Which of the following series is(are) convergent? 00 (1) Σ I) n 10 1 + 53 n 12 n=1 8 n - 8 (II) Σ ) ng n=1 n4 + 3 3 (III) Σ. n3 + n2 + + n=1 O I, II and III O II only I only O I and II O I and III

Answer:

2x (x - 4)

Step-by-step explanation:

Using the formula they gave us:

Cost of shipping = 2.79 + 0.38(8)

Cost of shipping = 2.79 + 3.04

Cost of shipping = 5.83(currency unit)

0.88 is the probability that the system functions. If the probability that c fails is 0.1 and the probability that d fails is 0.12

Let A be the probability that the system functions. Because of that, the probability that the system fails is:

P(system fails) = P(c fails or d fails) = P(c fails) + P(d fails) - P(c and d fail)

The above formula is true because of the addition rule of probability: we sum the probabilities of all the outcomes that satisfy the event, but we need to subtract the intersection (P(c and d fail)) because we would be adding it twice since it satisfies both conditions.

The given values are: P(c fails) = 0.1P(d fails) = 0.12 The intersection (P(c and d fail)) is not given, but we know that it can't be greater than either individual probability: P(c and d fail) ≤ min(P(c fails), P(d fails)) = min(0.1, 0.12) = 0.1

Then, we can calculate the probability that the system fails:

P(system fails) = P(c fails or d fails) = P(c fails) + P(d fails) - P(c and d fail)P(system fails) = 0.1 + 0.12 - 0.1 = 0.12

We know that the probability that the system functions is the complement of the probability that the system fails:

P(A) = 1 - P(system fails)P(A) = 1 - 0.12 = 0.88

We round to four decimal places: 0.88 is the probability that the system functions.  

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Answer:

he went on 16 rides and paid for 2 admission

Step-by-step explanation:

he went on 16 rides and paid for 2 admission

16-p

1) 7+9=16

2) It states that  "then subtract p from the result" so that means 16-p which is the final answer because we cannot further substitute p without a known result

the maximum and minimum values of f(x,y) on the ellipse occur at approximately (±0.445, ±0.364) and (±0.364, ±0.445), respectively.

To find the points on the ellipse 3x^2 + 2y^2 = 1 where f(x,y) = xy has its extreme values, we can use the method of Lagrange multipliers.

We want to find the points (x, y) on the ellipse where the gradient of f(x,y) is parallel to the gradient of the constraint function g(x,y) = 3x^2 + 2y^2 - 1. The gradient of f(x,y) is <y, x>, and the gradient of g(x,y) is <6x, 4y>. Thus, we need to solve the system of equations:

y = λ(6x)

x = λ(4y)

3x^2 + 2y^2 = 1

From the second equation, we get λ = x/(4y). Substituting into the first equation, we get y = (3/8)x^2. Substituting into the third equation, we get:

3x^2 + 2[(3/8)x^2]^2 = 1

3x^2 + (27/32)x^4 = 1

Multiplying both sides by 32, we get:

96x^2 + 27x^4 - 32 = 0

This is a quartic equation in x^2, which can be solved using standard methods. We can also note that the function f(x,y) = xy is symmetric with respect to the line y = x, so any extreme values on one side of this line will have a corresponding extreme value on the other side.

Therefore, the maximum and minimum values of f(x,y) on the ellipse occur at approximately (±0.445, ±0.364) and (±0.364, ±0.445), respectively.

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The TRUE statements about function g are C, D, and E. as the domain is all real numbers.

A continuous function is a mathematical model that possesses the following characteristics:

Thus, the TRUE statements about function g are:

C) The function is continuous.

D) As x approaches positive infinity, approaches positive infinity.

E) The domain is all real numbers.

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Answer:

I believe the answer is 45 cakes

Step-by-step explanation:

60min = 1hr

15 x 3 = 45

Answer:

I just need points I don't know your answer

Step-by-step explanation:

Answer:

x = 29

Step-by-step explanation:

The SQL aggregate function that gives the arithmetic mean for a specific column is `AVG()`.

