Answers
Answer:
Each term is a sum of the two previous terms like the fibonacci sequence, but the sum of the two starting terms of the lucas sequence is followed by 2 then 1, rather than 0 then 1 for the fibannaci sequence.
These are integer sequences.
The sum of the two previous terms can be represented by:
fn = fn-1 + fn-2.
These numbers can be obtained by adding the previous corresponding term of the fibonacci sequence by the next corresponding term to get the corresponding number of the lucas sequence.
Ln = { 2 if n = 0
1 if n = 1
Ln-1 + Ln-2 if n > 1
________________
Fn+1 + Fn-1 = Ln
___________________
f(0) = -1
f(1) = 2, f(2) = 1, f(3) = 3, f(4) = 4, f(5) = 7, f(6) = 11
________________________________
f(12) = 199
________
f(12) = f(11) + f(10) = (f(10) + f(9)) + (f(9) + f(8)) = .....
given f(n) = f(n-1) + f(n-2)
____________________
f(12) = f(1) + f(2) = f(2) + f(3) = f(3) + f(4) =
f(4) + f(5) = f(5) + f(6) = f(6) + f(7) =
f(7) + f(8) = f(8) + f(9) = f(9) + f(10) =
f(10) + f(11) = f(12) →
f(12) = 2 + 1 = 1 + [3] = 3 + [4] = 4 + [7] =
7 + [11] = 11 + [18] = 18 + [29] = 29 + [47] =
47 + [76] = 76 + [123] = 199
_____________________
Explicit formula
for n is an integer.
Nth term of the lucas sequence.
As you can see, the golden ratio
( 1 + √5 / 2) appears in here.
L(n) = ((1 + √5) / 2)ⁿ⁻¹ + ((1 – √5) / 2)ⁿ⁻¹
Related Questions
pls solve for x, will give brainliest to whoever
Answers
Answer:
60 degrees
Step-by-step explanation:
all angles of an equilateral triangle are 60 degrees
Answer:
x=60
Step-by-step explanation:
We know that since all sides are the same, all angles are the same.
x=angle
(180) is the amount of degrees when you add up all of the angles in the triangle
3x=180
x=60
(20,-6)(6,5) find the slope
Answers
ΔY
ΔX
=
5
4
= 1.25
θ =
arctan( ΔY )
ΔX
= 51.34019174591°
ΔX = 6 – -6 = 12
ΔY = 20 – 5 = 15
Distance (d) = √ΔX2 + ΔY2 = √369
= 19.209372712299
Equation of the line:
y = 1.25x + 12.5
or
y =
5 x
4
+ 25
2
When x=0, y = 12.5
When y=0, x = -10
the value of the 5 in the number 40.52 is _____ the value of the 5 in 115.78?
Answers
The value of each digit in a number is known as the place value. The value of the 5 in the number 40.52 is 10 times the value of the 5 in 115.78.
What is the place value of a digit in a number?The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.
Identification of 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 onThe tens mean multiply by 10The tenth means the tenth part of that digit which is that digit divided by 10The value of 5 in the given numbers can be written as,
The value of the 5 in the number 40.52 is 0.5.The value of the 5 in the number 115.78 is 5.Now, we can write the value of the two numbers as,
5 = 0.5 × x
x = 5/0.5
x = 10
Hence, the value of the 5 in the number 40.52 is 10 times the value of the 5 in 115.78.
Learn more about the Place Value here:
https://brainly.com/question/27734142
#SPJ2
Which statement is NOT TRUE when solving 5x - 4 = 26 *
O I need to add 4 to both sides of the equation.
O I need to divide both sides of the equation by 5.
O My answer is that x = 6
O My answer is that x = 4.4
Answers
Answer:
My answer is that x = 4.4
Step-by-step explanation:
The answer to the equation is 6, so the false one is the last one. All the other ones are true.
Find 0% of 152:
Find 100% of 152:
Find 50% of 152:
Find 25% of 152:
Find 75% of 152:
Answers
100% of 152:152
50% of 152:76
25% of 152:38
75% of 152:114
A factory can make 120 backpacks in 3 hours.
How long would it take to make 600 backpacks?
15 h
20 h
30 h
40 h
Answers
120 is 3 hrs and 600 is 5 times more so it’ll take 15 hrs
Noah wrote that 6+6 =12. Then he wrote that
6+6 -n =12 - n. Are his equations balanced? Explain.
Answers
Answer:
Hs equations are balancedStep-by-step explanation:
To check whether both equations are balanced, we will simplify
6+6 -n =12 - n
Add n to both sides of the equation using additive property
6+6-n+n = 12-n+n
6+6 +0 = 12+0
6+6 = 12 (This gives the other equation)
Since they are both equal, this shows that the equations are balanced
I need help with solving systems of linear equations through elimination.
