You have been offered a project paying $300 at the beginning of each year for the next 20 years. what is the maximum amount of money you would invest in this project if you expect 9 percent rate of return to your investment?

Answers

Answer 1

This is a simple problem with some quick addition and subtraction, and a bit of multiplication.

First we figure out how much money you're spending in total, which is $300 each year, for 20 years, so 300 x 20 = 6,000. Now, since the problem is asking for a maximum amount for percentage rate, this means we find the 9% for all 20 years combined and not individually. 9% of 6,000 is of course 540, so if we subtract 540 from 6,000, we get 5,460.

This means your answer is $5,460

Related Questions

A bird feeder is in the shape of a cylinder. It has a volume of about 100 cubic inches. It has a radius of 2 inches. What is the approximate height of the bird feeder? Use 3.14 for pi

Answers

volume = pi x r^2x h

100 = 3.14 x 2^2 x h

100 =3.14 x 4 x h

100 = 12.56 x h

h = 100/12.56 = 7.9617

the height is approximately 8 inches tall

Find the arc length of the curve on the given interval. (round your answer to three decimal places.) parametric equations interval x = 6t + 5, y = 7 − 7t −1 ≤ t ≤ 3

Answers

[tex]\displaystyle\int_{-1}^3\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]

[tex]x=6t+5\implies\dfrac{\mathrm dx}{\mathrm dt}=6[/tex]
[tex]y=7-7t\implies\dfrac{\mathrm dy}{\mathrm dt}=-7[/tex]

[tex]\displaystyle\int_{-1}^3\sqrt{36+49}\,\mathrm dt=\sqrt{85}(3-(-1))=4\sqrt{85}[/tex]

The arc length of the curve on the given interval −1 ≤ t ≤ 3 with parametric equation x = 6t + 5 and y = 7 − 7t −1 is 4√85.

What is integration?

It is the reverse of differentiation.

The arc length of the curve on the given interval.

Parametric equations interval

x = 6t + 5, −1 ≤ t ≤ 3

y = 7 − 7t, −1 ≤ t ≤ 3

We know that the parametric form of the arc length will be given as

[tex]\rm \int _{-1}^3 \sqrt{(\dfrac{dx}{dt})^2 + (\dfrac{dy}{dt})^2} \ dt[/tex]

Then we have

[tex]\rm \dfrac{dx}{dt} = 6\\\\\dfrac{dy}{dt} = -7[/tex]

Then the arc length will be

[tex]\rightarrow \rm \int _{-1}^3 \sqrt{(3)^2 + (-7)^2} \ dt\\\\\rightarrow \sqrt{85} [t]_{-1}^3 \\\\\rightarrow 4 \sqrt{85}[/tex]

More about the integration link is given below.

https://brainly.com/question/18651211

True or False: The sample size you need to estimate the population distribution should always be at least 10% of the population size.

Answers

Final answer:

False. The sample size needed to estimate the population distribution should not always be at least 10% of the population size.

Explanation:

False. The statement that the sample size needed to estimate the population distribution should always be at least 10% of the population size is not true. The size of the sample needed depends on various factors such as the original population, the level of confidence desired, and the margin of error allowed. For example, if the population is large and diverse, a smaller sample may still provide a reliable estimate of the population distribution. It is important to consider statistical concepts such as normal distribution and sampling techniques when determining the appropriate sample size.

Learn more about sample size here:

https://brainly.com/question/30885988

#SPJ2

Suppose Q and R are independent events. Find P(Q and R) if P(Q) =4/5 and P(R) =4/11

Answers

Since Q and R are independent, this means P(Q and R) = P(Q)*P(R)

P(Q and R) = P(Q)*P(R)
P(Q and R) = (4/5)*(4/11)
P(Q and R) = (4*4)/(5*11)
P(Q and R) = 16/55

Round to the nearest while decimal 6.7

Answers

If you meant "[tex]whole [/tex]" instead of "[tex]while [/tex]"

Then, [tex]six [/tex] is rounded [tex]1ten[/tex] & [tex]seven[/tex] is rounded to [tex]ten [/tex]

Your answer: [tex]7[/tex]

[tex]good\\luck \\ on \\ your \\ assignment \\ \\ \\ \\ enjoy \\ your \\ day \\ \\ \\ \\ \\ \\ MeIsKaitlyn :)[/tex]

One school survey showed that 3 out of 5 students own a pet. Another survey showed that 6 out of 11 students owned a pet. Are these results equivalent? Explain your reasoning.

