What is the Fibonacci sequence?
The Fibonacci sequence is a set of integers (the Fibonacci numbers) that starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers. The sequence follows the rule that each number is equal to the sum of the preceding two numbers.
The Fibonacci sequence begins with the following 14 integers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ...
Each number, starting with the third, adheres to the prescribed formula. For example, the seventh number, 8, is preceded by 3 and 5, which add up to 8.
The sequence can theoretically continue to infinity, using the same formula for each new number. Some resources show the Fibonacci sequence starting with a one instead of a zero, but this is fairly uncommon.
Example 1: Starting with 0 and 1, write the first 5 Fibonacci numbers.
Solution: The formula for the Fibonacci sequence is Fn= Fn-1+Fn-2
The first and second terms are 0 and 1, respectively.
F0 = 0 and F1 = 1.
F2 = F0 + F1 = 0+1 = 1 is the third term.
F3 = F2+F1 = 1 + 1 = 2 is the fourth term.
F4 = F3+F2 = 1+2 = 3 is the fifth term.
The Fibonacci sequence’s first five terms are 0,1,1,2,3.
Example 2: Find the Fibonacci series’ next term: 0, 1, 1, 2, 3, 5…
Solution: The preceding two Fibonacci terms are the next term in the series.
As a result, the word that must be used is – 3 + 5 = 8
Example 3: What is the significance of Fibonacci numbers?
Solution: In financial statement analysis, Fibonacci numbers are pretty helpful. In addition, the Fibonacci number series may be utilized to provide valuable proportions or ratios for business people.
Example 4: Find the 12th term of the Fibonacci sequence if the 10th and 11th terms are 34 and 55, respectively.
Solution: Using the Fibonacci Sequence recursive formula, we can say that the 12th term is the sum of the 10th term and the 11th term
12th term = 10th term + 11th term
= 34 + 55
= 89
The 12th term of the Fibonacci sequence is 89.
Example 5: The 14th term in the sequence is 377. Find the next term.
Solution: We know that the 15th term = the 14th term × the golden ratio.
F15 = 377 × 1.618034
≈ 609.99 = 610
The 15th term in the Fibonacci sequence is 610.
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If 7cakes cost $6.30 what is the cost of 12 such cakes
Answer:
$10.8
Step-by-step explanation:
First, to determine the price of one cake divide 6.30/7
You will determine one cake costs 90 cents.
So, multiply 0.90 by 12, and you get $10.8
How many times larger is (1.143 x 101) than (9 x 10−1)?
0.127
7.87
10.287
12.7
how did you get your answer?
(1.143 × 10¹) is 12.7 times larger than (9 × 10⁻¹). The correct option is the last option 12.7
Calculating magnitudeFrom the question, we are to determine the factor by which 1.143 × 10¹ is larger than 9 × 10⁻¹
To determine how many times larger the number is, we will divide 1.143 × 10¹ by 9 × 10⁻¹
Carrying out the division operation
(1.143 × 10¹) ÷ (9 × 10⁻¹)
= (1.143 ÷ 9) × (10¹ ÷ 10⁻¹)
= (1.143 ÷ 9) × (10¹ ÷ 10⁻¹)
= 0.127 × (10¹ ⁻ ⁽⁻¹⁾)
= 0.127 × (10¹ ⁺ ¹)
= 0.127 × (10²)
= 0.127 × 10²
= 12.7
Hence, (1.143 × 10¹) is 12.7 times larger than (9 × 10⁻¹). The correct option is the last option 12.7
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What’s the answer?
5x + 12(19 - x) = 19(1678)
Okay so for context there's 4 pounds of pears 3 pounds of grapes 6 pounds of pineapple and 3 pounds of oranges
OKAY NOW FOR THE ACTUAL QUESTION
Jorge wants to bring 2 pounds total of this fruit salad to a potluck dinner, how much of each ingredient should he use?
The total amount of each ingredient are as follows;
Pears = 1/2 pound
Grapes = 3/8 pounds
Pineapple = 3/4 pounds
Oranges = 3/8 pounds
How to Solve Ratio Problems?
We are given the amounts of fruits as;
4 pounds of pears
3 pounds of grapes
6 pounds of pineapple
3 pounds of oranges
Now, total pounds of fruits = 4 + 3 + 6 + 3 = 16 fruits
Ratio of pears = 4/16 = 1/4
Ratio of grapes = 3/16
Ratio of pineapple = 6/16 = 3/8
Ratio of oranges = 3/16
Thus. amount of each ingredient required are;
Pears = 1/4 * 2 = 1/2 pound
Grapes = 3/16 * 2 = 3/8 pounds
Pineapple = 3/8 * 2 = 3/4 pounds
Oranges = 3/16 * 2 = 3/8 pounds
Thus, the total amount of each ingredient are as follows;
Pears = 1/4 * 2 = 1/2 pound
Grapes = 3/16 * 2 = 3/8 pounds
Pineapple = 3/8 * 2 = 3/4 pounds
Oranges = 3/16 * 2 = 3/8 pounds
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5. Please help and show work
Please help on the middle!!
