25. A sequence of positive integers with 2020 terms is called an FT sequence if each term
after the second is the sum of the previous two terms. For example, if the first two
terms of an FT sequence are 8 and 7, the sequence would begin 8,7,15,22,37,....
For some positive integer m, there are exactly 2415 FT sequences where the first two
terms are each less than 2m and the number of odd-valued terms is more than twice
the number of even-valued terms. What is the value of m?
(A) 21
(B) 69 (C) 115 (D) 35 (E) 105

Answers

Answer 1

Answer:

The first term in the sequence is odd-valued and so there are m choices for it.2020 Gauss Contest Solutions Page 19

The second term in the sequence is even-valued and so there are m − 1 choices for it.

Thus, there are a total of m × (m − 1) FT sequences that begin with an odd-valued term

followed by an even-valued term.

Finally, we consider the FT sequences that begin with an even-valued term followed by an

odd-valued term (Parity #4).

Again, there are exactly twice as many odd-valued terms as there are even-valued terms in the

first 2019 terms (since the pattern repeats even, odd, odd).

However in this case, the 2020th term is even and so there are fewer than twice as many odd valued terms as there are even-valued terms.

Thus, there are m2 + m × (m − 1) FT sequences that satisfy the required conditions.

Since there are 2415 such FT sequences, we may solve m2 + m × (m − 1) = 2415 by trial and

error.

Evaluating m2 + m × (m − 1) when m = 30, we get 302 + 30 × 29 = 1770, and so m is greater

than 30.

When m = 33, we get 332 + 33 × 32 = 2145.

When m = 34, we get 342 + 34 × 33 = 2278.

When m = 35, we get 352 + 35 × 34 = 2415, as required.

Answer: (D)

Step-by-step explanation:


Related Questions

What is the slope of the line?

Answers

I used the points -1,-3 and 3,4

The slope I got was 7/4, so that should be the answer

The original price of concert tickets is $100.00. If there is a discount of 21%, what is the sale price?

Answers

Answer:

its 100 so it would literally just be 100 - 21

Step-by-step explanation:

Calculating permutations can be used in all of following except _____.

seating arrangements at a wedding
survey results
assisting computer programmers
placing items into a display

Answers

Answer:

Option C,  

Calculating permutations can be used in all of following except assisting computer programmers

Step-by-step explanation:

Permutations is basically used in cases where there is some sort of patterning involved in it.

In case of seating arrangements at a wedding, survey and placing items into a display some kind of pattern will be followed.

Hence, option C

Answer:

survey results

Step-by-step explanation:

I got it right

PLZ HELPPP

What is the radius of a cylinder that has a volume of 500 fts and that is 10 ft tall?

Answers

Answer:

4ft

Step-by-step explanation:

500=pir^2h

r^2=500/(10*pi)

r=3.989ft

Please help me! Thank you!

Answers

The correct answer is D

would 1, 2, 5, form a right angle​

Answers

Im assuming you mean the sides of a triangle which the answer would be no as 1+4 does not equal to 25. (A2+b2=c2) for a right triangle

On a certain day, the temperature in Seattle was -5° and the temperature in Houston was 10°. How many degrees lower was the temperature in Seattle?

Answers

Answer:

15 degrees lower

Step-by-step explanation:

When you are trying to find the difference between a negative and positive number, add both numbers and you will get the difference. In this case it was 15.

Sorry, math isn't my strongest suit, but i hoped this helped!

Hurry this is due in 45 minutes! I need help

Answers

Answer: B

Step-by-step explanation:

18%/38%= about 47%

( -1)×(-1)×(-1) 5 times equal to​

Answers

I think the answer is -5.

Which set of tokens represents 0?
Positive
Negative


Pls helpp!!

Answers

Answer:

C.

represent 0

hope it helps

How many meters are equal to 4,581 centimeters? Use how the placement of the decimal point changes when dividing by a power of 10 to help you.

Answers

Answer:

Step-by-step explanation:

How many meters are equal to 4,581 centimeters?

100cm = 1m

4581 cm = x

Use how the placement of the decimal point changes when dividing by a power of 10 to help you

Quickly please I can't answer it and I'm running out of time

Answers

362.8 meter^2

(rounded by the nearest tenth .79>.8)

Formula:

A=2⋅π⋅r⋅h+2⋅π⋅r^2

Equation:

2⋅ 3.14⋅ 5.3⋅ 5.6+ 2⋅ 3.14⋅ 5.3^2 =362.8 m^2

What is the inverse of the function
f(x)
19
13?
OA-110) =
319
OB. 5-1,5) =
19
T
319
Oc. 9-17)
OD. 1-16x) = leven

Answers

Answer:

A is correct ..............

What does A equal?

What does A equal?


Please answer both of the question!!

Answers

Answer:

5. 32,000

6. 0.006

Answer:

1=d

2=D

Step-by-step explanation:

Solve the following equation using the quadratic formula.

