A sequence can be generated by using an = 3a,-1

where a, = 12 and n is a whole number greater than 1.

What are the first four terms in the sequence?

Answer:

Substitute (–5, 0.5) into x – 4y = –7 to get  

✔ –5 – 4(0.5) = –7

.

Substitute (–5, 0.5) into 0.2x + 2y = 0 to get  

✔ 0.2(–5) + 2(0.5) = 0

.

Simplify the above equations to get  

✔ –7 = –7 is true and 0 = 0 is true; a solution.

Step-by-step explanation:

(–5, 0.5) a solution of the system of equations.

A system of equations is a set or collection of equations that you deal with all together at once.

Given are the equations, x – 4y = –7 and 0.2x + 2y = 0;

Substitute (–5, 0.5) into x – 4y = –7 to get  

–5 – 4(0.5) = –7

Substitute (–5, 0.5) into 0.2x + 2y = 0 to get  

0.2(–5) + 2(0.5) = 0

Simplify the above equations to get  

–7 = –7 and 0 = 0 is true

Hence, (–5, 0.5) a solution of the system of equations.

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The solution is Option A.

The sum of the three consecutive numbers is given by the equation

A = n + ( n + 1 ) + ( n + 2 ) = 147°

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be n

The value of the second number = n + 1

The value of the third number = ( n + 1 ) + 1

The value of the third number = n + 2

Substituting the values in the equation , we get

Now , the total sum of all the values is A = 147

Hence , the equation is A = n + ( n + 1 )° + ( n + 2 ) = 147

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The correct answer is C." is either rational or irrational" because it cannot be expressed as the ratio of two integers.

The product of a non-zero rational number and a non-zero irrational number is either rational or irrational, depending on the specific numbers involved.

let's assume that the non-zero rational number is a/b and the irrational number is c. If their product is rational, we can write

a/b×c=d/e

where d and e are integers with no common divisors. This means:

c = (d/b) × (e/a)

Both d/b and e/a are rational numbers, so their product is also a rational number. Therefore, expressing the irrational number c as the product of two rational numbers is a contradiction. 

For example, consider the rational number 2/3 and the irrational number √2.

Multiplying them gives:

(2/3) * √2 = (2√2)/3

It is an irrational number because it cannot be expressed as the ratio of two integers. Therefore answer (C) is either rational or irrational.

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Answer:

A

Step-by-step explanation:

The answer to this question is 0.

Apply the initial value theorem approach to calculate the values of ˙f(0) and f(0 ).

Imagine that, in this problem, f(t) and f(s) are a Laplace transform pair. These transform pairs are defined by:

f(t) = 3s 1 s 2 s 1 ,

and ˙f(0 ) = 0

The values of f(0 ) and ˙f(0 ) are given by: f(0 ):

s 1 = 3, s 2 = 1

and

\(f 0 = \frac{1}{2} (t - 0) - 0\)

First we must find a solution to the initial value problem. To do this, we need to find the functions ˙f(0 ) and g(t). The first thing we need is some knowledge about convolution. A convolution is simply the operation of taking the derivatives of two functions and adding them together, so it can be thought of as applying the difference operator (sometimes called "Difference") dx/dt

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The polynomial "625x⁴ 1,875x³ 5,625x² 16,875x 50,625" can be factored using the binomial theorem.

This polynomial can be written in the form of (a + b)ⁿ, where n is a positive integer.

The binomial theorem states that this polynomial can be expanded as a sum of terms involving powers of a and b, and the coefficients of these terms can be determined using combinatorial formulas. The polynomial "625x^4 1,875x^3 5,625x^2 16,875x 50,625" can be factored using the binomial theorem.

In this case, you have a binomial with a = 5x and b = 3. The exponent is 4, so the expansion will have 5 terms.

You can use the formula for the coefficients of the terms in the binomial expansion:

C(n, k) * a^(n-k) * b^k,

where C(n, k) is the binomial coefficient, equal to n! / (k! * (n-k)!).

Using this formula, you can find the coefficients of each term in the expansion.

The first term will have a coefficient of C(4,0) = 1, and it will be equal to (5x)⁴ * 3⁰ = 625x⁴.

