Determine if the sequence {an} converges, when 1. limit = 3 2. sequence does not converge an = 6 cos 5ηπ+1 15 n +7 a 1 3. limit = cos 7 and if it does, find its limit. 4. limit = 2 1 5. limit = 6 cos 7 6. limit = 3V3

Answer:

784000

Step-by-step explanation:

Given data

Profit =  700000

Let us begin by finding what 12% of  700000 is

=12/100* 700000

=0.12* 700000

=84000

Hence the profit made last years was

=84000+700000

=784000

Answer:

3

Step-by-step explanation:

because if N = 6, then you will have to substitute the n to n and then do the order of operation. first it will be 6+3=9 and then 9*5=45. then you will do 7*6=42 and then subtract 45-42=3

Answer:

3

Step-by-step explanation:

Okay, since we know what n equals to, all we have to do is insert 6 where n was:

\(5(6+3)-7(6)\)

Now we just need to simplify, so:

\(30 + 15 - 42\)

\(45-42\)

And we get our answer

\(= 3\)

Answer:

I would say the answer is C

Step-by-step explanation:

As per the regression equation, the value of intercept coefficient is 1.5707

Regression is a statistical technique used to determine the relationship between an independent variable and a dependent variable.

In this case, the regression statistics provided in table 6 show the results of estimating the model

=> Δln (Sales t) = b0 + b1Δln (Sales t −1) + εt,

where Δln (Sales t) is the change in the natural log of sales for Cisco Systems quarterly observations from 3Q:1991 to 4Q:2000.

The R-squared value of 0.0661 indicates that only about 6.61% of the variation in the change in the log of sales can be explained by the change in the log of sales from the previous quarter.

The standard error of 0.4698 indicates the average deviation between the actual and predicted change in the log of sales.

If the results show that the specification is correct, then the long-run change in the log of sales toward which the series will tend to converge can be determined by the intercept coefficient, which in this case is 1.5707.

To know more about regression here.

https://brainly.com/question/14184702

#SPJ4

Answer: C

Step-by-step explanation:

area of rectangle = (5--2) × (2--2) = 7 × 4 = 28

area of triangle = ((12-5) × (6--6)) ÷ 2 = (7 × 12) ÷ 2 = 84 ÷ 2 = 42

total area = 28 + 42 = 70

Answer:X=1

Step-by-step explanation:

The answer is:

x > 2

Work/explanation:

The inequality is:

\(\sf{2x+4 > 8}\)

To solve, start by subtracting 4 from each side:

\(\sf{2x > 4}\)

Divide each side by 2

\(\sf{x > 2}\)

The given function is f(x) = (x+3)^4 * (x-4)^3 * (x-6)^6. The interval on which f(x) is increasing is (4, ∞).

To determine the intervals on which f(x) is increasing or decreasing, we need to analyze the sign of f'(x), the first derivative of f(x). In this case, f'(x) can be calculated using the product and chain rules of differentiation:

f'(x) = 4(x+3)^3 * (x-4)^3 * (x-6)^6 + 3(x+3)^4 * (x-4)^2 * (x-6)^6 + 6(x+3)^4 * (x-4)^3 * (x-6)^5

Simplifying f'(x) and factoring out common terms, we get:

f'(x) = (x+3)^3 * (x-4)^2 * (x-6)^5 * [4(x-6) + 3(x+3)(x-4) + 6(x-4)]

We can now analyze the sign of f'(x) for different values of x:

Thus, the interval on which f(x) is increasing is (4, ∞).

To learn more about chain rules, visit:

https://brainly.com/question/22882675

#SPJ11

The given function is f(x) = (x+3)^4 * (x-4)^3 * (x-6)^6. The interval on which f(x) is increasing is (4, ∞).

To determine the intervals on which f(x) is increasing or decreasing, we need to analyze the sign of f'(x), the first derivative of f(x). In this case, f'(x) can be calculated using the product and chain rules of differentiation:

f'(x) = 4(x+3)^3 * (x-4)^3 * (x-6)^6 + 3(x+3)^4 * (x-4)^2 * (x-6)^6 + 6(x+3)^4 * (x-4)^3 * (x-6)^5

Simplifying f'(x) and factoring out common terms, we get:

f'(x) = (x+3)^3 * (x-4)^2 * (x-6)^5 * [4(x-6) + 3(x+3)(x-4) + 6(x-4)]

We can now analyze the sign of f'(x) for different values of x:

Thus, the interval on which f(x) is increasing is (4, ∞).

