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
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:
Please help me solve these questions!!!
b) A men earns Rs.50000 in a month. He spends 30% of his income on foood
2/5 on his child's Education,0.25% on transportation and rest he saves.
i) Find the amount that he spends on each topic.
ii)Find his saving percentage.
Answer:
[tex]\huge\mathfrak\pink{ here's your solution } \\ \\ im \: soo \: happy \: [/tex]
which of the following is true about the expression √3*√12
54:40
Maya is finding the area of the shaded triangle below.
A triangle has a base of 73 meters and a height of 10 meters.
If she considers 10 m to be the height of the triangle, what should she use as the triangle’s base?
22 m
25 m
52 m
73 m
Answer:
d) 73 m
Step-by-step explanation:
From the Question, we are told that:
Maya is finding the area of the shaded triangle below.
A triangle has a base of 73 meters and a height of 10 meters.
If she considers 10 m to be the height of the triangle, what should she use as the triangle’s base?
The area of a triangle = 1/2 × Base × Height
We are already told the base of the triangle from the question and this is 73 m
Option D, 73 m is the correct answer
Peter hired a cleaning company to clean his house. The cleaning company charges a fixed fee $15 plus $17 per hour to clean a house
PLS ACTUALLY HELP ME , I WILL MARK BRAINLIEST
Answer: 15/8
Step-by-step explanation:
The fuction f(t)= 500(0.8)^t models the size of a population of rats in an area t years after 2005. What does 0.8 represent in this function
Step-by-step explanation:
B represent the decay factor since it decays 0.2 every t year.
Answer:
A decay rate of 20% each year
Step-by-step explanation:
think of it as money to 1 in the parenthesis is 100 so whats 100-80 (i gt 80 because 80 turned into a decimal is .8) its 20 so its going to decay or go down 20% each year. hope this helps anyone :)
Samuel drove 84 miles in 6 hours. How far can he drive in 6 hours?
Answer:
the answer is 84 being how you asked the question but I dont think thats what you meant to ask. if thars wrong just tell me and ill answer it the way you need it
Step-by-step explanation:
Answer:
84 miles
Step-by-step explanation:
......help due in a minute
Answer:
The answer is ''C''
Hope this helps!! Have a great day! <3
Answer: D ( I really don’t have a good explanation for this question.)
Part C: Prove that the measure of ∠JKL is 90°.
The ratio of boys to girls in the 10th grade is 8 to 13. If there are 91 girls in 10th grade, then how many boys are there?
Answer: There are 56 boys in the 10th grade
Step-by-step explanation:
Step 1
ratio of boys to girls in the 10th grade is 8 :13
Number of girls= 91
To find the number of boys, we first find the total number of boys and girls in the 10th grade
Step 2
Now the total ratio= 8 +13=21
Number of girls = ratio of girls/ total ratio x Total number of students
91=13/ 21 x Total number of students
Total number of students =21 x 91 / 13 =147
Step 3
Therefore Number of boys =ratio of boys/ total ratio x Total number of student
8/21 x 147=56
How long will it take the population of a certain country to double if it’s annual growth rate is 7.3%?
7. Find the length of HP.
12
P
9
H
Step-by-step explanation:
hope it is helpful to you
Answer and Step-by-step explanation:
To find the length of HP, we must use the Pythagorean Theorem.
This theorem helps us solve for the sides of any right triangle.
The equation for the Pythagorean Theorem is:
[tex]a^{2}+ b^{2} = c^{2}[/tex], in which a and b are the legs, while c is the hypotenuse.
Let's plug in our values into the equation to find the length of HP.
We will use the variable x to represent HP.
[tex]9^{2}+ 12^{2} = x^{2} \\\\\\Square.the.9.and.the.12.\\\\\\81 + 144 = x^2\\\\\\Add.\\\\\\225 = x^2\\\\\\Square.both.sides.\\\\\\\sqrt{225} = \sqrt{x^2} \\\\\\15 = x = HP[/tex]
So, we get our answer to be 15.
The length of HP is 15.
#teamtrees #PAW (Plant And Water)
sum of 20 and 8 minus the product of 3 and 5
Answer and Step-by-step explanation:
The sum of 20 and 8 would look like
20 + 8
Then we have to subtract the product of 3 and 5 from the sum of 20 and 8.
(20 + 8) - 3(5)
^That is the expression^
The answer, when you evaluate the expression, is:
28 - 15 = 13
#teamtrees #PAW (Plant And Water)
x+y=1212
x-y=518
please help me with it
Here,
x+y=1212••••••[tex]\bold{equation~I }[/tex] x-y=518••••••[tex]\bold{equation~II }[/tex]ADDITIONALL,both two equation.
we get that,
x+y+x-y=1212+5182x=1730x=865so,
x-y=518865-y=518y=860-518y=347QUICK will give brainlist
What is the shape of each half of the pentagon?