The second term will have a coefficient of C(4,1) = 4, and it will be equal to (5x)³ * 3¹ = 1,875x³.

The third term will have a coefficient of C(4,2) = 6, and it will be equal to (5x)² * 3² = 5,625x².

The fourth term will have a coefficient of C(4,3) = 4, and it will be equal to (5x)¹ * 3³ = 16,875x.

The fifth term will have a coefficient of C(4,4) = 1, and it will be equal to (5x)⁰ * 3⁴ = 50,625.

So, the expanded form of the polynomial is 625x⁴ + 1,875x³ + 5,625x² + 16,875x + 50,625.

The polynomial "625x⁴ 1,875x³ 5,625x² 16,875x 50,625" can be factored using the binomial theorem, and

the expanded form of the polynomial is 625x⁴ + 1,875x³ + 5,625x² + 16,875x + 50,625.

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Answer:10

Step-by-step explanation:multiply and simplify

Answer:that is the slope intercept form

Step-by-step explanation: slope intercept form is y=mx+b

So, Lana gave away 26.32% of he Pokemon cards  to her little brother.

To find the percentage of cards Lana gave away, we can use the formula:(Quantity given away / Total quantity) * 100.

In this case, Lana gave away 125 cards out of her total collection of 475 cards.Plugging these values into the formula, we have:

(125 / 475) * 100 = 0.2632 * 100 = 26.32%.

Lana gave away 26.32% of her Pokemon cards to her little brother.

Alternatively, we can calculate the percentage by subtracting the remaining cards from the total and finding the ratio:

Percentage given away

= (Cards given away / Total cards) * 100

= (125 / 475) * 100

= 26.32%.

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Answer:

310

Step-by-step explanation:

\(80/\frac{1}{4} -10\\=80*4+10\\=320-10\\=310\)

Step-by-step explanation:

oh boy, the typing or the scan of the question did a lot of strange things in the description.

so, let's write this properly :

the sum S of all interior angles of a polygon with n sides is

S = 180×(n - 2)

in the given example this S = 1,620 (right ?).

so,

1620 = 180×(n - 2)

9 = n - 2

n = 11

the polygon has 11 sides.

Answer:

-$500

Step-by-step explanation:

Answer:

Step-by-step explanation:

100X5=500

500 Was deducted from the account

Answer:

The third one

Step-by-step explanation:

Answer:

-n+1

Step-by-step explanation:

h(n)-g(n) =n+2-2n-1 ,collect like terms

n-2n+2-1 = -n+1

Applying one of the properties of a parallelogram, the value of x is 10°, then 6x=60° and 12x=120°.

There are different quadrilaterals, for example square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, a parallelogram presents some properties that are presented below.

The figure of the exercise shows two adjacent angles. From the property: the adjacent angles are supplementary, you have:

6x+12x=180

18x=180

x=10°

Therefore, 6x= 6*10=60° and 12x=12*10=120°.

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A graph of this parallelogram is shown below.

The perimeter of a parallelogram is equal to 31.8 units.

In Mathematics and Geometry, the perimeter of a parallelogram can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

For the length, we have:

Distance UX = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance UX = √[(2 + 2)² + (3 + 5)²]

Distance UX = √80

Distance UX = 8.9 units

For the width, we have:

Distance WX = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance WX = √[(2 - 9)² + (3 - 3)²]

Distance WX = √49

Distance WX = 7 units.

P = 2(UX + WX)

P = 2(8.9 + 7)

P = 31.8 units.

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From the given information provided, the means of x₁, x₂,  and x₃ are 158.28, 41.3, and 43.75 respectively.

a. Handle the missing values using omission strategy:

The omission strategy involves removing any observation with missing values.

The resulting table after the omission strategy is as follows:

Obs x₁ x₂ x₃

1 248 3.5 3.8

2 55 150 74

3 196 4.5 32

4 134 6.2 63

We can see that one observation with missing values was removed, which was observation 5.

b. Handle the missing values using simple mean imputation strategy:

The simple mean imputation strategy involves replacing the missing values with the mean of the non-missing values.