SQL (Structured Query Language) aggregate functions are functions that operate on a set of values and return a single value as a result. These functions are used in SQL queries to perform calculations on groups of rows in a database table.

There are several common aggregate functions in SQL, including:

1. `COUNT()` - returns the number of rows in a table or the number of non-null values in a specific column.

2. `SUM()` - calculates the sum of values in a specified column.

3. `AVG()` - calculates the average value of values in a specified column.

4. `MAX()` - returns the maximum value in a specified column.

5. `MIN()` - returns the minimum value in a specified column.

Aggregate functions are typically used with the `GROUP BY` clause in SQL queries to group the data based on one or more columns and then apply the aggregate function to each group.

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The SQL aggregate function for calculating the arithmetic mean of a specific column is AVG.

The SQL aggregate function that gives the arithmetic mean for a specific column is AVG.

For example, if you have a table called 'students' with a column called 'grades', you can use the AVG function in SQL to calculate the average grade:

SELECT AVG(grades) FROM students;

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Hi

3*5000 +X*2500 = 25 000

15 000 + 2 500X = 25 000

                2 500X = 25 000 - 15 000

                       2 500 X = 10 000

                               x = 10 000 / 2 500

                                 X = 100/25

                                   X = 4

You need 4 post for  B

3*5000 + 4* 2 500 =  15 000 + 10 000 = 25 000

The length of arc AB using the measure circle are 5) 6.28 feet and 6) 18.84 feet.

To find the length of arc AB with a measure of 80°, use the formula:

length of arc AB = (measure of arc AB / 360°) x circumference of circle

The diameter of the circle is given as 9 feet, so the radius is 4.5 feet. The circumference of the circle is:

circumference = 2 x π x radius

circumference = 2 x 3.14 x 4.5

circumference = 28.26 feet

Using the formula:

length of arc AB = (80° / 360°) x 28.26

length of arc AB = 0.2222 x 28.26

length of arc AB = 6.28 feet

Rounding to the nearest hundredth:

length of arc AB ≈ 6.28 feet

To find the length of arc AB with a measure of 240°, use the same formula as above:

length of arc AB = (measure of arc AB / 360°) x circumference of circle

Using the same values for the diameter and radius of the circle:

length of arc AB = (240° / 360°) x 28.26

length of arc AB = 0.6667 x 28.26

length of arc AB = 18.84 feet

Rounding to the nearest hundredth:

length of arc AB ≈ 18.84 feet

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Answer:

Step-by-step explanation:

y + 9 = -5/2(x - 10)

y + 9 = -5/2x + 25

y = -5/2x + 16

The expression for the output of the system, when the input is delayed by 2, is given by\(y_d\)[n] = ((n - 2) + 1) * [(n - \(2)^2\)].

The given system has an input-output relationship represented by y[n] = (n + 1) * x[\(n^2\)]. To find the expression for the output when the input is delayed by 2, we substitute (n - 2) for n in the original expression. This accounts for the delay of 2 in the input signal. Thus, the expression becomes \(y_d\)[n] = ((n - 2) + 1) * [(n - \(2)^2\)].

Breaking down the expression further, ((n - 2) + 1) represents the scaling factor, which is the coefficient applied to the delayed input signal. It ensures that the output is scaled by the factor of (n - 2) + 1. [\((n - 2)^2\)] represents the delayed input signal squared. By substituting (n - 2) for n in the original expression, we are effectively shifting the input signal by 2 units to the right before squaring it.

Overall, the expression\(y_d\)[n] = ((n - 2) + 1) * [(n - 2\()^2\)] represents the output of the system when the input is delayed by 2.

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The expected number of dumplings that need to be eaten to find the first lucky dumpling is 40/3 or approximately 13.33.

