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
Semmy [17]
3 years ago
14

Bill is able to save $35/week after working part-time and paying his expenses. These two formulas show his weekly savings: f(1)

= 35, f(n) = f(1) + f(n-1) for n > 1 f(n) = 35n Which one of these formulas show the sequence written rercursively and which shows it written explicity? Justify your explanantions. Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations. Use the explicit formula to demonstrate the most direct method to find f(40). Explain why you chose that method and what your answer means. Show your calculations. Given the sequence of numbers: 5, 6, 8, 11, 15, 20, 26, 33, 41,… Explain whether or not this sequence can be considered a function.
Mathematics
1 answer:
Umnica [9.8K]3 years ago
4 0
1. We use the recursive formula to make the table of values:
f(1) = 35
f(2) = f(1) + f(2-1) = f(1) + f(1) = 35 + 35 = 70
f(3) = f(1) + f(3-1) = f(1) + f(2) = 35 + 70 = 105
f(4) = f(1) + f(4-1) = f(1) + f(3) = 35 + 105 = 140
f(5) = f(1) + f(5-1) = f(1) + f(4) = 35 + 140 = 175

2. We observe that the pattern is that for each increase of n by 1, the value of f(n) increases by 35. The explicit equation would be that f(n) = 35n. This fits with the description that Bill saves up $35 each week, thus meaning that he adds $35 to the previous week's value.

3. Therefore, the value of f(40) = 35*40 = 1400. This is easier than having to calculate each value from f(1) up to f(39) individually. The answer of 1400 means that Bill will have saved up $1400 after 40 weeks.

4. For the sequence of 5, 6, 8, 11, 15, 20, 26, 33, 41...
The first-order differences between each pair of terms is: 1, 2, 3, 4, 5, 6, 7, 8...since these differences form a linear equation, this sequence can be expressed as a quadratic equation. Since quadratics are functions (they do not have repeating values of the x-coordinate), therefore, this sequence can also be considered a function.
You might be interested in
Write the equation for the function graphed below.
avanturin [10]
Given the vertex of the parabola at point (2, -3):

The quadratic function in vertex form is:

f(x) = (x - 2)^2 - 3

where the vertex (h, k) is the minimum point = (2, -3).
6 0
3 years ago
Write 2, 330, 000 in scientific notation?
Genrish500 [490]

Answer:

2.33 × 10^6

Step-by-step explanation:

I just used a calculator, to be honest. It was super simple.

2.33 * 10^6

2.33 * (10*10*10*10*10*10)

which then equals 2,330,000

6 0
3 years ago
An artist can paint 4 paintings in 2 hours. What is the artist’s unit rate?
RUDIKE [14]

Answer: if we divide the numerator and denominator by two, we get that he can paint two paintings in one hour. His unit rate is 2:1.

4:2 divide by two to make the denominator 1

2:1 solution has 1 in the denominator

Step-by-step explanation:

3 0
2 years ago
Anna buys 12 pens and 20 pencils for a total cost of $16. One pen costs $0.40 more than a pencil. What would one pencil and one
vladimir2022 [97]

It is given in the question that

Anna buys 12 pens and 20 pencils for a total cost of $16. One pen costs $0.40 more than a pencil.

Let the cost of pencil is $ x .

Therefore cost of pen is

$(x+0.40)

According to the question

12(x+0.40)+20x =16

Distributing 12 and combining like terms, we will get

12x+4.8+20x=16\\32x = 11.2\\x = 0.35

Therefore cost of pencil is $0.35 and cost of pen is

0.35+0.40=0.75

3 0
3 years ago
A machine in an office can shred 65 sheets of paper every 5 seconds. How many sheets of paper can the machine shred in 60 second
Tema [17]

Answer:

780 sheets

Step-by-step explanation:

we know that

A machine can shred 65 sheets of paper every 5 seconds

so

using proportion

Find out how many sheets of paper can the machine shred in 60 seconds

7 0
3 years ago
Read 2 more answers
Other questions:
  • which set of numbers may represent the lengths of the sides of a triangle? A. 1, 3, 4 C. 5, 7, 9 B. 4, 4, 9 D. 8, 5, 3
    14·1 answer
  • triangle RST is congruent to triangle NPQ, RT=7x-5, NQ= 5x+11, find the length of side RT and side NQ
    14·2 answers
  • Which two rational numbers does square root of 14 lie between
    8·1 answer
  • What is the domain of the function graphed below?
    8·2 answers
  • Ana uses gcf and distributive property to rewrite 72+60
    14·2 answers
  • The original price is $40.90 and the sale price is 30% off what would be two different expressions for the equation?
    12·1 answer
  • Express the following in standard form.​
    7·1 answer
  • in the equation dy+3x=2, for what value of d is the graph of the equation parallel to the graph of x-3y=0? the y axis?
    12·1 answer
  • Multiply the factors which appear in both lists that you made in This gives you the HCF of 60 and 80
    11·1 answer
  • Solve by the elimination method. Check your work.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!