make an educated guess what is the limit of the sequence an= 5n2 n3 5 . then use the definition of a limit to prove that your guess is correct.

Step-by-step explanation:

So here we need to make two equations, as follows:

[tex]r + a = 37 \\ a = 2r - 5[/tex]

R being Robert and A being Aiden

Since we have A alone in the second equation, we can plug that into the first equation

R + (2R - 5) = 37

Let's add 5 to each side

R + 2R = 42

3R = 42

And lastly we will divide by 3 to get R alone

R = 14

Now that we know Robert scored 14 points, we can plug that into the first equation.

R + A = 37

14 + A = 37

Subtracting 14 from both sides

A = 23

The answer to the given problem is ∫3−5[2f(x) 6g(x)]dx = 108. This can be found by using the properties of integration and substituting the given values for the integrals of f(x) and g(x).

Given that:

∫3−5f(x)dx=6

∫3−5g(x)dx=3

We need to find: ∫3−5[2f(x) 6g(x)]dx

To solve this problem, we will use the properties of integration:

Property 1:

If c is a constant, then

∫cf(x)dx=c∫f(x)dx

Property 2:

If f(x) and g(x) are two functions, then

∫[f(x) + g(x)]dx = ∫f(x)dx + ∫g(x)dx

Using Property 1, we can rewrite the given equation as:

∫3−5[2f(x) 6g(x)]dx = ∫3−5[12f(x)g(x)]dx

Using Property 2, we can further simplify the equation as:

∫3−5[12f(x)g(x)]dx = ∫3−5[12f(x)]dx + ∫3−5[12g(x)]dx

Now we can substitute the given values:

∫3−5[12f(x)]dx + ∫3−5[12g(x)]dx = 12∫3−5f(x)dx + 12∫3−5g(x)dx

Substituting the given values for the integrals of f(x) and g(x), we get:

12∫3−5f(x)dx + 12∫3−5g(x)dx = 12(6) + 12(3)

Simplifying, we get:

12∫3−5f(x)dx + 12∫3−5g(x)dx = 12(6) + 12(3) = 12(9) = 108

Therefore, the answer is

∫3−5[2f(x) 6g(x)]dx = 108

The answer to the given problem is ∫3−5[2f(x) 6g(x)]dx = 108. This can be found by using the properties of integration and substituting the given values for the integrals of f(x) and g(x).

the complete question is :

if ∫3−5f(x)dx=6, and ∫3−5g(x)dx=3 , then ∫3−5[2f(x) 6g(x)]dx will be equal to  ?

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The first 4 terms of the sequence by the given recursive formula is found as: 6 , 13, 20, 27.

For the stated question:

f(n) :

f(1) = 6

f(n) = f(n - 1) + 7, if n > 1.

Thus,

First term, n = 1: f(1) = 6

Second term, n = 2:  

f(2) = f(2 - 1) + 7

f(2) = f(1) + 7

f(2) = 6 + 7

f(2) = 13

Third term: n = 3.

f(3) = f(3 - 1) + 7

f(3) = f(2) + 7

f(3) = 13 + 7

f(3) = 20

Fourth term: n = 4.

f(4) = f(4 - 1) + 7

f(4) = f(3) + 7

f(4) = 20 + 7

f(4) = 27

Thus, the first 4 terms of the sequence by the given recursive formula is found as: 6 , 13, 20, 27.

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The approximate energy requirement for the car when driven at 95 km/h is 789.47 kcal/km.

We have,

If a car averages 38 km/gal when driven at 95 km/h, we can calculate the fuel consumption in gallons per kilometer (gal/km).

Fuel consumption (gal/km) = 1 / (average fuel efficiency in km/gal)

Fuel consumption (gal/km) = 1 / 38

Now, to determine the energy requirement in kcal per kilometer (kcal/km), we multiply the fuel consumption by the energy released per gallon of gasoline:

Energy requirement (kcal/km) = Fuel consumption (gal/km) * Energy released per gallon (kcal/gal)

Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)

Now,

Fuel consumption (gal/km) = 1 / 38

Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)

Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)

≈ 789.47 kcal/km

Therefore,

The approximate energy requirement for the car when driven at 95 km/h is 789.47 kcal/km.

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The complete question:

"Burning gasoline in a car releases approximately 3 x 10^4 kcal/gal. If a car averages 38 km/gal when driven at 95 km/h, what is the energy requirement in kcal per kilometer (kcal/km) for the car?"

The minimum value of 3^{x²-4x+8} is 81. The solution has been obtained by using maxima-minima.

What is maxima-minima?

The extrema of a function are known as its maximum and minimum. The maximum and smallest values of a function within the predetermined set of ranges are known as maxima and minima. The function's maximum value and minimum value are referred to as the absolute maxima and absolute minima, respectively, for the function across the whole range.

We are given f(x) = 3^{x²-4x+8}

The function is minimum when {x²-4x+8} is minimum.

When the form of the equation is ax^2 + bx + c, then minimum is at -b/2a

Here, a = 1 and b = -4

So,

x = 4/2 = 2

So, {x²-4x+8} at x = 2 is

⇒(2)^2 - 4(2) + 8

⇒4 - 8 + 8

⇒4

So, the minimum value of f(x) is

3^4 = 81

Hence, the minimum value of 3^{x²-4x+8} is 81.

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Answer:

The symbol W denotes the whole number. The symbol Z denotes integers. The symbol N denotes all natural numbers or all positive integers. The symbol R denotes real numbers or any numbers that are not imaginary

i think you mean this , i hope is help

You can arrange 10 people in a circle in 362880 different ways if two arrangements are considered the same

In mathematics, a combination or combinations are all the possible groupings that can be made of a given number of elements, without repeating them and regardless of the order in which they are found.

Information about the problem:

As the table is round, the first person can take any seat, then the seat on the right can be taken by 1 of 9 people, then the next seat by 1 of 8 and so on until the 10th person has no choice of seats.

This is expressed by:

9*8*7*6*5*4*3*2

9!

362,880

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Answer:

Welcome to Brainly! I saw that this was your very first question. I will gladly assist you with your problem. (see explanation).

Step-by-step explanation:

The calculation of the estimated damaged items in the situation where 23,025 capacitors were produced is displayed below:

(5 times 23,025 capacitors) / (1,535 capacitors)

= 75

Therefore, when 23,025 capacitors are produced, 75 damaged products are expected.

Hope this helped!)

The percentage decrease from first to third year is; 47.725%

To find the percentage decrease, work out the difference (decrease) between the two numbers you are comparing. Thereafter, divide the decrease by the original number and then multiply the answer by 100.

Amount of car in 2010 = £18500

It depreciated by 15% in the first year. Thus;

Amount after first year = (100% - 15%) * 18500

= £15725

It depreciated by 18% in the second year. Thus;

Amount after second year = (100% - 18%) * 15725

= £12,894.5

It depreciated by 25% in the third year. Thus;

Amount after third year = (100% - 25%) * 12,894.5

= £9,670.875

Thus;

Decrease from first to third year = (18500 - 9670.875)/18500 * 100%

= 47.725%

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The world population in 2030 will be of 9.0062 billion.

The exponential formula for population growth is given below:

P(t) = P (0)e^rt

Here, P(t) is the population in t years from now P (0) is the population in the current year and r(decimal) is the growth rate, e=2.7 is the Eular number.

If the world population is 7.0 billion in 2012.

2012 is the initial year, P (0) =7

P(t) will be measured in billions of people.

The growth rate is constant at 1 .4%.

So that, r = 0.014

Now, the population in 2030 will be :

2030-2012=18 years after 2012, so this is P(18).

P(t)= 7e^rt

P(18) = 7e^0.0014*18

       = 9.0062

So, the world population in 2030 will be of 9.0062 billion.

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The world population will be 9.0062 billion in 2030.

The population growth exponential formula is as follows:

P(0)ert = P(t)

P(t) denotes the population in t years. P (0) is the current year's population, r(decimal) is the growth rate, and e=2.7 is the Euler number.

If the world population in 2012 is 7.0 billion.

The first year is 2012, and P (0) = 7.

The magnitude of P(t) will be measured in billions of people.

The rate of growth remains constant at 1.4%.

As a result, r = 0.014.

Now, in 2030, the population will be:

2030-2012 = 18 years after 2012, so P (18).

P(t)= 7e^rt

P(18) = 7e^0.0014*18

= 9.0062

As a result, the world population in 2030 will be 9.0062 billion people.

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a. The amount of rainfall received and level of water in the lake have casual and correlation relation.

b. The number of lights left on each day and the amount of the electric bill have casual and correlation relation.

c.  The increase of warm, sunny days and the number of ice cream vendors visible have not casual but correlation relationship.

d. The number of hours worked and how much money is made, have casual and correlation relation.

We have to shows a relationship that is correlated but not causal, a, b, c, or d.

a. The amount of rainfall received and level of water in the lake.

There have two events:

Event 1: The amount of rainfall

Event 2: The level of water

The both event are related to each other because when the rainfall heavily then the level of water increase

So the relation in the statement is casual and correlation.

b. The number of lights left on each day and the amount of the electric bill.

Event 1: The number of lights left on each day

Event 2: The amount of the electric bill

The both event are related because when the light left then the bill of electricity increases.