1.) 8x = 3y + 38
24= 6y + 9x
a. all real numbers
b. (4,-2)
c. (4,-4)
d. (6,3)
2.) 6 = 2x + y
7x = 3 - 3y
a. (15,-36)
b. (-5,6)
c. (0,0)
d. (-15,36)
3.) 11x = 5 + 10y
7y = -2x +45
a. (-5,10)
b. (5,5)
c. (14, -4)
d. No solution
Answers
Answer:
See explanation
Step-by-step explanation:
8x = 3y + 38
24= 6y + 9x
Rearrange;
3y - 8x = -38 * 2 -------(1)
6y + 9x = 24 * 1 -------(2)
6y - 16x = -76 -------(3)
6y + 9y = 24 -------(4)
Subtract (4) from (3)
-25y = -100
y= 100/25
y = 4
Substitute y =4 into(1)
3y - 8x = -38
3(4) - 8x = -38
12 -8x = -38
-8x = -38 - 12
x = 50/8 = 6 2/8
2) 6 = 2x + y
7x = 3 - 3y
Rearrange;
2x + y = 6 * 3 --------(1)
7x + 3y = -3 * 1 --------(2)
6x + 3y = 18 ---------(3)
7x + 3y = -3 ---------(4)
Subtract (4) from (3)
-x = 21
x = -21
Substitute x = -21 into (1)
2x + y = 6
2(-21) + y = 6
-42 + y = 6
y = 6 + 42
y = 48
3)
11x = 5 + 10y
7y = -2x +45
Rearrange
11x - 10y = 5 * 2 ---------(1)
2x + 7y = 45 * 11 ---------(2)
22x - 20y = 10 --------(3)
22x + 77y = 495 --------(4)
Subtract (4) from (3)
-97y = -485
y = 5
Substitute y =5 into (1)
11x - 10y = 5
11x - 10(5) = 5
11x - 50 = 5
11x = 5 + 50
11x = 55
x = 55/11
x = 5
Consider proving the following.
Given Right isosceles △ABC with leg length 2s, right isosceles △WXY with leg lengths s, CA¯¯¯¯¯¯¯¯∥WY¯¯¯¯¯¯¯¯¯
Prove △ABC is similar to △WXY.
A student says the first step of the proof is "Reflect △ABC in AB←→ to create △ABC′." Which of the following statements logically comes next?
1. Rotate △ABC′ 90∘ about point A.
2. Reflect △WXY in WX←→− to create △WXY′.
3. Translate △ABC′so that point A maps to point W.
4. Find the hypotenuse of △ABC′ in terms of s.
Answers
Answer: 2
Step-by-step explanation:
Match the equations to the lines below :
y = 1/2x - 1
y= -1/2x + 1
y= 1/2x + 1
y= -2x - 1
y= 2x - 1
y= -1/2x - 1
Answers
2.) y = -1/2 + 1 is C
3.) y = 1/2x + 1 is E
4.) y = -2x - 1 is A
5.) y = 2x - 1 is B
6.) y = -1/2x - 1 is D
Which ratio is equivalent to 10:4
5:2
14:6
1:4
3:6
Answers
Answer:
5:2
Step-by-step explanation:
10:4/2
5:2
Answer:
5.2
Step-by-step explanation:
divide 10:4 by 2 and you will get 5:2
PLEASE HELP WILL GIVE LOTS OF POINTS & BRAINLY!!
Answers
Answer:
the amplitude is 5
the period is 4 pi
Step-by-step explanation:
The total for some groceries at the store was $25.63. With 8% sales tax, what is the total? $
Answers
Answer:
$2.05
Step-by-step explanation:
just do the math bro
Answer:
$27.72
Step-by-step explanation:
I hope this helps!!!
I need help with this
Answers
Answer:
x = 104 degrees
Step-by-step explanation:
A line like this will always have a measure of 180 degrees, therefore when the two sides are combined, it must equal 180, which means you can set up an equation and x can be determined
72 + x + 4 = 180
76 + x = 180
-76 -76
x = 104 degrees
Hope this helps!
5 is 1% of what number?
Answers
Answer:
500
Step-by-step explanation:
well uh, 5 x 100 is 500 and it’s out of 100%.
Answer:
500
Step-by-step explanation:
The absolute value of -15 is -15 because -15 is 15 units to the left of zero
Answers
Answer: False
Step-by-step explanation: The absolute value of -15 is 15.
What is the scale factor of this dilation?
