Both functions log(n + 1) and log(n^2 + 1) are not o(log n). For large values of n, log(n + 1) is approximately equal to log n, and log(n^2 + 1) behaves like 2*log n, none of which grows strictly slower than log n.
To determine whether the functions log(n + 1) and log(n2 + 1) are o(log n), we'll use the definition of little-o notation. A function f(n) is said to be o(g(n)) if for any positive constant c > 0, there exists a threshold n0 such that for all n > n0, f(n) < c * g(n). In other words, f(n) grows slower than any constant multiple of g(n) as n approaches infinity.
Analysis for log(n + 1)
When n is very large, the +1 becomes negligible, and log(n + 1) behaves similarly to log n. Therefore,
log(n + 1) ≈ log n when n is large.
This implies that log(n + 1) is not o(log n) because it does not grow strictly slower than any multiple of log n.
Analysis for log(n2 + 1)
Using logarithm properties:
log(n2 + 1) < log(n2 + n2) = log(2n2) = log 2 + 2*log n.
As n grows, the constant term (log 2) becomes insignificant, and the function approaches the behavior of 2*log n. However, since there is a multiple of log n (which is 2*log n), this still means that log(n2 + 1) is not o(log n) because it grows faster, not slower, than log n.
In Ellen's math class, there are 2 boys for every 3 girls . What is the the following ratio of boys to girls in the class ?
A . 17/21
B . 14/21
C . 7/14
D. 11/17
What is 24/126 simplified
Analyzing the graphs of a periodic functions (need help)
In a study conducted for the state department of education, 30% of the teachers who left teaching did so because they were laid off. assume that we randomly select 16 teachers who have recently left their profession. find the probability that at least 7 of them were laid off.
At a certain time, the length of a rectangle is 5 feet and its width is 3 feet. At that same moment, the length is decreasing at 0.5 feet per second and the widthis increasing at 0.4 feet per second.
What is the length of the diagonal at that time?
How fast is the length of the diagonal changing? Is this length increasing or decreasing?
A local hamburger shop sold a combined total of 693 hamburgers and cheeseburgers on Wednesday. There were 57 fewer fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Wednesday
693-57 = 636
636/2 = 318
cheeseburgers sold = 318
hamburgers sold = 318 + 57 = 375
To determine the number of hamburgers sold on a specific day, an equation is set up and solved to find the value of hamburgers. In this scenario, 375 hamburgers were sold on Wednesday.
The question is asking how many hamburgers were sold on a specific Wednesday given the total combined sales of hamburgers and cheeseburgers and that fewer cheeseburgers were sold than hamburgers. To find the number of hamburgers sold, we can set up a system of equations. Let's define H as the number of hamburgers and C as the number of cheeseburgers. From the information provided, we have the following equations:
H + C = 693 (Total sales of both types of burgers)C = H - 57 (There were 57 fewer cheeseburgers sold than hamburgers)Substituting the second equation into the first gives us:
H + (H - 57) = 693
2H - 57 = 693
Adding 57 to both sides, we get:
2H = 693 + 57
2H = 750
Now divide both sides by 2:
H = 375
Therefore, 375 hamburgers were sold on Wednesday.
What is the inverse of y equals x squared + 2
Solve for v 14v-8v=24
The perimeter of a triangle is 133 inches. If one side of the triangle is five more than the shortest side, and the longest side is 14 more than the shortest side, find the lengths of the three sides?
side 1 = x
side 2 = x+5
side 3 = x+14
perimeter = side 1 + side 2 + side 3
133 = x + (x+5) + (x +14)
133=3x + 19
114=3x
x=114/3 = 38
side 1 = 38
side 2 = x+5 = 38+5 = 43
side 3 = x+14 = 38+14 = 52
38+43+52 = 133
side lengths are 38, 43 & 52
Choose the correct description of the graph of the inequality x − 3greater than or equal to 5
Answer:
Move all terms not containing x to the right side of the inequality. x≥8
Closed circle on 8, shading to the right.
If the measures of the angles of a triangle are in the ratio of 19:13:4, then the expressions 19x, 13x, and 4xrepresent the measures of these angles. Find these angle measures.
Find the area of the equilateral triangle if a side is 14√3 ft. Round to the nearest whole number.
Answer:
Answer is C
Step-by-step explanation:
Area of an equilateral triangle can be found by the following formula,
A=[tex]\frac{\sqrt{3}} {4} a^{2}[/tex]
Where "a" is the length of one side of the triangle.
Now we can substitute the value given to the equation above and find the area of the given equilateral triangle.
A=[tex]\frac{\sqrt{3}} {4}(14\sqrt{3})^ {2}[/tex]
=[tex]\frac{\sqrt{3}} {4} 196*3[/tex]
=[tex]\frac{\sqrt{3}*196*3} {4}[/tex]
=[tex]254.611[/tex]
A=[tex]255[/tex] square feet.
Answer is C
What is the area of parallelogram ABDC?
Answer:
9cm
Step-by-step explanation:
Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.
A newspaper finds that the mean number of typographical errors per page is
six
six. Find the probability that (a) exactly
four
four typographical errors are found on a page, (b) at most
four
four typographical errors are found on a page, and (c) more than
four
four typographical errors are found on a page.
(15+23)+7=15+(___+7)
The radius of a circular park is 114 yd. To the nearest yard, what is the circumference of the park?
circumference = 2 x pi x r
using 3.14 for pi
2 x3.14x114=715.92
round to 716 yards
Answer:
The circumference of a circle is 715.92 yd.
Step-by-step explanation:
Formula
[tex]Circumference\ of\ a\ circle = 2\pi r[/tex]
Where r is the radius of a circle.
As given
The radius of a circular park is 114 yd.
[tex]\pi = 3.14[/tex]
Put in the formula
[tex]Circumference\ of\ a\ circle = 2\times 3.14\times 114[/tex]
Circumference of a circle = 715.92 yd
Therefore the circumference of a circle is 715.92 yd.
The sum of differences between the group mean and the grand mean summed over all groups for a given set of observations is called _____ variance.
he IQ scores of 500 college football players are randomly selected. Which graph would be most appropriate for these data: histogram, bar chart, pie chart, multiple bar graph, or slack plot?
help me? idk the answer :P
Two examples where the law of detachment does not apply.
If the following statements are true, use the Law of Detachment to derive a new true statement.
1) If you are a penguin, then you live in the Southern Hemisphere.
2) You are a penguin.
Remember if p then q
The law of detachment, or modus ponens, doesn't apply when the antecedent is false or when premises lack conditional statements, making deductions invalid in these cases.
The law of detachment, also known as modus ponens, is a fundamental principle in classical logic that allows us to make valid deductions. However, there are situations where it does not apply:
Invalid Antecedent: In modus ponens, we start with a conditional statement (if-then statement) as our premise and then affirm the consequent. If the antecedent (the "if" part) of the conditional statement is false, the law of detachment cannot be applied. For example, if we have the statement "If it is raining, then the ground is wet" and we know that the ground is not wet, we cannot conclude anything about whether it's raining or not, as the antecedent is false.
Lack of a Conditional Statement: Modus ponens requires a conditional statement as its premise. If we are given unrelated or non-conditional premises, we cannot apply this rule. For instance, if we know that "John is a doctor" and "The sun is shining," we cannot use modus ponens to deduce anything because there is no conditional relationship between the statements.
In summary, while modus ponens is a valid and powerful inference rule in classical logic, it cannot be applied when the antecedent is false or when the premises do not involve conditional statements.
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Complete question below:
Could you provide two examples where the law of detachment does not apply in logic?
At what points does the helix r(t) = sin t, cos t, t intersect the sphere x2 + y2 + z2 = 65? (round your answers to three decimal places. if an answer does not exist, enter dne.)
To determine the intersection points of the helix and the sphere, we substitute the helix's parametric expressions into the sphere's equation, simplify, and solve for t, resulting in two points of intersection upon further substitution back into the helix's equation.
Explanation:The question asks at what points the helix r(t) = (sin t, cos t, t) intersects the sphere x2 + y2 + z2 = 65. To find the intersections, we substitute the parametric equations of the helix into the equation of the sphere. Thus, we get (sin2t) + (cos2t) + t2 = 65. Using the Pythagorean identity sin2t + cos2t = 1, the equation simplifies to 1 + t2 = 65, which further simplifies to t2 = 64. Solving for t, we find t = ±8. Thus, the helix intersects the sphere at the points generated by these t values, which can be found by substituting t back into the helix equations, resulting in (sin(8), cos(8), 8) and (sin(-8), cos(-8), -8), with approximate numerical values after calculations.
Consider the words typically associated with geometry. Are there any words that would be hard to precisely define? What words can you think of?
The words typically associated with geometry are:
Points, Lines, Plane, and angle.
We have,
In geometry,
There are some words that can be challenging to precisely define or may have different interpretations.
Here are a few examples:
- Point: While a point is commonly understood as a location with no size or dimension, providing an exact definition can be difficult without relying on terms like "location" or "position."
- Line: A line is often described as a straight path extending infinitely in both directions. However, defining it without using similar geometric concepts like "straight" or "infinitely" can be challenging.
- Plane: A plane is typically defined as a flat, two-dimensional surface that extends infinitely in all directions. However, explaining it without referencing terms like "flat" or "two-dimensional" can be complex.
- Angle: An angle is formed by two intersecting lines or line segments. Describing it precisely without using terms like "intersects" or "measures" can be difficult.
Thus,
These words require a level of understanding of basic geometric concepts and often rely on other geometric terms for precise definitions.
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20. Archetypes are a type of _______ that appear throughout history.
A. motif
B. prototype
C. foreshadowing
D. subgenre
Student Answer: A
Answer: Incorrect
Answer is B Prototype
For Penn Foster the answer you find the answer to this qrestion In the section called Analysis of “ Paul’s Case” 4 th paragraph an Archetype appears repeatedly throughout history -It’s a prototype . So the qrestion people are asking is. Archetypes are a type of _______ that appear throughout history? A. foreshadowing B. prototype C. subgenre D. motif
Answer true and correct B. PROTOTYPE
I made a hundred on this test for pf
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What is the number of square units in the area of the triangle whose vertices are points (2,0), (6,0), (8,5)
Answer: 10 square units.
Step-by-step explanation:
The area of triangle with vertices [tex](x_1,y_1),(x_2,y_2)\text{ and }(x_3,y_3)[/tex] is given by :-
[tex]A=\dfrac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)][/tex]
Given : The vertices of triangle : (2,0), (6,0), (8,5)
Then , the area of the triangle will be :_
[tex]A=\dfrac{1}{2}[(2)((0)-(5))+(6)((5)-(0))+(8)((0)-(0))\\\\\Rightarrow A=\dfrac{1}{2}[20]\\\\\Rightarrow A=10\text{ square units}[/tex]
Hence, the number of square units in the area of the triangle whose vertices are points (2,0), (6,0), (8,5) = 10
Which ratio is equivalent to 7 : 8?
A) 28 : 40
B) 21 : 24
C) 49 : 64
The Jurassic Zoo charges $14 for each adult admission and $9 for each child. The total bill for the 214 people from a school trip was $2081. How many adults and how many children went to the zoo?
a=adult
c=child
a+c=214
c=214-a
9c+14a=2081
9(214-a)+14a=2081
1926-9a+14a=2081
5a=155
a=155/5=31
31 adults
183 children
check
31*14 = 434
183*9=1647
1647+434=2081
With 400,000 sq ft or 16% of total office space. How much space did the city have
EASY 5 POINTS!!! You want to help build an awards podium for a track meet. If the podium has the dimensions shown, what is its volume?
Answer:
The volume is equal to [tex]18\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of each figure is equal to
[tex]V=LWH[/tex]
where
L is the length
W is the width
H is the height
Step 1
Find the volume of figure N 1
[tex]V1=1.5*2*3=9\ cm^{3}[/tex]
Step 2
Find the volume of figure N 2
[tex]V2=1.5*2*2=6\ cm^{3}[/tex]
Step 3
Find the volume of figure N 3
[tex]V3=1.5*2*1=3\ cm^{3}[/tex]
Step 4
Find the total volume
[tex]V=V1+V2+V3=9+6+3=18\ cm^{3}[/tex]
Answer:
[tex]\text{Volume of podium}=18\text{ ft}^3[/tex]
Step-by-step explanation:
We have been given a graph of podium for a track meet and we are asked to find the volume of our given podium.
To find the volume of podium we will find volume of each podium using volume of cuboid formula.
[tex]\text{Volume of cuboid}=l*b*h[/tex], where,
[tex]l=\text{ Length of cuboid}[/tex],
[tex]b=\text{ Breadth of cuboid}[/tex],
[tex]h=\text{ Height of cuboid}[/tex].
Upon substituting our given values in cuboid formula we will get,
[tex]\text{Volume of cuboid 1}=\text{3 ft*2 ft*1.5 ft}[/tex]
[tex]\text{Volume of cuboid 1}=9\text{ ft}^3[/tex]
[tex]\text{Volume of cuboid 2}=\text{2 ft*2 ft *1.5 ft}[/tex]
[tex]\text{Volume of cuboid 2}=6\text{ ft}^3[/tex]
[tex]\text{Volume of cuboid 3}=\text{1 ft*2 ft *1.5 ft}[/tex]
[tex]\text{Volume of cuboid 3}=6\text{ ft}^3[/tex]
Let us add volume of each cuboid to find the volume of our given podium.
[tex]\text{Volume of podium}=9\text{ ft}^3+6\text{ ft}^3+3\text{ ft}^3[/tex]
[tex]\text{Volume of podium}=18\text{ ft}^3[/tex]
Therefore, volume of our given podium is 18 cubic feet.
Which equation does the graph of the systems of equations solve? two linear functions intersecting at 4, 1 the answers are one fourthx + 2 = 2x − 7 one fourthx + 2 = −2x − 7 −one fourthx + 2 = 2x − 7 −one fourthx + 2 = −2x − 7
Sal bought three CDs for 1598 each a computer cable for 3995 and a case for his MP3 player for 2499 sales tax is 7% to the nearest cent what is the total cost of his purchases
Pleaseee helppppppp