Angelina wins money in a competition. She is given the choice as to how she is paid.
Choice 1: Get $1 the 1st day, 2$ the 2nd day, $4 the 3rd day, 8$ the 4th day, and so on
Choice 2: Get 1,000,000 today.
a) With which method of payment will angelina get more money?
c) After how many days will the money Angelina gets from Choice 1 be approximately $1, 000, 000?

Answers

Answer 1

Answer:

Choice 120 days

Step-by-step explanation:

You are being asked to compare the value of a growing infinite geometric series to a fixed constant. Such a series will always eventually have a sum that exceeds any given fixed constant.

__

a)

Angelina will get more money from the Choice 1 method of payment. The sequence of payments is a (growing) geometric sequence, so the payments and their sum will eventually exceed the alternative.

__

c)

For a first term of 1 and a common ratio of 2, the sum of n terms of the geometric series is given by ...

  Sn = a1×(r^n -1)/(r -1) . . . . . . . . . . series with first term a1, common ratio r

We want to find n such that ...

  Sn ≥ 1,000,000

  1 × (2^n -1)/(2 -1) ≥ 1,000,000

  2^n ≥ 1,000,001 . . . . add 1

  n ≥ log(1,000,001)/log(2) . . . . . take the base-2 logarithm

  n ≥ 19.93

The total Angelina receives from Choice 1 will exceed $1,000,000 after 20 days.


Related Questions

Given similar terms, solve for the missing variables (x)

Answers

Answer:

x=10

Step-by-step explanation:

the image above shows the work to solve the equation

the inverse of the function f(x)=-x+3

Answers

Answer: [tex]f^{-1}(x)=-x+3[/tex]

Step-by-step explanation:

To find the inverse of a function replace f(x) with x and replace the original x with y

[tex]f(x)=-x+3\\x=-y+3[/tex]

Now solve for y

[tex]x=-y+3[/tex]

First subtract 3 from both sides

[tex]x-3=-y+3-3\\x-3=-y[/tex]

Now divide both sides by -1 (this will make y positive)

[tex]\frac{x-3}{-1} =\frac{-y}{-1} \\-x+3=y[/tex]

Now replace y with the inverse of f(x), [tex]f^{-1}(x)[/tex]

The area of this figure.
square meters
10 m
2 m
12 m
7 m
4 m
4 m

Answers

Answer:

I believe it is 106 Square meters

Step-by-step explanation:

Easiest way to find area for these kind of shapes is to break them into smaller rectangles, this specific one can be broken 3 ways...

Right: 4m long, 7m tall

Top: 10 long, 5 tall *(12-7)*

Left: 4m long, 7m tall

*To find incomplete ones, you find clues in other sides, for instance the whole side was 12, the broken part was 7, therefor you just subtract 7 from 12, giving you 5 for the top.*

Then you just multiply...

4x7=28
4x7=28
10x5= 50

Now, you have the area for three individual smaller rectangles. So you simply add them together to get the whole shapes area...

28+28+50=106

Therefor, your answer should be 106 square meters- if I'm not mistaken.

Hope this helps, brainliest is appreciated if its right, trying to rank up :)

Have a great day! cx

~Mitsuna

Answer:

106

Step-by-step explanation:

Here's one way of finding the area:

Find the area of the entire outer rectangle. Then subtract the area of the samlle rectangle in the bottom middle.

A = LW - lw

A = (10 m)(12 m) - (2 m)(7 m)

A = 120 m² - 14 m²

A = 106 m²

Question on picture(how the question short bozo)

Answers

Answer: The correct answer is C.

Step-by-step explanation: C Shows multiple animals and shows plants. It also shows water which is needed in an ecosystem.

Hope this helps!

find the slope of the line that passes through the pints (2,7) and (2,6)

Answers

Answer:

Undefined Slope

Step-by-step explanation:

The points (2,6) and (2,7) are on the same vertical line of 2, which results in an undefined slope.

Answer:

m=undefined

Step-by-step explanation:

The formula to find the slope isn't very complicated. The formula is:

    y₂-y₁

m= --------

      x₂-x₁

You have the points (2,7) and (2,-6). In (2,7) 2 is your x and 7 is your y. Since (2,7) is your first coordinate set, we put 2 as our x₁ . We put 7 as our y₁ .

In (2,-6) 2 is your x and -6 is your y. Since (2,-6) is your second coordinate set, we put 2 as our x₂ . We put -6 as our y₂ .

Let's substitute all of these numbers in:

    -6-7       -13

m= -------  = -------

     2-2         0

So we have -13/0 .You would think that any number divided by                0 is 0, right?

                No. Any number divided by 0 is undefined.

                   

Therefore, you slope, m, would be:

m=undefined .

If 1/10 of a scarf is knit in 48 minutes.what fraction of a scarf is knit in 1 hour

Answers

Answer:

1/8

Step-by-step explanation:

i believe this is the answer

Write the word sentence as an equation.
5 is one-fourth of a number c. PLEASE HELP

Answers

1/4c=5 I think that’s the answer if not sorry

Select TRUE or FALSE for each of the statements below.



In hanger A, 2x + 5 = 16

In hanger B, y = 2400

In hanger C, 4z = 20.8 -4.4

in hanger D, w + 2/3 = 20/3 ÷ 2

Answers

Answer:

1 true

2 false

3 true

4 false

Step-by-step explanation:

How can we write the domain and range for a function that is not piece-wise such as y=x?​

Answers

Answer:

(−∞,∞)

Step-by-step explanation:

For every x value there is, there is an equivalent y value, thus there are infinite x and y values that satisfy this equation.

Hope this helps!!!

Can someone solve this?

Answers

Step-by-step explanation:

First box =25

Second Box = 0.25

If jamie completed 5 chores, about how much money did she earn?

Answers

Answer:

5(chore payment)

Step-by-step explanation:

since we dont know how much money the chore is worth it would be 5 times the money

What is the value of z?

Enter
your answer in the box.

Answers

Answer:

the value of z is 60 degree

4. Find the perimeter of the figure below. Use 3.14 for pi.
number answer.

Answers

Answer:

90.24 mm

Step-by-step explanation:

Circumference = 2πr

C = 2(3.14)(16)

C = 100.48 mm

Perimeter of the figure = 20 + 20 + 1/2 (circumference)

P = 40 + 1/2 (100.48)

P = 40 + 50.24

P = 90.24 mm

I hope this helps!

Two lines, A and B, are represented by equations given below: Line A: y = x − 2 Line B: y = 3x + 4 Which of the following shows the solution to the system of equations and explains why? (1 point) a (−3, −5), because the point does not lie on any axis b (−3, −5), because the point satisfies both equations c (−4, −8), because the point satisfies one of the equations d (−4, −8), because the point lies between the two axes

Answers

The solution to the system of equations is (-3, -5) because the point satisfies both equations

What is a linear function?

A linear function is in the form:

y = mx + b

Where m is the slope (rate of change) and b is the y intercept

Line A:

y = x − 2  (1)

Line B:

y = 3x + 4   (2)

Solving both equations simultaneously gives:

x = -3, y = -5

The solution to the system of equations is (-3, -5) because the point satisfies both equations

Find out more on linear function at: https://brainly.com/question/4025726

Use the graph of triangle JKL to answer a-b.

a.Reflect JKL over the x-axis. Record the coordinates of the original and new image below.

Pre Image: J:_____ K:_____
L: ______

Now Image: J:______ K:______

L:_______

b. Describe what happened to the x and y coordinates once they were reflected.

*ignore the erasing marks and the lines ^^

Answers

After reflection, the x-coordinates remains unchanged while the y-coordinates are negated.

Reflection of coordinates over the xy axis

The translation rule for reflecting the coordinate (x, y) over the x-axis is expressed as:

[tex](x, y) \rightarrow (x,-y)[/tex]

Given the following coordinates of the vertices from the figure J(-7, 7), K(-5, -2) and L(-2, 3)

If the coordinates ara reflected over the x-axis, the resulting coordinates will be  J(-7, -7), K(-5, 2), and L(-2, -3).

After reflection, the x-coordinates remains unchanged while the y-coordinates are negated.

Learn more on reflection here: https://brainly.com/question/26642069

A square is cut in half and the diagonal creating two equal triangles of each triangle has an area of 4.5 in.² what is the length in inches of the original square

Answers

8 Ft 9In i think dont kill me if its wrong

Find the value of X for these twi

Answers

Answer:

11: x=60   12:x=27

Step-by-step explanation:

For the first one, we know that all triangle angles add up to 180, so we take 180 and divide by 3 to get each of the angles and we get 60. For the second one, like I said earlier, all triangles add up to 180 so you add all the angles together and make them equal 180. You simplify and you get x=27

(also i changed my answer because I double checked it and it was wrong

Evaluate the expression 3^-2

Answers

Answer:

-9 is the answer for 3^-2

Originally, a department store bought a set of dishes at a cost of $57.68 and marked it up 125%. After a month, the set of dishes had not sold, so the store marked it down 50%. What was the discounted price?

Answers

Answer:

$64.89

Step-by-step explanation:

57.68 + 1.25 × 57.68

= 57.68 + 72.1

= 129.78

The original price was $129.78.

129.78 – 0.50 × 129.78

= 129.78 – 64.89

= 64.89

The discount price was $64.89.

The length and width of the park are measured in linear units. inches, miles, meters, etc the area is measured in square units. explain the reason for using square units for area of the park. (please hurry and make it not too long please )​

Answers

The area is measured in square units because it is the product of two units which gives square unit.

What is area?

Area is the amount of space occupied by a two dimensional shape or object.

The area of a rectangular park is gotten from the productiif the width and length, hence:

Area = length * width

The area is measured in square units because it is the product of two units which gives square unit.

Find out more on area at: https://brainly.com/question/25292087

All right answers = 20 points
Pls help

Answers

1. y= 5x -10
2. y= -5x + 10
3. y= -7x +4
4. y= 0x + 4
5. y= 9x + 0
6. y= 0x + 8
7. y= 7x -2
8. y= 0x + 7
9. y= 0x - 6
10. y= -6x +0

The perimeter of a rectangle is 168 m. Its length is five times its width. Find the length and width.

Answers

Answer:

Length of rectangle = 63 mWidth of rectangle = 21 m

Step-by-step explanation:

Given:

Perimeter of rectangle = 168 mLength of rectangle is five times the width

To Find:

Length and Width

Solution:

Let's assume width of rectangle x m and length of rectangle be 3x m. To calculate the dimensions of the rectangle we will use the formula of Perimeter of the rectangle

Perimeter of rectangle = 2(L + B)

Substituting the required values:

→ 168 = 2(3x + x)

→ 168 = 2(4x)

→ 168/2 = 4x

→ 84 = 4x

→ 84/4 = x

21 = x

Hence,

Length of the Rectangle = 3x = 3(21) = 63 mWdith of the rectangle = x = 21 m

Answer:

Length = 70 metre

Width = 14 metre

Step-by-step explanation :

As, it is given that, the perimeter of a rectangle is 168 m and its length is five times its width and we are to find the length and width of the rectangle. So,

Let us assume the width of the rectangle as w metre and therefore, the length will be 5w metre .

Now, According to the Question :

[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]

[tex]{\longrightarrow \qquad { {\sf{2 (5 w + w )= 168 }}}}[/tex]

[tex]{\longrightarrow \qquad { {\sf{2 (6 w )= 168 }}}}[/tex]

[tex]{\longrightarrow \qquad { {\sf{12 w = 168 }}}}[/tex]

[tex]{\longrightarrow \qquad { {\sf \: w = \dfrac{168}{12} }}}[/tex]

[tex]{\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ w = 14 }}}}}} \: \: \bigstar[/tex]

Therefore,

The width of the rectangle 14 metre .

Now, we are to find the length of the rectangle :

[tex]{\longrightarrow \qquad { { { \pmb {\frak{ Length = 5w }}}}}} \: \: [/tex]

[tex]{\longrightarrow \qquad { { { \pmb {\frak{ Length = 5 \times 14 }}}}}} \: \: [/tex]

[tex]{\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ Length = 70 }}}}}} \: \: \bigstar[/tex]

Therefore,

The length of the rectangle is 70 metre

can you please help me?

Answers

Answer:

24.00

Step-by-step explanation:

8 times tables

Toby thinks of a number less than 15. He divides it by 2 and then he adds 4. He then divides it by 3. His awnser is 3. 5

Answers

Answer:

The number he thought of was 13

Step-by-step explanation:

Revers the problem

3.5 * 3 = 10.5

10.5 - 4 = 6.5

6.5 * 2 = 13

The number was 13 if Toby thinks of a number less than 15. He divides it by 2 and then he adds 4.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Toby thinks of a number less than 15. He divides it by 2 and then he adds 4.

Let the number be x:

From the question:

Revers the problem

x =(3.5×3 - 4)×2

x = (10.5 - 4)×2

x = 6.5×2

x  = 13

Thus, the number was 13 if Toby thinks of a number less than 15. He divides it by 2 and then he adds 4.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ5

Solve the following proportions

Answers

6.5/40.3 = m/12.4
Cross multiply
40.3m = 6.5 x 12.4
40.3m = 80.6
Divide through by 40.3
m = 80.6/40.3
m= 2

m= 2

Answer:

[tex]6.5 \times 12.4 = 40.3 \: m \\ \frac{80.6}{40.3} = 2[/tex]

Help solve this circle

Answers

You're basically using the supplement angle to find the missing number.

Tyler has completed 60 pages in his
French workbook. This is 20% of the total
number of pages in the workbook.
How
many pages are in the workbook?

Answers

Answer:

300 pages

Step-by-step explanation:

this is the answer

HURRY PLEASE I WILL GIVE BRAINLIEST AND LOTS OF POINTS

Answers

Answer:

[tex]m = \dfrac{3}{4} [/tex]

Step-by-step explanation:

We would like to find the slope of the line of the given equation .

[tex]\longrightarrow y =\dfrac{3}{4}x -1 [/tex]

We know that slope intercept form of the line is given by ,

[tex]\longrightarrow y = mx + c [/tex]

where ,

m is the slope c is y intercept

Now we can compare the given equation with the slope intercept form to find the slope . You will see that 3/4 is present at the place of m .Therefore ,

[tex]\longrightarrow \underline{\underline{m=\dfrac{3}{4}}} [/tex]

Hence option C is correct choice .

Answer:

C. 3/4 (third option).

Step-by-step explanation:

Use the slope-intercept formula.

Slope-intercept formula:

→ y=mx+b

The m represents the slope.The b represents the y-intercept.

So, the slope is 3/4 and y-intercept is -1.

Therefore, the correct answer is C. 3/4.

I hope this helps! Let me know if you have any questions.

Tile the rectangle shown using square inches to find the area, and then use multiplication to confirm the area. Use paper to show your work.

Answers

Answer:

19 11/16

Step-by-step explanation:

5 1/4 x 3 3/4

Area = width x length


$1.68 for 8 ounces
$3.36 for 16 ounces
$3.60 for 20 ounces
$4.08 for 24 ounces
$5.44 for 32 ounces

Answers

What do you want me to do with that?

Answer:

what do you mean by this I don't get it

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