Placing these functions from slowest asymptotic growth to fastest asymptotic growth. f₇(n) < f₄(n) < f₀(n) < f₃(n) < f₅(n) < f₉(n) < f₂(n) < f₆(n) < f₁(n) < f₈(n).The exponents we got.
Given that,
Placing these functions from slowest asymptotic growth to fastest asymptotic growth,
Come to question,
f₇(n) < f₄(n) < f₀(n) < f₃(n) < f₅(n) < f₉(n) < f₂(n) < f₆(n) < f₁(n) < f₈(n).
(ln ln ln n) < (ln n + 2021) < ([tex]n^{lg n}[/tex] ) < ((n/lg n)⁸) < (n⁸ - n⁶ + n⁴ - n² + 1) < (n²⁰²¹) < ([tex]32^{n/5}[/tex]) < (3³ⁿ) < ([tex]16^{lgn}[/tex]) < ( 2021 ∛n)
Let's understand, lg n < n < exponential. on the basis of it,
f₇(n) comes first, it will be smaller than f₄(n), because ln n is > ln ln ln n.
f₄(n) comes second, it will be smaller than f₀(n), because O(n) functions are larger than O(log n).
f₀(n) comes third, it will be smaller than f₃(n), because O(n⁸) functions are larger than O([tex]n^{log n}[/tex]).
f₃(n) comes fourth, it will be smaller than f₅(n), because (n⁸ - n⁶ + n⁴ - n² + 1) will give more larger value than ((n/lg n)⁸), these both functions are O(n⁸).
f₅(n) comes fifth, it will be smaller than f₉(n), because n⁸< n²⁰²¹.
f₉(n) comes sixth, it will be smaller than f₂(n), because n²⁰²¹ is O(n), whereas [tex]32^{n/5}[/tex] = 2n is exponential, and exponential are larger than O(n).
f₂(n) comes seventh, it will be smaller than f₆(n), because 2n < 3³ⁿ, both are exponential (2 < 3).
f₆(n) comes eight, it will be smaller than f₁(n), because 3³ⁿ < [tex]16^{logn}[/tex], both are exponential (3 < 16).
f₁(n) comes ninth, it will be smaller than f₈(n), because [tex]16^{logn}[/tex] < 2021 ∛n, both are exponential (16 < 2021).
Complete question: Place these functions in order from slowest asymptotic growth to fastest asymptotic
growth. Justify the claimed order for each pair of consecutive functions that appear in your ordered
list. For instance, if you claim that
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Charlie has $3.15 in his bank which contains only nickels and dimes. There are 9 more nickels than dimes. Find the number he has of each kind.
Charlie has $3.15 in his bank which contains only nickels and dimes. There are 9 more nickels than dimes. Then Number of dimes =18
and Number of nickels =27
What is basic algebra ?Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.
Given that : Charlie has $3.15 in his bank which contains only nickels and dimes. There are 9 more nickels than dimes
Let d be the number of dimes
d + 9 = Number of nickels
A dime = 0.1
nickle is = 0.05
0.1d + 0.05d + 0.45 = 3.15
0.15d = 2.7
d = 18
Number of dimes =18
Number of nickels = 18 + 9
=27
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30 to 72 ratio problem
Answer: 5:12
Step-by-step explanation:
[tex]\displaystyle\\30:72=\\\\\frac{30}{72}=\\\\ \frac{6(5)}{6(12)}=\\\\ \frac{5}{12}=\\\\ 5:12[/tex]
what is the place value of the 5 in 836.15?
Answer:
The place value of 5 is HUNDREDTH
Explanation:
From the right-hand side, the place value of:
8 is Hundred
2 is Ten
6 is Unit
1 is Tenth
and finally, what we are required to tell,
5 is Hundredth.
I need to determine m∠z. Can anybody help with this?
Answer:
z = 134°
Step-by-step explanation:
You want to know the measure of exterior angle z given remote interior angles of the triangle are 77° and 57°.
Exterior angleThe exterior angle of a triangle is equal to the sum of the remote interior angles of the triangle. (It is useful to remember this.)
z = 77° +57°
z = 134°
__
Additional comment
As you know the value of the interior angle at C will be the supplement of the value of z: (180° -z). Then the sum of the interior angles is ...
77° +57° +(180°-z) = 180°
Add (z -180°) to both sides of this equation and you get ...
77° +57° +(180°-z) +(z -180°) = 180° +(z -180°)
77° +57° = z . . . . simplified
pls help need to anwser this question
Answer: y = -3x + 1
Step-by-step explanation:
Find the slope, rise/run:
-5 - (-17) / 2 - 6
-12/4 or -3
Find the y-intercept by substitution:
y = mx + b
-5 = -3(2) + b (Using the first coordinate)
1 = b
help plss its due today. the assignment is about equlvalent fractions and decimals
Answer: 87
Step-by-step explanation:
You would do 26/30 which gives 86.6666666 but we round up to 87
Answer:
0.86666...
Step-by-step explanation:
26/30=0.86666...
rounded to the nearest tenth is
0.9
A shot-putter throws a shot and its height is noted every 20 feet, the data is in the table below:
Feet Traveled Feet Above Ground
20 25
40 40
60 55
80 65
100 71
120 77
140 77
160 75
180 71
200 64
Please find the quadratic function of best fit for these data and, to the hundredths place, say how many feet the shot travels before striking the ground.
Best fit quadratic equation is: y = 77x + 140
Define quadratic equation.ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. An example of a quadratic equation is x² + 2x + 1. Here, an is greater than zero because if it equals zero, the equation will cease to be quadratic and change to a linear equation, such as bx+c=0. As a result, we cannot refer to this equation as a quadratic equation.
Given,
A shot-putter throws a shot and its height is noted every 20 feet
Best fit quadratic equation is:
y = 77x + 140
As after this equation, feet above ground is decreasing.
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What is the slope of the line created by this equation?
y = -6.3x+0
Answer:
-6.3 is your slope.
Step-by-step explanation:
Hello, there! Nice to meet you.
This is a pretty easy question, as it's written in y = mx + b form.
When it's written like this, the m in replacement is your slope value.
So, in this case, -6.3 is your slope.
If I had y = 3x + 6, then 3 would be the slope, but that's just an example.
Once more, the m value is your slope.
Hope this helped, and best of luck with the rest of your assignment! (:
Solve the triangle.
a= 10.0 ft, b= 11.0 ft, c = 13.0 ft
What is the measure of angle A?
A=⁰
(Round to two decimal places as needed.)
What is the measure of angle B?
B =°
(Round to two decimal places as needed.)
What is the measure of angle C?
c=°
(Round to two decimal places as needed.)
...
Answer:
Below in bold.
Step-by-step explanation:
Using the Cosine Rule:
a^2 = b^2 + c^2 - 2bc cos A
10^2= 11^2 + 13^2 -2.11.13 cos A
cos A = (11^2 + 13^2 - 10^2) / (2*11*13)
= 0.66434
m < A = 48.368 degrees
= 48.37 degrees to 2 D. P's.
By the Sine Rule:
a / sin A = b / sin B
10 / sin 48.368 = 11 / sin B
sin B = 11 * sin 48.368 / 10
= 0.82217
m < B = 55.303
= 55.30 degrees to 2 D,P's
So, m < C = 180 - 48.37 - 55.30
= 76.33 degrees
Which two graphs are increasing on all points of the domain?
Answer:
Step-by-step explanation:
the first one
Your friend says two different translations of the graph of the parent linear function can result in the graph of
f(x) = x - 2. Is your
friend correct? Explain.
Your friend claims that the graph of f(x) = x - 2 can be produced by two distinct translations of the graph of the parent linear function. The graph moves down by 2 units.
Given that,
Your friend claims that the graph of f(x) = x - 2 can be produced by two distinct translations of the graph of the parent linear function.
We have to find how much units the graph moves.
This linear equation's parent function is y=x.
The way your friend described this function wasn't exactly accurate.
If the function's transformation takes the form y=f(x)+c, the graph will move vertically up or down along the y-axis depending on the value of c.
The graph moves up if c>0.
The graph drops down if c>0.
When y=x-2 and y=f(x)+c are compared, we see that c = -2, which is smaller than 0, in the equation y=x-2.
Therefore, the graph moves down by 2 units.
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The Pencil Shop sells 20 pencils for $2.50 or single pencils for $0.13 each. Which option has the lesser price per pencil?
Answer:
20 pencils for $2.50 has the lesser price per pencil.
Step-by-step explanation:
$0.13 compared to $2.50 ÷ 20 = $0.125
$0.13 > $0.125
HELP PLEASE GIVING BRAINLIEST TO ONLYRIGHT ANSWER
Which graph shows a proportional relationship between x and y?
The graph C shows the proportional relationship between x and y.
What is meant by the term proportional relationship?A proportional relationship is defined as "y varies proportionally with x" or "y is directly proportional to x."
This implies that as x increases, y increases, and vice versa—and that the ratio among them always remains constant.The proportional relationship equation's graph is a straight line that follows the origin.Proportional relationships always are represented by equations of the form y=kx, in which k is the proportionality constant. That is, the connection between x and y always is multiplicative, with no additions or subtraction.For the given question;
The graph of the proportional relationship are given.
For the graph C, the relation tween x and y is said to be proportional because when the value of x increases the value of y decreases and also this line passes from the origin.
Thus, the graph C shows the proportional relationship between x and y.
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How can the square-root property be used to solve y2=6
Given the expression:
[tex]y^2=6[/tex]The first step to solve it using the square root property, is moving the coefficient on the right side of the equation to the left side, changing it's sign:
[tex]\begin{gathered} y^2=6 \\ \Rightarrow y^2-6=0 \end{gathered}[/tex]Now, remember the rule for conjugates:
[tex](a+b)(a-b)=a^2-b^2[/tex]in this case we have the following:
[tex]\begin{gathered} y^2=a^2 \\ \Rightarrow y=a \\ b^2=6 \\ \Rightarrow b=\sqrt[]{6} \end{gathered}[/tex]therefore, we can factor the expression like this:
[tex]\begin{gathered} y^2-6=0 \\ \Rightarrow(y-\sqrt[]{6})(y+\sqrt[]{6})=0 \end{gathered}[/tex]Finally, we have that the only values that make true the expression are:
[tex]\begin{gathered} y_1=\sqrt[]{6} \\ y_2=-\sqrt[]{6} \end{gathered}[/tex]I know the answer is 16 but can someone show me the steps as to how to get the answer? Also, we have not learned the l'hospital rule yet, so is there other way?
[tex]\lim_{n \to \\\pi /4} \frac{sec^4x-4}{x-\frac{\pi }{4} }[/tex]
The value of the given function, [tex] \displaystyle{\lim_{n \to \\ \frac{\pi}{4} } \frac{ {sec}^{4} x - 4}{x - \frac{\pi}{4} } }[/tex], found using L'Hospital's rule is; [tex] \displaystyle{\lim_{n \to \\ \frac{\pi}{4} } \frac{ {sec}^{4} x - 4}{x - \frac{\pi}{4} } = 16}[/tex]
What does L'Hospital's rule state?L'Hospital's rule states that if the limits [tex]\displaystyle{ \lim \limits_ {x \rightarrow c}f(x)} [/tex] = [tex]\displaystyle{ \lim \limits_{x \rightarrow c}g(x)} [/tex]= 0 or [tex]\pm \infty[/tex], g'(x) ≠ 0 for all x in I and x ≠ c, also, [tex]\displaystyle{ \lim \limits _ {x \rightarrow c}\frac{f ' (x)}{ g ' (x)} } \: exists, \: then;[/tex]
[tex]\displaystyle{ \lim \limits _ {x \rightarrow c}\frac{f (x)}{ g (x)} =\lim \limits _ {x \rightarrow c}\frac{f ' (x)}{ g ' (x)} } [/tex]
The given function is [tex] \displaystyle{\lim_{n \to \\ \frac{\pi}{4} } \frac{ {sec}^{4} x - 4}{x - \frac{\pi}{4} } }[/tex]
According to L'Hospital's rule, we have;
Where;
f(x) = sec⁴x - 4
[tex] \displaystyle g(x) = x - \frac{\pi}{4} [/tex]
[tex] \displaystyle f'(x) = \frac{4\cdot sin(x)}{cos^5(x)} [/tex]
g'(x) = 1
Therefore;
[tex] \displaystyle{\lim_{n \to \\ \frac{\pi}{4} } \frac{ {sec}^{4} x - 4}{x - \frac{\pi}{4} }= \frac{ \frac{4\cdot sin(x)}{cos^5(x)}}{1}=\frac{4\cdot sin(\frac{\pi}{4})}{cos^5(\frac{\pi}{4})} = 16}[/tex]
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The following table shows the monthly flow through a dam from October through April.
Solution:
Given the data below:
A) Mean monthly flow:
The mean monthly flow is evaluated as
[tex]\begin{gathered} \frac{total\text{ volume}}{total\text{ number of months}}=\frac{92+133+239+727+345+495}{6} \\ =\frac{2031}{6} \\ =338.5 \end{gathered}[/tex]Thus, the mean monthly flow is 338.5 KAF
B) Median monthly flow:
The median is evaluated as
[tex]undefined[/tex]PLEASE HELP QUICKLY!! WILL GIVE BRAINLIEST TO CORRECT ANSWER!!
Answer:
Grade A: 0.2
Grade B: 0.3
Grade C: 0.2
Grade D: 0.15
Grade F: 0.15
Step-by-step explanation:
You take the number of the grade and divide that by the total. The total is 20. A 4/20 = 0.2
Grade B 6/20 = 0.3 and so on
Answer:
For part b. its grade D so it says how much right so I think u need to times it or divide it or so sorry if this doesn't help u
if 4 tickets costs$40, how much does 8 tickets cost?
4 tickets----------------------------->$40
8 tickts------------------------------->$x
Using cross multiplication:
[tex]\begin{gathered} \frac{4}{8}=\frac{40}{x} \\ x=\frac{40\times8}{4} \\ x=80 \end{gathered}[/tex]8 tickets cost $80
In February, Robbins and Myers, Inc. executed a 2-for-1 split. Janine had 470 shares before the split. Each share was worth $69.48.
a. How many shares did she hold after the split?
b. What was the post-split price per share?
c. Show that the split was a monetary non-event for Janine.
In February, Robbins and Myers, Inc. executed a 2-for-1 split, then the
(a) . The shares did she hold after the split is 940 shares.
(b) . The post-split price per share is $34.74
(c) . Janine didn't gain or lose any money during the event.
Based on the given conditions,
In February, Robbins and Myers, Inc. executed a 2-for-1 split.
That means,
2 - for - 1 stock split.
= 2 / 1
= 2
(a) . How many shares did she hold after the split?
Then,
Janine had 470 shares before the split.
Each share was worth $69.48.
= 470 shares * 2
= 940 shares
Hence,
The shares did she hold after the split is 940 shares.
(b) . What was the post-split price per share?
Each share was worth $69.48.
Then,
= $69.48/2
= $34.74
Hence,
The post-split price per share is $34.74
(c) . Show that the split was a monetary non-event for Janine
We can write,
After the split, Janine had 940 share worth $34.74.
Since they doubled the amount of share, but decrease the amount of each share.
So,
Janine didn't gain or lose any money during the event.
Therefore,
Robbins and Myers, Inc. executed a 2-for-1 split,
(a) . The shares did she hold after the split is 940 shares.
(b) . The post-split price per share is $34.74
(c) . Janine didn't gain or lose any money during the event.
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pls pls help whoever gets it right gets marked brainliest
Which scatterplots have a nonlinear association? Select three options 
The association between two numerical variables measured for the same individuals is displayed in a scatterplot. One variable's values are displayed on the horizontal axis, and the other variable's values are displayed on the vertical axis. On the graph, each individual in the data is represented by a point.
Explain about the scatterplots?
The relationship between two economic phenomena, such as employment and output, inflation and retail sales, and taxes and economic growth, can be visually illustrated using scatter plots.
Spread Plots. Points on a scatter (XY) plot depict how two sets of data relate to one another. Each dot in this illustration represents a person's weight in relation to their height. (The information is displayed as "Cartesian (x, y) Coordinates")
Display a connection between the data and a trend. Display all data points, including outliers, minimum, and maximum values. can draw attention to relationships. the sample size and exact data values are retained.
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Choosing which types of assets you will invest in is known as
Solve the system by substitution.
a + b - 2c = 14
4b + c = -1
C = -5
Answer:
a = 3 ; b = 1 ; c = -5
Step-by-step explanation:
Solving system of equations by substitution method:a +b - 2c = 14 -----------------------------(I)
4b + c = -1 -----------------------------(II)
c = -5 ------------------(III)
Substitute c = -5 in equation (II) and find the value of 'b',
4b + (-5) = -1
4b = -1 + 5
4b = 4
b = 4 ÷ 4
[tex]\sf \boxed{b = 1}[/tex]
Substitute c = -5 and b = 1 in equation (I)
a + 1 - 2*(-5) = 14
a + 1 + 10 = 14
a +11 = 14
a = 14 - 11
[tex]\sf \boxed{a = 3 }[/tex]
Verification:a + b - 2c = 14
LHS = a + b - 2c
= 3 + 1 - 2*(-5)
= 3 + 1 + 10
= 14 = RHS
Hence verified.
Answer:
(3, 1, - 5 )
Step-by-step explanation:
a + b - 2c = 14 → (1)
4b + c = - 1 → (2)
c = - 5 → (3)
substitute c = - 5 into (2)
4b - 5 = - 1 ( add 5 to both sides )
4b = 4 ( divide both sides by 4 )
b = 1
substitute b = 1 and c = - 5 into (1)
a + 1 - 2(- 5) = 14
a + 1 + 10 = 14
a + 11 = 14 ( subtract 11 from both sides )
a = 3
solution is (3, 1, - 5 )
as a check substitute values into (1) and (2)
a + b + c = 3 + 1 - 2(- 5) = 4 + 10 = 14 ← correct
4b + c = 4(1) - 5 = 4 - 5 = - 1 ← correct
3. Use the equation V = abc where a = 5, b = 10, c = 3 to find the value of V.Show your work here:Choose the correct answersV = 120V = 50V = 150V = 60
Solution
[tex]V=abc[/tex]Where
[tex]\begin{gathered} a=5 \\ b=10 \\ c=3 \end{gathered}[/tex]Now,
[tex]\begin{gathered} V=abc \\ V=(5)(10)(3) \\ V=150 \end{gathered}[/tex]Therefore, V = 150
If you shift the linear parent function, f(x) = x, up 6 units, what is the equation
of the new function?
OA. g(x)= x+6
OB. g(x) = x-6
O C. g(x)=x
OD. g(x) = 6x
The required equation is g(x)=x+6
What is an equation?
An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign. A polynomial equation is the most common sort of equation. A mathematical equation is akin to a weighted scale. When equal weights of material (for example, grain) are placed in the two pans, the scale is balanced and the weights are said to be equal. To keep the scale in balance, if grain is withdrawn from one pan of the balance, an equal amount of grain must be removed from the other pan. In general, if the identical operation is done on both sides of an equation, it stays balanced.
The required equation is g(x)=x+6, when the parent function is 6 units up
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Felipe and Gregory are given the arithmetic sequence - 1, 6, 13, ..... Gregory wrote the explicit definition an = - 1 + 7(n - 1) for the sequence. Felipe wrote the definition as an = 7n -8. Which one of them is correct? Explain. Choose the correct answer below. O A. Only Felipe's definition is correct because it is simplified. Gregory's definition is not simplified, so it cannot be correct. O B. Only Gregory's definition is correct. The explicit definition of an arithmetic sequence is an = a, + d(n - 1), and only Gregory's definition is of that form. O C. Both are correct. Gregory's definition can be simplified to get Felipe's definition. O D. Both are correct. Gregory's definition uses n = 1 for the first term whereas Felipe's definition uses n = 0 for the first term, but both definitions describe the given sequence.
Answer: C. Both are correct. Gregory's definition can be simplified to get Felipe's definition.
Step-by-step explanation:
-1, 6, 13
[tex]a_n=a_1+(n-1)d\\\\d=a_2-a_1\\\\d=6-(-1)\\\\d=6+1\\\\d=7[/tex]
Hence,
[tex]a_n=-1+7(n-1)\\\\a_n=-1+7(n)-7(-1)\\\\a_n=-1+7n-7\\\\a_n=7n-8[/tex]
The figure MNP will be reflect across the line x = -2. If point M starts at (1, 2), what is the coordinate of M´?
The coordinates of the point M' is (-6,2) when the point M was reflected across x =-2.
Here, assume that there is a point A(a, b). This point is reflected across the line x = -2. When reflected across this line, the value of the y coordinate of this point A will not change, only the value of the x coordinates of the point A will change.
Here, the point M(1,2) is reflected across the line x = -2.
The coordinates of the reflected point M' are (a, b).
The value of will b will remains same as that of the point M.
Now, the location of a,
the distance between the line x = -2 and a will be same as that of the distance between 2 and x =-2 which is 4 units,
So, the location of a will be fours units away from x =-2 and in the opposite direction so, a = -6
So, the Point M' is (-6,2)
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Raul purchased a pair of shoes for $19.25 that normally sell for $55. What percent discount did he recieve?
He got a 61.5% Discount
if "f" varies directly with "m" and f = -19 when m=14, what is "f" when m=2? enter the number that belongs in the green box. reduce to the simplest form. f= - ?/?
solution
For this case we can use the following proportion rule:
[tex]\frac{-19}{14}=\frac{f}{2}[/tex]Then we can solve for f on this way and we got:
[tex]f=2\cdot(\frac{-19}{14})=-\frac{19}{7}[/tex]i need help with this
Answer:
32 feet
Step-by-step explanation:
See attached worksheet