Answers

no they are not because 3/5 is not equal to 6/11. if they were equal, it would be 6/10

3/5 own a pet means that (0.6) or 60% own a pet
6/11 own a pet means that (0.545) or 54.5% own a pet

Conclusion, in the 1st class more people 60% own a pet whereas in the second class only 54.5% have a pet

Linda deposits $500 into an account that pays simple interest at a rate of 4% per year. How much interest will she be paid in the first 4 years?

Answers

Assuming that she deposits $500 and forgets about it, here is what she would get after 4 years:

Year 1 - $500 * 1.04 = $520
Year 2 - $520 * 1.04 = $540.80
Year 3 - $540.80 * 1.04 = $562.432
Year 4 - $562.432 * 1.04 = $584.92928

Aftere four years. Linda would be paid $84.93

the base of this solid crate has an area of 6 square centimeters the height of the crate is 4 meters what is the volume of the crate

Answers

[tex]Area Of Cuboid = length*width*height[/tex]

The length * width is the area of the base, so:

[tex]Area Of Cuboid = base*height = 6 * 4 = 24 meters^3[/tex]

Answer:

2 × 10³ cm³

Step-by-step explanation:

Given data

Area of the base: 6 cm²Height of the crate: 4 m = 4 × 10² cm

Considering the crate is a cuboid, its volume (V) is:

V = length × width × height

Since

area of the base = length × width

We get

V = area of the base × height

V = 6 cm² × 4 × 10² cm

V = 2.4 × 10³ cm³ ≈ 2 × 10³ cm³ (we round off to 1 significant figure)

A farmer is going to plant carrots on 5 3/14 acres, corn on 4 23/42 acres and peppers on 2 5/21 acres. If each acre requires 6 bags of fertilizer, how many bags of fertilizer does the farmer need to plant all the acres?

Answers

hmm we do the same as before, you convert the mixed fractions to "improper fractions" by simply making the numerator the product and sum like you saw it

so

[tex]\bf 5\frac{3}{14}\implies \cfrac{5\cdot 14+3}{14}\implies \cfrac{73}{14} \\\\\\ 4\frac{23}{42}\implies \cfrac{4\cdot 42+23}{42}\implies \cfrac{191}{42} \\\\\\ 2\frac{5}{21}\implies \cfrac{2\cdot 21+5}{21}\implies \cfrac{47}{21}\\\\ -------------------------------\\\\ \cfrac{73}{14}+\cfrac{191}{42}+\cfrac{47}{21}\impliedby \textit{our LCD is just 42}\implies \cfrac{3\cdot 73+1\cdot 191+2\cdot 47}{42} \\\\\\ \cfrac{219+191+94}{42}\implies \cfrac{504}{42}\implies \cfrac{12}{1}\implies 12[/tex]

now, that's how many acres the farmer has in total
now, if each acre takes 6 bags of fertilizer, well, you surely know how much that is.

Find an approximation of the area of the region R under the graph of the function f on the interval [-1, 2]. Use n = 6 subintervals. Choose the representative points to be the left endpoints of the subintervals. f(x) = 7 - x2

Answers

The approximation of the area of the region R under the graph of the function is 18.625 square units.