To learn more about chain rules, visit:

https://brainly.com/question/22882675

#SPJ11

The inequality is x<10, which is true when `x=4`.

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to. An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a< b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

here, we have,

Given Data,

`x=4

so, from the given inequality, we get,

The inequality is x<10, which is true when `x=4`.

To learn more on inequality click:

brainly.com/question/24853349

#SPJ1

The required diameter of dwarf planet is \(10^{6} m\).

A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

Given:

The given statement is the diameter of 3 planet is

planet A= \(10^{9} m\)= 1000000000m

planet B=\(10^{7} m\)=10000000m

planet C= \(10^{8} m\)=100000000m

According to given question we have

A dwarf planet is discovered with a radius is 1/100 times of radius of planet C.

Radius of planet C =100000000/2=  50000000m

Radius of  dwarf planet = 1/100 times of radius of planet C.

Radius of  dwarf planet = 1/100 * 50000000m

Radius of  dwarf planet = 500000 m=\(5*10^{5} m\)

Diameter of dwarf planet =2*500000 m=1000000 m=\(10^{6} m\)

Therefore, the required diameter of dwarf planet is \(10^{6} m\).

Learn more details about statement here:

https://brainly.com/question/2285414

#SPJ1

An ordered rooted tree is a tree data structure in which each node has a specific parent-child relationship with its adjacent nodes. Each node in the tree has an address or path that specifies its location in the tree.

Given an ordered rooted tree T with vertex v at address 3.4.5.2.4, we can answer the following questions:

The level of a vertex in a tree is the number of edges on the path from the root to that vertex. In this case, the root is at address 3, and the path from the root to v has four edges: 3->4, 4->5, 5->2, and 2->4. Therefore, v is at level 5.

The parent of a vertex is the node that is immediately above it in the tree. In this case, the parent of v is the node at address 3.4.5.2. Therefore, the address of the parent of v is 3.4.5.2.

The siblings of a vertex are the nodes that have the same parent as the vertex. In this case, we do not have enough information to determine the number of siblings of v. We only know the address of v and its parent, but we do not know the structure of the tree beyond that.

The number of vertices in a tree can be calculated using the formula n = m + 1, where n is the total number of vertices and m is the number of edges. In this case, we know that the path from the root to v has four edges, so there are at least five vertices in the tree (including the root). However, we do not have enough information to determine the exact number of vertices in T, as there may be additional branches and nodes that are not specified.

Based on the address of v, we can determine some of the other addresses that must occur in the tree. For example, the address 3.4.5 must occur in the tree, as this is the parent of v. Additionally, the address 3.4 must occur in the tree, as this is the parent of 3.4.5. However, we cannot determine all of the other addresses that must occur in the tree without additional information about its structure.

To learn more about vertex click:

https://brainly.com/question/31159105

#SPJ1

We have here a perpendicular bisector of GH, so it divides this segment into two equal parts, that is. GB = 8, and BH = 8.

We also have that the formed triangles BCG and BCH are congruent since GB is congruent to BH And they share the same side BC. The angles Therefore, we have:

GH = GB + BH ---> GH = 8 + 8 = 16

GC = CH = 12 (since we have congruent figures here.)

In summary, we have that

GH = 16

CH = 12

Answer:

Step-by-step explanation:

We know that the perpendicular lines have negative-reciprocal slopes.

In other words, their product is - 1.

Find the slopes of AB and AC:

Find the the product of slopes and solve for b:

Answer:

31542

Answer:

x >4

Step-by-step explanation:

2x + 2 > 10

Subtract 2

2x+2-2> 10-2

2x > 8

Divide by 2

2x/2 > 8/2

x >4

Answer:

A, x>4

Step-by-step explanation:

Solve this like any other two step equations

2x + 2 > 10

Subtract 2 on each side

Now it becomes 2x > 8

Then divide 2'on each side

8/2=4

Therefore your answer is x>4

Which is answer A

Hope this helps!

Answer:

Total is 3

Step-by-step explanation:

AI-generated answer

Let's start by finding out how many marbles John had initially. We can do this by using the information given in the problem.

Let the original number of marbles be x.

John gave away 3/4 of his marbles, which means he has 1/4 of the original number of marbles left. We can express this as:

1/4 x = the number of marbles John has left

If we solve for x, we get:

4/1 * 1/4 x = 4/1 * the number of marbles John has left

x = 4 * the number of marbles John has left

Now we know that John had 4 times the number of marbles he has left.

