Victor Vogel is 27 years old and currently earns $65,000 per year. He recently picked a winning number in the Wisconsin lottery. After income taxes he took home $1,000,000. Victor put the entire amount into an account earning 5% per year, compounded annually. He wants to quit his job, maintain his current lifestyle and withdraw enough at the beginning of each year to replace his salary. At this rate, how long will the winnings last?

Got the explanation from classmates
N=??? I/Y=5 PV=1000000 PMT=-65000 FV=0
It will last 27 years.

Answer:

3/8

Step-by-step explanation:

Step 1: Find common denominators

1/2 = 4/8

2/4 = 4/8

Step 2: Evaluate

4/8 + 4/8 - 5/8

8/8 - 5/8

3/8

Alternatively, you can just plug this into a calc to evaluate and get your answer.

Answer:

3/8

Step-by-step explanation:

Look at the denominator:

2, 4, 8. The LCM (Lowest Common Multiple) is 8.

So this equation becomes

4/8+4/8-5/8=3/8

Answer:

D

Step-by-step explanation:

(x - 1)² = (x - 1)(x - 1)

x² - x- x + 1 = x² - 2x + 1

Answer:

a) 4.8

b) 2.96

c) 4.4

d) 1.44

e) 3.76

Step-by-step explanation:

What we will do is solve point by point, knowing the following:

Fx (x) = P (X <= x) = (x - 1) / 4

a) P (X <-a) = 0.95

Fx (a) = 0.95

(a -1) / 4 = 0.95

a = 1 + 0.95 * 4

a = 4.8

b) P (X <a) = 0.49

Fx (a) = 0.49

(a -1) / 4 = 0.49

a = 1 + 0.49 * 4

a = 2.96

c) P (X <a) = 0.85

Fx (a) = 0.85

(a -1) / 4 = 0.55

a = 1 + 0.85 * 4

a = 4.4

d) P (X> a) = 0.89

P (X <a) = 1 - 0.89 = 0.11

Fx (a) = 0.11

(a -1) / 4 = 0.11

a = 1 + 0.11 * 4

a = 1.44

e) P (X> a) = 0.31

P (X <a) = 1 - 0.31 = 0.69

Fx (a) = 0.69

(a -1) / 4 = 0.69

a = 1 + 0.69 * 4

a = 3.76

Answer:

45 square units

Step-by-step explanation:

To figure out the area of a trapezoid, the formula is. A= (b1 + b2)h ÷2 . b1 is the top side which is 7 units and b2 is the bottom side which is 11 units. The height (h) is a vertical line going from the top to the bottom which is 5 units. All you need to do now is plug in those numbers and solve the equation.

Answer: 45 square units

Step-by-step explanation:

This shape can be broken down into two diffrent peices

The first peice is the rectangle

The second peice is the triangle

And both of these peices area's added together will yeild the total area

The rectangle is 7 units long and 5 units high, so it has an area of (7X5) = 35

The triangle is a little bit more complicated, it's formula is (BaseXHeight)/4

So all we need to do is plug in The base of the triangle = 4

And the Height of the trianlge = 5

So the triangles area is... (4X5)/2= 10

35+10=45 square units

Answer:

the photo shows the answer ^D^ hope this helps~

Step-by-step explanation:

+also included the correct sign for confirmation xD

Answer:

up answer is correct :)

Step-by-step explanation:

Answer:

a) 50S + 30C ≤ 800

b) 1) MAX = S + C

   2) Max = 0.03S + 0.05C

   3) Max = 6S + 5C

Step-by-step explanation:

Given:

Total space = 800 square feet

Each sofa = 50 square feet

Each chair = 30 square feet

At least 5 sofas and 5 chairs are to be displayed.

a) Write a mathematical model representing the store's constraints:

Let S denote number of sofas displayed and C denote number of chairs displayed.

