Betty received $ 500,000 from a life insurance policy to be distributed to her as an annuity certain in 10 equal annual installments with the first payment made immediately. On the day she receives her third payment, she is offered a monthly perpetuity of X in lieu of the future annual payments. The first payment will be made in exactly one month. The effective annual rate of interest is 8 %. Determine the value of X.​

Answers

Answer 1

9514 1404 393

Answer:

annual payment: $68,995.13monthly payment in perpetuity: X = $2394.76

Step-by-step explanation:

a) For payments made at the beginning of the period, the annuity is called an "annuity due." The formula in the first attachment tells how to compute the payment for a given present value ($500,000), number of periods (N=10), and interest rate (i=0.08).

  pmt = $500,000/(1 +(1 -(1 +i)^(-N+1))/i) = $500,000/(1 +(1 -(1.08^-9))/.08)

  pmt ≈ $68,995.13 . . . . annual payment

__

b) After the first payment, the account balance is ...

  $500,000 -68,995.13 = $431,004.87

After subsequent payments, the account balance will be ...

  $431,004.87×1.08 -68,995.13 = $396,490.13 . . . after 2nd payment

  $396,490.13×1.08 -68,995.13 = $359,214.21 . . . after 3rd payment

The payment amount that can be made in perpetuity is the amount of the monthly interest on this balance:

  X = $359,214.21 × (0.08/12) = $2394.76

Betty Received $ 500,000 From A Life Insurance Policy To Be Distributed To Her As An Annuity Certain

Related Questions

Complete the sentence that explains why Write an Equation is a reasonable strategy for solving this problem. Because the answer may be _________ the numbers in the problem.

Answers

Answer:

4 e

Step-by-step explanation:

dz6dxrx xrrx6 xz33x4xr4x xrx

PLS
Write the equation of the piecewise function that is represented by its graph.

IS IT A, B, C, OR D

Answers

9514 1404 393

Answer:

  a) domain bounds are -1 ≤ x ≤ 1, x > 1

Step-by-step explanation:

In considering the definition of any piecewise function, the domain descriptions in the function definition must match the pieces shown in the graph.

Here, the right segment has no upper bound, so x > 1 is an appropriate description of its domain.

The left segment has the points at x=-1 and x=1 included, so the appropriate domain description for that is -1 ≤ x ≤ 1.

The one answer choice that combines these domain descriptions is ...

  [tex]\displaystyle f(x)=\begin{cases}x^2,&\text{if }-\!1\le x\le1\\\sqrt{x},&\text{if }x>1\end{cases}[/tex]

If 4 gallons of gasoline cost $13.76, how much will 11 gallons of gasoline cost?

Answers

Answer:

x=37.84

Step-by-step explanation:

We can write a ratio to solve

4 gallons        11 gallons

--------------- = ----------------

13.76              x dollars

Using cross products

4x = 11*13.76

4x=151.36

Divide by 4

4x/4 = 151.36/4

x=37.84

Lost-time accidents occur in a company at a mean rate of 0.8 per day. What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2

Answers

Answer:

0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.

Step-by-step explanation:

We have the mean during the interval, which means that the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Lost-time accidents occur in a company at a mean rate of 0.8 per day.

This means that [tex]\mu = 0.8n[/tex], in which n is the number of days.

10 days:

This means that [tex]n = 10, \mu = 0.8(10) = 8[/tex]

What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2?

This is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-8}*8^{0}}{(0)!} = 0.00034[/tex]

[tex]P(X = 1) = \frac{e^{-8}*8^{1}}{(1)!} = 0.00268[/tex]

[tex]P(X = 2) = \frac{e^{-8}*8^{2}}{(2)!} = 0.01073[/tex]

So

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00034 + 0.00268 + 0.01073 = 0.01375[/tex]

0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.

Ethan buys a video game on sale. If the video game usually costs $60, and it was on sale for 20% off, how much did Ethan pay? Round to the nearest whole dollar.

Answers

Ethan will pay $31.99 with the discount.

How? This is the answer because:

If 39.99 is 100%, and you are trying to find 20%...

1. you need to set it up as a ratio (of course, you do not need to do this, but it is easier for me to do it this way)

2. the ratio will look like this: 39.99/100% x/20%

3. all we need to do from here is to cross multiply!

4 39.99 x

---------- = ----------

100 20

-price is on the top and percent on the bottom

-you would now do 39.99 times 20

-then divide by 100

5. once you have 20% of 39.99, you need to subtract that answer from the total

6. 39.99 - 7.998 = 31.992 (you need to round to the nearest hundredth)

Hope this helps <3

Rate of change or rate of change

A farmer has 80 feet of wire mesh to surround a rectangular pen.
A) Express the area A of the pen as a function of x, also draw the figure of A indicating the admissible values ​​of x for this problem.
B) What are the dimensions of the maximum area pen?