Answer:
trapezoid
Step-by-step explanation:
Answer:
Trapezoids and diamonds but you really have to look closely
Step-by-step explanation:
In the XY coordinate plane, the slope of a line is 4 and it passes through the point (1,3). Find the equation of a line that is perpendicular to the given line and intersects it at the given point.
A. y=4x-1
B. y=-4x+7
C. y=1/4x -1
D. y=4x+13/4
E. y=-1/4x+13/4
Answer:
E?
Step-by-step explanation:
I'm sorry of this answer is wrong
Mrs. Lindsay doesn't have a cat crate and needs to take her cats to the vet. She's
going to make a box out of a 8 foot by 8 foot piece of cardboard. How many feet
should Mrs. Lindsay cut from the corners to have the maximum amount of space
inside the box?
Answer:
The amount to remove from each corner is a square, 4/3 ft by 4/3 ft.
Step-by-step explanation:
The piece of cardboard measures 8 ft by 8 ft.
Each corner will be cut to create the sides of the box.
Let the square cut from each corner measure x by x ft.
The base of the box will measure 8 - 2x by 8 - 2x, and the height of the box will be x.
V = (8 - 2x)^2 * x
V = 64x - 32x^2 + 4x^3
Now we differentiate and set the derivative equal to zero to find a maximum value.
64 - 64x + 12x^2 = 0
3x^2 - 16x + 16 = 0
(3x - 4)(x - 4) = 0
3x - 4 = 0 or x - 4 = 0
3x = 4 or x = 4
x = 4/3 or x = 4
The solution x = 4 must be discarded since 8 - 2x = 8 - 8 = 0, and the sides would have 0 length.
The amount to remove from each corner is a square, 4/3 ft by 4/3 ft.
During Christmas sale, a local store in Virginia has marked all items 20% off. George Walker bought a microwave that normally sells for $100 and a refrigerator that usually goes for $250. Calculate the total sale price.
Answer:
it looks like the answer to this problem is $280.
Step-by-step explanation:
i got this answer because you add $100 and $250 together. You will get $350. Then you take 20% of that total. So, 20% of 350 is 70. Now take 350-70, which = 280. and that should be your final answer.
SOMEONE PLS HELP IM CONFUSED , WILL MARK BRAINLIEST
Answer. multiply 13 and 64 then round to the nearest tenth
Step-by-step explanation:
I hope it helps :)
please help me!!!! pleasseeeee
Answer: I'm not to sure, but Khan Academy does a really good job at this. Anything apart of STEM they have a step by step video on.
Step-by-step explanation:
A password contains five digits, such as 17467. How many different passwords can be formed? Help please
Answer:
Step-by-step explanation:
100,000
The number of different passwords can be formed by; 1,00,000
How to identify the place value of a digit in a number?The place values on the left of the decimal point start as ones, tens, hundreds, and so on. The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths, and so on
Given that the password contains five digits, such as 17467.
In general total digits = 10 [ from 0 to 9]
If a password contains five digits, then by the fundamental principal of counting, then the total number of different passwords;
[tex]10^5[/tex] = 1,00,000
Hence, the number of different passwords can be formed by; 1,00,000
Learn more about place value here:
https://brainly.com/question/17983725
#SPJ2
what is the value of 11²
Answer: 121
11^2 = 11 x 11 = 121
Answer:
121
Step-by-step explanation:
To square a number, we have to multiply the number by itself. This means we'll multiply 11 by 11.
11 · 11 = 121
So, 11² = 121.
I hope this helps :)
can anyone help with these 4 questions?
Answer:
hablas español?? Si o no ?
Find a description this equation represents. Of the numbers 1, 2, 3, 4, and 5, which are solutions to the equation? 3x-8=7
Answer:
5
Step-by-step explanation:
3x - 8 = 7
collect like terms
3x = 8 + 7
3x = 15
divide both sides of the equation by 3
x = 15/3 = 5
A number has the same digit in its hundreds place and its hundredths place. How many times greater is the value of the digit in the hundreds place than the value of the digit in the hundredths place?
Answer:
372
Step-by-step explanation:
that's my answer hope it's help
Answer:
1000
Step-by-step explanation:
!!!!!!!PLEASE HELP I DNT UNDERSTAND!!!!!! WILL GIVE BRAINLYIEST
Answer:
11. 8/30
Step-by-step explanation:
add all the marbles
you get 30 marbles
then the probability of yellow being taken out is 8
Using Angle Relationships to Solve Equations
Answer:
x+x+4+3x-9=90
5x-5=90
5x=95
x=19
9. 19
10. 19+4=23
11. 3×19-9=48
Personal Finance
Which of these statements is false?
All states have state income taxes.
Different states have different tax rates.
Some states consider some income to be tax free.
Some states tax all taxable income at the same rate; they have a flat tax rate.
Answer:
Some states consider some income to be tax free. this statement is false
it would probably go with one of the first 2. they sound opposite of each other. probably go with the first 1?
sorry if I'm wrong