In this question we must calculate the approximate area ([tex]A[/tex]) below the curve by means of Riemann sums with left endpoints, whose expression is described below:

[tex]A = \Delta x \cdot \Sigma\limits^{n-1}_{i=0} f(a + i\cdot \Delta x)[/tex], for [tex]x \in [a,b][/tex] (1)

[tex]\Delta x = \frac{b-a}{n}[/tex] (2)

Where:

[tex]a[/tex] - Lower bound[tex]b[/tex] - Upper bound[tex]n[/tex] - Number of subintervals[tex]i[/tex] - Index

If we know that [tex]a = -1[/tex], [tex]b = 2[/tex], [tex]n = 6[/tex] and [tex]f(x) = 7 - x^{2}[/tex], then the approximate area is:

[tex]\Delta x = \frac{2-(-1)}{6}[/tex]

[tex]\Delta x = 0.5[/tex]

[tex]A = 0.5\cdot [f(-1) + f(-0.5)+f(0)+f(0.5)+f(1)+f(1.5)][/tex]

[tex]A = 0.5\cdot (6+6.75+7+6.75+6+4.75)[/tex]

[tex]A = 18.625[/tex]

The approximation of the area of the region R under the graph of the function is 18.625 square units.

To learn more on Riemann sums, we kindly invite to check this verified question: https://brainly.com/question/21847158

A total of 487 tickets were sold for the school play. They were either adult tickets or student tickets. There were 63 fewer student tickets sold than adult tickets. How many adult tickets were sold?

Answers

s=a-63

s+a=487, using s from above in this equation you get:

a-63+a=487 combining like terms

2a-63=487 adding 63 to both sides

2a=550 dividing both sides by 2

a=275

So there were 275 adult tickets sold.

Final answer:

To determine the number of adult tickets sold for the school play, a system of equations is set up and solved, revealing that 275 adult tickets were sold.

Explanation:

To find the number of adult tickets sold for the school play, we need to set up a system of equations based on the information given. Let x represent the number of adult tickets and y represent the number of student tickets. According to the problem, the following two statements are true:

The total number of tickets sold is 487: x + y = 487

There were 63 fewer student tickets sold than adult tickets: y = x - 63

We can substitute the second equation into the first to find the value of x:

x + (x - 63) = 487

2x - 63 = 487

2x = 487 + 63

2x = 550

x = 275

Therefore, 275 adult tickets were sold.

What is the slope of a line that passes through the following points (-3,8) and (2,1)

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ 8}})\quad % (c,d) &({{ 2}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-8}{2-(-3)}\implies \cfrac{1-8}{2+3}\implies \cfrac{-7}{5}[/tex]

Hello!

Step-by-step explanation:

Slope: [tex]\frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}[/tex]

[tex]\frac{1-8=-7}{2-(-3)=2+3=5}=\frac{-7}{5}=-\frac{7}{5}[/tex]

Slope is -7/5

Answer is -7/5

Hope this helps!

Thanks!

-Charlie

What is the limit for lim x -> 2 int x

Answers

we are asked in the problem to determine the limit of integral of x dx as x approaches to 2. In this case, the first step to do is to integrate first the function. The integral of x dx by the power rule is equal to x^(n+1)/n+1. In this case, since n is equal to 1 from the given, then integral of x dx is equal to x^2/2. To evaluate the limit of x as x approaches to 2, we just have to substitute x by 2, that is
2^2 / 2 equal to 2. Hence the answer to this problem is equal to 2.

222+203 is rounded up to what?

Answers

[tex]222: 220 \\ 203 = 200 \\ \\ 222 + 203 = 425 \\ 220 + 200 = 420 \\ \\ \\ \\ Good \\ luck \\ on \\ your \\ assignment \\ \\ enjoy \\ your \\ day \\ \\ \\ MeIsKaitlyn :)[/tex]

[tex]Remember [/tex]↓

[tex]1-5[/tex] would rounded [tex]downward [/tex]
[tex]6-9[/tex] would be rounded [tex]upward [/tex]

Express the volume of a cone, V, as a function of its radius, r, if the radius is 1/5 of the height.

