Suppose that a family wants to start a college fund for their child. if they can get a rate of 5.5% , compounded monthly, and want the fund to have a value of $35,450 after 20 years, how much should they deposit monthly? assume an ordinary annuity and round to the nearest cent. a. $81.38 b. $80.01 c. $11,829.97 d. $11,776.00 please select the best answer from the choices provided a b c d

Answer:

Step-by-step explanation:

25% = 1/4 of 100

100 represents 200 people here, that means that if 25 = 1/4 to 100, then it is 1/8 to 200. 25x8=200

If 25% = 50, since 50x4=200 and 1/4 = 25% of 100%.

50... ok......

50 = 25%

Now, because there are 5 parts in 25, let's divide 5 by 50, that is 10. That means that 5 = 10 in that 50. 5% = 10 people

So, if 25-15=10

and then 5% = 10 people

5%+5%=10

10+10=20

That means, that 20 people more liked the movie than disliked it.

The limit is equal to 1, so the Ratio Test is inconclusive. Further tests would be required to determine if the series converges absolutely or diverges.

To use the ratio test, we take the limit of the absolute value of the ratio of the (k+1)th term to the kth term:

lim as k approaches infinity of |(6(k+1)^4)/(6k^4)|

Simplifying this expression, we get:

lim as k approaches infinity of |(k+1)^4/k^4|

Using L'Hopital's rule, we can evaluate this limit:

lim as k approaches infinity of |4(k+1)^3/4k^3|

lim as k approaches infinity of |(k+1)/k|^3

Since the limit is less than 1, by the ratio test, the series converges absolutely.

Alternatively, we can use the root test, which involves taking the kth root of the absolute value of the kth term:

lim as k approaches infinity of |(6k^4 k)^(1/k)|

Simplifying this expression, we get:

lim as k approaches infinity of |6^(1/k) * k^(4+1/k)|

The exponent 4+1/k approaches 4 as k approaches infinity, so we can ignore the 1/k term. Taking the limit of just the k^(4) term, we get:

lim as k approaches infinity of |6^(1/k) * k^4|^(1/k)

Using the fact that lim as k approaches infinity of 6^(1/k) = 1 and lim as k approaches infinity of k^(4/k) = 1, we get:

lim as k approaches infinity of |6^(1/k) * k^4|^(1/k) = 1

Since the limit is less than 1, by the root test, the series converges absolutely.
To determine if the given series converges absolutely or diverges, we can use the Ratio Test. The series is given as:

Σ(6k^4 * k) for k = 1 to ∞

First, let's simplify the series:

Σ(6k^5) for k = 1 to ∞

For the Ratio Test, we need to compute the limit as k goes to infinity of the ratio of consecutive terms:

lim (k → ∞) (|a_(k+1)| / |a_k|)

For our series, a_k = 6(k+1)^5 and a_(k+1) = 6k^5. So we have:

lim (k → ∞) (|6(k+1)^5| / |6k^5|)

We can simplify by canceling the common factor of 6:

lim (k → ∞) ((k+1)^5 / k^5)

Now, let's take the limit:

lim (k → ∞) (1 + 1/k)^5 / 1 = 1^5 / 1 = 1

For the Ratio Test, if the limit is less than 1, the series converges absolutely; if it is equal to 1, the test is inconclusive; if it is greater than 1, the series diverges.

In this case, the limit is equal to 1, so the Ratio Test is inconclusive. Further tests would be required to determine if the series converges absolutely or diverges.

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Answer:

its too small to see

Step-by-step explanation:

Answer:

activity2

1. ( 14.4) adn

2.(0.616) adn

3.( 5-36) adn

Based on your question, you are asking about the property of expressions a, b, and c, where a ≠ 0. If a ≠ 0, then a/c = b/c. This property states that if you divide two equal expressions by the same nonzero value, the resulting expressions are still equal.

If a is greater than 0, then a/c is also greater than 0 because c is positive. Similarly, b/c is also positive because both b and c are positive. Therefore, a/c is greater than b/c, which can be written as a/c > b/c.

Based on your question, you are asking about the property of expressions a, b, and c, where a ≠ 0. If a ≠ 0, then a/c = b/c. This property states that if you divide two equal expressions by the same nonzero value, the resulting expressions are still equal.

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The volume of the cylinder is \(5725.28\ cm^3\).

According to the question:

The diameter of the cylinder \(d = 18\ cm\)

Therefore radius \(r\) = \(9\ cm\)

Height \(h = 2.5\times 9 = 22.5\ cm\)

To find:

The volume of the cylinder

We know that the volume of a cylinder is:

\(V = \pi r^2h\)

substitute the given values into this equation and take \(\pi = 3.1415\), we get:

\(V = 3.1415\times 9^2\times 22.5\ cm^3\)

\(V = 5725.28\ cm^3\)

Therefore, The volume of the cylinder is \(5725.28\ cm^3\).

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\( {c}^{2} - {b}^{2} = {a}^{2} \)

\( {34}^{2} - {30}^{2} = {256}^{2} \)

\( \sqrt{256} = 16\)

CB is 16 units.

To duplicate angle ABC, draw a line segment, position the compass on point A, and then draw an arc that intersects the line segment. Next, position the compass on point B, and then draw a second arc that intersects the first arc at a point on the line segment. Finally, position the compass on the point where the two arcs intersect, but without changing the width, and draw a third arc that intersects the line segment.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Common instruments used to measure angles are:

1. Protractor

2.Compass

3.Digital Angle finder

4.Angle finder

5.Clinometer

6. Inclinometer

You can take the following actions to copy angle ABC:

Create a line segment that will serve as the foundation for the new angle you're going to create.

Draw an arc that crosses the line segment you produced in step 1 by positioning the compass on point A.

Draw a second arc that crosses the previous arc at a point on the line segment by setting the compass on point B.

Place the compass on the intersection of the two arcs without adjusting the compass's width, then create another arc that crosses the line segment.

Point D is where the second arc crosses the line segment. To finish the new angle, join points D and C.

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To obtain a feasible solution, you would need to revise the assignment limits or add additional constraints that do not violate the given constraint.

Based on the constraint you provided, x21 + x22 + x23 + x24 ≤ 3, it means that the sum of variables x21, x22, x23, and x24, representing the number of tasks assigned to agents 1, 2, 3, and 4 respectively, cannot exceed 3.

This constraint implies that agent 3 can be assigned to a maximum of 2 tasks (since x23 ≤ 2), and agent 2 can be assigned to a maximum of 3 tasks (since x22 ≤ 3).

However, there seems to be a contradiction with the statement that "agent 3 can be assigned to 2 tasks" and "agent 2 can be assigned to 3 tasks" because the sum of these maximum assignments would already exceed 3, which is not feasible according to the constraint.

Therefore, To obtain a feasible solution, you would need to revise the assignment limits or add additional constraints that do not violate the given constraint, such as reducing the maximum number of tasks that can be assigned to agent 2 or agent 3, or adjusting the total number of tasks available for assignment.

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The language L3 is not regular. It can be proven using the pumping lemma for regular languages.

Here is the proof:

Assume L3 is a regular language.

Let w = xyβ, where β is a non-empty suffix of ω and x is a prefix of ω of length p or greater.

We can write w as w = xyβ = ωαββ R, where α is the suffix of x of length p or greater. Because L3 is a regular language, there exists a string v such that uviw is also in L3 for every i ≥ 0.

Let i = 0.

Then u0viw = ωαββR is in L3. By the pumping lemma, we have that v = yz and |y| > 0 and |uvyz| ≤ p. But this means that we can pump y any number of times and still get a string in L3, which is a contradiction.

Therefore, L3 is not a regular language.

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Step-by-step explanation:

1 and 1/8 and add 1 and 1/4.

Make the mixed fractions into improper fractions which is 9/8 add 5/4.

Make a common denominator which is 8 so leave 9/8 and turn 5/4 into 10/8.

Add em up which equals to 19/8

19/8 into a mixed number is 2 3/8

Answer: 32768 or \(8^5\).

Step-by-step explanation:

\(8^7\)= 8x8x8x8x8x8x8 = 2097152

\(8^2\)= 8x8 = 64

                                            Dividing Exponents

When you divide exponents with the same base. You subtract. So in this case, you subtract 7 by 2, (being exponents). The same base is 8. So your subtracting \(8^7\) by \(8^2\). Which will get you \(8^5\).

                                          Dividing Whole Numbers.

You are going to divide whole numbers. Its pretty self explanatory but I will do the math for you anyways.

64 goes into 2097152, 32768 times. Or we can say,

2097152 divided by 64 = 32768.

So the answer is 32768, or \(8^5\).

Answer: i think it’s D

Step-by-step explanation:

Answer:

(-1, -2) will be the solution.

Step-by-step explanation:

System of equations has been given as,

y = 3x + 1 ---------(1)

Input-output value table for the given line will be,

x       -2        -1          0          1

y      -5        -2         1           4

y = -x - 3 ----------(2)

Input-output value table for the given line will be,

x        -2         -1           0           1

y       -1          -2          -3         -4  

By plotting the given coordinates we can draw the straight lines.

And the point of intersection (common point) of these lines will be the solution of the given system of equations.

Hence, (-1, -2) will be the solution.

Answer:

2(a)=20t

Step-by-step explanation:

Mark me as brainliest

The Fabrienne's speed is x miles per hour. Then Henry's speed will be (x-11) miles per hour as he drives 11 miles per hour slower than Fabrienne.

Given that they started at the same spot and drove in opposite directions.

We know that when two objects move in opposite directions, we should add up their speeds to get the total speed.

So, the total speed of Fabrienne and Henry = x + (x-11) = 2x-11.

And they were 484 miles apart after 5.5 hours.

So, the distance traveled by Fabrienne after 5.5 hours = 5.5x.

And the distance traveled by Henry after 5.5 hours = 5.5(x-11).

Now, add up the distance traveled by both Fabrienne and Henry to get the total distance.

5.5x + 5.5(x-11)

= 48411x - 60.5

= 48411x = 484 + 60.511x

= 544.5x

= 49.5

Henry's speed (x-11) = 49.5 - 11 = 38.5 miles per hour.

Fabrienne's speed x = 49.5 miles per hour.

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Answer:

A) $1,209

Step-by-step explanation:

To calculate Stephanie's total premium, we need to multiply her base annual premium by the rating factor.

Base annual premium: $930

Rating factor: 1.30

Total premium = Base annual premium * Rating factor

Total premium = $930 * 1.30

Total premium = $1,209

Therefore, Stephanie's total premium is $1,209.  

Answer:

x=-1

Step-by-step explanation:

If you need help with math get the app mathaway its great.

The intervals on which function f(x) = sin x -1 increasing or decreasing is (0, π/2) (B).



The given function is f(x) = sin x -1, 0 < x < 2 π.

A sinusoidal function is a function that can be written in the form f(x) = a sin(bx + c) + d or f(x) = a cos(bx + c) + d, where a, b, c, and d are constants.

The graph of the given function is a sine curve shifted downward by 1 unit.

The function is increasing on the interval (0, π/2) because the slope of the curve is positive on this interval.

The function is decreasing on the interval (π/2, 3π/2) because the slope of the curve is negative on this interval.

The function is increasing again on the interval (3π/2, 2π) because the slope of the curve is positive on this interval.

Therefore, the correct answer is option B. (0, π/2).

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In graph theory, a vertex cover of a graph is a set of vertices that covers all the edges in the graph. On the other hand, an independent set is a set of vertices that have no edges connecting them.

In this context, it is important to note that a vertex cover and an independent set are mutually exclusive.

That is, a vertex cannot belong to both the vertex cover and the independent set simultaneously.

In many cases, the determination of the minimum size of a vertex cover is one of the fundamental problems in graph theory.

Similarly, the determination of the maximum size of an independent set in a graph is also a significant problem in graph theory. The problems are typically addressed using various algorithms and heuristics.

However, in some cases, it is possible to establish the relationship between the vertex cover and the independent set in a graph. For instance, if a graph is a bipartite graph, then the vertex cover and the independent set are the same size.

This result is known as König's theorem and is one of the most important results in graph theory. In conclusion, the fact that each vertex belongs to the vertex cover or the independent set is not a coincidence.

It is a fundamental property of graphs that has significant implications for various problems in graph theory.

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Answer:

Solving the equation \(x^2 - 6x + 10 = 0\) we get \(x=3+i \ , \ x=3-i\)

Step-by-step explanation:

Noah's step to solve the equation \(x^2 - 6x + 10 = 0\) are:

\(x^2 - 6x + 10 = 0\\x^2 - 6x = -10\\x^2 - 6x + 9 = -10 + 9\\(x-3)^2 = -1\)

The next step is to take square root on both sides because: \(\sqrt{x^2}=x\)

\(\sqrt{(x-3)^2}=\sqrt{-1} \\x-3=\pm\sqrt{-1} \\x=\pm(\sqrt{-1})+3 \\\)

Now, we know that: \(\sqrt{-1}=i\)

