PLEASE HELP ME 40 PTS!!!!!!
Which statement describes the sequence defined by a Subscript n Baseline = StartFraction n cubed minus n Over n squared + 5 n EndFraction?
The sequence diverges.
The sequence converges to 0.
The sequence converges to ∞.
The sequence converges to –∞.
Answers
Answer:
The sequence converges to infinity.
Step-by-step explanation:
[tex]a_n = \frac{n^3 - n}{n^2 + 5n}\\\\ \lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{n^3 - n}{n^2 + 5n}[/tex]
[tex]= \lim_{n \to \infty} \frac{n(n^2 - 1)}{n(n + 5)} \\\\= \lim_{n \to \infty} \frac{(n^2 - 1)}{(n + 5)}\\\\= \lim_{n \to \infty} \frac{n(n - \frac{1}{n})}{n(1 + \frac{5}{n})}\\\\= \lim_{n \to \infty} \frac{(n - \frac{1}{n})}{(1 + \frac{5}{n})}[/tex]
[tex]denominator = \lim_{n \to \infty} 1 + \frac{5}{n} = 1 + \lim_{n \to \infty} \frac{5}{n} = 1+0 = 1[/tex]
[tex]numerator = \lim_{n \to \infty} n - \frac{1}{n} = \infty[/tex]
Therefore,
[tex]\lim_{n \to \infty} a_n = \frac{ \infty}{1} = \infty[/tex]
The sequence diverges because the series divergence the limit tends to infinity does not exist option (A) is correct.
What is the convergent of a series?A series is convergent if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums get closer and closer to a certain number.
We have:
A sequence:
[tex]\rm a_n=\dfrac{\left(n^3-n\right)}{n^2+5n}[/tex]
As we know if the series converges the limit tends to infinity exist.
If the series divergence the limit tends to infinity does not exist.
Taking limit x tends to infinity:
[tex]\rm = \lim \:_{n\to \:\infty \:\:}\dfrac{\left n^3-n\right}{n^2+5n}[/tex]
[tex]\rm =\lim _{n\to \infty \:}\left(\dfrac{n^2-1}{n+5}\right)[/tex]
[tex]\rm =\lim _{n\to \infty \:}\left(\dfrac{n-\frac{1}{n}}{1+\dfrac{5}{n}}\right)[/tex]
[tex]\rm =\dfrac{\lim _{n\to \infty \:}\left(n-\dfrac{1}{n}\right)}{\lim _{n\to \infty \:}\left(1+\dfrac{5}{n}\right)}[/tex]
= ∞/1
= ∞ = does not exist.
Thus, the sequence diverges because the series divergence the limit tends to infinity does not exist option (A) is correct.
Learn more about the convergent of a series here:
brainly.com/question/15415793
#SPJ5
Related Questions
5. A parallelogram has vertices D(-1,1) E
(2,4) F(5. 1 )G(2,-2) Which description best describes the figure? A rectangle B trapezoid, C. Square, D. Kite
Answers
Answer:
C
Step-by-step explanation:
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 86 minutes with a mean life of 505 minutes. Of the claim is true, in a sample of 120 batteries, what is the probability that the mean battery life would be greater than 523.8 minutes
Answers
Answer:
0.0082 = 0.82% probability that the mean battery life would be greater than 523.8 minutes
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Standard deviation of 86 minutes with a mean life of 505 minutes.
This means that [tex]\sigma = 86, \mu = 505[/tex]
Sample of 120:
This means that [tex]n = 120, s = \frac{86}{\sqrt{120}}[/tex]
What is the probability that the mean battery life would be greater than 523.8 minutes?
This is 1 subtracted by the p-value of Z when X = 523.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{523.8 - 505}{\frac{86}{\sqrt{120}}}[/tex]
[tex]Z = 2.39[/tex]
[tex]Z = 2.39[/tex] has a p-value of 0.9918.
1 - 0.9918 = 0.0082
0.0082 = 0.82% probability that the mean battery life would be greater than 523.8 minutes
Original price of a book 18.50 discount 45%
Answers
Answer:
18.5-45%=10.175 Hope this helped! :)
joe mama is obama
Step-by-step explanation:
Kylie worked as an official for 45 soccer games last year. She made a graph of the number of games she worked during the first 6 months during the first 6 months of the year. How many more games did Kylie work during the first six months as shown on the graph than she did during the rest of the year?