3x^2+7x+8=6

Answers

That’s the answer

x = - 1/3, -2

The table shows the heights of students in a group
Student Height (in inches)

49

47

46

45

53
What is the mean height of the students in the group?
46 inches
48 inches
51 inches
53 inches

Answers

Answer:

The guy above me is wrong but I know the correct answer and the correct answer is 46 and you get this by adding all your numbers together then dIvide the number that you got by however many numbers you added together and that is how you get 46

PLEASE GIVE BRAINLIEST

Step-by-step explanation:

The length of the sides of a triangle is given. Determine
whether or not the triangle is right, acute, or obtuse.
6, 8, 10
a Right
b Acute
Obtuse

Answers

Answer:

The triangle is a right triangle

Step-by-step explanation:

For the triangle to be right, Pythagoras’ theorem must be obeyed

According to the theorem, the square of the longest side (the hypotenuse) equals the sum of the squares of the two other sides

Now, from the given side lengths, the highest value is 10;

squaring this, we have 10^2 = 100

Squaring and adding the other values, we have

6^2 + 8^2 = 36 + 64 = 100

This mean the values are equal and the Pythagoras’ theorem is obeyed

Hence, we can conclude that the triangle with the given side lengths is a right triangle

How do you know if something is congruent? (scale Factors)

Answers

example: Two polygons are congruent if they are the same size and shape - that is, if their corresponding angles and sides are equal.

Answer:

Two polygons are congruent if they are the same size and shape - that is, if their corresponding angles and sides are equal. Move your mouse cursor over the parts of each figure on the left to see the corresponding parts of the congruent figure on the right.

Step-by-step explanation:

Hailey saved up $357.45 in her Piggy Bank. She decided that she wanted to use $97.99 to buy Roller skates and $50.00 to buy the Glow In the Dark flashing wheels. How much money will Hailey have leftover?

Answers

Answer:

209.46

Step-by-step explanation:

subtract $357.45, $97.99, and $50 and

you'll get $209.46

17 and 18 please no links

Answers

Answer:

17) 135 degrees

Step-by-step explanation:

An octagon contains six triangle, or 1080 degrees, meaning each angle is 135 degrees.

Step-by-step explanation:

1. an octagon contain 6 triangles or 1080 degrees this means with 8 angles each angle is 135 degrees

The area of a rectangular carpet is 96 square feet. The length of the carpet is 12 feet. What is the width of the carpet?

A. 8 feet
B. 12 feet
C. 24 feet
D. 36 feet

Answers

Answer:

A. 8 feet

Step-by-step explanation:

96 = 12 (x)

96/12 = x

8 = x

us
Complete the square
to find the vertex
of this parabola.
x2-14x+4y+29=0
( , )

Answers

Answer:

y=3x+29

Step-by-step explanation:

4y=12x+29

4y/4=12x+29/4

y=3x+29

Answer:

(7,5)

Step-by-step explanation:

A circle has an area of in2. If it is dilated by a scale factor of 5/4, what is the area after dilation

Answers

The question is incomplete, let's take an hypothetical value for the Area of the circle ;

Let the are aid the circle = x in²

Answer:

Kindly check explanation

Step-by-step explanation:

The scale factor = 5/4

The initial area of square = x in²

The area of the circle after dilation will be :

Scale factor * initial area of circle

5/4 * x in²

Area after dilation = 5/4(x) in²

Just substitute the original value of the square for X in the solution to obtain the exact answer.

PLEASE HELP ME!!!!! #4,5!!!!

Answers

The answer for question 4:
a) 3(3n-1)=9n-3
b) 9n-3=96
9n=96+3
9n=99
n=11

Answer:

4a) 9n - 3

4b) n = 11

Step-by-step explanation:

3(3n - 1)

9n - 3

9n - 3 = 96

9n - 3 + 3 = 96 + 3

9n = 99

9n ÷ 9 = 99 ÷ 9

n = 11

HELP ASAP PLEASE!!!!!! No links! Explanation please!!! Brainliest to whoever answers first!

Answers

I believe the answer would be 54. I could of course be wrong so if I am, please correct me

At a water park, 4 out of 20 tickets sold were child tickets. What percentage of the tickets were child tickets?

Answers

Answer:

20%

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

Choose the measure that best represents the data. Explain your reasoning.

12, 15, 16, 18, 20, 90

Answers

The measure that would best represent the data set is 17. This because 17 is the mid range number making it not the smallest but not the biggest
Hope this helps!

1. On a scale drawing with a scale of 1 in to 25 feet, the height of a building is 8 inches on a
drawing. How tall is the actual building?
A. 200ft
B. 200in
C. 20ft
D. 20in

Answers

200ft, you just do 8x25

Answer:

A

Step-by-step explanation:

You multiply 8 and 25

URGENT!!! I’LL GIVE BRAINLIEST ANSWER

Answers

Answer:

a

Step-by-step explanation:

Answer:

A. QRP≅UTV

Step-by-step explanation:

Q is congruent with U.

