The first six values of the recursive function F(n+2) = 2F(n) + F(n+1) are 0, 1, 1, 3, 5, and 11.
We are given a recursive function:
F(0) = 0, F(1) = 1
F(n+2) = 2F(n) + F(n+1) , n ≥ 0
For n = 0:
F(0+2) = 2F(0) + F(0+1)
F(2) = 2(0) + 1
F(2) = 1
For n = 1:
F(1+2) = 2F(1) + F(1+1)
F(3) = 2(1) + 1
F(3) = 3
For n = 2:
F(2+2) = 2F(2) + F(2+1)
F(4) = 2(1) + 3
F(4) = 5
For n = 3:
F(3+2) = 2F(3) + F(3+1)
F(5) = 2(3) + 5
F(5) = 11
Hence, F(0) = 0, F(1) = 1, F(2) = 1, F(3) = 3, F(4) = 5, F(5) = 11.
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use the figure to find the ration in simplest form . AB/BC.
Answer: 3:2
Step-by-step explanation:
AB / BC = AB:BC
therefore, 6:4
6:4 simplified -> 3:2
Factorise the following:
X^2+2x
Answer:
x(x + 2)
Step-by-step explanation:
x² + 2x ← factor out the common factor x from each term
= x(x + 2)
If the two lines below are perpendicular and the slope of the red line is -7.
what is the slope of the green line?
OA
B. 7
O C.
C. -
D. -7
HEFF
5
10
Answer:
Step-by-step explanation:
10
Which describes the number and type of roots of the equation x^3 + 121x = 0
Answer:
x=0
Step-by-step explanation:
xx(x^2+121)=0
x=0
x^2+121=0
x=0
when y = 9 − 9x2 is rotated around the x-axis, a vertical strip of width δx creates a disk. the radius of this disk is r =
The radius of this disk r is ± 9 √(1 - 2x^2).
The radius of the disk created by rotating the strip of width δx around the x-axis can be found using the Pythagorean theorem. Consider a right triangle with the horizontal leg equal to δx, the vertical leg equal to the height of the strip (which is equal to 9 - 9x^2), and the hypotenuse equal to r. We have:
δx^2 + (9 - 9x^2)^2 = r^2
Expanding and simplifying the square on the right-hand side, we get:
δx^2 + 81 - 162x^2 + 81x^4 = r^2
Since δx is infinitesimal, we can neglect it compared to 81 and 162x^2. Thus,
r^2 ≈ 81 - 162x^2
Taking the square root of both sides, we get:
r ≈ ± 9 √(1 - 2x^2)
where the positive sign corresponds to the upper half of the disk and the negative sign corresponds to the lower half.
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please help if i don’t pass this i’m gonna cry
Therefore , the solution of the given problem of scale factor comes out to be new coordinate is (-4,5).
How can you find the scale factor of a dilation?To determine a dilated figure's scale factor, use the following simple formula: Scale factor is the product of the old shape's dimension and the new shape's dimension. A reduction is a scale factor that is more than zero but less than one, or 0 x 1.
Here,
Given :
=> dilation maps (2,3) to (4,6)
=> √(4-2)² + (6-3)²
=> √4 + 9
=>√13
Scale factor of dilation is :
=> 1/√13
and
=> (-6,3)
=> new coordinate is (-4,5)
Plot DEF with a scale factor of 2 with the origin (0,0) as the centre of dilation. To determine the new coordinates, add the scale factor of 2 to each x and y coordinate value as indicated in the formula above.
Therefore , the solution of the given problem of scale factor comes out to be new coordinate is (-4,5).
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Point C has coordinates (24, 16).
Point D has coordinates (10, 26).
What are the coordinates of the midpoint of line CD?
The coordinates of the midpoint of line CD is (17, 21).
A midpoint is a point that is equidistant from the endpoints of a line segment. It is the point that is exactly halfway between the two endpoints of the line segment.
The midpoint of a line segment is found by taking the average of the x-coordinates and the y-coordinates of the endpoints of the line segment. The coordinates of the midpoint can be determined using the formula below.
midpoint (x, y) = (x₁ + x₂/2, y₁ + y₂/2)
If point C has coordinates (24, 16) and point D has coordinates (10, 26), then the midpoint is:
midpoint (x, y) = (24 + 10/2, 16 + 26/2)
midpoint (x, y) = (34/2, 42/2)
midpoint (x, y) = (17, 21)
Therefore, the midpoint of line CD has the coordinates (17, 21).
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There are 120 students in the 6th grade 56% of them failed. How many failed, Round to the nearest whole number.
120 multiplied by 56% equals 67.2 students.
The number 67 becomes the result of rounding to the nearest whole number, which is 67.2.
Describe an example of a whole number.A collection of positive integers and zero, whole numbers are numbers without fractions. The set of integers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,... and it is denoted by the sign "W". Whole Numbers: W = 0 through 10 (inclusive).
How does math define a whole number?Absolute numbers those figures that contain zero and natural integers. neither a fraction nor a decimal. {0, 2, 3, 4, 5 6, 7, 8, 9,10, 11 …} Integer. A counting number, zero, or the negative.
The number of students who failed can be calculated by multiplying the total number of students by the percentage that failed:
120 students * 56% = 67.2 students
Rounding to the nearest whole number, 67.2 students becomes 67 students.
So, 67 students failed in the 6th grade.
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Overnight, the temperature in Chicago was just
–
7°F. But by the afternoon, the temperature had risen 9°F.
What was the temperature in Chicago that afternoon?
°F
The temperature in Chicago at afternoon is 16 °F if Overnight, the temperature in Chicago was just 7°F. But by the afternoon, the temperature had risen 9°F.
What is relation between celsius to fahrenheit ?
The relation between celsius to fahrenheit is (0°C × 9/5) + 32 = 32°F .
Given,
Overnight, the temperature in Chicago was just 7°F.
But by the afternoon, the temperature had risen 9°F.
So, given there was rise in the temperature
so,
the temperature in chicago could be = 7 + 9
= 16
Therefore, The temperature in Chicago at afternoon is 16 °F if Overnight, the temperature in Chicago was just 7°F. But by the afternoon, the temperature had risen 9°F.
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if ∫3−5f(x)dx=6, and ∫3−5g(x)dx=3 , then ∫3−5[2f(x) 6g(x)]dx=
The answer to the given problem is ∫3−5[2f(x) 6g(x)]dx = 108. This can be found by using the properties of integration and substituting the given values for the integrals of f(x) and g(x).
Given that:
∫3−5f(x)dx=6
∫3−5g(x)dx=3
We need to find: ∫3−5[2f(x) 6g(x)]dx
To solve this problem, we will use the properties of integration:
Property 1:
If c is a constant, then
∫cf(x)dx=c∫f(x)dx
Property 2:
If f(x) and g(x) are two functions, then
∫[f(x) + g(x)]dx = ∫f(x)dx + ∫g(x)dx
Using Property 1, we can rewrite the given equation as:
∫3−5[2f(x) 6g(x)]dx = ∫3−5[12f(x)g(x)]dx
Using Property 2, we can further simplify the equation as:
∫3−5[12f(x)g(x)]dx = ∫3−5[12f(x)]dx + ∫3−5[12g(x)]dx
Now we can substitute the given values:
∫3−5[12f(x)]dx + ∫3−5[12g(x)]dx = 12∫3−5f(x)dx + 12∫3−5g(x)dx
Substituting the given values for the integrals of f(x) and g(x), we get:
12∫3−5f(x)dx + 12∫3−5g(x)dx = 12(6) + 12(3)
Simplifying, we get:
12∫3−5f(x)dx + 12∫3−5g(x)dx = 12(6) + 12(3) = 12(9) = 108
Therefore, the answer is
∫3−5[2f(x) 6g(x)]dx = 108
The answer to the given problem is ∫3−5[2f(x) 6g(x)]dx = 108. This can be found by using the properties of integration and substituting the given values for the integrals of f(x) and g(x).
the complete question is :
if ∫3−5f(x)dx=6, and ∫3−5g(x)dx=3 , then ∫3−5[2f(x) 6g(x)]dx will be equal to ?
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How do you find the cov of X and Y?
Step-by-step explanation:
The covariance of two variables X and Y is a measure of the relationship between their changes. It is calculated as:
cov(X, Y) = (1/n) * sum((x_i - mean(X)) * (y_i - mean(Y)))
where n is the number of observations, x_i and y_i are the values of X and Y respectively for the i-th observation, mean(X) and mean(Y) are the means of X and Y respectively.
In Python, you can use the numpy library to calculate the covariance as follows:
import numpy as np
X = [x_1, x_2, ..., x_n]
Y = [y_1, y_2, ..., y_n]
cov = np.cov(X, Y)[0][1]
A measurement of the intensity and direction of the linear relationship between two random variables, X and Y, is called covariance. A definition of covariance is:
Cov(X, Y) is equal to E[(X - E(X))(Y - E(Y))].
where E[...] is the anticipated value operator and E(X) and E(Y) is the expected values of X and Y, respectively.
If Cov(X, Y) is positive, X and Y have the propensity to rise or fall together. Cov(X, Y) is a measure of the tendency for two variables to move in opposite directions. When Cov(X, Y) equals 0, X and Y are said to be uncorrelated.
You must be aware of the expected values as well as the joint probability distribution of X and Y in order to compute the covariance of X and Y.
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The composite figure above is made from an isosceles triangle and a rectangle. What is the area of the composite figure?
Answer:
Area of the composite figure is 516
Step-by-step explanation:
picture above
Write the following in usual form : (i) 4.567 × 108 (ii) 3.00856 × 103
Step-by-step explanation:
4.567×10^8 = 4567000000 is the right answer.3.00856×10^3 = 3008.56 is the right answer.Solve for the given variable. 9(4 + c) = 99
PLEASEEEEEEEEEEEEEEEE HURRY
Vocabulary How is a ratio table used to graph equivalent ratios?
A. Find the value of each ratio as a fraction and plot the fractions on a number line.
B. Find the differences of the values in the ratio table and plot the differences on a number line.
C. Use the values in the ratio table to write coordinate pairs for the points on the graph.
D. Use the equivalent ratio in lowest terms to plot the numerator on the x-axis and the denominator on the y-axis, then connect the two points.
Answer:
D. Use the equivalent ratio in lowest terms to plot the numerator on the x-axis and the denominator on the y-axis, then connect the two points.
which data set is represented by the modified box plot? box and whisker plot on a number line from 70 to 140 in increments of 5. the whisker ranges from 79 to 115. the box ranges from 88 to 106 with the vertical bar inside the box at 95. one dot mark above one hundred and thirty-six. responses 92, 88, 100, 136, 106, 59, 88, 86, 98, 115 92, 88, 100, 136, 106, 59, 88, 86, 98, 115 100, 88, 100, 136, 106, 79, 88, 86, 100, 115 100, 88, 100, 136, 106, 79, 88, 86, 100, 115 92, 88, 100, 127, 106, 79, 88, 86, 98, 115 92, 88, 100, 127, 106, 79, 88, 86, 98, 115 92, 88, 100, 136, 106, 79, 88, 86, 98, 115
The data set represented by the modified box plot is: 92, 88, 100, 136, 106, 79, 88, 86, 98, 115.A graphical depiction of a set of numerical data is a modified box plot.
The figure is made by drawing a box between the data's upper and lower quartiles with whiskers extending from each end of the box to the minimum and maximum values. The median is represented by the vertical bar inside the box.
In this scenario, the data is displayed on a number line with a whisker spanning from 79 to 115 and a range of 70 to 140 in 5 increments. The box runs from 88 to 106, with 95 being the median.
The single dot mark above 136 is an anomaly. The values in the data set are: 92, 88, 100, 136, 106, 79, 88, 86, 98, 115.
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6. A factory produces 32 tables in an 8-hour day. Calculate how many 8 tables are produced: a) in 1 hour b) in 3 days c) in a 5-day week 6 minutes hours
a) In 1 hour, 32 tables / 8 hours = 4 tables are produced in an hour.
b) In 3 days, 32 tables/day * 3 days = 96 tables are produced in 3 days.
c) In a 5-day week, 32 tables/day * 5 days = 160 tables are produced in a 5-day week.
d) 6 minutes hours: Not a valid unit of time to perform the calculation. Showing work is not applicable.
What is an example of a unitary method?
We can use the unitary approach to calculate 100% of an amount. For instance, if 10% of the marbles in a pot are 35, then the total number of marbles in the pot will be 35 x 10%, or 350.
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The density function of a continuous non-negative random variable (X) is defined for x > 0 as follows: fˣ(x) = C · x₄ · (1 - x)
1. Evaluate the constant, C. 2. Derive expected value, E[X] 3. Find the second moment, E[X²] 4. Determine Var [X]
Simply multiply each value of the discrete random variable by the probability associated with that value to obtain the expected value, E(X), or mean. E(X)=xP is the formula's notation (x).
How do you find ex and Var X?
It is common to refer to the long-term average or mean (symbolized as ) as the expected value of a discrete random variable X, denoted by the symbol E(X).
Thus, if you conducted an experiment again throughout time, you could anticipate this average result. If you toss three fair coins, for instance, let X be the number of heads you receive.
The expected value of X is the average number of heads you would anticipate receiving after three fair coin tosses if you were to perform this experiment a significant number of times.
f(x) = 4x³,0 < x < 1
Domain of f(x) = 4x³,0 < x < 1 : Solution : 0 < x < 1
Interval notation : (0,1)
Range of 4x³ ,0 < x < 1;
Solution : 0 < f(x) < 4
Interval Notation : (0,4)
Axis interception points of 4x³,0 <x <1.
Asymptotes of 4x³. 0 < x < 1;
Extreme Points of 4x³ . 0<x < 1:
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(25 POINTS IF YOU DO THIS AND BRAINLIST) Write 4 sentences about how you found x and y describe the steps you took to find the answers.
Answer:
x = 9/2, y = 15/4
Step-by-step explanation:
The line intersecting two distinct points on both sides of the triangle are parallel
So the corresponding angles are equal
Also, we have a common angle at point A
So, both the triangles are similar by AAA criteria
Now, the sides will be proportional as the triangles are similar
4/7 = 5/5+y = 6/6+x
Solving this, we get y = 15/4 units
and x = 9/2 units
a bag has 5 blue pens, 2 red pens, 2 green pens and 1 yellow pen. what is the probability of drawing 2 successive red pens?
The probability of drawing 2 successive red pens is [tex]\frac{1}{66}[/tex]
What do you mean by Probability?Probability is a branch of mathematics that deals with the likelihood or chance of an event happening. It is a number between 0 and 1 that indicates the likelihood of an event occurring, with 0 meaning that an event is impossible and 1 meaning that an event is certain to occur.
Probability is used to model and make predictions about real-world situations such as the outcome of a coin flip, the results of a survey, or the success of a marketing campaign. It is also used in many fields including statistics, finance, engineering, and sciences to make decisions based on uncertain data.
Probabilities can be calculated using various methods, such as counting, Bayes' theorem, and simulation. In general, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
The probability of drawing a red pen on the first draw is 2/12 = 1/6. After the first red pen is drawn, there is 1 red pen left in the bag, so the probability of drawing another red pen is 1/11.
Therefore, the probability of drawing 2 successive red pens is 1/6 * 1/11 = 1/66.
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Help pleasee asap 15 points!!
Answer:
They are supplementary angles
is it A, B,C or D I wasen't here for the assigment in class
Answer:
C :minimum value of -4
Step-by-step explanation:
the curve is a u shape so its a minimum value
if its a n shape it wouldve been a maximum value
the curve goes on -4 so its -4
If$ 1= Rs 115.45(buying rate) and $1= Rs 116.20 (Selling rate). Find the profit while
selling and buying $800
Answer:
[tex]600[/tex]
[tex] 6 \times {10}^{2} [/tex]
if ln(x) = 3.23 , what is the value of x
If ln(x) = 3.23 , the value of x is 25.28.
Therefore the answer is 25.28.
If ln(x) = 3.23, then x can be found by using the exponential function.
The natural logarithm function, represented by ln(x), gives the power to which e (approximately equal to 2.71828) must be raised to equal x. So, if ln(x) = 3.23, it means that e^3.23 = x.
The exponential function is the inverse of the natural logarithm, so if ln(x) = 3.23, then
x = e^(ln(x))
= e^(3.23).
Using a calculator, we can find that e^(3.23) ≈ 25.28.
So, the value of x is approximately 25.28.
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Find the perimeter of the composite figure.
A) 46.9
B) 42.9
C) 23.5
D) 31.9
Answer:
A
Step-by-step explanation:
half circle diameter = 9-(-1) =10
so perimeter = 2π r=20π =62.8
1/2 of it = 31.4
triangle 3 sides: 10, 4.5
10²+4.5² = long line's sqaure
so long line is 11
so perimeter for triangle without the line shared with semicircle = 11+4.5 =15.45
total =31.4+15.45 =46.85
If x is a real number, find the minimum value of 3^{x²-4x+8}
The minimum value of 3^{x²-4x+8} is 81. The solution has been obtained by using maxima-minima.
What is maxima-minima?
The extrema of a function are known as its maximum and minimum. The maximum and smallest values of a function within the predetermined set of ranges are known as maxima and minima. The function's maximum value and minimum value are referred to as the absolute maxima and absolute minima, respectively, for the function across the whole range.
We are given f(x) = 3^{x²-4x+8}
The function is minimum when {x²-4x+8} is minimum.
When the form of the equation is ax^2 + bx + c, then minimum is at -b/2a
Here, a = 1 and b = -4
So,
x = 4/2 = 2
So, {x²-4x+8} at x = 2 is
⇒(2)^2 - 4(2) + 8
⇒4 - 8 + 8
⇒4
So, the minimum value of f(x) is
3^4 = 81
Hence, the minimum value of 3^{x²-4x+8} is 81.
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The number of songs enjoyed from Eminem by all Learn4Life students is normally distributed with a mean of 7.0 songs and a standard deviation of 1.5 songs.
What is the probability an individual student likes between 5.5 and 8.5 songs from Eminen?
Answer:
≈84,13%
Step-by-step explanation:
To find the probability of a student liking between 5.5 and 8.5 songs from Eminem, we need to find the standard normal deviate (z-score) for each of these values and then use a standard normal table to find the area between these z-scores.
For 5.5 songs:
z = (5.5 - 7.0) / 1.5 = -1.0
For 8.5 songs:
z = (8.5 - 7.0) / 1.5 = 1.0
The area between -1.0 and 1.0 on a standard normal distribution table is approximately 0.8413. This means that the probability of an individual student liking between 5.5 and 8.5 songs from Eminem is approximately 84.13%.
Find the mEF . -2x+41 and 7x+5
Based on the chord of a circle theorem, the length of Ef is: 33.
What is the Chord of a Circle Theorem?If the arcs of a circle have the same measurement, then their corresponding chords will also have the same measurement based on the chord of a circle theorem.
Therefore, since arcs CD and EF are congruent, then:
CD = EF
Substitute and find x:
-2x + 41 = 7x + 5
-2x - 7x = -41 + 5
-9x = -36
-9x/-9 = -36/-9
x = 4
Length of EF = 7x + 5 = 7(4) + 5
Length of EF = 33 units.
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12^2+5^2=x^2 Find the missing side of each triangle. Round to the nearest tenth if necessary.
Answer:
x = 13
Step-by-step explanation:
x² = 5² + 12²
x² = 169
x = √169 = 13
Jake knows that 8×5=40 . Select the three statements that are true.
Answer:
8 multiplied by 5 equals 40.
8 is a factor of 40.
40 can be divided by 8 with no remainder.
Step-by-step explanation:
