The sequence converges to a limit of 1/2.
We have,
Let's simplify the nth term of the sequence:
an = (n^2 + 3n) / (2n^2 + 5)
Dividing both the numerator and denominator by n^2, we get:
an = (1 + 3/n) / (2 + 5/n^2)
As n approaches infinity, the terms 3/n and 5/n^2 both tend towards zero.
Therefore, we have:
an = (1 + 0) / (2 + 0) = 1 / 2
The nth term of the sequence simplifies to a constant value of 1/2 as n approaches infinity.
Since the nth term converges to a specific value (1/2), the sequence itself is convergent.
The limit of the sequence is 1/2.
Thus,
The sequence converges to a limit of 1/2.
Learn more about sequence convergence here:
https://brainly.com/question/29394831
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The complete question:
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the sequence diverges, enter DIVERGES.)
Consider the sequence defined by the nth term an = (n^2 + 3n) / (2n^2 + 5).
Wilbur has a bag of coins. The bag contains 10 dimes, 5 nickels, and 1 penny. He will randomly select 2 coins from the bag, one at a time, without replacement. What is the probability that Wilbur will select a dime first and then a penny? A) 0.1 B) 0.04167 C) 0.03906 D 0.04444
a hill rises 10 meters over horizontal distance of 8 meters
calculate the slope
Answer:
Slope = 5/4
Step-by-step explanation:
GCF of 10 and 8 is 2, divide both values by two and have the 10 as the rise and 8 as the run.
85 miles on 8 gallons of gas
Answer:
11.6 miles per gallon
Step-by-step explanation:
Answer:
11.6 miles per gallon
Step-by-step explanation:
just divide
The depth of the Mariana Trench is 10,911m. Convert the depth to kilometers.
Answer:
Step-by-step explanation:
Now I didnt solve the question but if you do a google search on how many metres in a kilometre, then divide km by metres
Answer: 10.911
Step-by-step explanation:
how many numbers are between k and n
Answer:
n-k-1
Step-by-step explanation:
n is bigger than k. It asks BETWEEN k and n. so, since n is bigger than k, n-k. since it says BETWEEN, you subtract 1 after that
got it?
=)
oh and the reason i am strict about BETWEEN, is because when it said between, then its discluding k and n.
If it says FROM k and n, then you both include k and n, and that would result of adding 1 instead of subtracting 1.
solve the following inequality.
6.3r < -45.36
which graph shows the correct solution?
A) Open circle pointing to the right, starting from -72 to infinity
B) Open circle pointing to the left, starting from -72 to infinity
C) Open circle pointing to the right, starting from -7.2 to infinity
D) Open circle pointing to the left, starting from -7.2 to infinity
Can u help please??
Answer:
D. Open circle, point is at -7.2 pointing to the left.
Step-by-step explanation:
Got it right on Edge 2021! Hope I helped <3
O SYSTEMS OF EQUATIONS AND MATRICES
Solving a word problem using a 3x3 system of linear equations....
Over the last 3 evenings, Latoya received a total of 96 phone calls at the call center. The second evening, she received 2 times as many calls as the third
evening. The third evening, she received 8 fewer calls than the first evening. How many phone calls did she receive each evening?
Answer:
Find the midpoint of the line segment joining the points R(,) and S(,).
Step-by-step explanation:
Whata 7,500lb= to tons what's it
Answer:
3.75 tons djdhdjrjrhejejjwjwjsjs
Answer:
3.75 US tons
Step-by-step explanation:
1 ton =2000 pounds
so 7,500÷2000 =3.75
The large Ferris wheel makes a revolution in 60 seconds. The small Ferris wheel makes one revolution in 20 seconds. How many seconds will pass before Jeremy and Deborah are both at the bottom again?
Answer:
120 seconds
Step-by-step explanation:
60 20
120 40
180 60
80
100
120
help me please i’ll give u a cookie
Answer:
the answer is B
Step-by-step explanation:
i just did this.
What is 5/8 divided by 1/4?
Answer: 2.5
Step-by-step explanation: If you do 5/8 divided by 1/4 in the calculator it is 2.5.
What is the sum of 16.5 x 10 exponent 4
The following are a list of variables that will almost certainly vary across students in a large undergraduate introductory statistics course.
(a) Favorite beverage
(b) Year of birth
(c) Typing speed
(d) Handedness (e.g., left or right handed)
(e) Age
(f) Occupation
(g) Self-report of Assertiveness
For questions 1a to 1d that follow choose the variable or variables that best represent the level of measurement.
a) Which variables would typically be measured on a nominal scale of measurement?
b) Which variable would likely be measured on an interval, but not a ratio scale?c) Which two variables are most likely to be measured on a ratio scale?d) As typically measured, which variable represents at least an ordinal scale of measurement, but probably not a true interval scale?
Step-by-step explanation:
a. nominal scales
occupation
Favorite beverage
b. Interval but not ratio.
Typing speed
c. ratio scale.
age
Handedness (e.g., left or right handed)
d. Ordinal scale of measurement but not a true interval scale.
Self-report of Assertiveness
year of birth
Can someone help please?
Answer:
f htsbfzsrgbbbbbbbbbbbbbbbbbbbbbb
Step-by-step explanation:
fxmynhyxmyrjnbvd
0.16
As a repeating fraction
Answer:
0.16161616161616161616161616161616161616161616161616
Step-by-step explanation:
just keep adding whats repeating or put a bar on top of the 16
which number is the additve inverse of -5
Answer:
Additive inverses add to 0. The additive inverse of a number is the opposite of the number.
If anyone is willing to try and answer this go ahead
Answer:
X intercept: x = 4 or in point form (4,0)
Zero for the function at (4, 0)
Y intercept : y = 160 or in point form (0,160)
slope = -40 mph
Step-by-step explanation:
The y-intercept, x-intercept are directly obtained from the graph by noticing the points on the axes where the line crosses them.
The slope is calculated using the points (0, 160) and (4, 0) and the formula for the slope of the segment that joins them:
slope = (y2 - y1)/(x2 - x1) = (160 - 0) / (0 - 4) = -160/4 = -40
and the units of the slope are miles over hour (that is miles per hour or mph)
Restless Leg Syndrome and Fibromyalgia
People with restless leg syndrome have a strong urge to move their legs to stop uncomfortable sensations. People with fibromyalgia suffer pain and tenderness in joints throughout the body. A recent study indicates that people with fibromyalgia are much more likely to have restless leg syndrome than people without the disease. The study indicates that, for people with fibromyalgia, the probability is 0.33 of having restless leg syndrome, while for people without fibromyalgia, the probability is 0.03. About 2% of the population has fibromyalgia. Create a tree diagram from this information and use it to find the probability that a person with restless leg syndrome has fibromyalgia.
Answer:
The probability that a person with restless leg syndrome has fibromyalgia is 0.1833.
Step-by-step explanation:
Denote the events as follows:
F = a person with fibromyalgia
R = a person having restless leg syndrome
The information provided is as follows:
P (R | F) = 0.33
P (R | F') = 0.03
P (F) = 0.02
Consider the tree diagram attached below.
Compute the probability that a person with restless leg syndrome has fibromyalgia as follows:
[tex]P(F|R)=\frac{P(R|F)P(F)}{P(R|F)P(F)+P(R|F')P(F')}\\\\=\frac{(0.33\times 0.02)}{(0.33\times 0.02)+(0.03\times 0.98)}\\\\=0.183333\\\\\approx 0.1833[/tex]
Thus, the probability that a person with restless leg syndrome has fibromyalgia is 0.1833.
eight water faucets having the same rate of flow,fill a tank in 27 minutes.If two faucets are turned off,how long will the remaining 6water faucets take to fill the tank?
Answer:
36 minutes
Step-by-step explanation:
If x is the flow rate of each faucet, then 8x is the flow of eight faucets, and the volume of the tank is:
V = (8x) (27)
V = 216x
When there are six faucets, the time is:
216x = (6x) t
t = 36
the sum of a interior angle measures of a polygon is 5220. How many sides does the polygon have
9514 1404 393
Answer:
31
Step-by-step explanation:
The relationship between sides and the sum of angles is ...
sum of angles = (sides - 2)·180°
Filling in the given value and solving for "sides", we get ...
5220 = (sides -2)180
29 = sides -2 . . . . . . . . . divide by 180
31 = sides . . . . . . . . . . . . add 2
The polygon has 31 sides.
Answer:
31
Step-by-step explanation:
5220/180=29+2=31
Y=3x+10 slope and y intercept
Answer:
The slope is 3 and the y-intercept is 10
Step-by-step explanation:
Answer:
Slope: 3
y-intercept: ( 0 , 10)
Step-by-step explanation:
y=mx+b
y=3x+10
Hope this Helps!!!
What is the area of a rectangle with sides measuring 2x+3 and 3x-1 feet
In the diagram, m∠3 = 120° and m∠12 = 80°. Which angle measures are correct? Check all that apply.
m∠1 = 60°
m∠13 = 80°
m∠6 = 80°
m∠5 = 60°
m∠10 = 120°
m∠ 14 = 100°
Answer:
Its A, B, D, and F
Step-by-step explanation:
On edge2021
an equivalent ratio to the tape diagram shown is to
Answer:
it is 16 to 32
Step-by-step explanation:
if you divided 16 by 8 and 32 by eighth you get 2:4
HELPP ！I'm stucked at question b. can somebody help me? I'm not sure when should I change the sign thank you!
Answer:
dang
Step-by-step explanation:
that looks hard
The equation Ax + By = 14 goes through the coordinates (-7, -4) and (14, 2).
What are the values of A and B?
Answer:
A=-6
B=7
Step-by-step explanation:
We want to solve for the values of A and B.
let us substitute the values of the coordinates, that is x and y into the expression and obtain the two equations.
then we solve simultaneously
-7A-4B=14---------1
14A+2B=14--------2
-14A+-8B=28---------3
14A+2B=14------------2
0-6B=42
6B=42
B=42/6
B=7
put B=7 in eqn 1 we have
-7A-4(7)=14---------1
-7A-28=14
-7A=14+28
-7A=42
A=42/-7
A=-6
The values of A and B are 3 and -7 respectively
In order to determine the values of A and B,
First, we will determine the equation of the line passing through the coordinates (-7, -4) and (14, 2).
Using the formula for determining the equation of a line with two given points,
[tex]\frac{y-y_{1} }{x -x_{1} } =\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
From the question
x₁ = -7
y₁ = -4
x₂ = 14
y₂ = 2
Putting these values into the equation,
We get
[tex]\frac{y--4}{x--7} =\frac{2--4}{14--7}[/tex]
∴ [tex]\frac{y+4}{x+7} =\frac{2+4}{14+7}[/tex]
[tex]\frac{y+4}{x+7} =\frac{6}{21}[/tex]
This becomes,
[tex]6(x+7) = 21(y+4)[/tex]
Clearing the brackets
[tex]6x + 42 = 21y + 84[/tex]
Then,
[tex]6x -21y = 84 -42[/tex]
[tex]6x -21y = 42[/tex]
Dividing through by 3
We get
[tex]3x - 7y = 14[/tex]
∴ The equation of the line that goes through the coordinates (-7, -4) and (14, 2) is [tex]3x - 7y = 14[/tex]
Now, we will compare the above equation to the equation given.
The given equation is Ax + By = 14
By comparing
A = 3 and B = -7
Hence, the values of A and B are 3 and -7 respectively
Learn more here: https://brainly.com/question/21967006
Mr. Waxman is helping with deliveries for a shipping company. The graph shows a linear model for his delivery times on different days. (A) Identify two points on the line and write the coordinate pairs below. (B) Use your two points to find the slope, and make sure to show your work. (C) Use your slope from Part B and find the equation of the line in point-slope form. Show your work and work through the steps to transform the equation from point-slope form into slope-intercept form. (D) Based on the equation you found in Part C, predict how long it take Mr. Waxman to deliver his packages on Day 0. Approximately how much did his delivery time decrease per day? 2 SEE A
Answer:
See below
Step-by-step explanation:
Note: missing graph is attached
SolutionA) The two points are:
(4, 19) and (7, 7)B) Slope formula: m = (y2-y1)/(x2-x1)
m = (7 - 19)/(7-4)m = -12/3m = -4C) Point-slope formula:
y - y1 = m(x - x1)Using one of the points we get:
y - 19 = -4(x - 4)D) Delivery time on Day 0:
y - 19 = -4(0 - 4)y - 19 = 16y = 16 + 19y = 35 minutesDelivery time decreases by the value of the slope which is 4 minutes per day
Help lol I don’t know what to do
Answer:B
Step-by-step explanation:
=========================================
Explanation:
n = some unknown number
2n = twice a number
4+2n = four more than twice a number
4+2n = 8 since the "is" means "equals"
Below is a diagram showing the word problem broken up in a table form
12. It takes Daphne 25 minutes to assemble a model plane. During her work
minutes for lunch and one 15 minute break. Which inequality could Daphne use to determine the number
of model planes, p, she can assemble in her 8 hour work day?
A. 25p – 45 > 8
B. 25p + 45 2 8
C. 25p – 45 < 480
D. 25p + 45 < 480
Answer:
25p+45 < 480
Step-by-step explanation:
When the author visited Dublin, Ireland (home of Guinness Brewery employee William Gosset, who first developed the t distribution), he recorded the ages of randomly selected passenger cars and randomly selected taxis. The ages can be found from the license plates. (There is no end to the fun of traveling with the author.) The ages (in years) are listed below. We might expect that taxis would be newer, so test the claim that the mean age of cars is greater than the mean age of taxis. Use α= 0.05 significance level to test the claim that in Dublin, car ages and taxi ages have the same variation.
Car Ages 4 0 8 11 14 3 4 4 3 5 8 3 3 7 4 6 6 1 8 2 15 11 4 1 6 1 8
Taxi Ages 8 8 0 3 8 4 3 3 6 11 7 7 6 9 5 10 8 4 3 4
Answer:
The Decision Rule
Fail to reject the null hypothesis
The conclusion
There is no sufficient evidence to support the claim that the mean age of the cars is greater than that of taxi
Step-by-step explanation:
From the question we are told that
The data is
Car Ages 4 0 8 11 14 3 4 4 3 5 8 3 3 7 4 6 6 1 8 2 15 11 4 1 6 1 8
Taxi Ages 8 8 0 3 8 4 3 3 6 11 7 7 6 9 5 10 8 4 3 4
The level of significance [tex]\alpha = 0.05[/tex]
Generally the null hypothesis is [tex]H_o : \mu_1 - \mu_2 = 0[/tex]
the alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 > 0[/tex]
Generally the sample mean for the age of cars is mathematically represented as
[tex]\= x_1 = \frac{\sum x_i }{n}[/tex]
=> [tex]\= x_1 = \frac{4+ 0+ 8 +11 + \cdots + 8 }{27}[/tex]
=> [tex]\= x_1 = 5.56[/tex]
Generally the standard deviation of age of cars
[tex]\sigma _1 = \sqrt{\frac{\sum (x_i - \= x)^2}{n_1} }[/tex]
=> [tex]\sigma _1 = \sqrt{\frac{(4 - 5.56)^2 + (0 - 5.56)^2+ (8 - 5.56)^2 + \cdots + 8}{ 27} }[/tex]
=> [tex]\sigma _1 = 3.88 [/tex]
Generally the sample mean for the age of taxi is mathematically represented as
[tex]\= x_2 = \frac{\sum x_i }{n}[/tex]
=> [tex]\= x_2 = \frac{8 +8 +0 + \cdots + 4 }{20}[/tex]
=> [tex]\= x_2 = 5.85 [/tex]
Generally the standard deviation of age of taxi
[tex]\sigma _2 = \sqrt{\frac{\sum (x_i - \= x)^2}{n_1} }[/tex]
=> [tex]\sigma _2 = \sqrt{\frac{(8 - 5.85)^2 + (8 - 5.85)^2+ (0 - 5.85)^2 + \cdots + 8}{ 20} }[/tex]
=> [tex]\sigma _2 = 2.83 [/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{(\= x_ 1 - \= x_2 ) - 0}{\sqrt{\frac{\sigma^2_1}{n_1} + \frac{\sigma^2_2}{n_2} } }[/tex]
=> [tex]t = \frac{(5.56 - 5.85 ) - 0}{\sqrt{\frac{(3.88)^2}{27} + \frac{(2.83)}{20} }}[/tex]
=> [tex]t = -0.30 [/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n_1 + n_2 -2[/tex]
[tex]df = 27 + 20 -2[/tex]
[tex]df = 45[/tex]
From the t distribution table the [tex]P(t > t )[/tex] at the obtained degree of freedom = 45 is
[tex]P(t > -0.30 ) = 0.61722067[/tex]
So the p-value is
[tex]p-value = P(t > T) = 0.61722067[/tex]
From the obtained values we see that the p-value > [tex]\alpha [/tex] hence we fail to reject the null hypothesis
Hence the there is no sufficient evidence to support the claim that the mean age of the cars is greater than that of taxi