) * |J|

Substituting the pdfs of x and y, we have:

f(u, v) = Beta(x; α, β) * Beta(y; αβ, γ) * (1/v)

Replacing x and y with their respective inverse transformations:

f(u, v) = Beta(u/v; α, β) * Beta(v; αβ, γ) * (1/v)

This is the joint pdf of u and v when x and y are independent random variables following beta distributions.

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The warning approach is an example of Detection of error type prevention.

Error is a conscious or unconscious departure from a standard of conduct. A bug is a mistake in computer data. A software bug is an error, flaw, failure, or fault that results in an unwanted behavior from a computer program or system or leads it to deliver an inaccurate or unexpected outcome. Errors caused by bugs may have repercussions. The majority of defects are caused by faults and blunders in a program's source code, in its design, or in the parts and operating systems that these programs rely on.

After pressing submit or a PAR or KC quiz, D2Lprovides a warning if you have not saved your answers to one or more questions before grading your assignment. Since you are still permitted submit a quiz with unanswered questions, using a warning approach is an example of Detection type of error prevention

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Step-by-step explanation:

sin(x)×csc(x) - cos²(x) = sin²(x)

csc(x) = 1/sin(x) (basic definition)

therefore,

sin(x)×csc(x) = sin(x) × 1/sin(x) = 1

1 - cos²(x) = sin²(x)

1 = sin²(x) + cos²(x)

and that is again a basic definition based on the standard circle with radius = 1. there we have the Pythagoras principle, as sin and cos are the legs of a right-angled triangle, with radius 1 being the Hypotenuse.

More than 50% of the bottles meet the specifications.

To determine the proportion of bottles that meet the specifications, we need to calculate the process capability index (Cpk).

The formula for Cpk is:

Cpk = min((USL - X) / (3* σ), (X - LSL) / (3 * σ))

Given:

USL = 3 + 0.150 = 3.150 ounces

X = 3.042 ounces

σ = 0.034 ounce

So, Cpk = min((3.150 - 3.042) / (3 * 0.034), (3.042 - 2.850) / (3 * 0.034))

   = min(0.108 / 0.102, 0.192 / 0.102)

   = min(1.059, 1.882)

   = 1.059

To determine the proportion of bottles that meet the specifications, we can use the following table:

Cpk Value       Proportion within Specifications

-----------------------------------------------

< 1.00          Poor

1.00 - 1.33     Fair

1.33 - 1.67     Good

> 1.67          Excellent

Since the Cpk value is 1.059, it falls within the range of 1.00 - 1.33, which corresponds to a "Fair" proportion within specifications.

Therefore, slightly more than 50% of the bottles meet the specifications.

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The surface area of the rectangular prism is 362 square inches.

Surface area refers to the total area of all the faces or surfaces of a three-dimensional object. It is measured in square units and is calculated by adding the area of each individual face or surface. The formula for calculating the surface area of different 3D shapes varies depending on the shape, but the basic concept remains the same - adding the areas of all the faces or surfaces that make up the object. Surface area is an important concept in fields such as mathematics, engineering, and physics, and is used in the design and analysis of various structures and objects.

To find the surface area of a rectangular prism with length (l) = 16 inches, width (b) = 7 inches, and height (h) = 3 inches, we use the formula:

SA = 2lb + 2lh + 2wh

Substituting the values, we get:

SA = 2(167) + 2(163) + 2(7*3)

SA = 224 + 96 + 42

SA = 362

Therefore, the surface area of the rectangular prism is 362 square inches.

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