Next, John receives another bag of marbles containing 2/4 (which is the same as 1/2) of the original number of marbles.

We can express this as:

1/2 x = the number of marbles in the new bag

To find the total number of marbles John has now, we can add the number of marbles he has left to the number of marbles in the new bag:

Total number of marbles = the number of marbles John has left + the number of marbles in the new bag

Total number of marbles = 1/4 x + 1/2 x

Total number of marbles = (1/4 + 1/2) x

Total number of marbles = (3/4) x

We know that x = 4 times the number of marbles John has left, so we can substitute this into the equation:

Total number of marbles = (3/4) * 4 * the number of marbles John has left

Total number of marbles = 3 * the number of marbles John has left

Therefore, the total number of marbles John has now is 3 times the number of marbles he has left.

Tell me in the commets if you didn't understand a word or something in the equation. :)

Consequently, the room has a 7 meter width. The room's length is

\(= 7 * 3 meters = 21 meters\)

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

Given that the length of the rectangular space is three times its breadth

The chamber has a 56-meter perimeter.

Assume that the room's width is x.

As a result, the room is three times as long.

The room's perimeter is now equal to 2(3x + x).

\(Here, 2(3x + x) = 56\\ 2 * 4x = 56\\ 8x = 56\\ x = 7.\)

Consequently, the room has a 7 meter width.

The room's length is

\(= 7 * 3 meters\\= 21 meters\)

To know more about Rectangle visit:
https://brainly.com/question/29123947

#SPJ4

Answer:

m = -11

Explanation:

\(\sf slope \formula:\boxed{\frac{\sf y2-y1}{\sf x2-x1} }\)

using this formula:

\(\rightarrow \frac{-9-2}{6-5}\)

\(\rightarrow -11\)

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

To determine if the function f(x) = (x+3)/(x²-9) is continuous at x=3, we need to check if the limit of the function exists as x approaches 3 from both the left and the right, and whether this limit is equal to the value of the function at x=3.

First, we can check the limit as x approaches 3 from the left:

lim x→3- f(x) = lim x→3- (x+3)/(x²-9) = (-3)/(0-) = ∞

Next, we can check the limit as x approaches 3 from the right:

lim x→3+ f(x) = lim x→3+ (x+3)/(x²-9) = (6)/(0+) = ∞

Since both one-sided limits are infinite, the limit as x approaches 3 does not exist.

Therefore, the function f(x) = (x+3)/(x²-9) is not continuous at x=3.

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

To know more about continuity visit:

brainly.com/question/21447009

#SPJ1

Before you can multiply two matrices together, the number of COLUMN in the first matrix must equal the number of rows in the second matrix.

The entries of a matrix are a rectangular array of numbers (or other mathematical objects). Standard operations like addition and multiplication can be performed on matrices. A matrix over a field F is often just a rectangular array of F's constituent elements.  Real and complex matrices are those whose entries are real or complex numbers, respectively.

The entries or elements of the matrix are its numbers, symbols, or phrases. In a matrix, the terms "rows" and "columns" refer to the horizontal and vertical rows of entries, respectively.

learn more about matrix here :

brainly.com/question/28180105

#SPJ4

Mean is used to measure the center of a set of values. It is good for summarizing values which are generally pretty similar to each other.

Mean is more usually referred to as the average. It is calculated by adding up all of the values and dividing by the total number of values. It is a good way for summarizing the center of values which are commonly very similar to each other.

The mean is the most often used measure of central tendency since it uses all values in the data set to give us an average. For data from skewed distributions, the median is better than the mean because it is not influenced by large values.

Learn more about mean at: https://brainly.com/question/30090607

#SPJ4

Although part of your question is missing, you might be referring to this full question: _________ is used to measure the center of a set of values. It is good for summarizing values that are generally pretty similar to each other.

Answer:

if I am correct I believe it should be 1153.5 calories

The value of x based on the equation given as 3(4x + 6) = 9x + 12 is -2.

It should be noted that an equation shows that relationship between the variables that are given or illustrated in the data.

The value for x based on the equation will be:

3(4x + 6) = 9x + 12

Open bracket

12x + 18 = 9x + 12

Collect like terms

12x - 9x = 12 - 18

3x = -6

Divide

x = -6/3

x = -2

Therefore, x is -2.

Learn more about equations on:

brainly.com/question/13763238

#SPJ1

Answer:

NULL ; TRUE

Step-by-step explanation:

The sampling distribution is on the assumption that the null hypothesis is true .

The null hypothesis is a general statement that states that there

is no relationship between two phenomenon's under

consideration or that there is no association between two groups.

#SPJ4

Learn more about on

https://brainly.com/question/23056080

The sampling distribution is based on the assumption that the null hypothesis is TRUE.  

A null hypothesis is a general statement that something is. There is no relationship between the two phenomena under or consider that there is no relationship between the two groups.  

The sampling distribution is based on the assumption that the null hypothesis is TRUE.

Learn more about sampling distribution here

https://brainly.com/question/15713806

#SPJ4

Answer:

B

Step-by-step explanation:

many different values of x lead to the same value of y.

hence, many-to-one.

but it does not mean that all values of x have to lead to the same value of y. it could be, but it is not demanded. so, it is not necessarily a horizontal line.

and this does not give us any information about the power of x involved. so, we cannot make any statement about linear or non-linear function.

The equation x² + 4x + 9 = 0 are complex numbers: x = -2 + i√5 and x = -2 - i√5.

To find the solutions for the equation x² + 4x + 9 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Comparing this equation with the given equation x² + 4x + 9 = 0, we can see that a = 1, b = 4, and c = 9.

Plugging in these values into the quadratic formula, we have:

x = (-4 ± √(4² - 4(1)(9))) / (2(1))

x = (-4 ± √(16 - 36)) / 2

x = (-4 ± √(-20)) / 2

Since the value inside the square root is negative, we know that the solutions will involve complex numbers. Simplifying further, we have:

x = (-4 ± i√20) / 2

x = (-4 ± 2i√5) / 2

Simplifying the expression by dividing both the numerator and denominator by 2, we get:

x = -2 ± i√5

for such more question on quadratic

https://brainly.com/question/17482667

#SPJ8

The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.

We have,

d=(2,4)

and e=(4k,3k)

Then,

d×e= (2 * 3k) - (4 * 4k) = -10k

Area of parallelogram = |d×e|

= |-10k|

= 10

As we know, area of parallelogram can also be given as,

|d×e| = |d||e| sin θ

where, θ is the angle between the two vectors.

Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ

⇒ 10 = √20 √25k^2 sin θ

⇒ 10 = 10k sin θ

∴ k sin θ = 1

Therefore, sin θ = 1/k

Hence, the value of k is 1.

Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,

| a . (b × c)|

Here, a=(1,1,2),

b=(5,3,λ), and

c=(4,4,0)

Therefore,

b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k

= -4i + 4λj + 8k

Now,| a . (b × c)|=| (1,1,2) .

(-4,4λ,8) |=| (-4 + 4λ + 16) |

=| 12 + 4λ |

Therefore, the volume of the parallelepiped is 12 + 4λ.

Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].

Here, a=(1,1,2) and

c=(4,4,0).

Then, a + c = (1+4, 1+4, 2+0)

= (5, 5, 2)

Now, projecting (a+c) onto c, we get,

projc(a+c) = [(a+c).c / |c|^2] c

= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)

= (4,4,0.5)

Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)

= (1,1,1.5)

Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).

Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

To know more about orthogonal visit

https://brainly.com/question/32250610

#SPJ11

The equation is f(x) = x² – 8x + 5. Then the y-intercept is at (0, 5) and the function crosses the x-axis twice. Then the correct options are A, D, and E.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The quadratic equation is given below.

f(x) = x² – 8x + 5

Convert the equation into vertex form, then the equation will be

f(x) = x² – 8x + 5

f(x) = x² – 8x + 16 – 16 + 5

f(x) = (x – 4)² – 16 + 5

f(x) = (x – 4)² – 11

The graph of the function is given below.

From the graph, the y-intercept is at (0, 5) and the function crosses the x-axis twice.

Then the correct options are A, D, and E.

More about the equation of parabola link is given below.

https://brainly.com/question/20333425

#SPJ6

The 33rd term of the given Arithmetic progression will be -132.

What is an Arithmetic progression?

A series of numbers is called a "arithmetic progression" (AP) when any two subsequent numbers have a constant difference. Arithmetic Sequence is another name for it.

Given, first term= a1= 28

and, a93 = -432

we know that, a93 = -432

                   a + 92d = -432 (where d is the common difference)

                  28 + 92d = -432

                     92d = -432-28

                             = -460

                       d = -460/92 = -5.

Now, we can find the a33,

               a33 = a + 32d

                       = 28 + (32× -5)

                       = 28-160

                       = -132.

Learn more about Arithmetic progression from the link given below:

https://brainly.com/question/6561461

#SPJ4