The means of x₁, x₂, and x₃ are calculated as follows:

mean of x₁ = (248 + 55 + 196 + 134) / 4 = 158.25

mean of x₂ = (3.5 + 150 + 4.5 + 6.2) / 4 = 41.3

mean of x₃ = (3.8 + 74 + 32 + 63) / 4 = 43.75

The resulting table after the simple mean imputation strategy is as follows:

Obs x₁ x₂ x₃

1 248 3.5 3.8

2 55 150 74

3 196 4.5 32

4 134 6.2 63

5 158.25 41.3 43.75

We can see that all missing values were replaced, which were x₁ in observation 5 and x₃ in observation 3.

Question - The following table contains 3 variables and 5 observations including some missing values x₁ x₂ x₃ 248 3.5 3.8 55 150 74 196 4.5 32 134 6.2 63 a. Handle missing values using omission strategy. b. Handle missing values using simple mean imputation strategy. How many missing values are replaced? What are means of x₁, x₂, and x₃?

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Step-by-step explanation:

I hope this will help uuuuuuu

6 meters is the slant height of the square pyramid.

The formula for a square pyramid's surface area may be used to calculate the slant height:

Surface area = base area + (0.5 x perimeter x slant height)

In this instance, we are aware that the base's side length is 5 meters, and the surface area is 85 square meters.

The base area is equal to (side length)2, or the area of a square, hence the base area is:

The base area = 5², or 25 square meters.

In addition, we can calculate the base's perimeter by multiplying the side length by four:

Perimeter: (4 * 5) = 20 metres

We can now enter the variables we already know into the algorithm to find the slant height:

85 = 25 + (0.5 x 20 x slant height)

60 = 10 x slant height

slant height = 6 meters

Therefore, the slant height of the square pyramid is 6 meters.

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Answer:

Step-by-step explanation:

The coefficients are

2x + 4y + 1z + 8

2, 4 and 1

Since the 1 is usually invisible, it might not be included.

Hope this helps!

The system of equation that can be used to represent the price of each pound of raspberries and grapes is as follows:

44x + 43y = 217

45x + 18y = 144

Brayden runs a farm stand that sells raspberries and grapes. Yesterday, Brayden sold 44 pounds of  raspberries and 43 pounds of grapes for a total revenue of 217 dollars.

Today, he sold  45 pounds of  raspberries and 18 pounds of grapes for a total revenue of 144 dollars.

Therefore, the system of equation that can be used to describe the price of each pound of raspberries and grapes can be represented as follows:

let

x = price of each pounds of raspberries

y = price of each pound of grapes

Therefore, the system of equation is as follows

44x + 43y = 217

45x + 18y = 144

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The polynomial that passes through the given points is \(P(x) = (5x^2 - 13x + 8) / 6.\)

To find a polynomial that passes through the given points (1, 1), (2, 4), and (4, 10) using Lagrange interpolation, we can construct a polynomial of degree two since we have three points.

The Lagrange interpolation formula states that for a set of distinct points (xi, yi), the polynomial P(x) that passes through these points is given by:

P(x) = Σ [yi * Li(x)], where Li(x) = Π [(x - xj) / (xi - xj)], for i ≠ j.

Let's calculate the polynomial:

For the point (1, 1):

L1(x) = [(x - 2)(x - 4)] / [(1 - 2)(1 - 4)] = (x - 2)(x - 4) / 3

For the point (2, 4):

L2(x) = [(x - 1)(x - 4)] / [(2 - 1)(2 - 4)] = -(x - 1)(x - 4) / 2

For the point (4, 10):

L3(x) = [(x - 1)(x - 2)] / [(4 - 1)(4 - 2)] = (x - 1)(x - 2) / 6

Now, we can substitute the values into the Lagrange interpolation formula:

P(x) = 1 * (x - 2)(x - 4) / 3 + 4 * -(x - 1)(x - 4) / 2 + 10 * (x - 1)(x - 2) / 6

Simplifying, we get:

\(P(x) = (x^2 - 3x + 2) / 3 - 2(x^2 - 5x + 4) / 2 + 5(x^2 - 3x + 2) / 6\\P(x) = (x^2 - 3x + 2) - (x^2 - 5x + 4) + (5x^2 - 15x + 10) / 6\\P(x) = (5x^2 - 13x + 8) / 6\)

Therefore, the polynomial that passes through the given points is \(P(x) = (5x^2 - 13x + 8) / 6.\)

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The conditional probability that Eric is a high-risk driver, given that he has had no traffic accidents in the past three years, is very low. Generally, insurance companies use the number of traffic violations and/or the number of claims a driver has had within a certain time period as indicators of their riskiness.

