find the future value of an ordinary annuity of $110 paid at the end of each quarter for five years if interest is earned at a rate of 6% compounded quarterly ....round to 2 decimal places

Answers

Answer 1

Given:

Amount paid is, p = $110.

Interest rate is, r = 6%=0.06.

Nmber of years, t = 5 years.

Number of times per year is, n = 3 (each quarter).

The objective is to find the future values compounded quarterly.

The general formula to find the compound interest is,

\(A=P(1+\frac{r}{n})^{n(t)}\)

Substitute the given values in the above equation.

\(\begin{gathered} A=110(1+\frac{0.06}{3})^{3(5)} \\ A=110(1+0.02)^{15} \\ A=148.05 \end{gathered}\)

Hence, the future value is .


Related Questions

Please help-!! hurry​

Please help-!! hurry

Answers

Answer:

180

Step-by-step explanation:

Need help With This anyone please help am confused on this one very much

Need help With This anyone please help am confused on this one very much

Answers

Step-by-step explanation:

(2×8² - 2²×8)/(2×8)

before we start typing things into the calculator, we see that the fraction can be simplified :

(2×8² - 2²×8)/(2×8) | divide top and bottom by 2

(8² - 2×8)/8 | divide top and bottom by 8

(8 - 2)/1 = 6/1 = 6

pls help!!
Q:In a random sample, 8 students were asked how long it takes them to get ready for school in the morning. The times are listed below, compute the following:
22 29 21 24 27 28 25 36

Range:
Variance:
Std Deviation:

Answers

The required statistical parameters has been computed as follows:

Range = 15.

Standard deviation, SD = 4.4441.

Variance = 19.75.

How to calculate the range?

Mathematically, the range of a data set can be calculated by using this formula;

Range = Highest number - Lowest number

Range = 36 - 21

Range = 15.

How to calculate the mean?

Mathematically, the mean for these data sets would be calculated by using this formula:

Mean = [F(x)]/n

F(x) = 22 + 29 + 21 + 24 + 27 + 28 + 25 + 36

F(x) = 212.

Mean = 212/8

Mean = 26.5

Next, we would calculate the standard deviation by using this formula:

SD = √(1/n × ∑(xi - u₁)²)

SD = √(1/5 × ∑(22 - 26.5)² + 1/5 × ∑(29 - 26.5)² + 1/5 × ∑(21 - 26.5)² + 1/5 × ∑(24 - 26.5)² + 1/5 × ∑(27 - 26.5)² + 1/5 × ∑(28 - 26.5)² + 1/5 × ∑(25 - 26.5)² + + 1/5 × ∑(36 - 26.5)²)

Standard deviation, SD = 4.4441.

In Statistics, the standard deviation of a data sample is the square root of the variance and this is given by this mathematical expression:

Variance = δ²

Variance = 4.4441²

Variance = 19.75.

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androy12 answer na dito​

Answers

Answer:

hindi ko po kilala yan

Step-by-step explanation:

pero salamat sa points ☺️☺️

There are 5 pens in a container on your desk. Among them, 3 will write well but 2 have defective ink cartridges. You will select 2 pens (without replacement) to take to a business appointment. Select the most appropriate statement for each part (a-e) when considering calculating the probability that both pens are defective.
a. Let X: the number of defective pens selected. X is a random variable. [Select ]
b. For each pen chosen from the container, we can consider "Defective" as the success and "Working" as the failure since we are interested in both pens being defective. [ Select] -
c. X is well approximated by a Binomial Random Variable X-Bin(n=2. pi=2/5) True
d. If the first pen was replaced before the second pen was selected (sampling with replacement), then X would be very well approximated by a Binomial Random Variable X-Bin(n=2, pi=2/5) True
e. Had you been drawing 2 pens (without replacement) from a container of 25 pens, X would be better approximated by a Binomial Random Variable.

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Total Number of pens = 5

Number of defective pens = 2

Number of non-defective pens = 3

A.) number of defective pens selected :

X : {0, 1, 2}

It is possible that no defective pen will be selected ; 1 defective will be chosen or both pens are defective.

2.)

Defective as Success (since selecting a defective pen is the point of interest.

3.)

Since selection is done without replacement

Probability of success per selection is different for each selection ;

Number of defective = 2

Number of observations = 5

P(success on first selection) = 2/5

P(success on second selection) = 1/4

Hence, X is not well approximated by a binomial random variable.

4.) if selection is done with replacement ; then then the probability of success per selection will be the Same for each selection made. Hence, X will be well approximated by a binomial Random variable.

5.) If sampling is done without replacement, then the the hypergeometric function will be a more effective approximation.

What is the equation of the line that passes through the point (7,6) and has a slope of 0

Answers

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

Given,

The points which the line passes, (x₁, y₁) = (7, 6)

Slope of the line, m = 0

We have to find the equation of the line:

We know that,

y - y₁ = m(x - x₁)

So,

y - 6 = 0(x - 7)

y - 6 = 0

y = 6

That is,

The equation of the line that passes through the point (7, 6) with slope 0 is y = 6

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\(\( y=\int_{-2}^{x} \sqrt{3 t^{4}-1} d t \)\)

Answers

The value of intergal  \(y=\int_{-2}^{x} \sqrt{3 t^{4}-1} d t\) is

\(y=\frac{1}{6} \sqrt{(3x^{2}-1)^{2}} - \frac{1}{6} \sqrt{(3(-2)^{2}-1)^{2}} \)\)

What is integral?

In mathematics, an integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals, together with derivatives, are the two main tools used in calculus and are used to calculate areas, volumes, and their generalizations.

The integral \(y=\int_{-2}^{x} \sqrt{3 t^{4}-1} d t\)  can be evaluated by first completing the square and then using the substitution method.

Completing the square gives us \(( 3 t^{4} -1 = (3t^{2} -1)^{2} \)\).

We can now make the substitution \(( u = 3 t^{2} -1 \)\)).

Differentiating, we get \(( du = 6t dt \)\)).

Therefore, the integral can be written as\(y=\int_{-2}^{x} \sqrt{(3t^{2}-1)^{2}} \frac{du}{6t} \)\).

Solving the integral, we get:

\(y = \frac{1}{6} \sqrt{(3t^{2}-1)^{2}} +C \)\)

Substituting back into the equation, we get the answer as:

\(y=\frac{1}{6} \sqrt{(3x^{2}-1)^{2}} - \frac{1}{6} \sqrt{(3(-2)^{2}-1)^{2}} \)\)

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Which operation symbol could be placed in the circle so that B is a non linear function of T?

B= t___t

A. +

B. -

C. x

D. division sign

Answers

It can be deduced that a non linear function is a function where the graph isn't a line.

What is a non linear function?

Your information is incomplete as the circle isn't given. Therefore, an overview of the non linear function will be given.

A non linear function simply means a function where the graph is not a line. In this case, they do not have a constant slope.

A non linear function is a function shows graph isn't a line or part of a line. In such a case, the graph isn't a straight line.

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Which operation symbol could be placed in the circle so that B is a non linear function of T? B= t___tA.

find the value of each variable in the parallelogram

find the value of each variable in the parallelogram

Answers

Answer:

1. x = 15°

2. y = 12

Step-by-step explanation:

1. Determination of the value of x.

(5x – 5) + 110 = 180 (Adjacent angles add up to 180)

5x – 5 + 110 = 180

5x + 105 = 180

Collect like terms

5x = 180 – 105

5x = 75

Divide both side by 5

x = 75/5

x = 15°

2. Determination of the value of y.

3y – 4 = 2y + 8 (opposite sides are equal)

3y – 4 = 2y + 8

Collect like terms

3y – 2y = 8 + 4

y = 12

What is the volume of the rectangular prism?
1/3ft

Answers

Answer:V=whl

Step-by-step explanation:

L=Length

W= Width

H= Height

If n is equal to the unknown number, which of the following proportions can be used to find 135% of 48?

Answers

Answer:

ITS C-    135/100 = n/48

Step-by-step explanation

i know

Answer:

c

Step-by-step explanation:

Find the surface area and volume of a sphere.
A = 4 r²
V = 4/3r³
A sphere has a radius of 4 inches.
Area (to the nearest tenth) =
Volume (to the nearest tenth) =
sq. in.
cu. in.

Answers

\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies SA=4\pi (4)^2\implies SA\approx 201.1~in^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies V\approx 268.1~in^3\)

Is it possible for PQ to have two
distinct midpoints, M₁(a, b) and M₂(c,d)?

Answers

A line segment cannot have two distinct mid points.

What is midpoint of a line?

The midpoint of a line is the middle point of a line segment.

It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

Coordinate of midpoint of a line divided by ratio

for external division: (x,y) = ([(mx2 + nx1) / (m + n )], [(my2 + ny1)/(m+n)])

for internal division: (x, y) = ([(mx2 - nx1) / (m -n)], [(my2 - ny1)/(m - n)])

where;

m, and n are ratio of line divisionx, and y are the coordinates of the midpoints

Thus, a line segment cannot have two distinct mid points.

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Question A class of 25 students took a spelling test. Two students scored 100 on each test, nine students scored 95 on each test, ten students scored 90 on each test, three students scored 80 on each test and one student scored 70. What is the average score of the spelling test rounded to one decimal place? Enter your answer in the box.

Answers

The average score of the spelling test is 90.6%

To find the average score of the test, we need to add up all the scores and divide by the total number of students. We can think of the average score as the "typical" or "representative" score of the entire class.

First, let's add up all the scores:

2(100) + 9(95) + 10(90) + 3(80) + 1(70) = 200 + 855 + 900 + 240 + 70 = 2265

Next, we divide by the total number of students:

Average score = (2 + 9 + 10 + 3 + 1) / 25 * 100% = 25 / 25 * 100% = 90.6%

Therefore, the average score of the spelling test is 90.6% when rounded to one decimal place.

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Which of the following is not a function?
A{ (0,1), (1,2), (2,3), (3,4)}
B.{(0,2), (1,3), (4,3), (1,2)}
C.{(1,3), (4,2), (2,0), (3,4)}
D.{(1,2), (2,2), (3,2), (4,2)}

Answers

Answer:

  B.  {(0,2), (1,3), (4,3), (1,2)}

Step-by-step explanation:

A relation is not a function if the same input value maps to multiple output values. Essentially, if any x is repeated, it is not a function.

The second set, {(0,2), (1,3), (4,3), (1,2)}, has x-values of 0, 1, 4, 1, so 1 is repeated. It is not a function.

A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.

Answers

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

Finding the equation perpendicular to the tangent

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

The smallest slope on the curve

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

The equation of the tangent line

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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answer the number 2 only

answer the number 2 only

Answers

The missing variables on item 2 are given as follows:

\(o = 12\sqrt{3}\)i = 24.

What are the trigonometric ratios?

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

Sine = length of opposite side to the angle/length of hypotenuse of the triangle.Cosine = length of adjacent side to the angle/length of hypotenuse of the triangle.Tangent = length of opposite side to the angle/length of adjacent side to the angle = sine/cosine.

For the angle of 60º, we have that:

o is the opposite side.12 is the adjacent side.

Hence the length o is given as follows:

tan(60º) = o/12.

\(\sqrt{3} = \frac{o}{12}\)

\(o = 12\sqrt{3}\)

Applying the Pythagorean Theorem, the length i is given as follows:

i² = 12² + \((12\sqrt{3})^2\)

i² = 576

i² = 24²

i = 24.

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Answer:

o = 12√3

i = 24

Step-by-step explanation:

From observation of the given right triangle, we can see that two of its interior angles measure 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, the triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

Side a is opposite the 30° angle (shortest leg).Side a√3 is opposite the 60° angle (longest leg).Side 2a is the hypotenuse (longest side).

In triangle #2, the shortest leg is 12 units.

As "a" is the shortest leg, the scale factor "a" is 12.

The side labelled "o" is the longest leg opposite the 60° angle. Therefore:

\(o = a\sqrt{3}=12\sqrt{3}\)

The side labelled "i" is the hypotenuse of the triangle. Therefore:

\(i= 2a = 2 \cdot 12=24\)

Therefore:

o = 12√3i = 24

Please help! 20 pts and brainliest!! An isosceles triangle has an angle that measures 124°. Which other angles could be in that isosceles triangle? Choose all that apply. 124, 28, 65, 41

Answers

Answer:

Step-by-step explanation:

In an isosceles triangle, by definition two of the three sides of the triangle are equal to one another. Therefore, the angles opposite to these sides must also be equal. And considering the Triangle Sum Theorem, the angles of a triangle must add up to 180 degrees, the angle that measures 124 degrees cannot be be equal to another angle due to the fact that the sum of them would exceed 180. Therefore let x be the angle:

124+2x=180

2x=56x=28

Please brainlest!

Select the correct answer. Which expression is equivalent to this polynomial? 16x² +4​

Answers

Answer:

(4x+2)(4x-2)

Step-by-step explanation:

Answer:

(4x+2)(4x-2)

Step-by-step explanation:

center at (2, -2) and twice the area of the circle (x, -7)² + (y, -7)² =7​

Answers

Answer:

\((x-2)^2+(y+2)^2=14\)

Step-by-step explanation:

Equation of a circle

\((x-a)^2+(y-b)^2=r^2\)

where:

(a, b) is the center of the circle.r is the radius of the circle.

Given equation:

\((x-7)^2+(y-7)^2=7\)

Therefore:

center = (7, 7)radius = √7

Area of a circle

\(\sf A=\pi r^2\)

where:

r is the radius.

Therefore, the area of a circle with radius √7 is:

\(\implies \sf Area=\pi \left(\sqrt{7}\right)^2=7 \pi\:\:square\:units\)

Therefore, a circle with twice the area would be:

\(\implies \sf Area = 2 \cdot 7 \pi = 14 \pi \:\: square\:units\)

Therefore, its radius would be:

\(\begin{aligned}\implies \sf \pi r^2 & = \sf14 \pi\\\sf r^2 & = \sf 14\\\sf r & = \sf \sqrt{14}\end{aligned}\)

So the equation of a circle with a center at (2, -2) and a radius of √14 is:

\(\implies (x-2)^2+(y-(-2))^2=\left(\sqrt{14}\right)^2\)

\(\implies (x-2)^2+(y+2)^2=14\)

A model of a telescope has a height of 15 inches and and a diameter of 3.5 inches. If the actual diameter is 10 inches, find its actual height.

Answers

Answer:

The actual height of telescope is 42.85 inches

Step-by-step explanation:

Given that:

Height of model of telescope = 15 inches

Diameter of model of telescope = 3.5 inches

Actual diameter of telescope = 10 inches

Actual height of telescope = x

Ratio of model's diameter to height :: Ratio of actual diameter to height

3.5 : 15 :: 10 : x

Product of extreme = Product of mean

3.5*x = 10*15

3.5x=150

Dividing both sides by 3.5

\(\frac{3.5x}{3.5}=\frac{150}{3.5}\\x=42.85\)

Hence,

The actual height of telescope is 42.85 inches

Nicks lunch cost $14.75 tax was 1.03 and he left a tip of 2.50 how much did he pay for his lunch

Answers

Answer:

$18.28

Step-by-step explanation:

To complete this problem is a straightforward answer:

First, you add 14.75 + 1.03 which equals $15.78 then, you'll want to add 2.50 to 15.78 and there you have your answer!!

A charitable nonprofit organization wants to test two methods of fundraising. From a list of 1,000 past donors, half will be sent literature about the successful activities of the charity and asked to make another donation. The other 500 donors will be contacted by phone and asked to make another donation. The percentage of people from each group will be compared. (Select all that apply.)
A) After the donation collection period, calculate the average or total amount collected from the 500 donors in the treatment group.
B) After the donation collection period, compare the average or total amount collected from each of the two treatment groups.
C) A placebo is not being used.
D) Randomly select 100 donors to receive the literature and 900 donors to receive the phone call.
E) A placebo is being used for the remaining 900 donors.
F) Randomly select 500 donors to receive the literature and 500 donors to receive the phone call.

Answers

Answer:

The correct selections are:

B) After the donation collection period, compare the average or total amount collected from each of the two treatment groups.

C) A placebo is not being used

F) Randomly select 500 donors to receive the literature and 500 donors to receive the phone call.

Step-by-step explanation:

What this question requires from you, is to identify the correct characteristics of the study described. Let us explain why each of the selections was made.

B) After the donation collection period, compare the average or total amount collected from each of the two treatment groups: The purpose of the study is to determine the difference in the effectiveness of two methods of fundraising. Therefore at the end of the study, the average total amount raised from each group will be compared to determine which was more effective.

C) A placebo is not being used: Placebos are sham treatments used in a control group without their knowledge. The placebos do not produce any effect similar to the results anticipated the actual treatment. Here, no group is given sham treatment, there is no "control" group given placebos hence placebos are not used.

F) Randomly select 500 donors to receive the literature and 500 donors to receive the phone call: To remove any form of bias in the study, the selection of the groups is done at random, and the number of participants in each group is the same, so as to maintain uniformity during the comparison.

The right statement selection will be of these are:

A) After the donation collection period, compare the average or total amount collected from each of the two treatment groups.

C) A placebo is not being used.

F) Randomly select 500 donors to receive the literature and 500 donors to receive the phone call.

Use a random number generator to choose from a list of \(1000\) past donors, half will be i.e.,\(=\frac{1000}{2} =500\) will be sent literature, and the other 500 donors will be contacted by phone.

And the percentage of people from each group will be compared i.e. we make the total amount from each of the two treatment groups.

In this case, Placebo is not used.

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Lightfoot Inc., a software development firm, has stock outstanding as follows: 20,000 shares of cumulative preferred 2% stock, $20 par, and 25,000 shares of $100 par common. During its first four years of operations, the following amounts were distributed as dividends: first year, $3,000; second year, $5,000; third year, $34,500; fourth year, $71,000.

Answers

The amount of Dividends of $3,000, $5,000, $34,500, and $71,000 were distributed to the 20,000 preferred and 25,000 common shareholders of Lightfoot Inc. over the first four years of operations.

To calculate the dividend per share of the preferred and common stock of Lightfoot Inc., the total amount of dividends paid out over the first four years must first be determined. This can be done by adding the given amounts of $3,000, $5,000, $34,500, and $71,000 to get a total of $113,500. To find the dividend per share for the preferred stock, the total dividend is divided by the number of shares (20,000) which gives a dividend per share of $5.68. To find the dividend per share for the common stock, the total dividend is divided by the number of shares (25,000) which gives a dividend per share of $4.54.

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What is the simplified expression for 4 to the 4 power x 4 to the 3 power over 4 to the 5 power

Answers

Answer:

42 or 4^2

hope this helps

Answer:

4^12

Step-by-step explanation:

What is the volume of a solid that is 3 inches wide, 4
inches tall, and 2 inches deep?
24 in.2
24 in.3
26 in.2
26 in. 3

Answers

Answer:

24 in^2

Step-by-step explanation:

3 x 4 x 2 = 24 in^2

Answer:

3×4×2 = 24 in^3

Although it depends on the shape

Type the correct answer in the box. Use numerals instead of words. Find the missing side length, x. 18° 18° 20 B D The value of the missing side length labeled as x is _____​

 Type the correct answer in the box. Use numerals instead of words. Find the missing side length, x.

Answers

Answer:

7.2

Step-by-step explanation:

20/12 = 12/x

20x = 144

x = 144/20

x = 7.2

Check to make sure your answer is right:

20/12 = 1.66666666667

12/7.2 = 1.66666666667

Last week, Jason ran 26.1. He wants to run further this week. He plans to run 2.4 miles to the park, four times around the park, and 2.4 miles back from the park. To represent that inequality. He wrote: 2.4 + 4p + 2.4 __ 26.1
Which inequality symbol should be use? Why?

Answers

Step-by-step explanation:

>

Since he wanted to run farther this week so the last week 26.1 which is the distance he ran is less than the distance of this week

Hope this helps...

Answer:

Use the greater than symbol.

His goal does not include running exactly 26.1 miles; he needs to run more than 26.1 miles.

Equality should not be part of the solution set.

Step-by-step explanation:

A rectangular garden has an area of 3/5 square miles. If its length is 7/8 miles, what is its
width?
Input your answer as a fraction.

Answers

Answer:

\(\frac{24}{35}mi\)

Step-by-step explanation:

Area = length • width

area = \(\frac{3}{5}mi^{2}\)

length = \(\frac{7}{8} mi\)

width = x

\(\frac{3}{5} = \frac{7}{8} x\)                   multiply both sides by \(\frac{8}{7}\) (the reciprocal of \(\frac{7}{8}\))

\((\frac{8}{7})(\frac{3}{5}) = x\)

x = \(\frac{24}{35}\)

Answer:

24/35 is your answer

Divide 3/5 by 7/8 to get the answer of 24/35

What is the simplified value of the expression below rounded to the nearest hundredth? StartFraction 3.5 times 2 + 9 over 10.4 minus 1.4 times 2 EndFraction 0.28 0.89 1.91 2.11

Answers

Answer:

The answer is 2.11~! I hope I helped <3

Step-by-step explanation:

3.5x2=7   7+9=16   1.4x2=2.8   10.4-2.8=7.6   16/7.6=2.10526315789

but we simplify so, 2.10526315789 rounded to the nearest hundredth is 2.11~!

 

Answer:

2.11

Step-by-step explanation:

I got it correct on the test

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