Answer: I just points so rate this a 10
Step-by-step explanation:
Answer:
owi4w85e963696w95witote5iw47e
Is there a difference between [tex]-\frac{x}{y}[/tex] and [tex]\frac{-x}{-y}[/tex] ?
Do they mean different things?
There is a difference between the expressions -x/y and -x/-y
How to determine if there is a difference between the expression?The expressions are given as:
-x/y and -x/-y
When the expression -x/-y is evaluated, we have:
-x/-y = x/y
This means that
-x/y = -x/y
-x/-y = x/y
When the above expressions are compared, we can see that both expressions are not equal
Hence, there is a difference between the expressions -x/y and -x/-y
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Two angles are complementary if their sum is 90°. A larger angle measures three degrees less than
twice the measure of the smaller angle. If x represents the measure of the smaller angle and these two
angles are complementary, find the measure of each angle.
Answer:
31 and 59
Step-by-step explanation:
We can figure this out by putting the words into an equation
"three degrees less than twice the measure of the smaller angle"
we know the smaller angle = x, so:
twice the smaller angle=2x
3 degrees less=-3
you then put those into an equation where they all add up to equal 90 and simplify
x+2x-3=90
3x-3=90
3x=93
x=31
you then plug that into the equation we would have for the second angle:
2x-3
2(31)-3
62-3
59
the first angle would be 31 and the second angle would be 59
:D
Lucia walked of the length of the Tremont Trail before
stopping for a rest. How far had Lucía walked on the trail?
Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail
We are told in the question that
Linda walked 3/4 of the length of the Tremont Trail before stopping for a rest.
From the question, the length of the Tremont Trail = 3 1/2 miles
Hence, the distance (how far )Linda has walked =
3/4 of 3 1/2 miles
= 3/4 × 3 1/2 miles
= 3/4 × 7/2 miles
= 21/8 miles
= 2 5/8 miles or 2.625 miles
Therefore, Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail.
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Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 19 of the 59 boxes on the shelf have the secret decoder ring. The other 40 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that both of them have the secret decoder ring?
The probability that both of the boxes one would select had the decoder ring is 9.9%.
Given, the store manger gives the surety that 19 out of 59 boxes on the shelf have the secret decoder ring.
The boxes on the shelf which have a different gift inside is = 40 boxes.
If one randomly selects two boxes from the shelf to purchase, the probability that both of them have the secret decoder ring = ?
You can imagine that someone used invisible link to label each box with a number, and knows that boxes number 1 through 19 have decoder rings, while boxes number 20 through 59 have other gifts.
There are 59×58/2
= 3422/2
= 1711 possible sets of two boxes that one could select, but there are only 19 × 19/2
= 342/2
= 171 possible sets of two boxes with decoder rings.
The fraction of possible pairs of boxes where both boxes have the secret decoder ring is:
= 171/1711
= 0.099 = 9.9%
Hence there is 9.9% probability that both of the boxes one might select had a decoder ring.
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what is (8^5)^4 (answer must include an exponent )
Answer:
[tex]8^{20}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then
[tex](8^5)^{4}[/tex] = [tex]8^{5(4)}[/tex] = [tex]8^{20}[/tex]
The length of a rectangle is 1 fr more than double the width, and the area of the rectangle is 45 ft^2. Find the dimensions of the rectangle.
The length and width of rectangle is 10 feet and 4.5 feet.
This problem is related to the area and perimeter of plane figures. We have to find the dimensions of the rectangle using the data given.
Given, the length is 1 feet more than twice the width.
Let the width be a feet.
So, length = (2a+1) feet
Now according to question,
[tex](2a+1)(a)=45\\[/tex]
⇒ [tex]2a^{2} +a-45=0[/tex]
On solving the above quadratic equation we get a=4.5 feet.
So, length = 10 feet.
The dimension of rectangle is 10 feet × 4.5 feet.
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How do I solve this problem?
On Friday, 4/7 of Parkden School chose pasta for lunch, 1/5 chose pizza and the rest chose salad. What fraction of the pupils chose salad?