A:2/3
B:1 1/2
C:3
D:5
Please hurry it’s timed
Answers
Answer:
1 1/2
B
Step-by-step explanation:
Question is in the Picutre attached.
Answers
11 b = 5, what is a
B. 25
C, 75
D. 125
Answers
Answer:
2.2
Step-by-step explanation:
Question 2 (1 point)
(07.01)
Solve 3x−5 = 9. (1 point)
a
x = −3
b
x = 2
c
x = 7
d
x = 8
Answers
Answer:
All options are wrong.................
A figure is shown.
What is the measure, in degrees, of
PLEASE HELP ME
Answers
explanation: 59+4x=180
4x=121
121 would be that angle and the other side as well because 59+121=180
hey so don’t trust me on this but i’m like 95 percent sure it’s right
How are these triangles congruent??????
Answers
Answer:
These triangles are congruent.
Step-by-step explanation:
These triangles are congruent because they have same length.
hope this helps u!
the amount people pay for cable service varies quite a bit but the mean monthly fee is $142 and the standard deviation is $29. the distribution is not normal many people pay about $76 for basic cable and about $160 for premium service but some pay much more. a sample survey is designed to ask a simple random sample of 1,500 cable service customers how much they pay. let x hat be the mean amount paid.
Part a: what are the mean an standard deviation of the sample distribution of x hat show your work and justify your reasoning.
Part b: what is the shape of the sampling distribution of x hat justify your answer.
Part C: what is the probability that the average cable service paid by the sample of cable service customers will exceed $143? show your work.
Answers
Answer:
a) By the Central Limit Theorem, the mean is $142 and the standard deviation is $0.7488.
b) By the Central Limit Theorem, approximately normal.
c) 0.0901 = 9.01% probability that the average cable service paid by the sample of cable service customers will exceed $143
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean monthly fee is $142 and the standard deviation is $29.
This means that [tex]\mu = 142, \sigma = 29[/tex]
Part a: what are the mean an standard deviation of the sample distribution of x hat show your work and justify your reasoning.
Sample of 1500(larger than 30).
By the Central Limit Theorem
The mean is $142
The standard deviation is [tex]s = \frac{29}{\sqrt{1500}} = 0.7488[/tex]
Part b: what is the shape of the sampling distribution of x hat justify your answer.
By the Central Limit Theorem, approximately normal.
Part C: what is the probability that the average cable service paid by the sample of cable service customers will exceed $143?
This is 1 subtracted by the pvalue of Z when X = 143. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{143 - 142}{0.7488}[/tex]
[tex]Z = 1.34[/tex]
[tex]Z = 1.34[/tex] has a pvalue of 0.9099
1 - 0.9099 = 0.0901
0.0901 = 9.01% probability that the average cable service paid by the sample of cable service customers will exceed $143
I need help with this I will mark you if it’s not wrong
Answers
Answer:
C
Step-by-step explanation:
May I please have brainliest
Answer:
The answer is C
Step-by-step explanation:
I subtracted 29 from 180, and then i added 5 since it is subtracting
Find two consecutive numbers whose sum is 55
Answers
Answer:
27 and 28
Step-by-step explanation:
Answer and Step-by-step explanation:
27 and 28.
27 plus 28 equals 55.
To know which numbers to use, we have to find two numbers that would produce a number that would include the digit of the second number in 55. Then, we find numbers that add up to 5, then minus by 1.
#teamtrees #WAP (Water And Plant)
For each expression, use a property to write an equivalent expression. Tell which property you used.
1. (ab)c =
2. 3y + 4y =
3. 6 x 7 =
Answers
Answer:
1. is the answer
Step-by-step explanation:
Because i did the test
Jonas has 3 more than two times the number of video games that Amber has. Amber has 12 games. How many does Jonas have? To solve this problem using algebra, which of the following is one step that you will take?
Answers
Answer:
36
Step-by-step explanation:
So Jonas has ? number of games.
Multiply 12 by 3.
You get thirty-six.
So Jonas has thirty-six games.
One step you take is multiplying 12 by 3.
I hope this helps! :)
!!!ANSWER IMEDDIATELY!!! What is the area of this trapezoid?
Answers
Answer:
A
Step-by-step explanation:
I worked it out :)
Ay anyone willing to help me with my work kinda lost
Answers
Okaayyy
Set B has the greater mode
Write an equation for the function whose graph is described.
The shape of f(x) = |x|, but shifted 19 units up and then reflected in the x-axis
Answers
Answer:
f(x)=-|x|+19
Step-by-step explanation:
so shifted 19 units up means
abosolute value of x + 19
and reflected in the x axis means that you have to put the - before the abosolute value.
so -|x|+19