As Eric has had no accidents or traffic violations, the probability that he is a high-risk driver is very low. However, this does not mean that the probability is zero. There are many other factors which can contribute to a driver's risk, such as age, gender, experience, and location.

If Eric is an experienced driver, who has been driving for many years with no traffic accidents, then the probability of him being a high-risk driver will be lower than the average driver. On the other hand, if Eric is a new driver, or is located in an area with a high rate of traffic accidents, then the probability of him being a high-risk driver may be higher than the average driver.

Overall, the conditional probability that Eric is a high-risk driver, given that he has had no traffic accidents in the past three years, is very low. However, this probability can change depending on other factors, such as his age, experience, and location.

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Answer:

2in

Step-by-step explanation:

Since we are not given the type of polygon, let the polygon be an hexagon. An hexagon is a 6 sides shape. The perimeter of the shape will be the sum of all the sides of the polygon

Perimeter of the polygon = 6L

Length is the length of the side

Given

Perimeter of the polygon = 12in

Substitute and get L

P = 6L

12 = 6L

L = 12/6

L = 2in

Hence the length of side x of the polygon is 2in

Answer:

Dolly Parton

Step-by-step explanation:

hopes this helps please mark brainliest

The values of the variables x, y, and z obtained from the simplifying the square root indicates that we get;

w = 4, x = 6, y = 1, and z = 5

A square root can be simplified by making the values under the square radical as small as possible, such that the value remains a whole number.

The expression can be presented as follows;

(6·√(27) + 12·√(15))/(3·√(3)) = x·√y + w·√z

\(\frac{6\cdot \sqrt{27} + 12 \cdot \sqrt{15} }{3\cdot \sqrt{3} } = \frac{6\cdot \sqrt{9}\cdot \sqrt{3} + 12\cdot \sqrt{15} }{3\cdot \sqrt{3} } = \frac{18\cdot \sqrt{3} + 12\cdot \sqrt{15} }{3\cdot \sqrt{3} } = 6 + 4\cdot \sqrt{5}\)

Therefore, we get;

6 + 4·√5 = x·√y + w·√z

Comparison indicates;

6 = x·√y and 4·√5 = w·√z

Which indicates;

x = 6

√y = 1, therefore; y = 1

w = 4

√z = √5, therefore; z = 5

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You should obtain the value of 296.1 Btu/s for the power required by the compressor.

The power required by the compressor can be calculated by considering the energy balance during the compression process.

First, we need to determine the change in enthalpy of the R-134a during the compression. The enthalpy change can be calculated using the heat loss and the mass flow rate of the R-134a.

Given:
- Initial temperature (T1_R134a) = 100.0 °F
- Initial pressure (P1_R134a) = 100 psia
- Final temperature (T2_R134a) = 320.0 °F
- Final pressure (P2_R134a) = 300 psia
- Mass flow rate (mdot_R134a) = 5.0 lbm/s
- Heat loss (Q_loss) = 10 Btu/lbm

To calculate the enthalpy change, we can use the property table for R-134a or the specific heat capacity relationship.

Next, we calculate the work done by the compressor. The work done is equal to the change in enthalpy of the R-134a multiplied by the mass flow rate.

Finally, we convert the work done from Btu/s to the desired unit, which is also Btu/s.

Let's calculate it step by step:

1. Convert the initial and final temperatures from Fahrenheit to Rankine:
  T1_R134a = 100.0 °F + 459.67 °R
  T2_R134a = 320.0 °F + 459.67 °R

2. Determine the specific enthalpies at the initial and final states using the property table for R-134a or specific heat capacity relationship.

3. Calculate the change in enthalpy:
  ΔH = (H2 - H1)

4. Calculate the work done by the compressor:
  W = ΔH * mdot_R134a

5. Convert the work done to power:
  Power = W / mdot_R134a

6. Convert the power from Btu/s to the desired unit, Btu/s.

By following these steps, you should obtain the value of 296.1 Btu/s for the power required by the compressor.

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