Answer:
i think is 7/12
because if 4/7 chose pasta,1/5 chose pizza then we add 7+5=12 then we sudstract 12-4-1 = 7.
hope that helps
An unknown distribution has a mean of 80 and a standard deviation of 12. A sample size of 95 is drawn randomly from the population.
Find the probability that the sum of the 95 values is less than 7,450. (Round your answer to 4 decimal places)
The probability that the sum of the 95 values is less than 7450 is 0.1002
Given Data :
An unknown distribution has a
Mean (μ) = 80
Standard Deviation (σ) = 12
Sample Size (n) = 95
is drawn from the population.
∑X ≈ N (95 * 80, [tex]\sqrt{95}[/tex] * 12)
= N (7600, 116.96)
The Probability that the sum of the 95 values is less than 7450 is given as follows :
P(∑x < 7450) = P [(∑x - μ) / s] < [(7450 - 7600) / 116.96
= P(Z < -1.282) = 0.1 (From Z table)
Hence, the probability that the sum of the 95 values is less than 7450 is 0.1002
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Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 20. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 80 and 120? (b) What percentage of people has an IQ score less than 60 or greater than 140? (c) What percentage of people has an IQ score greater than 160?
Using the Empirical Rule, the percentages are given as follows:
a) 68%.
b) 5%.
c) 0.15%.
What does the Empirical Rule state?It states that, for a normally distributed random variable, approximately:
68% of the values in the distribution are within 1 standard deviation of the mean.95% of the values in the distribution are within 2 standard deviations of the mean.99.7% of the values in the distribution are within 3 standard deviations of the mean.For item a, 80 and 120 are within one standard deviation of the mean, hence:
68% of people has an IQ score between 80 and 120.
For item b, the bounds are within two standard deviations of the mean, hence 5% of the observations are outside this interval, that is:
5% of people has an IQ score less than 60 or greater than 140.
For item c, 160 is three standard deviations above the mean. Considering the symmetry of the normal distribution, 0.3/2 = 0.15% of people has an IQ score greater than 160?.
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the distance between two cities on a map measures 3.75 inches. the scale shows that 2 inches is equal to 50 miles . how many miles apart are the cities
Which equation best represents the graph shown below? Explain in detail how you arrived at your answer by stating each of the mathematical transformations necessary to produce the graph.
please I need help
In the graph we have a parabola, and its equation is y = (x - 2)^2 - 3
How to find the equation of the graphed function?
In the graph, we can see a parabola.
We only need to identify 3 parts, which are the two x-intercepts (if it has) and the y-intercept.
Remember that if the vertex and the y-intercept. Remember that if the vertex is (h, k) and the leading coefficient is a, then we can write the equation as:
y = a*(x - h)^2 + k
In the image we can see that the vertex is (2, -3), then:
y = a*(x - 2)^2 - 3
And the y-intercept is y = 1, then if we evaluate in x = 0 we should get y = 1, replacing that we get:
1 = a*(0 - 2)^2 - 3
1 = a*4 - 3
1 + 3 = a*4
4/4 = a = 1
Then the quadratic equation is y = (x - 2)^2 - 3
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.Solve 2x−1<4 or −5x−3>−3 and write the solution in interval notation.
The interval notation is { 5/ 2 < x > 0 }
How to determine the valueGiven the inequalities;
2x−1<4−5x−3>−3To determine the value of x, we have;
2x - 1 < 4
collect like terms
2x < 4 + 1
2x < 5
Make 'x' the subject
x < 5/ 2
−5x −3 > −3
collect like terms
-5x > -3 + 3
-5x > 0
x > 0
Thus, the interval notation is { 5/ 2 < x > 0 }
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A shopkeeper allows a discount of 10% on the marked price of an article.What was the marked price of the article which costs him 1800 and makes profit of 15%.
Answer:
$243 is his profit
Step-by-step explanation:
Answer: $4100
Step-by-step explanation:
discount = [tex]\frac{1800}{90}[/tex]×100 = 2000
profit = [tex]\frac{115}{100}[/tex]×2000 = 2300
market price = 2300 + 1800 = 4100
Please help!!!!!!! thx xxx
Start by dividing both sides by G, giving us
[tex]\frac{F}{G}=\frac{m_{1} m_{2} }{d^{2} } }[/tex]. Multiply both sides by d^2. [tex]\frac{F}{G}(d^{2})=m_{1} m_{2}[/tex].
Finally, divide both sides by m2.
[tex](\frac{F}{G}\div{m_{2}}) (\frac{d^{2} }{m_{2} } )=m_{1}[/tex]
Hope this helps! This was a tough problem for me too.
7. Alicia and Dexter are each walking on a straight path. For a particular -second window of time, each has their velocity (in feet per second) measured and recorded as a function of time. Their respective velocity functions are plotted in .
Figure 1.4.14. The velocity functions and for Alicia and Damon, respectively.
Determine formulas for both and .
What is the value and meaning of the slope of ? Write a complete sentence to explain and be sure to include units in your response.
What is the value and meaning of the average rate of change of on the interval ? Write a complete sentence to explain and be sure to include units in your response.
Is there ever a time when Alicia and Damon are walking at the same velocity? If yes, determine both the time and velocity; if not, explain why.
Is is possible to determine if there is ever a time when Alicia and Damon are located at the same place on the path? If yes, determine the time and location; if not, explain why not enough information is provided.
(a) The formula for velocity functions is:
f(t)=0.4t+4
g(t)=0.9t
(b) The slope of the v-t graph gives us the acceleration which as found above is 0.4 ft/sec². The slope of the v-t graph gives us the acceleration which as found above is 0.9 ft/sec².
(c) Damon is accelerating with 0.9 ft/sec² in intervals [4,8].
(d) Both are walking at a velocity of 7.2 ft/sec at t=8 sec.
What is velocity?
The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.(a) For Alicia,
m=(Δv/Δt)=(8-4)/(10-0)=4/10=0.4
f(t)=0.4t+4
for Damon,
m=(Δv/Δt)=(9-0)/(10-0)=9/10=0.9
g(t)=0.9t
The formula for velocity functions is:
f(t)=0.4t+4
g(t)=0.9t
(b) Value and meaning of the slope is
m for Alicia =0.4
Slope is determined (Δv/Δt)=(8-4)/(10-0)=4/10=0.4 ft/sec².
So, the slope of the v-t graph gives us the acceleration which as found above is 0.4 ft/sec².
m for Damon=0.9
Slope is determined (Δv/Δt)=(9-0)/(10-0)=9/10=0.9 ft/sec².
So, the slope of the v-t graph gives us the acceleration which as found above is 0.9 ft/sec².
(c) Value and meaning of the average rate of change on the interval:
the average rate of change of Δ on the interval [4,8] =
[tex]\frac{Velocity\ at\ 8\ sec - Velocity\ at\ 4\ sec}{Time\ interval\ (8-4)\ sec}[/tex]
=(7.2-3.6)/(8-4)=(3.6/4)=0.9 ft/sec²
So, Damon is accelerating with 0.9 ft/sec² in intervals [4,8].
(d) Let both are walking with the same velocity at t sec.
So, Let's equate their velocities
0.4t+4=0.9t
t=4/0.5 = 8 sec
The velocity of Alicia at 8 sec = 0.4(8)+4 = 7.2 ft/sec
The velocity of Damon at 8 sec = 0.9(8) = 7.2 ft/sec
So, both are walking at a velocity of 7.2 ft/sec at t=8 sec.
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Nine hundred ninety two hundred thousandths wrote in decimal form
Answer:
I think the answer is 9.920 please be careful with your answer I think it 9.920 because it says nine hundred and ninety two thousands so therefor the decimal need to be in between 9 and 9 I hope you get this correct!
step-by-step explanation:
Which linear equation represents the information shown in the table?
x y
–6 –1
0 0
12 2
Question 21 options:
y = –1/4x
y = 6x
y = 1/6x
y = –2x
Answer:
Only one equation fits all the information on the table which is:
y = 1/6x
Answer:
y = 1/6x
Step-by-step explanation:
To find the equation, let's see if each option works by plugging in x into each equation.
y = –1/4x
Plug -6 into x
y = –1/4(-6)
y = 1.5
y = –1/4x doesn't work because we didn't get -1.
y = 6x
Plug -6 into x
y = 6(-6)
y = -36
y = 6x doesn't work because we didn't get -1.
y = 1/6x
Plug 1/6x into x
y = 1/6(-6)
y = -1
Let's see if the other x values work.
Plug 0 into x
y = 1/6(0)
y = 0
Plug 12 into x
y = 1/6(12)
y = 2
y = 1/6x works.
y = –2x
Plug -6 into x
y = –2(-6)
y = 12
y = -2x doesn't work because we didn't get -1.
y = 1/6x is the only linear equation that worked and got all y values, so that is your answer.
Hope that helped and have a lovely rest of your day!
Rewrite the following statement using a number in scientific notation.
My new music player has a capacity of gigabytes 400. (Recall that giga means billion.)
My new music player has a capacity of _ enter your response here bytes.
(Use scientific notation. Use the multiplication symbol in the math palette as needed.)
4 x 10¹¹
Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.
