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).
Harry drove 5 hours on the freeway. then decreased his speed by 20 miles per hour and drove for 3 more hours on a country road. if his total trip was 396 miles, than what was his speed on the freeway?
Answer:
What are the options
Step-by-step explanation:
The supermarket has 30 aisles. 60% are empty, without any shoppers. How many empty aisles are there in the supermarket?
Answer:
18
Step-by-step explanation:
to find the percentage of something you change the percent to a decimal and multiply it by the other number, so in this case you have 0.6*30 and you get 18.
hope this helped :))
Can anyone please solve this question
Keiko is going for a walk.she takes 3 hours to walk 7.5 miles.what is her speed
Answer:
2.5 mph
Step-by-step explanation:
Which equation has the solution x = 9?
Select each correct answer.
+7= 8
4+ 5x = 18
81 – 3 = 6
х
2x – 3 = 15
24 – 2x = 13
3x + 2 = 25
Answer:
2x – 3 = 15
Step-by-step explanation:
2 * 9 = 18 - 3 = 15. correct
+7 = 8, no I don't really now what you mean by this...
81 - 3 = 6x? > (81 - 3 = 78) = (6 * 9 = 54), no, please tell me if I'm interpreting this right.
4 + 5x = 18 > 5 * 9 = 45 + 4 = 49, no
2 * 9 = 18, 24 - 18 = 6, no
3 * 9 = 27 + 2 = 29, no
I only have 30 minutes left
Answer:
what is the question?
Step-by-step explanation:
U only posted a picture of a half paragraph
A box contains three types of fruits:
apples, bananas, and pears. There are
20 pieces of fruit in all. Of these, 3 are
apples and 11 are bananas. What is the
ratio of pears to bananas?
А
6 3 11
B 11 26
C 3: 11
D
11: 3
Ο Α
o
D
Answer:
d
Step-by-step explanation:
Fin the equation of the line whose slope is 3, and passes through point (2,
4). Write it in point-slope.
y + 4 = 3(x - 2)
y - 4 = 3(x + 2)
y - 4 = 3( x - 2)
y-2 = 3(x - 4)
Answer:
use the point slope formula.. just memorize this formula.. you'll need to so often y-y1 = m(x + x1) and know it's name There is another one that is similar in form and name
Step-by-step explanation:
M = 3
P1 =(x1, y1 ) = (2,4)
plug it into the point slope formula
y-4 = 3(x+2)
the second choice looks pretty good
It is very important that you
and avoid errors to happen.
Review
Instruction:
Factor each of the following quadratic expression.
1. x² + x
2. 5x2 - 25x
3. x2 - 16
4. x² + 4x + 4
5. x2 - 5x + 6
Step-by-step explanation:
Given expressions:
1. x² + x
2. 5x² - 25x
3. x² - 16
4. x² + 4x + 4
5. x² - 5x + 6
Problem: Factor each of the quadratic expression
Solution:
A quadratic expression is an expression whose highest power is two.
1. x² + x
For this expression:
x² + x
Factorizing x since it is a common term;
x(x + 1)
2. 5x² - 25x
For this expression;
Factorize 5x since it common to both of them;
5x(x - 5)
3. x² - 16
For this expression;
Apply the differences of two squares;
x² - 16
x² - 4²;
Note; x² - y² = (x-y)(x+y)
So, x² - 4² = (x-4)(x + 4)
4. x² + 4x + 4
To solve this,
Find two numbers whose product will be 4 and sum also 4;
x² + 4x + 4 = x² + 2x + 2x + 4
= x(x + 2) + 2(x + 2)
= (x + 2)(x + 2)
5. x² - 5x + 6
To factorize this expression, simply find two numbers whose sum is -5 and product is 6;
x² - 5x + 6 = x² - 3x - 2x + 6
= x (x - 3) -2(x - 3)
= (x -2)(x-3)
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
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:
what is 5 divided by 1 4/7
which number is the estimated square root of 15 closest to
Answer:
3.87 that should be the answer
A hotel manager records the number of bookings made at various prices during July.
What type of correlation does the graph show?
A. strong positive correlation
B. weak positive correlation
C. strong negative correlation
D. weak negative correlation
E. no correlation
Answer:
C. strong negative correlation
Step-by-step explanation:
I would say the answer is C. a strong negative correlation.
Firstly, the graph is 'going downwards', meaning that the relationship is negative. This is because one variable decreases when the other is increased. I think it is a strong relationship because the trend is quite clear through the points and the slope is moderately steep.
Hope this helped!
3. A recipe for apple cider calls for 4 cups of apple juice and 3 cups of water. Which equation can be used to find x, the percent of apple juice in the recipe?
Answer:
what are the options
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
More on Linear Equations & Linear Systems: Question 1
How many solutions does the system of equations below
have?
y - 2x + 2
y-r-1
Select one:
none
infinitely many
O o o o
one
two
Answer:
21
Step-by-step explanation:
Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a
mean of 100 and a standard deviation of 15.
106 124
The area of the shaded region is (Round to four decimal places as needed.)
Answer:
The area of the shaded region is 0.2898.
Step-by-step explanation:
Let X represent the IQ scores of adults.
It is provided that [tex]X\sim N(100,15^{2})[/tex].
Compute the probability of an adult having an IQ between 106 and 124 as follows:
[tex]P(106<X<124)=P(\frac{106-100}{15}<\frac{X-\mu}{\sigma}<\frac{124-100}{15})[/tex]
[tex]=P(0.40<Z<1.60)\\=P(Z<1.60)-P(Z<0.40)\\=0.94520-0.65542\\=0.28978\\\approx 0.2898[/tex]
*Use a z-table.
Thus, the area of the shaded region is 0.2898.