So the relation in the statement is casual and correlation.

c. The increase of warm, sunny days and the number of ice cream vendors visible.

Event 1: The increase of warm, sunny days.

Event 2: The number of ice cream vendors visible.

The both events are related to each other because it is possible that in one place have many vendors in other hand some place have no vendors.

So this statement is not casual but there have correlation between them.

d. The number of hours worked and how much money is made.

Event 1: The number of hours worked.

Event 2: How much money is made.

Both event are related to each other because if a person worked extra hours he/she will be paid according to this.

So the relation in the statement is casual and correlation.

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The z-score for an observation of 200 is approximately -2.000.

Here are the steps to calculate the z-score for an observation of 200 based on a normal distribution with a mean of 500 and a standard deviation of 150:

        x - μ = 200 - 500 = -300

        -300 / 150 = -2

        -2 ≈ -2.000

So, the z-score for an observation of 200 is approximately -2.000.

A z-score is a measure of how many standard deviations a given value is from the mean of a dataset. It is calculated by subtracting the mean of the dataset from a given value and dividing the result by the standard deviation of the dataset.

In the case of a normal distribution with a mean of 500 and a standard deviation of 150, a z-score of -2 would indicate that an observation of 200 is 2 standard deviations below the mean. This information can be used to determine the proportion of data within the dataset that is above or below a certain value, or to make comparisons between different datasets.

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The slope of the curve at P is -60, and The equation for the tangent line at P is 60x + y = 245.

a) To find the slope of the curve, the derivative of a function f(x) at the given point is a slope of the curve

Slope of the given curve y = -5 - 2x² at the point P(5, -55) is the derivative f'(x) at P(5, -55)

m = f'(x) = dy/dx

= 0 - 2(2x)

Since the derivative of a constant is zero and the derivative of x² is 2x

f'(x) at P(5, -55) is 0 - 6(2 × 5)

= 0 + (- 6 × 10) = -60

b) To find an equation of the tangent line at P(5, -55) for the curve y = -5 - 2x²

The equation of tangent line in for the function f(x) at P (x1, y1) is (y - y1) = m (x - x1)

x1 = 5 and y1 = -55, f(x) = -5 - 2x² and slope of tangent m = -60

The equation of the tangent line is (y + 55) = - 60(x - 5)

⇒ y + 55 = -60x + 300

⇒ 60x + y = 300 - 55

The equation of tangent is 60x + y = 245.

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The value of x and y for which the graph has undefined slope is y = 0 or x = 2

Given y²(2 - x) = x³

We are asked to determine the point on the curve which has an undefined slope.

Undefined slope means dy/dx = ∞

                                   Now, y²(2 - x) = x³

                               Differentiating both sides

                                   2y dy/dx (2-x) - y² = 3x²

                                                       dy/dx = (3x² + y²)/2y(2-x)

So, (3x² + y²)/2y(2-x) = ∞

For this 2y(2-x) = 0

We can see that the possible cases  y = 0 or x = 2

Hence for y = 0 or x = 2, the slope of the graph is undefined.

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Alicia will have £2,238.93 in her account after 10 years if she invests £2130 in a 0.5% account.

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.

Here,

principal=£2,130.00

rate=0.5%
time=10 years

Compound interest earned=£108.93

Total amount=£2,238.93

Alicia will have £2,238.93 in the account after 10 years when she invests £2130 into an account that pays 0.5%.

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Complete question:

Alicia invests £2815 into an account that pays 1% compound interest per year. Work out how much Alicia will have in the account after 10 years.

The actual height of the rocket is 576 inches.

Cross multiply is to multiply the numerator of each side of a proportion by the denominator of the other side.

A ratio box is a visual tool that can be used to solve proportion problems. To use a ratio box to solve this problem, we can set up the following ratio:

1/12 : 48 inches : : x : actual height

where x is the unknown value that we want to find.

To solve for x, we can cross-multiply and simplify the equation:

1/12 * actual height = 48 inches

actual height = 48 inches * 12/1

actual height = 576 inches

So the actual height of the rocket is 576 inches.

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Answer:

scenario: GCF =15

15(30x+45 15+15)

15(2x+3) answers

Answer:

Step-by-step explanation:

I dont understand the question?

Answer: 3:2

Step-by-step explanation:

AB / BC = AB:BC

therefore,  6:4  

6:4 simplified -> 3:2

Answer:

Step-by-step explanation:

[tex] {4}^{2} + (10 \times 2) \\ 16 + (10 \times 2) \\ 16 + 20 \: \: \: \: \: \: \: \: \: \: \: \\ 36 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]4^2+(10\times2)[/tex]

[tex]4^2+20[/tex]

[tex]16+20[/tex]

[tex]=\boxed{36}[/tex]

The coordinates of C’ if the trapezoid is reflected across the y-axis is

(- 5, 3).