Answers

Answer:

Step-by-step explanation:

A). Let the dimensions of the rectangular pen are,

Length = l

Width = x

Since, farmer has the wire measuring 80 feet to surround the the pen.

Perimeter of the pen = 80 feet

2(l + x) = 80

l + x = 40

l = 40 - x ------(1)

Area of the rectangular pen = Length × width

                                               = lx

By substituting the value of l from equation (1),

Area (A) of the pen will be modeled by the expression,

A = (40 - x)

A = 40x - x²

B). For maximum area of the pen,

Derivative of the area = 0

[tex]\frac{d}{dx}(A)=0[/tex]

[tex]\frac{d}{dx}(A)=\frac{d}{dx}(40x-x^2)[/tex]

         = 40 - 2x

And (40 - 2x) = 0

x = 20

Therefore, width of the pen = 20 feet

And length of the pen = 40 - 20

                                     = 20 feet

Dimensions of the pen should be 20 feet by 20 feet.

Hari earns Rs 4300 per month. He spends 80% from his income. How much amount does he save in a year? ​

Answers

Answer:

Hari saves $ 10,320 in a year.

Step-by-step explanation:

Given that Hari earns $ 4300 per month, and he spends 80% from his income, to determine how much amount does he save in a year, the following calculation must be performed:

100 - 80 = 20

4300 x 0.20 x 12 = X

860 x 12 = X

10320 = X

Therefore, Hari saves $ 10,320 in a year.

If (-3)^-5 = 1/x, what is the value of x?

Answers

Answer:

-243

Step-by-step explanation:

(-3) (-3) (-3) (-3) (-3) = - 243

[tex]\frac{1}{-243 }[/tex]

Solve 8x + c = k for x

Answers

Answer:

x = 1/8(k-c)

Step-by-step explanation:

8x + c = k

Subtract c from each side

8x +c-c = k-c

8x = k-c

Divide each side by 8

8x/8 = (k-c)/8

x = 1/8(k-c)

Answer:

x-1/8(k-c)

Step-by-step explanation:

A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 47 states. What is the probability that she selects the route of three specific​ capitals?

Answers

Answer:

1 / 97290

Step-by-step explanation:

The number of ways of selecting 3 specific route capitals from 47 states can be obtained thus :

Probability = required outcome / Total possible outcomes

Total possible outcomes = 47P3

Recall :

nPr = n! / (n-r)!

47P3 = 47! / (47-3)! = 47! / 44! = 97290

Hence, probability of selecting route if 3 specific capitals is = 1 / 97290

Describe the system of equations
How many solutions does this system have.

Answers

Answer:

Step-by-step explanation:

One solution, at the point of intersection, (3,3)

You wish to create a 5 digit number from all digits; 0 1 2 3 4 5 6 7 8 9
Repetition is not allowed
* 0 cannot be first as it does not count as a place value if it is first. Ie. 027 is a 2 digit number

How many even numbers can you have?

Answers

Answer:

10234

Step-by-step explanation:

one is the smallest number so its first

and then you can place zero

after that just place the second smallest number

and so on

Find the sum of the geometric series given a1=−2, r=2, and n=8.
A. -510
B. -489
C. -478
D. 2

Answers

Answer:

A. -510

Step-by-step explanation:

We are given the variable values:

a = -2r = 2n = 8

Geometric series formula:

[tex]s = \frac{a( {r}^{n} \times - 1) }{r - 1} [/tex]

Plugging in values we have:

[tex]s = \frac{ - 2( {2}^{8} - 1) }{2 - 1} [/tex]

Simplifying the equation we are left with:

[tex] \frac{ - 2(255)}{1} = - 510[/tex]

I need help ASAP please no links

Answers

Answer: D' = (1, -1)

Step-by-step explanation:

When dilating by a 1/2 you take a point and divide the x and y of the point in half. So D before is (2,-2) and then divide that by a 1/2, which gives us our answer (1, -1).

Simplify
x * x^5 / x^2 * x

Answers

it’s x^3, i guess hope this helps

How do I figure this question out

Answers

Answer:

Orthocenter would be in the middle of the shape.

Step-by-step explanation:

B.