Answers
Answer:
11 More Games.
(I did the quiz too)
Answer:
11
Step-by-step explanation:
I did this on my map test, it's right
Provide the remaining principal parts for the verb below.
Present: shake
Present Participle:
Past:
Past Participle:
Answers
Past : Shook
Past Participle: Shaken
NEED HELP!
A water tank at a filtration plant is built in the shape of an inverted cone with height 5.2
m and diameter 5 m at the top. Water is being pumped into the tank at a rate of 1.2 m3
/min.
Find the rate at which the water level is rising when there is 8π m3
of water
Answers
Answer:
The rate of change is
6.2 × [tex]10^{-3}[/tex] [tex]ms^{-1}[/tex] = 0.37 [tex]\frac{m}{min}[/tex]
Answer ^ ^ ^ ^ ^ ^ ^
Explanation: it broke itself
Can side lengths 3, 4, and 5 form a right triangle
Answers
Answer:
Yes it can! Plz the Brainliest!
Step-by-step explanation:
A right triangle is defined as a triangle with sides in the ratio 3:4:5. Pythagorean Doubles are triangles whose sides have had a ratio of the whole numbers as their sides. Even if the sides are multiplied by any number, the result is still a right triangle with sides in the ratio 3:4:5. For instance, 6, 8, and 10 are all numbers.
Please help very urgent
Answers
Answer:
1) A={0,2,4,12,14,20}
2) 6
3) W={1,3,5,9,21,23,39}
4) 7
The table slow shows Larry's scores on 6 different math tests. What is Larry's mean score on the 6 tests?
Test: 1 2 3 4 5 6
Score: 88 78 76 86 92 96
Answers
Answer:
86
Step-by-step explanation:
Can someone tell e where to plot this? (PLEASE NO FILE ANSWER). !!!
Answers
Step-by-step explanation:
x<5
This means that we want to graph all the numbers less than 5, but not 5 itself. So the circle is selected onto the 5 mark, we make it open, and we make the graph go to the left of the circle.
Answer:
1.Make the circle open
2.put the dot on 5
3. change direction
Step-by-step explanation:
A solid dot on a number line graph indicates that the given number should be included as a possible solution, whereas an open dot indicates that the given number cannot be a solution. For example, if you graph x > 7, you place an open dot at 7.
Have a nice day! :-)
Find the measure of angle x in the figure below:
BRAINLIEST PLEASE HELP SHOW WORK AN WILL MAKE BRAINLY
Answers
Answer:
See attached photo!
Step-by-step explanation:
Background information:
Veteran Betterment has a set of blueprints which show the complete building design layout. The blueprint shows a scale factor of 0.5 inches to 7.5 feet. Please use this scale factor and the information on the blueprint to answer the following questions about the dimensions of the real building.
Look at the picture attached:
What will the height of the building in the real world be?
What will the area of the roof in the real world be?
Answers
4 inch • 6.5 inches = 30 feet • 48.75 feet = 1,462.5 sq ft
write each improper fraction as a mix numbet 19/4
Answers
Answer:
4 3/4
Step-by-step explanation:
On the image, if you scroll, there are questions and answers. I just need one example on how to get to those answers. I’m not sure how to do these types of problems. If you can help I’d appreciate it! Thank you!!
Answers
Answer:
Step-by-step explanation:
#27). 6k² = 48
k = √8 = 2√2
x = [tex]\frac{8}{2\sqrt{2} }[/tex] = 2√2 cm
y = [tex]\frac{12}{2\sqrt{2} }[/tex] = 3√2 cm
#29). 16k² = 48
k = √3
x = [tex]\frac{8}{\sqrt{3} }[/tex] = [tex]\frac{8\sqrt{3} }{3}[/tex] cm
y = [tex]\frac{12}{\sqrt{3} }[/tex] = 4√3 cm
A circular path 4 feet wide has an inner diameter of 250 feet. How much farther is it around the outer edge of the path than around the inner edge? Round to nearest hundredth. Use 3.14 for π.
The outer edge of the path is ??? feet farther around than the inner edge.
Answers
Answer:
25.13
Step-by-step explanation:
the inner circle is 1570.8 and the outer is 1595.93
Hope this helps! :)
Have a great weekend!! :)
Answer:
50.24 ft
Step-by-step explanation:
diameter = 250 ----- radius = 125 (radius of the smaller circle)
125+4 = 129 ( radius of the bigger circle)
129-125 = 4
4² x pi = 16x 3.14 = 50.24
In ΔWXY, the measure of ∠Y=90°, WY = 5, XW = 13, and YX = 12. What ratio represents the cosine of ∠X?