\(x=\pm(i)+3\\x=3+i \ , \ x=3-i\)

So, Solving the equation \(x^2 - 6x + 10 = 0\) we get \(x=3+i \ , \ x=3-i\)

The steps for Noah finishing his work have been shown below and the solution is;

x = 3 + i and x = 3 - i

Noah's work is;

x² - 6x + 10 = 0

x² - 6x = -10

x² - 6x + 9 = -10 + 9

(x - 3)² = -1

Now, the next step would be to take the square root of both sides to obtain;

x - 3 = √(-1)

Now, we are told that the solution to x² = -1 are i and -i. Now, x² = -1 can also be written as;

x = √(-1)

Thus, the solution to x = √(-1) is i and -i.

Thus;

x - 3 = i and x - 3 = -i

Thus;

x = 3 + i and x = 3 - i

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The dilated quadrilateral, using center B and a scale factor of 1/2, is A'B'C'D'.

To dilate a quadrilateral ABCD using center B and a scale factor of 1/2, we can follow these steps:

Draw line segments from the center of dilation (B) to each vertex of the quadrilateral (A, C, and D).

Measure the distance from B to each vertex (AB, BC, BD) and multiply each distance by the scale factor (1/2).

From the endpoints of the original line segments, construct new line segments with the scaled distances obtained in the previous step.

Connect the endpoints of the newly constructed line segments to form the dilated quadrilateral A'B'C'D'.

The resulting quadrilateral A'B'C'D' will be a scaled-down version of the original quadrilateral ABCD, with center B as the center of dilation and a scale factor of 1/2.

Note: Since I am a text-based AI and cannot provide visual illustrations, it would be helpful to refer to a geometric software or draw the quadrilateral on paper to visualize the steps described above.

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By exhaustion theorem the lines that would be included in the proof are:

55 = (5)(11), so 55 is composite.

56 = (2)(28), so 56 is composite.

57 = (3)(19), so 57 is composite.

Therefore, to prove the theorem by exhaustion, we only need to show that the three integers in this range, namely 55, 56, and 57, are composite. The lines that show the prime factorization of each integer and conclude that they are composite are the ones that would be included in the proof.

The reason being that the theorem states that every integer in the range from 55 through 57 is composite.

The line that shows the factorization of 54 is not relevant to this theorem, as 54 is not in the range from 55 through 57. The line that shows the factorization of 58 is also not relevant, as 58 is not in the range from 55 through 57, and therefore does not contribute to proving the theorem.

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Answer:

A spring stretches 2.5 inches for each ounce of weight. Use this information for problems 9-11. 9. Determine a function that represents this situation.

Step-by-step explanation:

Hello!

We have the following expression:

Let's multiply and simplify it, look:

We multiply a*a*a, so we can rewrite it as a³. The same with b*b as b².

So, the answer in the simplified form is:

6a³ + 4b²

The sum of two rational numbers is rational because the sum of any two fractions with rational numerators and denominators can be expressed as a fraction with a rational numerator and denominator.

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. For example, 1/2, -3/4, 6/5, and 0 are all rational numbers.

When we add two rational numbers together, we can use the following formula:

a/b + c/d = (ad + bc) / bd

where a, b, c, and d are integers and b and d are not equal to zero.

This formula tells us that the sum of two rational numbers is also a rational number. The numerator of the sum is found by cross-multiplying the fractions, and the denominator of the sum is found by multiplying the denominators.

For example, if we want to add 1/2 and 2/3 together, we can use the formula above:

1/2 + 2/3 = (1 x 3 + 2 x 2) / (2 x 3) = 7/6

Therefore, the sum of 1/2 and 2/3 is 7/6, which is also a rational number. This formula can be used to prove that the sum of any two rational numbers is also a rational number.

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A rational number is a number that can be written as \(\dfrac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b\not=0\).

If one number is \(\dfrac{a}{b}\) and the other is \(\dfrac{c}{d}\), where \(b,d\not=0\), their sum is \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\). Since the set of integers is closed under addition and multiplication, we can write that \(\dfrac{ad+bc}{bd}=\dfrac{e}{f}\) where \(e,f\in\mathbb{Z}\) and \(f\not=0\), thus proving the sum of two rational numbers is a rational number.

Answer:

(a) kilometer

(b) Kilograms

(b) Milliliters

Answer:

(a)= kilometer

(b)= kilogram

(c)= millimeters

Step-by-step explanation:

You need to try and figure out which answer is more reasonable.