The mathematical model will be:

50S + 30C ≤ 800

At least 5 sofas are to be dispayed: S ≥ 5

At least 5 chairs are to be displayed: C ≥ 5

b)

1) Maximize the total pieces of furniture displayed:

S + C = MAX

2) Maximize the total expected number of daily sales:

MAX = 0.03S + 0.05C

3) Maximize the total expected daily profit:

Given:

Profit on sofas = $200

Profit on chairs = $100

Max Expected daily profit =

Max = (200S * 0.03) + (100C * 0.05)

Max = 6S + 5C

Answer: h(t) = g(t) between 4 and 5 seconds

Step-by-step explanation:

h(t) = -16t² + 90t + 75

g(t) = 31 + 32.2t

[tex]\begin{array}{c|c|c|c|c}\qquad&\underline{\quad t=2\quad }&\underline{\quad t=3\quad}&\underline{\quad t=4\quad }&\underline{\quad t=5\quad }\\h(t)&191&201&179&125\\g(t)&95.4&127.6&159.8&192\end{array}\right][/tex]

Notice that g(t) is increasing from t=2 to t=5, while h(t) is increasing from t=2 to t=3 and then decreasing.  

At t=4, h(t) > g(t)

At t = 5, g(t) > h(t)

therefore, the two lines must intersect at a point between t=4 and t=5.

You can graph this to verify the answer.

Answer:

Step-by-step explanation:

(x+yi)+4+6i=7-2i

x+yi=7-2i-4-6i

x+yi=3-8i

equating real and imaginary parts

x=3,y=-8

B.

x+yi=5+9i+(-8+11i)

x+yi=5+9i-8-11i

x+yi=-3-2i

equating real ,and imaginary parts

x=-3

y=-2

The value of x  and y for equation A is

[tex]x=3, y=-8[/tex]

The value of x  and y for equation B is

[tex]x=-3 , y=20[/tex]

Given :

[tex](x + yi) + (4 + 6i) = 7 - 2i[/tex]

find the value of x  and y in the given equation

Lets open the parenthesis and combine like terms

Equate the real and imaginary part to solve for x  and y

[tex]\left(x+4\right)+\left(y+6\right)i=7-2i\\x+4=7\\x=3\\\\y+6=-2\\y=-2-6\\y=-8[/tex]

The value of x=3  and y=-8

Now we do the same with second equation

[tex](x + yi) - (-8 + 11i) = 5 + 9i\\\\x+8+yi-11i=5+9i\\\left(x+8\right)+\left(y-11\right)i=5+9i\\x+8=5\\x=-3\\\\y-11=9\\y=9+11\\y=20[/tex]

The value of x  and y is x=-3 and y=20

Learn more : brainly.com/question/18552411

Answer:

GCF - 16

Step-by-step explanation:

48 - 1, 2, 3, 4, 6, 8, 12, 16

32 - 1, 2, 4, 8, 16

Hope this helps! :)

Answer:

16

Step-by-step explanation:

48=3*16

32=2*16

Answer:

1.411764706

Step-by-step explanation:

24/17=1.411764706

Answer:

Step-by-step explanation:

C. 5x/4-2=3x/2-4

 5x/4 -2=6x/4-4

   +4       +4

5x/4+2=6x/4

-5x/4

2=x/4

*4

x=8

Answer:

your answer is C

Step-by-step explanation:

Answer:

  $36,450.46

Step-by-step explanation:

The amortization formula can be used to figure this. For quarterly payment A, the principal invested must be P for interest rate r and compounding n times per year for t years.

  A = P(r/n)/(1 -(1 +r/n)^(-nt))

  2300 = P(0.0045/4)/(1 -(1 +0.0045/4)^(-4·4))

  2300 = P·0.06309934

  P = 2300/0.06309934 = 36450.46

You need $36,450.46 in your account today so that you can withdraw $2300 quarterly for 4 years.

Answer:

[tex]\frac{6}{5} =\frac{x}{12}[/tex]

Step-by-step explanation:

Write a proportion in the form:

Height/side= height/side

The side lengths are 5 and 12.

The height (of the 5 side) is 6.

The proportion can be written as:

[tex]\frac{6}{5} =\frac{x}{12}[/tex]

Answer:

Step-by-step explanation:

Given

the sample space for box A

green balls = 5

red balls= 7

sample size= 5+7= 12

the sample space for box B

green balls = 3

red balls= 3

yellow balls= 6

sample size= 3+3+6= 12

The probability of drawing a green ball from box A= 5/12

The probability of drawing a green ball from box B= 3/12= 1/4

Therefore the probability of picking a green ball from either of the boxes at random is =[tex]=\frac{5}{12} *\frac{1}{4}[/tex][tex]=\frac{5}{48}[/tex]

Hi !!

For f(x) = 3/x + 4 , B is correct.

• f(-3) = 3/(-3) + 4

f(-3) = - 1 + 4

f(-3) = 3

• f(-2) = 3/(-2) + 4

f(-2) = -1,5 + 4

f(-2) = 2,5

• f(1) = 3/(1) + 4

f(1) = 3 + 4

f(1) = 7

• f(2) = 3/(2) + 4

f(2) = 1,5 + 4

f(2) = 5,5

• f(3) = 3/(3) + 4

f(3) = 1 + 4

f(3) = 5

Answer:

A

Step-by-step explanation:

I did the test and it is the only one that makes sense

Answer:

a

Step-by-step explanation:

Answer:

  $1170

Step-by-step explanation:

Let x and y represent the numbers of economy and deluxe seats sold. The constraints are ...

And the objective function we want to maximize is ...

  p = 40x +35y

__

I find it convenient to graph the equations and locate the objective function line as far from the origin as possible. The graph is shown, along with the solution.

Here, it's even simpler than that. The profit per seat is the greatest for economy seats, so Roland's should sell as many of those as they can. The only limit is that 6 seats must be deluxe. The remaining 30-6=24 can be economy. So, the profit will be maximized for ...

  24 economy seats and 6 deluxe seats

The corresponding profit will be ...

  24(40) +6(35) = 1170

The maximum profit from one tour is $1170.

Answer:

y ≤ 2/5x - .5

Step-by-step explanation:

Well it is a solid line with it shaded down meaning the inequality starts with

y ≤,

And by look at the y axis we can tell that the line crosses the y axis at -.5 which is the y intercept.

And by looking at the line we can tell the slope is 2/5.

Hence, the inequality is y ≤ 2/5x - .5

Answer:

There are about 3.281 * 3.281 = 10.764 square feet in one square meter. Therefore, 22.5 square feet is 22.5 / 10.764 = 2.09 square meters.

Answer:

938 feet

Step-by-step explanation:

b/c every angle of a rectangle is 90° u can u Pythagorean theroem to solve the question

a*a+ b*b=c*c

900*900+264*264=c*c

c=√879,696

c=938feet

Answer:

938 feet

Step-by-step explanation:

Well to solve this we need to use the Pythagorean Theorem,

[tex]a^2 + b^2 = c^2[/tex].

So we have a and b which are 900 and 264,

and we need to find c or the walking distance.

So we plug in 900 and 264 for a and b.

[tex](900)^2 + (264)^2 = c^2[/tex]

So, 900*900 = 810,000

264 * 264 = 69696

810000 + 69696 = 879696

So now we have,

879696 = c^2

To get the c by itself we do,

[tex]\sqrt{879696} = \sqrt{c}[/tex]

= c = 937.921105424

c = 938 rounded to the nearest foot

Thus,

the solution is 938.

Hope this helps :)

Answer:

The lower bound of the confidence interval is 0.6922.

Step-by-step explanation:

We have to calculate a 94% confidence interval for the proportion.

The sample proportion is p=0.7167.

[tex]p=X/n=860/1200=0.7167[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.7167*0.2833}{1200}}\\\\\\ \sigma_p=\sqrt{0.000169}=0.013[/tex]

The critical z-value for a 94% confidence interval is z=1.8808.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.8808 \cdot 0.013=0.0245[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.7167-0.0245=0.6922\\\\UL=p+z \cdot \sigma_p = 0.7167+0.0245=0.7412[/tex]

The 94% confidence interval for the population proportion is (0.6922, 0.7412).

Answer:

A.

Step-by-step explanation:

From Step 3 to Step 4, Simon added -42 to both sides.

This is the addition property of equality: as long as you add the same thing to both sides, the equation remains equal.

A.

Answer: 200 ft²

Step-by-step explanation:

The area of a rectangle is length times width

So, simply do 25 * 8 = 200

Hey there! :)

Answer:

A = 200 ft².

Step-by-step explanation:

Use the formula A = l × w to determine the area of a rectangle:

A = 25 × 8

Multiply:

A = 200 ft².

Answer:

B. 4

Step-by-step explanation:

We are looking for the coefficient of the term x⁵. When we see it in the polynomial as 4x⁵, our coefficient and answer would then be 4.

Answer:

A) 0.1855

B) 0.0010376

C) 0.0001297

D) 0.006363

E) 0.000007629

Step-by-step explanation:

In calculation of a probability, we normally take the ratio of the number of ways to meet a certain condition (i.e. the numerator) divided by the number of ways to pick from a pool (i.e. the denominator).