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

A reflection through the axis and is given by the following transformation rule:

(x, y) -------> (-x, y)

We have the following point:

C = (5, 3)

Now, Applying the transformation rule we have:

(5, 3) -------> (-5, 3)

So, C' is given by:

C '= (- 5, 3)

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Answer:

50/11

Step-by-step explanation:

because 50/11=4.54

               [tex]\sqrt[3]{100} =4.64[/tex]

              so 4.54<4.64

Answer:

hyy can you my friend,,,,

Answer:(-4,0)

Step-by-step explanation:

Step-by-step explanation:

The covariance of two variables X and Y is a measure of the relationship between their changes. It is calculated as:

cov(X, Y) = (1/n) * sum((x_i - mean(X)) * (y_i - mean(Y)))

where n is the number of observations, x_i and y_i are the values of X and Y respectively for the i-th observation, mean(X) and mean(Y) are the means of X and Y respectively.

In Python, you can use the numpy library to calculate the covariance as follows:

import numpy as np

X = [x_1, x_2, ..., x_n]

Y = [y_1, y_2, ..., y_n]

cov = np.cov(X, Y)[0][1]

A measurement of the intensity and direction of the linear relationship between two random variables, X and Y, is called covariance. A definition of covariance is:

Cov(X, Y) is equal to E[(X - E(X))(Y - E(Y))].

where E[...] is the anticipated value operator and E(X) and E(Y) is the expected values of X and Y, respectively.

If Cov(X, Y) is positive, X and Y have the propensity to rise or fall together. Cov(X, Y) is a measure of the tendency for two variables to move in opposite directions. When Cov(X, Y) equals 0, X and Y are said to be uncorrelated.

You must be aware of the expected values as well as the joint probability distribution of X and Y in order to compute the covariance of X and Y.

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The equation of the line in point-slope form and in​ slope-intercept form are both y = 1/2x.

1. Point-Slope Form: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

2. Slope-Intercept Form: y = mx + b, where m is the slope of the line and b is the y-intercept.

3. Standard Form: Ax + By = C, where A and B are coefficients that define the slope and y-intercept of the line.

If a line has a slope of 1/2 and passing through the origin, then:

m = 1/2

(x1, y1) = (0,0)

Plug in the values in the point-slope form and in​ slope-intercept form.

point-slope form

y - y1 = m(x - x1)

y - 0 = 1/2(x - 0)

y = 1/2x

slope-intercept form

y = mx + b

y = 1/2x + b

Substitute the values of x and y and solve for the y-intercept, b.

0 = 1/2(0) + b

b = 0

y = 1/2x + 0

y = 1/2x

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Answer:

They are supplementary angles

12.5ml of a 60% solution is required to create 50ml of a 15% amount solution. You can compute this using a proportion.

50% x 15% = 7.5 ml, and 7.5 ml x 60% = 12.5 ml

12.5ml of a 60% solution is required to create 50ml of a 15% solution. You can compute this using a proportion. To begin with, we must ascertain how much of the 15% solution is required to make 50ml. To accomplish this, multiply 50 ml by 15%, which yields the answer of 7.5 ml. This means that to make 50ml, 7.5ml of the 15% solution is required. The next step is to calculate how much of the 60% solution is needed to create 7.5ml. To do this, divide 7.5 ml by 60%, which yields the result 12.5 ml. This indicates that in order to create 50ml of the 60% solution, 12.5ml of the 60% solution

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Seema left 6/11 of the book for reading over the weekend.

To calculate the part of the book left for reading during the weekend, we need to subtract the part of the book Seema read during the weekday from the total book.

If Seema reads 5/11 of the book during the weekday, then:

This means 6/11 of the book is left for reading during the weekend. It is important to note that the fraction of the book read during the weekday and the fraction left for reading during the weekend add up to the total book. This means that 11/11 of the book will be read by Seema in total.

This question should be written as:

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Overhead Rate * Labor Hours , additional overhead should she expect to incur.

What is additional overhead ?

Overhead refers to the ongoing costs to operate a business but excludes the direct costs associated with creating a product or service. Overhead costs can be fixed, variable, or a hybrid of both.

To determine the additional overhead that Angie should expect to incur if she books one more catering job requiring 350 labor hours, The overhead rate is the amount of overhead costs per labor hour.

If we have the overhead rate, we can calculate the additional overhead as follows:

Additional Overhead = Overhead Rate * Labor Hours

Overhead Rate * Labor Hours , additional overhead should she expect to incur.

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