400 billion in scientific notation = 4 x 10¹¹
We can complete the sentence as,
My new music player has a capacity of 4 x 10¹¹
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For the equation, find three ordered pair solutions by completing the table. Then use any two of the ordered pairs to graph the equation.
For the linear function x - y = 3, three ordered pairs are given as follows:
x = 3, y = 0.x = 1, y = -2.x = 0, y = -3.Using points (3,0) and (0,-3), the graph of the function is given at the end of the problem.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the function is:
x - y = 3.
In standard notation:
y = x - 3.
Hence three pairs of points are given as follows, replacing the value of x in the equation to find y.
x = 3, y = 0.x = 1, y = -2.x = 0, y = -3.The graph of the function is given at the end of the answer.
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Use f(x) = |x|
f(x) is shifted down 4 and right 3 to create h(x)
Which answer shows the correct function for h(x)
The function f(x) = |x|, after shifting it down by 4 units and right by 3 units can be written as -
(y - 4) - |x - 3| = 0
What is Modulus function?The modulus function can be written as follows -
|x| = x [for x ≥ 0]
|x| = - x [for x < 0]
Given that a function f(x) = |x| which is shifted down by 4 units and right by 3 units. Therefore, we can write -
y = f(x) = |x|
Change in y - coordinate = y + 4.
Change in x - coordinate = x - 3.
We will plot the graph of h(x) after the doing the given changes in the coordinates.
Now, we have -
y = |x|
y - |x| = 0
Change in y - coordinate can be written as -
(y + 4) - |x| = 0
Change in x - coordinate can be written as -
(y - 4) - |x - 3| = 0
Now, the graph of both f(x) and and h(x) is attached at the end.
Therefore, the function f(x) = |x|, after shifting it down by 4 units and right by 3 units can be written as -
(y - 4) - |x - 3| = 0
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Ettwice is three times as old as mavis. the sum of their age is 60. how old each
the answer to your question is Ettwice is 45 years old and Mavis is 15 years old. hope this helps
Step-by-step explanation:
15 * 3 = 45
45 + 15 = 60
HELPP!!
Ryan collects rainwater in a barrel for his garden. The barrel is filled with 15 gallons of water. Ryan used 6.8 gallons to water his garden in June and 5 and one-eighth gallons in July. How much water is left in the barrel?
1.) 3.075 gallons
2.) 5.125 gallons
3.) 5.178 gallons
4.) 16.675 gallons
Subtracting the initial amount of water from the amount used, the remaining amount of water is given by:
1.) 3.075 gallons.
How to find the remaining amount of water in the barrel?
To find the remaining amount of water in the barrel, we have to subtract the initial amount by the amount used.
We have that:
The initial amount was of 15 gallons.The amount used was of: 6.8 + 5 + 1/8(relative to the one-eight) = 11.925 gallons.Hence the remaining amount is:
15 - 11.925 = 3.075 gallons.
Which means that option 1 is correct.
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Answer: 3.075 gallons
Step-by-step explanation:
Oscar buys a bag of cookies that contains 7 chocolate chip cookies, 8 peanut butter cookies, 9 sugar cookies and 7 oatmeal cookies.
What is the probability that Oscar reaches in the bag and randomly selects a peanut butter cookie from in the bag and randomly selects a peanut butter cookie from
the bag, eats it, then reaches back in the bag and randomly selects a sugar cookie?
Give your answer as a fraction, or accurate to at least 4 decimal places.
The probability that Oscar reaches into the bag and randomly selects a peanut butter cookie from the bag and randomly selects peanut butter cookie from the bag eats it, then reaches back in the bag and randomly selects a sugar cookie is 0.07.
What is probability?
Probability is the branch of mathematics concerning numerical descriptions of how probable an event is to do, or how likely it's that a proposition is true. The probability of an event is a number between 0(zero)(zero) and 1(one), where, roughly speaking, 0(zero) indicates the impossibility of the event and 1(one) indicates certainty.The more advanced the probability of an event, the more likely it's that the event will do.These generalities have been given a self-evident fine formalization in probability proposition, which is used extensively in areas of study similar to statistics, mathematics, wisdom, finance, gambling, artificial intelligence, etc.
P(sugar | oatmeal) = (7/25)(6/24) = 0.07
The probability that Oscar reaches into the bag and randomly selects a peanut butter cookie from the bag and randomly selects peanut butter cookie from the bag eats it, then reaches back in the bag and randomly selects a sugar cookie is 0.07.
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$2,000 is the average price of a square foot. How much would you have to pay if you want to buy a 2 bedroom (1,200 sq ft) apartment in Manhattan ?
Answer:
$2,400,000
Step-by-step explanation:
Just multiply them together