A directed segment ST¯¯¯¯¯ is partitioned from S (−5,0) to T in a 32 ratio at point M (10, 15). What are the coordinates of point T? (20, 25) (15, 20) (7, 3) (5, 15
Answer:
[tex]T = (20,25)[/tex]
Step-by-step explanation:
Given
[tex]S = (-5,0)[/tex]
[tex]M = (10,15)[/tex]
[tex]Ratio = 3:2[/tex]
Required
Determine the coordinate of T
Line division by ratio is calculated using:
[tex]M(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]
Where:
[tex](x_1,y_1) = (-5,0)[/tex]
[tex](x,y) = (10,15)[/tex]
[tex]m:n = 3:2[/tex]
So, we have:
[tex](10,15) = (\frac{3 * x_2 + 2 * -5}{3+2},\frac{3 * y_2 + 2 * 0}{3+2})[/tex]
[tex](10,15) = (\frac{3x_2 -10}{5},\frac{3y_2}{5})[/tex]
Multiply through by 5
[tex]5 * (10,15) = (\frac{3x_2 -10}{5},\frac{3y_2}{5}) * 5[/tex]
[tex](50,75) = (3x_2 -10,3y_2)[/tex]
By comparison:
[tex]3x_2 - 10 = 50[/tex]
[tex]3y_2 = 75[/tex]
[tex]3x_2 - 10 = 50[/tex]
[tex]3x_2 = 50 + 10[/tex]
[tex]3x_2 = 60[/tex] --- Divide through by 3
[tex]x_2 = 20[/tex]
[tex]3y_2 = 75[/tex]
[tex]y_2 =75/3[/tex] --- Divide through by 3
[tex]y_2 =25[/tex]
Hence:
The coordinates of T is
[tex]T = (20,25)[/tex]
Find the value of the power.
3 exponent 5
Answer:
243
Step-by-step explanation:
3*3*3*3*3=243
Answer:
243
Step-by-step explanation:
Help me please!!..,,
Answer:
A.
Step-by-step explanation:
1.5 x 0.1 = 0.15
0.15 inches
Dont know if this is for sure right. Hope it is.
5) The price of a gallon of gas was $4.00. The price went up by 10% and then went down by 10%. Antonio thinks that since the price both rises and falls by 10%, the price of a gallon of gas is back to $4.00. His teacher tells him that he is incorrect. Explain why Antonio's reasoning is incorrect. (1 point) Determine the price of a gallon of gas after the 10% rise and 10% fall. (1 point) Total of 2 points. *
Answer:
Antonio is wrong because 10% of 4.00 is .40 and if the price goes up then the price is $4.40 and since the price is going down by ten percent, ten percent if $4.40 is .44 and therefore the price is $3.96.
helllllppppp pleaseeeeee
Answer:
2nd choice
Step-by-step explanation:
The slope is 2/3 (rise/run) and the y-intercept is -2
When you put those values into f(x) = mx + b, you get f(x) = 2/3x - 2
Help me out please I need help
The temperature in Denver is -4 degrees
Celsius and the temperature if Tampa is 38
degrees Celsius. What is the difference
3) between these two temperatures?
Answer:
34 degrees Celsius
Step-by-step explanation:
For this question, you just find the sum of the two temperatures:
-4+38 = 34
The company is interested in which confidence intervals associated with 1 (very satisfied) contain the proportion 0.25, or 25%. Determine which confidence levels satisfy this. (Select all that apply.)
Hi, you've asked an incomplete question. However, I provided a brief explanation about confidence interval and confidence level.
Explanation:
The term confidence interval and confidence level are not the same but they are related. Confidence interval refers to a range of values that makes up part of the statistic's mean data which contains an unknown population parameter.
However, the Confidence level is the level of certainty that the confidence interval would contain the true population parameter if a random sample is drawn.
16. (a) Find the Highest Common Factor (HCF) of 30 and 42.
Answer: 6
Step-by-step explanation: By checking the factors of both numbers, you see that 6 is their greatest common factor.
30: 1, 2, 3, 5, 6, 10, 15, 30
42: 1, 2, 3, 6, 7, 14, 21, 42
Hope this helps!
Round to the nearest hundredth 13.459
Answer:
13.46
Step-by-step explanation:
The correct response is 13.46.
Since 9 is greater than 5, we replace the 5 in the hundreths place with a 6.
The variables x and y are related proportionally. When x = 8, y = 20. Find y when x = 80.
Answer:
y = 200
Step-by-step explanation:
Use the equation y = kx, where k is a constant.
Plug in the given x and y values, then solve for k:
y = kx
20 = k(8)
2.5 = k
Then, plug in k and the given x value, and find y:
y = 2.5x
y = 2.5(80)
y = 200
So, y = 200 when x = 80
UM WHAT I NEED SOME ADMINS LOOK
Answer:
LOL UGH THAT KEEPS HAPPENING TO ME
Step-by-step explanation:
Answer:
try reloading the page or check your internet
Step-by-step explanation:
The mean output of a certain type of amplifier is 466 watts with a standard deviation of 10 watts. If 32 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 1.6 watts? Round your answer to four decimal places.
Answer:
0.8186
Step-by-step explanation:
The formula to use to solve this question is given as:
z = (x-μ)/σ/√n, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
n is the random number of samples
P(z < (x-μ)/σ/√n)
(x-μ) = 1.6 watts
σ = 10 watts
n = 32 amplifiers
Hence,
P(z < 1.6/10/√32)
P(z < 1.6/1.767766953)
P(z < 0.9050966799)
Approximately to 2 decimal places)
P(z < 0.91)
= 0.81859
Rounded to four decimal places, the probability that the mean of the sample would differ from the population mean by less than 1.6 watts is 0.8186.