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

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:

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 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

Hurry this is due in 45 minutes! I need help

Answers

Answer: B

Step-by-step explanation:

18%/38%= about 47%

Solve the following equation using the quadratic formula.

3x^2+7x+8=6

Answers

That’s the answer

x = - 1/3, -2

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!

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

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:

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

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.

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

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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 ..............

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:

Which set of tokens represents 0?
Positive
Negative


Pls helpp!!

Answers

Answer:

C.

represent 0

hope it helps

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:

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:

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!

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

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

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:

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

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

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

( -1)×(-1)×(-1) 5 times equal to​

Answers

I think the answer is -5.

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

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

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!

Please help me! Thank you!

Answers

The correct answer is D

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

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
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