Answers
Answer:
The ratio of cosine X = 12 : 13
Step-by-step explanation:
Given;
∠Y=90°
length WY = 5
length XW = 13
length YX = 12
Check the image uploaded for the solution.
hypotenuse is
How did u get 4/3. Because I’m confused
Answers
Factor the algebraic expression (x - 1)2
- (y - 2)2
Answers
Answer:
2(x-y+1) Is The Awnser
A total of 494 tickets were sold for the school play. They were either adult tickets or student tickets. There were 56 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answers
494=x+x-56
494=2x-56
550=2x
275=x
The number of adult tickets sold will be 275.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that a total of 494 tickets were sold for the school play. They were either adult tickets or student tickets. There were 56 fewer student tickets sold than adult tickets.
Assume that the number of adult tickets sold are [x] and the student tickets sold are [y]. Then -
x + y = 494
y = x - 56
So, we can write the equation as -
x + x - 56 = 494
2x = 550
x = 275
Then, we can find [y] as -
y = 275 - 56 = 219
y = 219
Therefore, the number of adult tickets sold will be 275.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
17. The present age of a father and his son is 50yrs and 20yrs respectively. How many years ago
the product of their ages was 451.
Answers
Answer:
9 yrs ago
Step-by-step explanation:
(50-x)(20-x) = 451
x^2-70x + 1000 = 451
x^2-70x + 549 = 0
(x-9)(x-61) = 0
x = 9 (if it was 61 yrs ago, the father and son both wouldnt be a live)
Select from the following pairs of events all the pairs that are independent.
A. Draw a 2 of clubs from a standard deck of 52 cards, keep it, then draw a 2 of diamonds.
B. Draw a 3 of spades from a standard deck of 52 cards, replace it, then draw a 5 of hearts.
C. Roll a number cube. Then roll again if the first roll is a 6.
D. Roll a 2 on a number cube and spin a 3 on a spinner.
E. Events A and B, where P(A) = 0.4, P(B) = 0.2, and P(A and B) = 0.8.
F. Events A and B, where P(A) = 0.1, P(B) = 0.5, and P(A and B) = 0.05.
Answers
Answer:
A.) Independent
B.) Independent
C.) Dependent
D.) Independent
E.) Dependent
F.) Independent
Step-by-step explanation:
To find - Select from the following pairs of events all the pairs that are independent.
A. Draw a 2 of clubs from a standard deck of 52 cards, keep it, then draw a 2 of diamonds.
B. Draw a 3 of spades from a standard deck of 52 cards, replace it, then draw a 5 of hearts.
C. Roll a number cube. Then roll again if the first roll is a 6.
D. Roll a 2 on a number cube and spin a 3 on a spinner.
E. Events A and B, where P(A) = 0.4, P(B) = 0.2, and P(A and B) = 0.8.
F. Events A and B, where P(A) = 0.1, P(B) = 0.5, and P(A and B) = 0.05.
Proof -
We know that,
Independent events are the events that does not depend on the previous events.
Also,
If A and B are two independent events, then
P(A and B) = P(A) * P(B)
Now,
A.)
Draw a 2 of clubs from a standard deck of 52 cards, keep it, then draw a 2 of diamonds.
Here,
Event 1 - Draw a 2 of clubs from a standard deck of 52 cards
Event 2 - keep it, then draw a 2 of diamonds.
These Events are independent
Because
Event 1 is about picking a card that is club
Event 2 is about picking a card that is diamond
And Diamond and spades are 2 different types of card in a pack of standard deck.
So, they are not related to each other.
So,
Both the Events are Independent.
B.)
Draw a 3 of spades from a standard deck of 52 cards, replace it, then draw a 5 of hearts.
Event 1 is about picking a card that is spade
Event 2 is about replacing the card to heart.
These Events are independent
Because
And spade and heart are 2 different types of card in a pack of standard deck.
So, they are not related to each other.
So,
Both the Events are Independent.
C.)
Roll a number cube. Then roll again if the first roll is a 6.
Event 1 is Roll a number cube.
Event 2 is Roll again if the first roll is 6.
These Events are Dependent
Because
Event 2 is dependent on Event 1.
If Event 1 given no 6 then Event 2 would not happen
If Event 1 given 6 then Event 2 would happen.
