If f is a function such that f(0) = 2, f(1) = 3, f(x + 2) = 2f(x) - f(x + 1) for every real x, then f(5) is
Answers
To find f(5), we can use the given recursive formula: f(x + 2) = 2f(x) - f(x + 1). We can apply this formula repeatedly to find f(5).
f(3) = 2f(1) - f(2) = 2(3) - f(2)
f(4) = 2f(2) - f(3) = 2f(2) - (2(3) - f(2)) = 3f(2) - 6
f(5) = 2f(3) - f(4) = 2(2f(1) - f(2)) - (3f(2) - 6) = 4f(1) - 4f(2) + 6
We know that f(0) = 2 and f(1) = 3, so we can substitute those values in:
f(1) - f(0) = 1
f(2) - f(1) = -f(0) + 4
f(3) - f(2) = -2f(0) + 5
f(4) - f(3) = 4f(0) - 11
We can solve this system of equations to find f(2) and f(4):
f(2) = -1
f(4) = -7
Now we can substitute these values into the expression we found for f(5):
f(5) = 4f(1) - 4f(2) + 6 = 4(3) - 4(-1) + 6 = 22
Therefore, f(5) = 22.
Hello! Based on the given information, let's find the value of f(5) using the provided recursive formula:
f(x + 2) = 2f(x) - f(x + 1)
We have f(0) = 2 and f(1) = 3. To find f(5), we'll first find f(2), f(3), and f(4).
For f(2), let x = 0:
f(2) = 2f(0) - f(1) = 2(2) - 3 = 4 - 3 = 1
For f(3), let x = 1:
f(3) = 2f(1) - f(2) = 2(3) - 1 = 6 - 1 = 5
For f(4), let x = 2:
f(4) = 2f(2) - f(3) = 2(1) - 5 = 2 - 5 = -3
Finally, for f(5), let x = 3:
f(5) = 2f(3) - f(4) = 2(5) - (-3) = 10 + 3 = 13
So, f(5) is 13.
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Related Questions
5) The floor of a room is in the shape of
a rectangle. The room is c meters long
and the width of the room is 2cm less
than its length.
a) write in terms of c;
i) the width of the floor
ii) the area of the floor
b) If the area of the room is 15cm²,
write down an equation in c to show
this information.
c) Use the equation to find the length
and width of the room.
Answers
Answer: a) i) The width of the floor can be expressed in terms of c as: w = c - 2 cm.
ii) The area of the floor can be expressed in terms of c as: A = c * (c - 2) cm^2.
b) If the area of the room is 15 cm^2, then we can write the equation as:
c * (c - 2) = 15.
c) Solving for c, we get:
c^2 - 2c - 15 = 0.
Using the quadratic formula, we find that:
c = 5 or c = -3.
Since the length of the room cannot be negative, we choose c = 5.
Therefore, the length of the room is 5 cm and the width of the room is 3 cm.
Step-by-step explanation:
Graph the solution to this inequality on the number line.
−4m+3>11
Answers
Subtract numbers
-4m>11-3
Evaluate and subtract
-4m>8
Divide by -4
Solution
M<-2
Answer: The person above me is correct. Here is a picture if you still dont get it..
Step-by-step explanation:
whats is the answer for 2y-x=5
Answers
Answer:
That's the answer in the photo.
3. Consider the following system: →0.85→0.85→ Determine the probability that the system will operate under each of these conditions: a. The system as shown. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.) b. Each system component has a backup with a probability of .85 and a switch that is 100 percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places. c. Each system component has a backup with a probability of .85 and a switch that is 90 percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)
Answers
a. The probability that the system will operate as shown is approximately 0.6141.
b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.
c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.
a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:
Probability = 0.85 × 0.85 × 0.85
Probability ≈ 0.6141
The probability that the system will operate as shown is approximately 0.6141.
b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:
Probability = 0.85 × 0.85 × 0.85
Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.
c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:
Probability = 0.85 × 0.90 × 0.85
Probability ≈ 0.6485
The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.
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Riley is saving up to buy a new television. She needs a total of $1,161.59. Riley has saved $200.39 already and earns $80.10 per week at her job. How many weeks does Riley need to work to save enough money to buy the new television?
Answers
Answer:
12 weeks
Step-by-step explanation:
I will use x to describe the amount of weeks.
200.39 (amount already have) + 80.10x (amount per week) = 1161.59 (total amount needed)
Now, just solve for x.
80.10x = 961.2
x = 12
the 2012 national health and nutrition examination survey reports a 95% confidence interval of 99.8 to 102.0 centimeters for the mean waist circumference of adult women in the united states. what is captured by this confidence interval?
Answers
95% confidence interval represents that the true mean waist circumference of all adult women in the United States falls within the range of 99.8 to 102.0 centimeters .
Confidence interval is equal to 95%
As reported by the 2012 National Health and Nutrition Examination Survey.
In the United States,
Mean waist circumference of adult women =99.8 to 102.0 centimeters
Randomly sample a large number of adult women from the United States.
And calculate their mean waist circumference.
95% of the time the true mean waist circumference of all adult women.
In the United States would be captured by the interval of 99.8 to 102.0 centimeters.
Confidence interval only applies to the population of adult women in the United States and cannot be extrapolated to other populations or groups.
Confidence interval is based on the specific sample and methodology used in the survey .
May not necessarily represent the true population parameter with complete accuracy.
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What is the distance, X between Jon's house and Maria's house?
Answers
Answer:
20ft
Step-by-step explanation:
Origami Is the Japanese art of paper folding the diagram below represents an unfolded paper Kabuto a Samurai warriors helmet which of the following are pairs of congruent segments
Answers
In general, two congruent segments have the same measure. Since no more information about the figure is given, we would need to estimate the measurement of each of its segments.
A) Notice that
\(\begin{gathered} FR=RN \\ and \\ RN=RT+TN \\ \Rightarrow FR=RT+TN \\ \Rightarrow FR\ne TR \end{gathered}\)B)
\(\begin{gathered} BC=PO=IJ=LM \\ \Rightarrow BC=PO \end{gathered}\)C)
\(\begin{gathered} RI^2=RU^2+UI^2 \\ \Rightarrow RI\ne RU \end{gathered}\)D)
\(\begin{gathered} RI=RM=RC=RO \\ \Rightarrow RI=RM \end{gathered}\)E)
\(\begin{gathered} IK=MK=CA=AO \\ \Rightarrow IK=MK \end{gathered}\)Thus, the answers are options B, D, and E.If TGS = KEL, which angle in KEL corresponds to T?
Answers
Hello.
If ΔTGS ≅ ΔKEL, then angle ∠T ≅ ∠K because:
∠T ≅ ∠K
∠G ≅ ∠E
∠S ≅ ∠L
Answer:
Then it is K
But you aren't giving me a lot of information
to work with here, so I answered it the best I know-how.
Step-by-step explanation:
:) Hope you enjoy it :)
which expressions below does not give the area of this figure
Answers
Answer:
The answer is vv
Step-by-step explanation:
The 3rd answer, ab+ac, that expression is wrong. ac+bc may be correct or wrong,
Which equation represents a circle with a center of (6,-3) and a radius of 4?
Answers
Answer: (x-6)2 + (y+3)2=4
Step-by-step explanation:
I’m smart like dat cuh
The answer is (x-6)^2+(y+3)^2=4
The areas of three circles are shown.
Circle X
Circle Y
Circle z
A=9x cm?
A-
cm?
A = 27.5 cm
Not drawn to scale
Which list shows the circles in order from greatest area to least area?
A. Circle Z, circle Y, circle X
B. Circle Y, circle Z, circle X
C. Circle X, circle Z, circle Y
D. Circle X, circle Y, circle z
Answers
Answer:
C. Circle X, circle Z, circle Y
Step-by-step explanation:
Given
Circles X, Y and Z
Required
Order from greatest to highest
First, we need to simplify the given areas;
For Circle X
\(A = 9\pi\)
Take \(\pi\) as 3.14
\(A = 9 * 3.14\)
\(A = 28.26\)
For Circle Y
\(A = \frac{\sqrt3}{2}\)
This gives
\(A = \frac{1.732}{2}\)
\(A = 0.866\)
For Circle Z
\(A = 27.5\)
By comparing the above areas;
X has the largest area; followed by Z and then Y
Hence,
option C answers the question
Answer:
x,z,y
Step-by-step explanation:
Prb. 2. A polymer sample has the following weight fraction distribution
wₓ=kx³ x=1,2,3,4,5 only
where wₓ is the weight fraction of x-mer. Calculate xₙ,x and the polydispersity index. Show all your work.
Answers
The weight fraction distribution of the polymer sample suggests a polydispersity index of 979/225, with xₙ and x both equal to 5.
xₙ, x, and the polydispersity index is calculated by determining the values of k, xₙ, and x based on the given weight fraction distribution.
First, we consider the weight fractions for each x-mer:
w₁ = k(1)³ = k
w₂ = k(2)³ = 8k
w₃ = k(3)³ = 27k
w₄ = k(4)³ = 64k
w₅ = k(5)³ = 125k
Since the sum of all weight fractions should be equal to 1, we set up the following equation:
w₁ + w₂ + w₃ + w₄ + w₅ = 1
k + 8k + 27k + 64k + 125k = 1
225k = 1
Solving for k:
k = 1/225
Now, we find the xₙ and x values. The weight fraction distribution is given by the equation wₓ = kx³.
For xₙ, we find the highest x value for which the weight fraction is non-zero. In this case, we see that w₅ = 125k, which is non-zero. Therefore, xₙ = 5.
For x, we find the x value at which the weight fraction distribution reaches its peak. We determine this by finding the maximum weight fraction among all x-mer fractions. In this case, we observe that w₅ = 125k is the highest weight fraction. Therefore, x = 5.
Finally, we calculate the polydispersity index (PDI). The polydispersity index is defined as the ratio of the weight average molecular weight (Mw) to the number average molecular weight (Mn). It is calculated using the following formula:
PDI = Mw / Mn
In our case, we express Mw and Mn using the weight fraction distribution:
Mw = Σ(wₓ * x) = w₁ * 1 + w₂ * 2 + w₃ * 3 + w₄ * 4 + w₅ * 5
= k * 1 + 8k * 2 + 27k * 3 + 64k * 4 + 125k * 5
= k + 16k + 81k + 256k + 625k
= 979k
Mn = Σ(wₓ) = w₁ + w₂ + w₃ + w₄ + w₅
= k + 8k + 27k + 64k + 125k
= 225k
Substituting the values of k from earlier:
Mw = 979 * (1/225)
Mn = 225 * (1/225)
PDI = Mw / Mn
= (979/225) / (225/225)
= 979/225
Therefore, the polydispersity index (PDI) is 979/225, and xₙ = 5 and x = 5 based on the given weight fraction distribution.
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————-PLEASE HELP————
Oscar has a $2,500 balance on his credit card that accumulates 14.5% interest compounded annually. Which of the following could be used to find the balance on the card after 5 years?
Answers
Answer:
35$
Step-by-step explanation:
It will take 10 years and 11 months to payoff the balance. The total interest is $2,574.43
Can someone PLEASE help me? I need help ASAP. Show work please
Answers
The volume of the triangular prism is 32.8 m³.
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
To find the volume of the triangular prism, we need to use the formula:
Volume = (Area of base) x Height
We are given the surface area of the prism, which includes the area of all five faces. However, we only need the area of the two triangular faces, since the base of the prism is a triangle.
The area of a triangle is given by the formula:
Area = (base x height) / 2
Substituting the given values, we have:
Area of each triangular face = (4.1 m x 2 m) / 2 = 4.1 m²
The total area of the two triangular faces is therefore:
2 x 4.1 m² = 8.2 m²
Now, we can use the formula for the volume of a prism:
Volume = (Area of base) x Height
Substituting the given values, we have:
Volume = (8.2 m²) x 4 m = 32.8 m³
Therefore, the volume of the triangular prism is 32.8 m³.
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If f(x) = -3x - 9, what is the value of f(6)?
Answers
Answer:
-27
Step-by-step explanation:
if f(6) you plug it into x
-3(6)-9
-18-9
-27
what is the product of 7/11 and 3/7
Answers
Answer:
3/11
Step-by-step explanation:
when you multiply 2 fractions you multiply the numerators and the denominators
(7/11 )*(3/7) = 7*3/11*7 now 7 can simplify so we have 3/11
Answer.
together is 0.27272727272
Step-by-step explanation:
hope it helps if not let me know comment
To make a fruit smoothie, Olivia uses 4 blueberries, 3 strawberries, 1 banana, 5 orange slices, and 2 slices of mango. What is the ratio of blueberries to banana?
Answers
Thus, the ratio for the number of blueberries to banana is 4:1.
Define about the ratios of the numbers?A ratio in mathematics is a correlation of at least two numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or integer that is dividing is referred to as the consequent.
A ratio compares two numbers by division. Comparing one quantity to the total, for example the dogs that belong to all the animals in the clinic, is known as a part-to-whole analysis. These kinds of ratios occur considerably more frequently than you might imagine.
The given data for preparing fruit smoothie:
4 blueberries, 3 strawberries, 1 banana, 5 orange slices, and 2 slices of mango.
Then,
ratio of blueberries to banana:
blueberries/banana = 4/1
Thus, the ratio for the number of blueberries to banana is 4:1.
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Help asap: use the number line to find the coordinate of p that represents the weighted average of the set of points such as point c has a weight of 3, and point e has a weight of 5
Answers
The coordinates weighted average is 6.
How is the weight average calculated?The whole query is as follows:
The weights of the coordinates 3 and 8 are 2 and 3, respectively. Additionally, we must determine the weighted average.
The parameters are as follows:
Three has a weight of two.
The weight of coordinate 8 is 3.
Next, the weight average is determined as follows:
Weight average is equal to the product of the weight and the coordinates.
We thus have:
Average weight: (3 * 2 + 8 * 3)/(2 + 3)
Assess the quotient.
Average weight = 6
Consequently, the coordinates' weighted average is 6
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what is 0.8w+3.6 factored
Answers
Answer:
4(0.2w + 0.9)
Ronald bought 1.5 pounds of red apples and 0.75 pounds of yellow apples. He bought 1.6 times as many pounds of green apples as red apples and yellow apples combined.
How many pounds of green apples did Ronald buy?
Answers
Answer:
To find the number of green apples he bought, We do the following:
calculate the total mass of red and yellow apples bought 1.5+0.75=2.25 poundsSince the mass of green apples bought was 1.6 times the combined mass of yellow and red apples bought we get;2.25×1.6=3.6pounds He bought 3.6 pounds green applessolve the following system of equations. if there is no solution, write dne in each coordinate of the ordered triplet. if there are an infinite number of solution, write each coordinate in terms of z . z. x 7
Answers
DNE in each coordinate of the ordered triplet are y is -7 , DNE ,y is-2.
Whais the explanation?1.) 2+3 = y + 12
Make y the formula's subject after adding the LHS.
5 = y + 12
Y = 5 - 12
Y = - 7
The answer to the equation is -7
2.) 2 + 13 = 1 +8
The equation cannot have a solution since there is no unknown variable and the sum of the numbers on the left hand side (LHS) does not equal the sum of the numbers on the right hand side (RHS).
3.) y - 7 = 2 - 11
RHS is added, and y is become the formula's subject.
Y - 7 = -9
Y = -9 + 7
Y = -2
The equation's answer is -2.
The complete question is:Solve the following system of equations. If there is no solution, write DNE in each coordinate of theordered triplet. If there are an infinite number of solution, write each coordinate in terms of z.2+3 = y + 12
2 + 13 = 1 +8
y - 7 = 2 - 11
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2. A restaurant employs five people. The two cooks work 36 hours
each per week for R36 an hour, and the three waiters work
30 hours each per week for R28 an hour. What does the
restaurant pay its five employees in total per week?
Answers
Answer:
Total amount = R5112
Step-by-step explanation:
Let the cooks be C.
Let the waiters be W.
Given the following data;
Number of cooks, C = 2
Number of waiters, W = 3
a. To find the amount earned by each cook;
C = 36 * R36 = R1296
b. To find the amount earned by each waiter;
W = 30 * R28 = R840
c. To find the total amount earned by the employees;
Total amount = 2C + 3W
Total amount = 2(1296) + 3(840)
Total amount = 2592 + 2520
Total amount = R5112
Is 1/-4 the same as -1/-4
Answers
tell me how to solve 3 1/2 x 2 3/4
Answers
Answer:
9.625
Step-by-step explanation:
(3 1/2) x (2 3/4) = 9.625
Answer:
.........................
I NEED HELP ASAP PLZZZ HELPP
PLZZ I need this done in like 10 minutes
Answers
Answer:
a) $60
b) $132
Step-by-step explanation:
one ticket costs $48/4 = $12
a) 5 tickets will cost 5*12 = $60
b) 11 tickets will cost 11*12 = $132
Answer:
you answer is b 11 movie tickets
Find the area. Give your answer as a simplified radical.
Answers
First we need to know the measure of the side, we can use the next trigonometric function
AE=2
\(\tan (30)=\frac{AE}{BE}=\frac{2}{BE}\)we isolate the BE
\(BE=\frac{2}{\tan(30)}=2\sqrt[]{3}\)the area of triangle ABE
\(A_{\text{ABE}}=\frac{1}{2}\cdot2\cdot2\sqrt[]{3}=\text{ }2\sqrt[]{3}\)For the total area of the rhombus is
\(A=4(2\sqrt[]{3})\)\(A=8\sqrt[]{3}\)4. There are major chords built on what three notes (with all white notes and no accidentals)? O CFG O ABC GEB OCDE
Answers
The three major chords built on white notes without accidentals are:
1. C major chord (C, E, G)
2. F major chord (F, A, C)
3. G major chord (G, B, D)
These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.
Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.
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When Mei was born, her parents gave her 6 dolls
to start her collection. Each year, she receives
4 new dolls as gifts. What function, f(x), models
the total number of dolls in her collection after x
number of years?
f(x) =
Plz help I will mark brainliest
Answers
If her parents had given her six dolls to begin her collection. She receives four brand-new dolls as presents every year. After x years, the function f(x) models that she would have a total of f(x) =6+4x. dolls in her collection.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that, When Mei was born, her parents gave her 6 dolls to start her collection. Each year, she receives 4 new dolls as gifts.
The function, f(x), models the total number of dolls in her collection after x number of years is,
f(x) =6+4x.
Thus, if her parents had given her six dolls to begin her collection. She receives four brand-new dolls as presents every year. After x years, the function f(x) models that she would have a total of f(x) =6+4x. dolls in her collection.
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Find the area of the figure.
area
units2
Answers
Answer:
\(33 units^{2}\)
I counted the squares.