R is congruent with T.

P is congruent with V.

Let me know if that helps!

In a piggy bank, the number of nickles is 8 more than half the number of quarters. The value of the coins is $21.85. Determine the number of nickels.

Answers

Answer:

The number of nickels is 47

Step-by-step explanation:

1 nickel is 5 cents while 1 quarter is 25 cents

let the number of nickels be n and the number of quarters be q

From the question;

the number of nickels n is 8 more than half the number of quarters (q/2)

n = q/2 + 8

(n-8) = q/2

q = 2(n-8) = 2n - 16 ••••(i)

let us convert $21.85 to cents

there are 100 cents in $1

Thus; $21.85 will be 21.85 * 100 = 2185 cents

1 nickel is 5 cents; so n nickels will be 5 * n = 5n cents

1 quarter is 25 cents; so q quarters will be 25 * q = 25q cents

The addition of both will give 2185 cents

Thus;

5n + 25q = 2185 ••••••(ii)

Substitute equation i into ii

5n + 25(2n-16) = 2185

5n + 50n - 400 = 2185

55n = 2185 + 400

55n = 2,585

n = 2,585/55

n = 47 nickels

Other Questions
Why is a sandy shore hot on a summer day?A. The sand is heated through thermal conduction,B. The sand is chemically heated.C. The sand is heated through radiation.D. The sand is heated through convection. 38. The number of bottles a machine fills is proportional to the number of minutes themachine operates. The machine fills 250 bottles every 20 minutes. Create a graph thatshows the number of bottles, y, the machine fills in x minutes. Directions: Identify the instruments described.Write your answer on the blanks provided.1. These are instruments that areplucked, strummed and bowed.2. It is a one -stringed fiddle instrumentof Bilaans also called Kugot.3. It is a bamboo polychordal tubezither of the Bagobo.4. It is a ring flute of Bilaan andTiruray, Maguindanao, Samal, Tausug and Yakan5. It is a lip-valley flute.Need answer today please ill mark u Could someone help with this question? If g(x) = 2 log (2x) what is g(3) The catapults are 14.5 m, end text apart, as shown. From catapult A, there is a 96 degree angle between catapult B and the target. From catapult B, there is a 58degree angle between catapult A and the target.How far should catapult B throw the snowball to reach the target?Do not round during your calculations. Round your final answer to the nearest tenth of a meter.Thank you very much. Use cubic regression to find a function that fits the following points (1,4),(2,9),(3,34),(-2,-11) What point is closest to x axis A carton of milk in the shape of a rectangular prism has a leak. The dimensions of the carton are 8 inches by 4 inches by 3 inches. If the rate in which the milk is leaking is 6 cubic inches per minute, how long would it take for the milk carton to completely empty? how can a chemical reaction be compared to shuffling a deck of cards? The excerpt is taken from Patrick Henry's famous "Give me liberty or give me death" speech to the Second Virginia Convention in 1775. Which sentence suggests that Patrick Henry believed British rule in the American colonies was tyrannical?A. The question before the House is one of awful moment to this country. B. For my own part, I consider it as nothing less than a question of freedom or slaveryC. Should I keep back my opinions at such a time, through fear of giving offence, I should consider myself as guilty of treason towards my countryD. We are apt to shut our eyes against a painful truth, and listen to the song of that siren till she transforms us into beastsE. For my part, whatever anguish of spirit it may cost, I am willing to know the whole truth; to know the worst, and to provide for it For the week of June 6, Melvin Mince, the manager of Melvins Hotel in North western Illinois, budgeted 600 hours for room attendants to clean rooms. This budget was based on a work standard of cleaning one room every 36 mins. The rooms attendants actually worked 660 hours cleaning 1,050 rooms. The budgeted wage rate for room attendants is $3.40 per hour. The wages paid to room attendant totaled $2,178.00.1. What is the amount of the budget variance?2. What is the amount of the volume variance?3. What is the amount of the efficiency variance?4. What is the amount of the rate variance? HELP MEEE PLEASE ILL MARK BRIANLIST!!!! Evaluate the expression when n =4 n^2 - 5n+6 The woman baked some cookies, and we ate them quickly.Which is adverb?? Charged particles from the Sun follow Earths magnetic field to the poles where they create the _______________. Which of these is a type of social engineering attack?Select one:O Packet SnifferO Port ScanO PhishingO Ping Sweep PLS HELP Find the value of x. *A and B are midpoints. Find the perimeter of the figure below. Figure not drawn to scale Write the equation of the line if the line passes through (4,4) and the y-intercept is -4.y = 2x - 4y = 2x - 2None of these answers are correct.y = 8x + 4y = 2x + 4