A graph of 2 functions is shown below. graph of function f of x equals negative 11 by 3 multiplied by x plus 11 by 3 and graph of function g of x equals x cubed plus 2 multiplied by x squared minus x minus 2 Which of the following is a solution for f(x) = g(x)? (2 points) x = −2 x = 1 x = 0 x = −1

Answers

9514 1404 393

Answer:

  (b)  x = 1

Step-by-step explanation:

A graph shows the solution to f(x) = g(x) is x = 1.

__

We want to solve ...

  g(x) -f(x) = 0

  x^3 +2x^2 -x -2 -(-11/3x +11/3) = 0

  x^2(x +2) -1(x +2) +11/3(x -1) = 0 . . . . . factor first terms by grouping

  (x^2 -1)(x +2) +11/3(x -1) = 0 . . . . .  . the difference of squares can be factored

  (x -1)(x +1)(x +2) +(x -1)(11/3) = 0 . . . . we see (x-1) is a common factor

  (x -1)(x^2 +3x +2 +11/3) = 0

The zero product rule tells us this will be true when x-1 = 0, or x = 1.

__

The discriminant of the quadratic factor is ...

  b^2 -4ac = 3^2 -4(1)(17/3) = 9 -68/3 = -41/3

This is less than zero, so any other solutions are complex.

When a fridge is imported, a customs value of 10% must be paid for its value. If the value of the fridge after paying the customs value is rs. 55,000/-. What is the value before paying customs duty?

Answers

Answer:

55000×100/90

61,111.111

Zoe has 4 pounds of strawberries to make pies. How many ounces of strawberries Is this?
64 oz.
60 oz.
68 oz.
72 oz.

Answers

Answer: 64 ounces (choice A)

Work Shown:

1 pound = 16 ounces

4*(1 pound) = 4*(16 ounces)

4 pounds = 64 ounces

Game consoles: A poll surveyed 341 video gamers, and 95 of them said that they prefer playing games on a console, rather than a computer or hand-held device. An executive at a game console manufacturing company claims that the proportion of gamers who prefer consoles differs from . Does the poll provide convincing evidence that the claim is true

Answers

Answer:

proportion of gamers who prefer console does not differ from 29%

Step-by-step explanation:

Given :

n = 341 ; x = 95 ; Phat = x / n = 95/341 = 0.279

H0 : p = 0.29

H1 : p ≠ 0.29

The test statistic :

T = (phat - p) ÷ √[(p(1 - p)) / n]

T = (0.279 - 0.29) ÷ √[(0.29(1 - 0.29)) / 341]

T = (-0.011) ÷ √[(0.29 * 0.71) / 341]

T = -0.011 ÷ 0.0245725

T = - 0.4476532

Using the Pvalue calculator from test statistic score :

df = 341 - 1 = 340

Pvalue(-0.447, 340) ; two tailed = 0.654

At α = 0.01

Pvalue > α ; We fail to reject the null and conclude that there is no significant evidence that proportion of gamers who prefer console differs from 29%

A rope is 56 in length and must be cut into two pieces. If one piece must be six times as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary.

Answers

Answer:

48, 6

Step-by-step explanation:

The ratio of the pieces is 6 to 1

Add them together to get the total

6+1 = 7

Divide the total length by 7

56/7 = 8

Multiply the ratios by 8

6*8 = 48

 1*8 = 6

The peices are 48 and 6

Write the point-slope form of an equation of the line through the points (-2, 6) and (3,-2).

Answers

Answer:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

Step-by-step explanation:

Hi there!

Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope

1) Determine the slope

[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-2, 6) and (3,-2):

[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]

Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

2) Plug in a point [tex](x_1,y_1)[/tex]

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

I hope this helps!


The population, P(t), in millions, of a country, in year t, is given by the formula P(t) = 24 + 0.4t. What are the values of the population for t = 10, 20,
and 30?

Answers

Answer:

B. 28, 32, 36 millions

Step-by-step explanation:

Given:

P(t) = 24 + 0.4t

Where,

P(t) = population in millions

t = number of years

✔️Value of the population when t = 10:

Plug in t = 10 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(10)

P(t) = 24 + 4

P(t) = 28 million

✔️Value of the population when t = 20:

Plug in t = 20 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(20)

P(t) = 24 + 8

P(t) = 32 million

✔️Value of the population when t = 30:

Plug in t = 30 into P(t) = 24 + 0.4t

P(t) = 24 + 0.4(30)

P(t) = 24 + 12

P(t) = 36 million

4 people take 3 hours to paint a fence assume that all people paint at the same rate How long would it take one of these people to paint the same fence?​

Answers

Answer:

12

Step-by-step explanation:

Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height 5h. Use cylindrical shells to compute the volume V of a napkin ring of height 5 h created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h .