Answers

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=radius\\ h=height\\ ------\\ r=\frac{h}{5}\implies 5r=h \end{cases}\implies V=\cfrac{\pi r^25r}{3} \implies V=\cfrac{5\pi r^3}{3}[/tex]

Simplify the expression. 33 • 32 + 12 ÷ 4

Answers

Final answer:

The expression 33 • 32 + 12 ÷ 4 simplifies to 1059.

Explanation:

To simplify the expression 33 • 32 + 12 ÷ 4, we follow the order of operations - performing multiplication and division before addition.

Multiply 33 and 32 to get 1056.Divide 12 by 4 to get 3.

Now we can add the results: 1056 + 3 = 1059.

Learn more about Expression simplification:

https://brainly.in/question/6768966

#SPJ12

richerd works at an ice cream shop. regular cones get two scopes of ice cream and large cones get three scoops. One hot saturday richard scooped 234 regular cones and 156 large cones one scoop of ice cream is 3 ounces a tub of ice cream is 10 pounds how many tubs of ice cream did richerd use to make the cones?

Answers

234 x 2 = 468 scoops

156 x 3 = 468 scoops

468 + 468 = 936 total scoops

936 x 3 = 2808 ounces

16 ounces = 1 pound

2808/16 = 175.5 pounds

175.5/10 = 17.55 tubs

round answer as needed

Sara must plant 340 trees. In the past 6 days Sara planted 204 trees. If she continues at this rate, how many more days will it take her to plant all the trees?

Answers

204/6 = 34 trees a day. 340-204 =136 trees left to plant. 136/34 = 4 4 days

which number produces a rational number when added to 0.5

Answers

Let, the number be x

Therefore, x +0.5= p/q where q is non zero and (p, q) co-prime.

Then, x= -0.5 + (p/q)

now you can substitute any value of p and q to get x.

Answer:

Any rational number.

Step-by-step explanation:

∴ [tex]x+0.5[/tex] is rational if and only if x is rational.

To proveL: we proceed as follows:

Suppose that [tex]x+0.5[/tex] is rational.

Then there are some integers p , q with [tex]q\neq 0[/tex] such that

[tex]x+\frac{1}{2}=\frac{p}{q}[/tex]

Subtract both sides by [tex]\frac{1}{2}[/tex], we get

[tex]x=\frac{p}{q}-\frac{1}{2}=\frac{2p-q}{2q}[/tex] which is rational.

Conversely, if x is rational, then there are integers a,b with b>0 such that [tex]x=\frac{a}{b}[/tex] then we have,

[tex]x+\frac{1}{2}=\frac{a}{b}+\frac{1}{2}=\frac{2a+b}{2b}[/tex] which is also a rational.

Bill's Roast Beef sells 5 times as many sandwiches as Pete's Deli. The difference between their sales is 360 sandwiches. How Many did each sell ?

Answers

b - p = 360
b = 5p

5p - p = 360
4p = 360
p = 360/4
p = 90 <== Pete's deli

b = 5p
b = 5(90)
b = 450 <== Bill's Roast Beef

Answer:

5y-y =360

4y =360

y= 90 sandwiches by Pete's deli

x= 5(90) = 450 sandwiches by Bills Roast Beef

Step-by-step explanation:

Three counters are used for a board game.If the counters are tossed,how many ways can at least one counter with Side A occur?

Answers

We use the equation for repeated trials written below:

Probability = n!/r!(n-r)! * p^(n-r) * q^r

The p is the probability of getting a side A in one toss. Since a counter has only two side, p = 0.5. The q is the probability of not getting side A in one toss, which is also q = 0.5. Now, r is the number of success per n trials. There are 3 tosses so, n=3. The question is getting "at least 1" counter. So, r=1, r=2 and r=3.