To answer this question, we need to understand the concept of the expected number. The expected number is the average number of times an event is expected to occur if an experiment is repeated a large number of times.

The expected number of dumplings to be eaten to find the first lucky dumpling is the sum of the products of the probability of finding a lucky dumpling on the nth try and the number of dumplings eaten up to that point. In mathematical notation, we can write it as:

Expected number = (3/40) x 1 + (37/40) x (3/37) x 2 + (37/40) x (33/37) x (3/36) x 3 + ...

Simplifying this expression, we get:

Expected number = 40/3

This means that, on average, the group will need to eat about 13 or 14 dumplings before they find the first lucky one.

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To determine the number of smaller boxes that would contain the same amount of cereal as a larger box, we set the expressions representing the cereal content equal to each other. Solving the equation, we find that 15 smaller boxes are required to match the cereal quantity in the larger box.

To find the number of smaller boxes that equal the same amount of cereal in a larger box, we need to equate the two expressions and solve for n.

Setting the expressions equal to each other:

10 + 6.3n = 7 + 6.5n

Simplifying the equation:

6.3n - 6.5n = 7 - 10

-0.2n = -3

Dividing both sides by -0.2:

n = -3 / -0.2

n = 15

Therefore, 15 smaller boxes would equal the same amount of cereal as the larger box.

The problem states that the expressions 10 + 6.3n and 7 + 6.5n represent the amount of cereal in the new larger box. The variable n represents the number of smaller boxes.

To find how many smaller boxes are equivalent to the larger box, we need to set the two expressions equal to each other and solve for n. This equation represents the balance between the amount of cereal in the larger box and the combined amount of cereal in the smaller boxes.

By simplifying the equation and solving for n, we find that 15 smaller boxes are needed to equal the same amount of cereal as the larger box.

This means that if the cereal manufacturer wants to package the same amount of cereal as the larger box, they would need to use 15 smaller boxes instead. This calculation helps the manufacturer determine the number of smaller boxes needed to maintain the same quantity of cereal while changing the box size.

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Answer:

The answer is option A) r and s

Set c = {north america, south america, europe, asia, australia, africa, antarctica}. Set-builder notation: c = {x | x is continent and x ∈ {north america, south america, europe, asia, australia, africa, antarctica}}.

What is set ?

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines,etc.

a) The set c = {north america, south america, europe, asia, australia, africa, antarctica} can be written in set-builder notation as:

c = {x | x is a continent and x ∈ {north america, south america, europe, asia, australia, africa, antarctica}}

b) The set-builder notation can be read as "the set c, such that x is a continent and x is an element of the set {north america, south america, europe, asia, australia, africa, antarctica}".

Set c = {north america, south america, europe, asia, australia, africa, antarctica}. Set-builder notation: c = {x | x is continent and x ∈ {north america, south america, europe, asia, australia, africa, antarctica}}.

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An angle or angle pair that satisfies the condition is angle F and its adjacent angle, creating a linear pair.

A linear pair consists of two adjacent angles that share a common vertex and a common side. In this case, the given condition states that the vertex of the linear pair is F. Therefore, we can consider angle F and its adjacent angle as a valid example of a linear pair whose vertex is F.

The two angles in a linear pair always add up to 180 degrees. By considering angle F and its adjacent angle, we can observe that their measures sum up to 180 degrees, satisfying the condition of a linear pair. This relationship holds true for any linear pair, and angle F in combination with its adjacent angle is just one example of such a pair.

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To have $600,000 in 40 years with a 5.7% annual interest rate compounded monthly, you should invest approximately $437.39 each month. The interest earned can be calculated by subtracting the total amount invested from the final goal amount.

To calculate the monthly investment amount, we can use the formula for the future value of a series of regular deposits:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value (goal amount) of $600,000,

P is the monthly investment amount,

r is the monthly interest rate (5.7% divided by 12),

n is the total number of periods (40 years multiplied by 12 months).

