1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dimas [21]
2 years ago
10

Here is a variation on a classic riddle: Jayden has a dog-walking business. He has two plans. Plan 1 includes walking

Mathematics
1 answer:
Anna35 [415]2 years ago
8 0

Answer:

Mrs. Maroney should choose plan 1

Step-by-step explanation:

<u>Plan 1: </u>

Plan 1 includes walking a dog once a day for a rate of $5 per day.

In 2 weeks (14 days), Jayden will earn

\$5\cdot 14=\$70

<u>Plan 2:</u>

Plan 2 also includes one walk a day but charges 1 cent for 1 day, 2 cents for 2 days, 4 cents for 3 days, and 8 cents for 4 days and continues to double for each additional day.

So,

a_1=1\\ \\a_2=2\\ \\a_3=4\\ \\a_n=2a_{n-1}=a_1\cdot 2^{n-1}\\ \\r=2

Hence,

a_{14}=a_1\cdot 2^{14-1}=1\cdot 2^{13}=2^{13}=8,192

Find the sum S_{14}=a_1+a_2+\dots+a_{14}:

S_{14}=\dfrac{a_1(1-r^n)}{(1-r)}\\ \\S_{14}=\dfrac{1\cdot (1-2^{14})}{1-2}=\dfrac{-16,384}{-1}=16,384\text{ cents }=\$163.84

Since $70<$163.84, Mrs. Maroney should choose plan 1

You might be interested in
Find the constant rate of change for each linear function and interpret its meaning
Marina CMI [18]

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

and to get it, we simply need two points off of the straight line, hmm let's use the ones in the picture below.

(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}}\implies \cfrac{2}{4}\implies \cfrac{1}{2}

3 0
2 years ago
HelP me plz i'll give brainliest or whatever
aivan3 [116]
The answer is d

explanation: its right in between 50 and 60 making it 55, and the picture is showing it as an angle.
3 0
3 years ago
What are 2 fractions closer to 1 than to 0?
solniwko [45]
1 and 1/2, 1 and 1/3
3 0
3 years ago
Read 2 more answers
Solve the quadratic equation by factoring. 9x^2+24x+20=4
const2013 [10]

D. -4/3

Let's solve your equation step-by-step.

9x2+24x+20=4

Step 1: Subtract 4 from both sides.

9x2+24x+20−4=4−4

9x2+24x+16=0

Step 2: Factor left side of equation.

(3x+4)(3x+4)=0

Step 3: Set factors equal to 0.

3x+4=0 or 3x+4=0

x= −4 /3

Hope This helps

5 0
3 years ago
Skyscraper Windows
Musya8 [376]

Answer:

A.) $2,166

B.) $10,545

C.) (n/2)(3.5 + 0.5n) × 38

Step-by-step explanation:

Floor - - - - - - - - - - 1 - - - - - - - 2 - - - - - - - 3

Cost / window - - $2.00 - - - $2.50 - - - $3.00

Cost of washing first floor = $2 × 38

Cost of second floor is: (2 + 0.5) × 38

Cost of third floor is: (2 + 2 × 0.5) × 38

Cost of n floor : (2 + (n - 1) × 0.5) × 38

Therefore,

Total cost :

(2 + (2 + 0.5) + (2 + 2*0.5) + ... + (2 + (n - 1)*0.5)) × 38

Using Arithmetic progression for the sequence :

2, (2 + 0.5), (2 + 2*0.5),..., (2 + (n - 1)*0.5)

first term 'a' = 2; common difference 'd' = 0.5

Sum of the first n terms of arithmetic sequence terms is:

S = (n/2)(2a + (n - 1)d) ; Where a = 2 and d = 0.5

S = (n/2)(2*2 + (n - 1)*0.5)

S = (n/2)(4 + 0.5n - 0.5)

S = (n/2)(3.5 + 0.5n)

To wash all windows with n stories :

S × 38 windows

A.) To wash all windows : stories = 12

n = 12

(12/2)(3.5 + 0.5(12)) × 38

6(3.5 + 6) × 38 = $2,166

B.) if building is 30 stories tall:

n = 30

(30/2)(3.5 + 0.5(30)) × 38

15(3.5 + 15) × 38 = $10,545

C.) If building is n stories tall :

(n/2)(3.5 + 0.5n) × 38

4 0
3 years ago
Other questions:
  • What is the answer ?
    9·1 answer
  • Help plzz i need the answer fast
    9·2 answers
  • A student collects 12 ladybugs for a science project. This is 9 fewer than the number of ladybugs the students collected yesterd
    7·2 answers
  • A sample of 56 research cotton samples resulted in a sample average percentage elongation of 8.63 and a sample standard deviatio
    13·1 answer
  • What should be added to 8 to make the sum 0
    11·2 answers
  • The Porter family budget in the new city is shown in the graph. Of the seven expenses shown, which of the following is fixed?
    9·1 answer
  • Which equation shows the distributive property?
    8·1 answer
  • About 0.5 of all the students in the fifth grade are girls. If the fifth grade has 80 ​students, how many of the students are gi
    9·1 answer
  • The number of boys in a club is 10 more than half the number of girls.
    5·1 answer
  • Rewrite each equation below so that it is solved for y.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!