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
labwork [276]
2 years ago
12

The infinite sequence $T=\{t_0,t_1,t_2,\ldots\}$ is defined as $t_0=0,$ $t_1=1,$ and $t_n=t_{n-2}+t_{n-1}$ for all integers $n&g

t;1.$ If $a,$ $b,$ $c$ are fixed non-negative integers such that\begin{align*} a&\equiv 5\pmod {16}\\ b&\equiv 10\pmod {16}\\ c&\equiv 15\pmod {16}, \end{align*}then what is the remainder when $t_a+t_b+t_c$ is divided by $7?$ You can use a LaTeX renderer to see what this says.
Mathematics
1 answer:
katrin [286]2 years ago
6 0

t_n are the Fibonacci numbers,

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

Taken modulo 7, we get the sequence

0, 1, 1, 2, 3, 5, 1, 6, 0, 6, 6, 5, 4, 2, 6, 1, ...

that repeats with period 16 (this is known as the 7th Pisano period).

This is to say,

t_a\equiv t_{16n+5}\equiv t_5\equiv5\pmod7

t_b\equiv t_{16n+10}\equiv t_{10}\equiv6\pmod7

t_c\equiv t_{16n+15}\equiv t_{15}\equiv1\pmod7

so that

(t_a+t_b+t_c)\equiv(5+6+1)\equiv\boxed5\pmod7

You might be interested in
P= 2 and r= 6 workout the value of Q, when Q =5p +2r
arlik [135]

Answer:

Q=5(2)+2(6)

Q=10+12

Q=22

22 is your answer

Step-by-step explanation:

3 0
3 years ago
**URGENT I WILL MARK BRAINLIEST**
hram777 [196]
It’s 50% in savings
5 0
3 years ago
Find the value of n.<br><br> n+27<br><br> 11n<br><br> The value of n is ? units.
Kipish [7]

Answer:2.7=n

Step-by-step explanation:

n+27=11n

Move the variable to one side so subtract n

27=10n

Divide by 10

2.7=n

I'm not sure if this what you were asking for

6 0
3 years ago
Andre and Morgan are both headed to Florida for vacation. Andre will drive 70 miles per hour. Morgan will drive 55 miles per hou
babymother [125]

Answer:

The number of hours Moran wold have driven before Andre catches up with him is 14 hours

Step-by-step explanation:

The given information are;

The speed with which Andre will drive = 70 miles per hour

The speed with which Morgan will drive = 55 miles per hour

The time of departure of Morgan = 3 hours before Andre departs

Let the time at which Andre catches up with Morgan be, t

We have, from the definition of distance traveled;

Distance traveled =Speed × Time

The distance Morgan would have driven in t hours = 55 × t

Given that to catch up with Morgan, Andre has to travel the same distance, and that Andre starts 3 hours late, we have;

The distance Andre would  drive when Morgan has driven for t hours = 70 × (t - 3)

Therefore, since the distance at the point they meet is the same distance for them both, we have;

55 × t = 70 × (t - 3)

55 × t = 70 × t - 210

210 = 70 × t - 55 × t  = 15 × t

t = 210/15 = 14 hours

Therefore, Morgan would have driven for 14 hours before Andre catches uo with him.

4 0
3 years ago
Need help will give thanks and brainliest
Lina20 [59]

Answer : y = 11x + 24

7 0
2 years ago
Read 2 more answers
Other questions:
  • Hi everyone can someone help me out with this question please
    6·1 answer
  • Find the equation of a line through (2,-4) and (-7,-4)
    9·1 answer
  • <img src="https://tex.z-dn.net/?f=x%2B%28-17%29%3D-1%20%3Cbr%3E%0A" id="TexFormula1" title="x+(-17)=-1 &amp;#10;" alt="x+(-17)=-
    8·1 answer
  • Problem PageQuestion The area covered by a certain population of bacteria increases according to a continuous exponential growth
    10·1 answer
  • Describe what type of information can be determined from a pie chart
    9·2 answers
  • Which phrases can be used to represent the inequality? Check all that apply. One-half + k greater-than 18
    11·1 answer
  • 17 Cos B +15=0 <br><br>Write the value of x,y,r​
    5·1 answer
  • Ohhh so your a master chef name every meal on the McDonald's menu
    14·2 answers
  • What is the area of the shaded triangle?
    5·1 answer
  • REMEMBER THAT THE RISE TESTS DO NOT GO TOWARDS YOUR GRADE, THEY ARE ONLY FOR THE SHOOLS TO SEE HOW WELL THEY ARE TEACHING YOU.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!