So what are the number of ways the flip of a coin 17 times can come out?

A coin has a head and tail, so each toss will have two possible results. If we toss once, we have 2 possible results. If we toss, twice we have 2² = 4 possible results.

If we toss thrice, we have 2³ = 8 possible results, etc.

Thus, for 17 tosses, we will have 2^(17) = 131072 possible results.

A) To achieve the probability of getting 9 heads, we will use combination formula;

C(n, k) = n! / (k!(n - k)!)

In this case, n = 17 and k = 9

So,

P(9 heads) = 17! / (9!(17 - 9)!) = 24310

Thus,

P(9 heads in 17 tosses of a fair coin) = 24310/131072 = 0.1855

B) Similar to A above;

P(2 heads) = 17! / (2!(17 - 2)!) = 136

Thus,

P(2 heads in 17 tosses of a fair coin) = 136/131072 = 0.0010376

C) Similar to A above;

P(1 tail) = 17! / (1!(17 - 1)!) = 17

Thus,

P(1 tail in 17 tosses of a fair coin) = 17/131072 = 0.0001297

D) probability of getting 14 or more heads?

Since, there are 17 tosses, this will be;

P(14 or more heads in 17 tosses) = P(14 heads in 17 tosses) + P(15 heads in 17 tosses) + P(16 heads in 17 tosses) + P(17 heads in 17 tosses)

P(14 heads) = 17! / (14!(17 - 14)!) = 680

P(15 heads) = 17! / (15!(17 - 15)!) = 136

P(16 heads) = 17! / (16!(17 - 16)!) = 17

P(17 heads) = 17! / (1!(17 - 17)!) = 1

Thus;

P(14 heads in 17 tosses) = 680/131072 = 0.005188

P(15 heads in 17 tosses) = 136/131072 = 0.0010376

P(16 heads in 17 tosses) = 17/131072 = 0.0001297

P(1 head in 17 tosses) = 1/131072 = 0.00000763

P(14 or more heads in 17 tosses) = 0.005188 + 0.0010376 + 0.0001297 + 0.00000763 = 0.006363

E) Similar to A above;

P(17 tails) = 17! / (17!(17 - 17)!) = 1

Thus,

P(17 tails in 17 tosses of a fair coin) = 1/131072 = 0.000007629

Answer:

D. 564.44 cm^3

Step-by-step explanation:

V = (1/3)(pi)r^2h

V = (1/3)(3.14159)(7 cm)^2(11 cm)

V = 564.44 cm^3

Answer:

yes, (0,-2) is the answer when graphing this equation.

Step-by-step explanation:

Answer:

yes.

Step-by-step explanation:

Answer:

-.15 km/ minute * 60 minutes

-9 km

Step-by-step explanation:

The rate is -.15 km per minute

We have 60 minutes

distance = rate  times time

change in elevation is the same as the distance change

change in elevation = -.15 km/ minute * 60

   change in elevation =-9 km

Answer:

(0.15 km/min) * (60 min)

Step-by-step explanation:

We see that the plane descends 0.15 kilometres every minute over the span of 60 minutes.

Use the distance-rate-time formula: d = rt, where d is the distance, r is the rate, and t is the time.

Here, our rate is r = 0.15 km/min and our time is t = 60 minutes. Then the total change in elevation is:

d = rt

d = 0.15 * 60 = 9 km

Note that we disregard the negative sign from -0.15 km/min because the question is asking for the change in elevation. Change is never a negative value.

Hence, the expression will be: 0.15 * 60, which simplifies to 9 km.

~ an aesthetics lover

Step-by-step explanation:

he operation of sorting fractions in ascending order: 18/46, 28/41, 29/38, 29/44, 32/30 ... terms equivalents: 18/46=(2×3^2)/(2×23)=((2×3^2)÷2)/((2×23)÷2)=9/23; 28/41 already reduced to ... by the largest exponents: LCM (9, 28, 29)=2^2×3^2× 7×29=7308 Calculate LCM, the least ... /10 </13 </19

Answer:

A quadralateral is any shape that has 4 sides ...

Step-by-step explanation:

rectangle

square

rhombus

Answer: A quadrilateral is a two dimensional shape(closed) with four sides.

Step-by-step explanation: The sides do not have to be equal.

Square

Rectange

Trapazoid

Diamond

Any four sided shape. They will classify as a quadrilateral as long as two of the shapes are not the same.