By substituting the given values into the formula, we can solve for P:

$600,000 = P * [(1 + 0.057/12)^(40*12) - 1] / (0.057/12)

Solving this equation, we find that P ≈ $437.39.

To determine the interest earned, we can subtract the total amount invested from the final goal amount:

Interest = $600,000 - (P * n)

For the second part of the question, the monthly investment amount to have $600,000 in 20 years would be different. To calculate the savings after 10 years, we would need to compute the future value of the amount invested after 20 years for an additional 10 years with the given interest rate.

However, the specific values for these calculations are not provided in the question.

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The answer is 1.72.

Division is splitting into equal parts or groups.

Given that 18.92 divided by 11

Let’s have a simple division.

18.92 : 11 = 1.72

Hence, 18.92 divided by 11 equal to 1.72

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Answer:

\(h_t=9ft\)

Step-by-step explanation:

From the question we are told that:

Height of child \(h_c=3ft\)

Height of child's shadow  \(h_c_s=2ft\)

Height of tree's shadow \(h_t_s=6ft\)

Since position of Sun remains constant  

Generally the equation for Height of tree h_t mathematically given by

 \(h_t=f_{ts}\frac{h_c}{h_c_s}\)

 \(h_t=6*\frac{3}{2}\)

 \(h_t=9ft\)

The sum of the interior angle measures of the polygon 34-gon will be 5,760°. Then the correct option is C.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The sum of the interior angle will be the product of 180° and the difference between the sides of the polygon and 2. Then we have

⇒ (n - 2) × 180°

The sum of the interior angle measures of the polygon 34-gon will be given as,

⇒ (34 - 2) × 180°

⇒ 32 × 180°

⇒ 5,760°

The sum of the interior angle measures of the polygon 34-gon will be 5,760°. Then the correct option is C.

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Answer:

12

Step-by-step explanation:

you would need to use BODMAS to work this out

as a result you would work out the value in the brackets which would equal to -1 so the question would look like this: 10-2(-1)

next you would do the multiplication due to the fact it comes next in the order

so you would end up with 10+2 which would equal to 12

Hope this helps

Answer:

12

Step-by-step explanation:

First we do 4-5 because of Order of Operations. So we get -1

Then we do multiplication because of Order of Operations and we get -2*-1=2

So now we do 10+2 and we get 12.

You may be asking why I did -2*-1.

It honestly doesn't matter.

Let's say I did 2*-1. We get -2.

Then we do 10-(-2) and If you subtract a negative, it's just adding basically. So we can put it as 10+2 and we get 12.

Find the length of side CD and then subtract from 7 to get side FC. Using the pythagorean theorem, you can find x.

5² - 3² = 16²

square root of 16 = 4

7 - 4 = 3

//

3² + 3² = 18²

square root of 18 = 4.242640687

round as you wish.

The probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes is 0.33 or 33%.

Uniform distribution is a probability distribution where all outcomes are equally likely. In this case, the time it takes to wash dishes is uniformly distributed between 8 and 17 minutes. This means that any time between 8 and 17 minutes is equally likely to occur.

To find the probability that a randomly selected event of washing dishes will take a person between 12 and 15 minutes, we need to find the area under the curve of the uniform distribution function between 12 and 15 minutes.

Since the distribution is uniform, the area under the curve between 12 and 15 minutes is simply the width of the interval divided by the total width of the distribution. Mathematically, we can express this as:

P(12 ≤ X ≤ 15) = (15 - 12) / (17 - 8)

P(12 ≤ X ≤ 15) = 3 / 9

P(12 ≤ X ≤ 15) = 0.33 or 33%.

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Answer:

x=6

Step-by-step explanation:

44+3x=5x+2x+20

collect like terms:

44+3x=7x+20

move the terms :

3x-7x=20-44

collect like terms calculate :

-4x=-24

divide both sides:

x=6 is the final answer