Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an
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:
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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).
Someone please help me with this I’m almost finished I just need this one PLEASEEEE
Answer:
2.7
Step-by-step explanation:
you substitute x in f(x) with 3 then get your answer which is 10 then substitute 10 for x in the formula g(x)
Solving a System of Linear Inequalities
Given the system of inequalities:
4x - 5y = 1
Which shows the given inequalities in slope-intercept
form?
Answer:
y = 4/5x -1/5
Step-by-step explanation:
4x -5y = 1
-5y = -4x + 1
5y = 4x - 1
y = 4/5x - 1/5
Jeffrey thinks that the largest place value that 8.21 and 19.5 have in common is the tens place Austin thinks that the largest place value they have in common is the ones place
Answer:
Austin is correct.
Step-by-step explanation:
19.5 has a tens, ones, and tenths place. 8.21 has a ones, tenths, and hundredths place.
Answer:
Neither are correct.
Step-by-step explanation:
8.21:
Tens Place - 0
Ones Place - 8
Tenths Place - 2
Hundredths Place - 1
19.5:
Tens Place - 1
Ones Place - 9
Tenths Place - 5
Hundredths Place - 0
None of the places are in common, so neither Jeffery nor Austin is correct.
You play a game using fair dice and fair coins. First you flip 72 coins. For each coin that is a heads, you roll 5 six-sided dice. You sum all the six-sided dice you roll to calculate your total score. What is the expected total score from this game
Answer:
630
Step-by-step explanation:
Given that:
First flip = 72 coins
For each coin which is a head, you roll = 5, six-sided dice
Thus, the expected sum on a single six-sided dice = [tex]\sum x P(x)[/tex]
[tex]\sum x P(x)[/tex] = [tex]\dfrac{1}{6}\times (1+2+3+4+5+6)[/tex]
[tex]\sum x P(x)[/tex] = 3.5
Thus, the expected sum on the five six-sided dice = 5 × 3.5 = 17.5
However, for a single flip :
The expected sum = P(heads) × expected sum on 5 dice + P(tails) × expected sum on 0 dice.
Expected sum = [tex]\dfrac{1}{2} \times 17.5 + \dfrac{1}{2} \times 0[/tex]
Expected sum = 8.75
Hence, the expected total score from this game = 72 × 8.75 = 630
Write an example that is not an integer
Answer:
1/2, 1/4 3/72, .50, .25, etc.
Step-by-step explanation:
An INTEGER is a whole number, positive or negative. A number that ISN'T an integer is a fraction or decimal.
Matt was standing 3 feet from the edge of the pool he walked away from the pool for four seconds then he was 12 feet away from the edge of the pool
Answer: graph b
Step-by-step explanation:
Seven cards are selected from a standard deck of cards. a) Determine the probability that exactly 5 of them are hearts. b) Determine the probability that there are 3 hearts and 3 diamonds. c) Determine the probability that there are 3 hearts, 3 diamonds and 1 spade. d) Determine the probability that there are 2 Aces and 2 Kings. e) Determine the probability that there are 2 Aces and 3 Kings.
Answer:
a
[tex]P(A_1) = 0.007[/tex]
b
[tex]P(A_2) = 0.016[/tex]
c
[tex]P(A_3) = 0.008[/tex]
d
[tex]P(A_4) = 0.004[/tex]
e
[tex]P(A_5) = 0.0002[/tex]
Step-by-step explanation:
From the question we are told that
The number of cards selected is n = 7
Generally in a standard deck of cards
The total number of cards is N = 52
The number of hearts is h = 13
The number of diamonds is d = 13
The number of spade is s = 13
The number of Ace is a = 4
The number of kings is k = 4
Considering question a
The number of ways to selected 5 hearts out of the 13 hearts is mathematically represented as
[tex]G = ^{13}C_5[/tex]
Here C means combination so
The number of cards that is not hearts is 52 - 13 = 39
Generally the number of ways of selecting the reaming 2 cards is
[tex]H = ^{39}C_2[/tex]
Generally the number of ways to select the 7 cards from the 52 deck of cards is
[tex]V = ^{52}C_7[/tex]
Generally the probability that exactly 5 of the 7 cards are hearts is mathematically represented as
[tex]P(A_1) = \frac{G * H}{V}[/tex]
=> [tex]P(A_1) = \frac{^{13}C_5 * ^{39}C_2}{^{52}C_7}[/tex]
=> [tex]P(A_1) = 0.007[/tex]
Considering question b
The number of ways to selected 3 diamonds out of the 13 diamonds is mathematically represented as
[tex] B = ^{13} C_3 [/tex]
The number of ways to selected 3 hearts out of the 13 hearts is mathematically represented as
[tex]K = ^{13}C_3[/tex]
The number of cards that is not hearts or diamond is 52 - (13 +13) = 26
Generally the number of ways of selecting the reaming 1 cards is
[tex]M = ^{26}C_1[/tex]
Generally the probability that there are 3 hearts and 3 diamonds is
[tex]P(A_2) = \frac{B * K * M}{V}[/tex]
=> [tex]P(A_2) = \frac{^{13}C_3 * ^{13}C_3 * ^{26}C_1}{^{52}C_7}[/tex]
=> [tex]P(A_2) = 0.016[/tex]
Considering question c
The number of ways to selected 1 spade out of the 13 spade is mathematically represented as
[tex]J = ^{13}C_1[/tex]
Generally the probability that there are 3 hearts, 3 diamonds and 1 spade is
[tex]P(A_3) = \frac{B * K * J}{V}[/tex]
=> [tex]P(A_3) = \frac{^{13}C_3 * ^{13}C_3 * ^{13}C_1}{^{52}C_7}[/tex]
=> [tex]P(A_3) = 0.008[/tex]
Considering question d
The number of ways to selected 2 Aces out of the 4 Aces is mathematically represented a
[tex]U = ^{4}C_2[/tex]
The number of ways to selected 2 Kings out of the 4 Kings is mathematically represented a
[tex]R = ^{4}C_2[/tex]
The number of cards that is not Aces or Kings is 52 - (4 +4) = 44
Generally the number of ways of selecting the reaming 3 cards is
[tex]S = ^{44}C_3[/tex]
Generally the probability that there are 2 Aces and 2 Kings is
[tex]P(A_4) = \frac{U * R * S}{ V}[/tex]
=> [tex]P(A_4) = \frac{ ^{4}C_2 * ^{4}C_2 * ^{44}C_3}{ ^{52}C_7}[/tex]
=>[tex]P(A_4) = 0.004[/tex]
Considering question e
The number of ways to selected 3 Kings out of the 4 Kings is mathematically represented a
[tex]P = ^{4}C_3[/tex]
Generally the number of ways of selecting the reaming 2 cards is
[tex]Q = ^{44}C_2[/tex]
Generally the probability that there are 2 Aces and 3 Kings is
[tex]P(A_5) = \frac{U * P * Q }{V}[/tex]
=> [tex]P(A_5) = \frac{ ^{4}C_2 * ^{4}C_3 * ^{44}C_2 }{^{52}C_7}[/tex]
=> [tex]P(A_5) = 0.0002[/tex]
2+1x1000000000000000000
Answer:
30000000000000000.. ....
if you have a class RIGHT NOW ethier google classroom are zoom let me crash it if yall board
Answer:
i have a class now but i will get in trouble sry
Step-by-step explanation:
Answer:
Meeting ID: 851 5556 0217
Step-by-step explanation:
i hate school proceed as you wish good sir! :)
meeting starts at 11:10 btw
What is the slope of line passing through (2, 7) and (4, - 6)?
Answer:
The slope is -13/2x + 20. In decimal form, -6.5x + 20
What is 4/9 - 1/3 =
help
Answer:djjdd
Please I love free points secy
Step-by-step explanation:
Ok but guys is 10009
What is the simplest form of
N3240215
bº?
b20)
(Assume that a 20
and
18ab3
* 1864
O 162ab3
162ab4
RETRY
done
Answer:
A
and the answer to part b is
C
Step-by-step explanation:
Answer:
the other man is right
Step-by-step explanation:
a then c so have nice day love yall
We
Shannon makes and sells picture frames. She charges different rates depending on the material she uses for the frame Shannon sold a frame
for $45. Which type of frame did Shannon sell? Use the drop-down menus to show and explain your answer
Frame Prices
Wood frame
$18
Metal frame
1.5 times wood frame rate
2.5 times wood frame rate
Silver-plated frame
Shannon bought the Choose
frame because 45
Choose...
= $18, which is the wood frame rate.
Answer: Shannon sold the silver plated frame because 45 divided by 2.5 = $18, which is the wood frame rate.
Step-by-step explanation:
I know this because 45 divided by 2.5 = $18 And that’s the silver plated frame.
(1,0) (2,1) put into standard form
Answer:
(1,0) (2,1) = (0) (2,1) = (0) (2) = 0
Step-by-step explanation:
1,0 is multiplication which would be 0 and the same applies for 2,1 which would be 2. 0 x 2 is 0 you know it's multiplication because there's no symbol between the parenthesis.
Ellie read an article claiming that 10% of people in her county were senior citizens, and she thought that it may be higher for residents in her city. She took a random sample of 225 people from her city and found that 36 of them were senior citizens. She wants to test H0:p=0.10 versus Ha:p > 0.10, where p is the proportion of people in her city that are senior citizens. Assuming that the conditions for inference have been met.
Required:
Calculate the test statistic for Ellie's significance test.
Answer:
The value is [tex]z = 3[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion of senior citizens is [tex]p = 0.10[/tex]
The sample size is [tex]n = 225[/tex]
The number of senior citizens is k = 36
The null hypothesis is [tex]H_o : p = 0.10[/tex]
The alternative hypothesis is [tex]H_a : p > 0.10[/tex]
Generally the sample proportion is mathematically represented as
[tex]\^{p} = \frac{k}{n}[/tex]
=> [tex]\^{p} = \frac{ 36 }{225}[/tex]
=> [tex]\^{p} =0.16[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\^{p} - p }{\sqrt{\frac{p(1 -p )}{n} } }[/tex]
=> [tex]z = \frac{0.16 - 0.10 }{\sqrt{\frac{p(1 -0.10)}{225} } }[/tex]
=> [tex]z = 3[/tex]
Answer:
P-value ≈ 0.0588
Step-by-step explanation:
mass and weight math
Answer: There is 1,000 milligrams in 1 gram.
Answer:
1000mg
Step-by-step explanation:
to be honest that's the obvious answer
and in advance
1kg=1000000mg
1kg=1000g
1g=1000g
NEED HELP WITH MATH! Will Give Brainliest! Image is below.
Answer:
I BELIEVE the answer is 3.
Step-by-step explanation:
However, I could be wrong, but I do know it's between 1 and 3.
-167-(-12)=
answer it idk
Answer:
155
Step-by-step explanation:
All you do is subtract negetive 167 and take -12 away from 167.
In developing their warranty policy, an automobile company estimates that over a 1-year period 17% of their new cars will need to be repaired once, 7% will need repairs twice, and 4% will require three or more repairs. If you bought two cars from this company, what is the probability that neither will need repair over a 1-year period
Answer:
Step-by-step explanation:
OVER A 1-YEAR PERIOD, it is estimated that
17 + 7 + 4 = 28% of new cars will need repairs (ranging from one repair to infinity number of repairs)
This means that the remaining percentage of new cars will NOT need any repairs over the 1-year period.
This percentage is 100 - 28 = 72%
The question is reframed thus: If you bought 2 cars from this company, what is the probability that none of them will need repair over the 1-year period?
What is the probability that none of the 2 cars falls within the 28% of cars which will need repair in the 1-year period?
72% = 72/100 = 0.72
this is the probability that a single car will not need repairs
the probability that 2 cars from this company will not need repair over a year is 0.72 ÷ 2 = 0.36
a bowl contains 4 yellow marbles, 5 red marbles, 1 blue marbles, and 3 green marbles. find the probabilityof the given outcome
Answer:
bowl of colorful marbels
Step-by-step explanation:
bowl+marbels
Zach mows lawns. He charges $5 plus $3 per hour. Alex also mows lawns He charges $2 plus $4 per hour. How many hours do they need to work to make the same amount
Answer:
They both need to work 3 hours to get the same amount of $14.
Step-by-step explanation:
If you have a graphing calculator handy, just graph the two expressions 3x + 5 and 4x + 2 and look for the point where they intersect. If you don't have a graphing calculator set up the equation 3x + 5 = 4x + 2. Subtract 4x from both sides to get -x + 5 = 2. Then subtract 5 from both sides to get -x = -3. Since x shouldn't be negative, divide both sides by -1. You do this because just like x is 1x, -x is -1x. After dividing, you should get x = 3.
A regional office of the Internal Revenue Service randomly distributes returns to be audited to the pool of auditors. Over the thousands of returns audited last year, the average amount of extra taxes collected was $356 per audited return. One of the auditors, Jeffrey Jones, is suspected of being too lenient with persons whose returns are being audited. For a simple random sample of 30 of the returns audited by Mr. Jones last year, an average of $340 in extra taxes was collected.
Required:
Assuming a normal population of extra taxes collected with a standard deviation of $90, do the suspicions against Mr. Jones appear to be justified?
Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the justification against Mr. Jones appears not to be justified
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = \$ 356[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = \$340[/tex]
The standard deviation is [tex]\sigma = \$ 90[/tex]
The null hypothesis is [tex]H_o : \mu = \$ 35 6[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne \$ 35 6[/tex]
Let assume the significance level is [tex]\alpha = 0.05[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 340 - 356 }{\frac{90 }{\sqrt{30} } }[/tex]
=> [tex]t =-0.9737 [/tex]
Generally the sample size from the question is small that it is not greater than 30 hence we use t-test
Now the degree of freedom is mathematically represented as
[tex]df = n- 1[/tex]
=> [tex]df = 30- 1[/tex]
=> [tex]df= 29[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 P (t > -0.9737 )[/tex]
Generally from the t-distribution table , the probability of -0.9737 at a degree of freedom of [tex]df= 29[/tex] for a two -tailed test is
[tex]P (t > -0.9737 ) = 0.33825793[/tex]
Hence p-value is
[tex]p-value = 2*0.33825793[/tex]
[tex]p-value = 0.676 [/tex]
From the value we obtained we see that [tex]p-value > \alpha[/tex] hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the justification against Mr. Jones appears not to be justified
(-7, 13); slope = -2 Write the equation of the line in slope-intercept form with the given point and slope or two points.
Answer:
y=-2x-1
Step-by-step explanation:
13=-2*-7+b
13=14=b
-1=B
The equation of the line in the slope-intercept form will be 2x+y+1=0.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that,
The coordinate of the points are (x,y) = (-7, 13)
Slope, m = -2
The standard equation of a line is,
y = mx+c
Substitute the given coordinate value in order to find the intercept value as
13=-2×-7+c
13-14=c
-1=c
Put the values in the standard equation,
y = mx+c
y=-2x-1
Thus, the equation of the line in the slope-intercept form will be 2x+y+1=0.
Learn more about the linear equation here:
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A 190-second song is divided into 3 parts, the beginning, the middle, and the end. The beginning is 1/6 as long as the end. The middle part is 1/2 as long as the end. Find the length of each part.
The beginning is ____ seconds
The middle is _____ seconds
The end is ______ seconds
Answer:
The beginning part is 19 seconds.
The middle part is 57 seconds.
The end part is 114 seconds.
Step-by-step explanation:
First, you have to form expressions. Let the end part be x :
Beginning = (1/6)x
Middle = (1/2)x
End = x
Next, you have to add up altogether equals to 190 :
(1/6)x + (1/2)x + x = 190
(5/3)x = 190
x = 190 ÷ (5/3)
x = 114 s
Lastly, you have to substitute the x-value into the expressions :
Beginning = (1/6)(114) = 19 s
Middle = (1/2)(114) = 57 s
End = 114 s
Answer:
b is 19 seconds
m is 57 seconds
e is 114 seconds
Step-by-step explanation:
total = b + m + e
total = 1/6e + 1/2e + e
190 = 1/6e + 1/2e + e
190 = 10/6e
190 * 3/5 = e
114 = e
(1/6)e = b = (1/6)(114) = 19
(1/2)e = m = (1/2)(114) = 57
Find the area and the perimeter of the figure
Answe ASAP test ina couple minutes
Answer:
Area of rectangle = (l×b)
=14×6
=84 metre²
Perimeter of rectangle= 2×(l+b)
=2×(14+6)
=2×20
40 metre/cm {as it is not given}
Step-by-step explanation:
Hope this helps you
Crown me as brainliest
Answer:
Step-by-step explanation:
To find the area you need to multiply the two length and height.
14 x 6
This would equal 84.
For the perimeter you add all the sides. Since there are four sides to a rectangle and a square, you add 2 of the corresponding sides to the equation.
14+14+6+6
Or
2(14+6)
Or
2(14) + 2(6)
Which equals 40.
Which statement correctly describes the expression ( - 15)3?
Answer: One factor is positive and one is negative, so the product will be negative.
Answer:
One factor is positive and one factor is negative, so the product will be negative
Step-by-step explanation:
If you see there (-15)3 so -15 is a negative number and 3 is a positive and when you multiple a negative number with a positive number it becomes negative.
5. If three times a number is increased by 4, the result is -8.
Step-by-step explanation:
Hey there!
Let the unknown number be x. Then;
According to the question;
3x+4= -8
3x = -12
x = -12/3
Therefore, x = -4
Check:
3*-4 +4 = -8
-12+4 = -8
-8= -8 (True).
Hope it helps...
Determine the measure of < 7
o 53
o 133
o 127
o 47
Y-4>3 solve the question
Answer:
y>7
Step-by-step explanation:
y-4>3
+4 +4
y>7