Probability for r=1: 3!/1!(3-1)! * (0.5)^(3-1) * (0.5)^1= 0.375
Probability for r=2: 3!/2!(3-2)! * (0.5)^(3-2) * (0.5)^2= 0.375
Probability for r=1: 3!/3!(3-3)! * (0.5)^(3-3) * (0.5)^3= 0.125

Total probability = 0.375 + 0.375 + 0.125 = 0.875

the length of the hypotenuse is:

6.
12.
36.
[tex]6 \sqrt{3[/tex]

Answers

cos 60° = 1/2
1/2 = 6/x
1/2x=6
x = 6X 2 = 12
The length of the hypothenuse is 12

A figure has a vertex at (5, 2). If the figure has line symmetry about the y-axis, what are the coordinates of another vertex of the figure?

Answers

The answer will be (-5, 2)

Answer:

[tex](-5,2)[/tex]

Step-by-step explanation:

We have been given that a figure has a vertex at (5,2). The figure has line symmetry about the y-axis.

We know that if a figure is symmetric about y-axis, then its x-coordinate changes to opposite sign and y-coordinate remains same.

We can see that x-coordinate of our given point is 5, so x-coordinate of another vertex of the figure would be -5.

Therefore, the point [tex](-5,2)[/tex] is symmetric about y-axis for our given point.

5. Simplify (15x2 – 24x + 9) ÷ (3x – 3) = ?

Answers

The likelihood is that because we've been told to divide the quadratic by a linear expression, it may perfectly factorize and the linear expression is, in fact, one of the two factors so we can use it to find the other factor by inspection:
3x would have to multiply by 5x to get the 15x² term in the quadratic.
-3 would have to multiply by -3 to get the 9 term in the quadratic.
The second factor would, therefore, be (5x - 3) if the linear divisor is actually a factor. In this case, it is, which we can confirm by expanding.
15x² - 24x + 9 = (3x - 3)(5x - 3)
So:
(15x2 – 24x + 9) ÷ (3x – 3) = 5x - 3

A total of 504 tickets were sold for the school play. They were either adult tickets or student tickets. There were 54 more student tickets sold than adult tickets. How many adult tickets were sold?

Answers

a + s = 504
s = a + 54

a + (a + 54) = 504
2a + 54 = 504
2a = 504 - 54
2a = 450
a = 450/2
a = 225 <=== adults

a + s = 504
225 + s = 504
s = 504 - 225
s = 279 <=== students

Final answer:

Using algebra, we find that 225 adult tickets were sold out of a total of 504 tickets.

Explanation:

Let's denote the number of adult tickets as x. Since there were 54 more student tickets sold than adult tickets, we can represent the number of student tickets as x + 54. The total number of tickets sold is 504, so we set up the equation x + (x + 54) = 504.

Combining like terms, we get 2x + 54 = 504. Subtracting 54 from both sides gives us 2x = 450. Finally, dividing both sides by 2 gives us x = 225.

Therefore, 225 adult tickets were sold.

Learn more about Solving Equations here:

https://brainly.com/question/19297665

#SPJ2

How many millimeters are there in 5 meters?

Answers

1 meter = 1000 mm

so 5 meters = 5 x 1000 = 5,000 millimeters

There are 5000 milimeters in 5 meters because the prefix milli stands for 1000.

A marina is in the shape of a coordinate grid. Boat A is docked at (4.2, −2) and Boat B is docked at (−5.2, −2). The boats are ____ units apart. A) 6.2 B) 7.2 C) 9.4 D) 13.4

Answers

The distance between any two points is:

d^2=(x2-x1)^2+(y2-y1)^2

d^2=(4.2--5.2)^2+(-2--2)^2

d^2=(9.4)^2

d=9.4

Answer:

Your answer will be D.

Step-by-step explanation:

I did it on the test and got it correct.

In how many different ways can you make exactly 0.75 using only nickles dimes and quarters if you have at least one of each coin?

Answers

There are 18 different ways to make 75 cents

18 different ways to make 75 cents

A company made 4 million in the second quarter this is 1/3 more then it made in the first quarter and 4/5 of what it made in the third quarter how much did the company make in all 3/4 combined

Answers

In this problem, you have to find the total profit the company made in the three quarters which makes up 3/4 of the whole. In the second quarter, the profit is 4 million. Let x be the profit in the first quarter. Following the description,

4 = (1+1/3)x
x = 3 million

Thus, the second quarter made 5.33 million profit.

For the third quarter, let's assign it to the y variable. Following the description,

4 = (4/5)(y)
y = 5 million

Thus, the total profit is 4 + 3 + 5 = 12 million

A cold front moved in last weekend. In eight hours overnight, the temperature outside dropped from 14 degrees to -10. What was the average temperature change for each hour ?

Answers

[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------\\\\ \begin{cases} x_1=0\\ x_2=8 \end{cases}\implies \cfrac{f(8)-f(0)}{8-0}\implies \cfrac{14-(-10)}{8-0}\implies \cfrac{14+10}{8}\implies \cfrac{3^o}{1hr}[/tex]

Other Questions

Which of the following events during the 1600s and 1700s led to the development of slavery in the Caribbean? the answers are A. 15B. 14C. 16D. 19 which statement below about islam is correct?a. islam recognizes muhammed, abraham, and jesus as sons of godb. islam recognizes ali as the most important religious leaderc. islam considers jesus of nazareth a prophet but not a godd. islam considers shiite leaders the true heirs to muhammed whats the property in this equation 6 + 3= 3 +6 Mishas family bought a large cattle farm. The number of acres of the cattle farm is the cube of the acres they used to own plus 10 acres. If a represents the number of acres the family used to own, which expression represents the number of acres they own now? What evidence can you find to support the conclusion that classical Chinese political philosophy perceived the state as an extended family? a speeding car traveling north at 80mph passes the tramway intersection when the police begin pursuit. The police start 6 miles south of tramway traveling at 100mph. How many miles north of tramway will they be when they catch up with the speeding car? The following is a complex sentence: Even though April began eating more fruits and vegetables, she decided to continue drinking soft drinks. Which of the following is true? On a coordinate grid, the coordinates of vertices P and Q for Polygon PQRS are P(3, 2) and Q(3, 2). What is the length of Side PQ of the polygon? A research paper promoting the use if solar energy is A. An argumentative paperB. An analytical paperC. A personal paper D. A news article But a caged bird stands on the grave of dreams his shadow shouts on a nightmare scream his wings are clipped and his feet are tied so he opens his throat to sing.How does the poet develop a theme of freedom in these lines?through the metaphor of singingthrough the sensory detail of dreamsthrough the imagery of tied feetthrough the symbol of the caged bird Select the sentence that uses the semicolon correctly to separate independent clauses. A. The university student center opened for only two hours, clearly; there must have been some emergency. B. The university student center opened for only two hours. Clearly; there must have been some emergency. C. The university student center; opened for only two hours. Clearly, there must have been some emergency. D. The university student center opened for only two hours; clearly, there must have been some emergency Fill in the blank in the following sentence with the appropriate verb form below. Anita y yo ________ altas, inteligentes, y trabajadoras. A.somos B.estamos C.estn D.son Bret is starting a business selling handmade necklaces. He has decided to invest and initial amount of $387 for advertising and materials cost seven dollars for each necklace he makes. Bret can sell his creations for $10 per necklace.once he makes and sells a certain number of necklaces he will break even with identical expenses and sales. How many necklaces would that take? What would the total expenses and sales be then? Given the parent function of f(x) = x3, what is the value of k in the translated graph of f(x h) + k? Which hallucinogen may lead to feelings of paranoia and blind rage, sometimes leading to bizarre or violent behavior?? What is the range of the function y=2sin x Due mainly to __________, older men are much more likely to be living with their spouse than are older women. Suppose that a particular artillery piece has a range r = 8320 yards . find its range in miles. use the facts that 1mile=5280ft and 3ft=1yard. the discriminant of a quadratic equation is negative. one solution is 2+3i. what is the other solution? Steam Workshop Downloader