Answers

Answer:

V = 1/6 π ( 5h)^3

Step-by-step explanation:

Height of napkin rings = 5h

Compute the volume V of a napkin ring

let a = 5

radius = r

express answer in terms of h

attached below is the detailed solution

Round each of the following numbers to four significant figures and express the result in standard exponential notation: (a) 102.53070, (b) 656.980, (c) 0.008543210, (d) 0.000257870, (e) -0.0357202

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Rounding each number to 4 significant figures and expressing in standard notation :

(a) 102.53070,

Since the number starts with a non-zero, the 4 digits are counted from the left ;

102.53070 = 102.5 (4 significant figures) = 1.025 * 10^2

(b) 656.980,

Since the number starts with a non-zero, the 4 digits are counted from the left ; the value after the 4th significant value is greater than 5, it is rounded to 1 and added to the significant figure.

656.980 = 657.0 (4 significant figures) = 6.57 * 10^2

(c) 0.008543210,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

0.008543210 = 0.008543 (4 significant figures) = 8.543 * 10^-3

(d) 0.000257870,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

0.000257870 = 0.0002579 (4 significant figures) = 2.579 * 10^-4

(e) -0.0357202,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

-0.0357202 = - 0.03572 (4 significant figures) = - 3.572* 10^-2

Reasoning by induction

Question 1 options:

1)

develops a general conclusion based on observations of cases.


2)

develops a general conclusion based on given information.


3)

starts with assumptions that are known to be valid to draw another new truths.


4)

uses patterns to create logical proofs.

Answers

Answer:

1because the occasion of cases

Which expression is equivalent to 9+y+y+3

Answers

Answer:

b

Step-by-step explanation:

You only need to add the real numbers and the ys.

Answer:

12 + 2y

Step-by-step explanation:

9+y+y+3

Combine like terms

9+3   + y+y

12 + 2y

Riley wants to make 100ml of 25% saline but only has access to 12% and 38% saline mixtures. x= 12% y=38%

Answers

Answer:

x = 50

y = 50

Step-by-step explanation:

[tex]\begin{bmatrix}x+y=100\\ 0.12x+0.38y=25\end{bmatrix}[/tex]

.12(100-y) + .38y = 25

x = 50

y = 50

Please helppppppppp!!!!

Answers

Terminal point for 4π/3

(cos4π/3 ,sin4π/3)

{cos(π+π/3) ,sin(π+π/3)}= (-cosπ/3 ,-sinπ/3)

or ,(- 1/2, -√3/2)

OPTION C

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patron at a resort ranch took part in a supervised horseback trail ride. Prior to the ride, the patron executed a valid release that enumerated the inherent risks of horseback riding and, by its terms, relieved the resort from liability from any loss, damage, or injury to the guest's person or property suffered during the ride attributable to the negligence of the ranch or its employees. The patron was injured by a fall from the horse. The horse reared in response to negligent behavior of another rider. The patron filed suit against the ranch and the other rider for damages resulting from his injuries that totaled $400,000. At trial, it was determined that the ranch was 75 percent at fault for the patron's injuries due to its selection and training of the horse and that the other rider was 25 percent at fault. The applicable jurisdiction recognizes the validity of such releases and has enacted both a modified comparative negligence statute and pure several liability statute. How much can the patron recover from the other rider View Policies Current Attempt in Progress In January, Dieker Company requisitions raw materials for production as follows: Job 1 $910, Job 2 $1,700, Job 3 $800, and general factory use $650. Prepare a summary journal entry to record raw materials used. (Credit account titles are automatically indented when amount is entered. Do not indent manually.) Date Account Titles and Explanation Debit Credit Jan. 31 enter an account title for the journal entry on January 31 enter a debit amount enter a credit amount enter an account title for the journal entry on January 31 enter a debit amount enter a credit amount enter an account title for the journal entry on January 31 Which table has a constant of proportionality between y and x equal to 0.3? A sporting goods manufacturer budgets production of 45,000 pairs of ski boots in the first quarter and 30,000 pairs in the second quarter of the upcoming year. 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According to Turner and Wilson (2018), Information Literacy consists oftasks EXCEPT...A applying previous knowledge.C. finding appropriate informationB. determining information need.2. Outlining your problem, developing research questions, selecting keywords adeveloping concept charts are activities during...D. using information ethicallyA. communicating information.B. determining information need.C. evaluating search results.D. finding appropriate resources,3. Asking questions such as what, why, where and how is an effective way toA. craft your research questions.B. develop good keywordsC. find good informationD. understand your topic,4. In asking "what" questions, you intend to find...A. answers and solutions. 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