So, They are related to each other
So,
Both the Events are Dependent.
D.)
Roll a 2 on a number cube and spin a 3 on a spinner.
Event 1 is Roll a 2 on a number cube
Event 2 is spin a 3 on a spinner
These Events are independent
Because
Cube and spinner are two different objects.
So, they are not related to each other.
So,
Both the Events are Independent.
E.)
Events A and B, where P(A) = 0.4, P(B) = 0.2, and P(A and B) = 0.8.
These Events are Dependent
Because
P(A and B) = P(A)*P(B)
⇒0.8 = 0.4*0.2
⇒0.8 = 0.08
But they are not equal
So, they are not independent Events.
F.)
Events A and B, where P(A) = 0.1, P(B) = 0.5, and P(A and B) = 0.05.
These Events are independent
Because
P(A and B) = P(A)*P(B)
⇒0.05 = 0.1*0.5
⇒0.05 = 0.05
They are not equal
So, they are independent Events.
which of the functions below could have created this graph?
A. F(x)=x^8+4x+20^2
B. F(x)=x^9+12x^8+x^7
C. F(x)=-x^6+x^3-x^2
D. F(x)=-x^7+4x^3-2x^2
Answers
Answer:
The answer is probably A, but you typed it in wrong so I do not know. I can only guess because the others do not seem to be correct either. I have graphed them on Desmos. The screenshot is below.
Step-by-step explanation:
How often are you required to make payments on an auto loan?
Option A Once a week.
Option B Every other week.
Option C Once a month.
Option D Every time you get a paycheck.
Answers
Answer:
C is the answer
Step-by-step explanation:
hope this helps
PLEASE PLEASE PLEASE HELP What is the measure of
T
175°
H
57°
F
Answers
Answer:
m<G = 59°
Step-by-step explanation:
Recall: the angle formed outside a circle when 2 secants intercept is equal to half of the difference of the intercepted arcs
m<G = ½(arc TE - arc HF)
m<G = ½(175 - 57)
m<G = ½(118)
m<G = 59°
Does anyone know he answers for 2 and 3? Need full work and explanations
Answers
Answer:
this is the answer of 2 and
Find the height and slant height of the cone. Round your answers to the nearest whole number.
Answers
Answer:
Height = 4 cm and slant height = 5 cm
Step-by-step explanation:
Given that,
The surface area of the cone, A = 75.4 cm²
Radius, r = 3 cm
The surface area of the cone is given by the formula as follows :
[tex]A=\pi r^2+\pi rl[/tex]
Put all the values,
[tex]75.4=3.14\times 3^2+3.14\times 3\times l\\\\75.4=28.26+9.42l\\\\75.4-28.26=9.42l\\\\47.14=9.42l\\\\l=\dfrac{47.14}{9.42}\\\\l=5\ cm[/tex]
Also,
[tex]l^2=r^2+h^2\\\\h=\sqrt{l^2-r^2}\\\\h=\sqrt{5^2-3^2}\\\\h=4\ cm[/tex]
Hence, the height of the cone is 4 cm and the slant height is 5 cm.
Which number has more than two factors?
A. 29
B. 19
C. 23
D. 25
Pls Answer Fast
Answers
Answer:
Step-by-step explanation:
The answer is 25 (D)
The factors of 25 are 1, 5, and 25, thus being more than two factors.
Hopes this helped!
Simplify c^3d^4/c^2d
Answers
Answer:
I think the answer is :-
[tex]c {d}^{3} [/tex]
The simplification of c^3d^4/c^2d is cd^3.
What is simplification of an expression?Simplification of an expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression.
For the given situation,
The expression is c^3d^4/c^2d.
The simplification is as
⇒ [tex]\frac{c^{3}d^{4} }{c^{2}d }[/tex]
⇒ [tex]\frac{(c^{2})( c)(d^{3} )(d)}{c^{2} d}[/tex]
⇒ [tex]cd^{3}[/tex]
Hence we can conclude that the simplification of c^3d^4/c^2d is cd^3.
Learn more about simplification of an expression here
https://brainly.com/question/13730519
#SPJ2
6. A vertex is a point where _____ or more edges meet.
Answers
Answer:
2
Step-by-step explanation:
I WILL GIFT YOU 30 Brainly (On Jesus)
Answers
Answer:
since highest degree is 2 the degree of a polynomial is also 2.
since the highest exponent is 2 the leading coefficient is 1.
Step-by-step explanation: