The sequence is monotone.The sequence is bounded.The sequence diverges.The answer is DIV.
Let's consider the sequence an = (Xn - 1)! (6n+1)! and describe its behavior. We will also determine whether the sequence is monotone and bounded, and then figure out whether the sequence converges or diverges. If it converges, we will also determine the value it converges to.
Behavior of the sequence an:The sequence an can be simplified as follows:an = (Xn - 1)! (6n+1)! = Xn!/(Xn) (6n+1)! = 6n+1/Xn (6n+1)!We can see that 6n+1 is less than 6(n+1)+1 for all values of n.
This implies that 6n+1 is the smallest number in the sequence (6n+1)! for every n. Additionally, Xn is always greater than or equal to 1, so an+1/an = Xn/(Xn+1) is always less than or equal to 1.
Hence, the sequence is monotone.The sequence is bounded:Since Xn is a sequence of positive integers, the sequence 6n+1/Xn is always greater than 0.
Also, we know that n! grows slower than exponential functions, so 6n+1! grows faster than exponential functions. This implies that 6n+1/Xn (6n+1)! is bounded by some exponential function of n.
Hence, the sequence an is bounded.Divergence or convergence of the sequence an:Since the sequence an is bounded and monotone, it is guaranteed to converge.
We can apply the monotone convergence theorem to find the limit of the sequence:lim n→∞ (6n+1/Xn (6n+1)!) = lim n→∞ (6n+1)/Xn lim n→∞ (6n+1)!
The limit of (6n+1)/Xn is 6 because Xn is a sequence of positive integers and n! grows slower than exponential functions.
The limit of (6n+1)! is infinity because it grows faster than exponential functions.
Hence, the limit of an is infinity. Therefore, the sequence diverges. The answer is DIV.
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Kathy bought a total of 60 cupcakes. Supreme cupcakes cost $12 each and regular cupcakes cost $3 each. She spent a total of $90. Which system of equations will determine the number of supreme (s) and regular (r) cupcakes that Kathy purchased?
Answer:
s + r = 60 and 12s + 3r = 90
Step-by-step explanation:
I just took the quiz and it said this is correct
Which point is a reflection of (12, −8) across the y-axis on a coordinate plane? A (8, 12) B (−8, 12) C (−12, −8) D (12, 8)
Answer:
option A
Step-by-step explanation:
thats the answer!!!
The expenses E and income I for making and selling T-shirts with a
school logo are given by the equations E = 535 +4.50n and I = 12n,
where n is the number of T-shirts.
Expenses: Slope=
Y-Intercept =
income: Slope=
Y-Intercept
Can you please help me with this question I keep getting the wrong answer
Answer:
14
Step-by-step explanation:
The diameter of a circle is 8 inches. What is the area?
d=8 in
Give the exact answer in simplest form.
Step-by-step explanation:
Radius = Half of Diameter
r = 8/2
= 4 in.
Area of Circle =
[tex]\pi {r}^{2} \\ = \pi( {4}^{2} ) \\ = 16\pi \: {in}^{2} [/tex]
On the main floor of the Kodak hall at Eastman theater the number of seats per row increases at a constant rate Steven counts 31 seats in row three and 37 seats in row six how many seats are there in route 20
Answer:
67
Step-by-step explanation:
no
Follow the process of completing the square to solve x2 - 10x + 8 = 0. What is the value of the constant that will be isolated on the right side of the equation in step 3? -8 -12 -32
Answer:
25
Step-by-step explanation:
Given the expression x^2 - 10x + 8 = 0.
According to completing the square method
Subtract 8 from both sides
x^2 - 10x + 8 - 8 = 0 - 8
x^2 - 10x = -8
Complete the square
Add the square of half of coefficient of x to both sides
Coefficient of x = -10
Half of Coefficient of x = -10/2
Half of Coefficient of x = -5
Square of Half of Coefficient of x = (-5)^2
Square of Half of Coefficient of x = 25
Add (-5)^2 to both sides
x^2 - 10x + (-5)^2 = -8 + (-5)^2
(x-5)^2 = -8 + 25
(x-5)^2 = 17
Hence the required constant that was added is 25
What will the answer be?
Answer:
hi!
Step-by-step explanation:
Laura is the fund-raising manager for a Local charity. She is Ordering caps for an upcoming charity walk. the company that makes the caps charges six dollars per cap plus a $25 shipping fee Laura has a budget of $1000 what is the greatest number of cats so she can buy
Answer:
162 caps.
Step-by-step explanation:
Let x be the number of caps.
We have been given that cost of one cap is $6, so cost of x caps will be equal to 6x.
We are also told that the company charges an amount of $25 for shipping, so total cost of buying x caps will be equal to the cost of x caps plus shipping charges ().
Since Laura has a budget of $1,000, so cost of x caps will be less than or equal to 1,000. We can represent this information in an equation as:
Now let us solve for x.
Let us divide both sides of our inequality by 6.
what percent of 272 is 34?
BRAINLIEST AND 50 POINTS UP FOR GRABS: PLEASE LEAVE DETAILED ANSWERS
Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(3, −6), Q(0, 9), and R(−3, 0). Triangle P'Q'R' has vertices P'(1, −2), Q'(0, 3), and R'(−1, 0).
Plot triangles PQR and P'Q'R' on your own coordinate grid.
Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R'? Explain your answer. (4 points)
Part B: Write the coordinates of triangle P"Q"R" obtained after P'Q'R' is reflected about the y-axis. (4 points)
Part C: Are the two triangles PQR and P''Q''R'' congruent? Explain your answer. (2 points)
Answer:
Triangle P' Q' R' is half the size of the original triangle.
-The scale factor is probably 1/3.
Part B: P'(1, −2), Q'(0, 3), and R'(−1, 0).
Part C: No, the triangles are not congruent. If the second triangle didn't have a dilation, and instead have a reflection of the first triangle, then it would be congruent.
Step-by-step explanation:
:)
Find the value of the variables in the simplest form
Answer:
y = 2
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
y² = ([tex]\sqrt{2}[/tex] )² + ([tex]\sqrt{2}[/tex] )² = 2 + 2 = 4 ( take the square root of both sides )
y = [tex]\sqrt{4}[/tex] = 2
4 cards are drawn from a deck of shuffled cards without
replacement.
Find the probability that:
a) All are kings
b) All are red cards
a) The probability of drawing all kings from a shuffled deck of cards without replacement is approximately 0.0000014, or 1.4 in 1 million.
b) The probability of drawing all red cards from a shuffled deck without replacement is approximately 0.000000103, or 1.03 in 10 million.
a) Probability of drawing all kings:
To calculate the probability of drawing all kings, we need to determine the total number of possible outcomes and the number of favorable outcomes. Let's break it down step by step:
Step 1: Total number of possible outcomes
In a standard deck of 52 playing cards, there are four kings. When we draw one card, there are 52 cards to choose from. For the second draw, only 51 cards remain, and so on. Therefore, the total number of possible outcomes for drawing four cards without replacement is:
52 × 51 × 50 × 49 = 649,740
Step 2: Number of favorable outcomes
Since we want all four cards to be kings, there are only four kings in the deck. When we draw the first card, there is a 4/52 chance of it being a king. For the second card, the probability reduces to 3/51 since there are three kings remaining out of 51 cards. Similarly, for the third and fourth cards, the probabilities become 2/50 and 1/49, respectively. Therefore, the number of favorable outcomes is:
(4/52) × (3/51) × (2/50) × (1/49) = 1/270,725
Step 3: Calculating the probability
Finally, we can calculate the probability of drawing all kings by dividing the number of favorable outcomes by the total number of possible outcomes:
P(all kings) = (1/270,725) / (649,740) ≈ 0.0000014
b) Probability of drawing all red cards:
Similarly, let's calculate the probability of drawing all red cards from the deck. We follow the same steps:
Step 1: Total number of possible outcomes
When we draw the first card, there are 26 red cards in a deck of 52. For the second draw, there are 25 red cards remaining out of 51, and so on. Hence, the total number of possible outcomes for drawing four cards without replacement is:
26 × 25 × 24 × 23 = 358,800
Step 2: Number of favorable outcomes
Since we want all four cards to be red, there are 26 red cards in the deck. The probability of drawing a red card for the first draw is 26/52. For the second draw, the probability becomes 25/51, for the third draw it is 24/50, and for the fourth draw, it is 23/49. Thus, the number of favorable outcomes is:
(26/52) × (25/51) × (24/50) × (23/49) ≈ 0.037
Step 3: Calculating the probability
The probability of drawing all red cards is the ratio of the number of favorable outcomes to the total number of possible outcomes:
P(all red cards) = (0.037) / (358,800) ≈ 0.000000103
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Select all the TRUE sentences!!!
Answer:
The last two.
Step-by-step explanation:
Answer:
A and C
Step-by-step explanation:
two particles travel along the space curves r1(t) = t, t2, t3 r2(t) = 1 6t, 1 30t, 1 126t . find the points at which their paths intersect. (if an answer does not exist, enter dne.)
Two particles are traveling along space curves defined by the equations r₁(t) = (t, t², t³) and r₂(t) = (1/6t, 1/30t, 1/126t). We need to find the points at which their paths intersect.
To find the points of intersection, we need to solve the system of equations formed by equating the components of the two space curves.
Comparing the x-components, we have:
t = 1/(6t) => t² = 1/6 => t = ±√(1/6).
Comparing the y-components, we have:
t² = 1/(30t) => t³ = 1/30 => t = ±∛(1/30).
Comparing the z-components, we have:
t³ = 1/(126t) => t⁴ = 1/126 => t = ±∜(1/126).
Combining all the solutions, we have four possible values for t: √(1/6), -√(1/6), ∛(1/30), and -∛(1/30). However, we need to check if these values are valid for all components of the curves.
By substituting these values of t into the equations, we find that only the value t = √(1/6) yields valid points of intersection: (√(1/6), 1/6, 1/√6) and (-√(1/6), 1/6, -1/√6).
Therefore, the points at which the paths of the particles intersect are (√(1/6), 1/6, 1/√6) and (-√(1/6), 1/6, -1/√6).
Please note that the other values of t do not yield valid points of intersection, so they are not considered as solutions in this case.
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Peterkin park has a square fountain with a walkway aroind it. The fountain measures 12 feet on each side. The walkway is 3 1/2 feet wide.Find the area of the walkway
Answer: 829.44 ft²
Step-by-step explanation:
Correction - The walkway is 31.2 feet wide.
To solve this, first find the area of the fountain:
Area of a square = Length * Width
= 12 * 12
= 144 ft²
The find the area of the walkway including the fountain:
= 31.2 * 31.2
= 973.44 ft²
To find the area of the walkway alone, subtract the area of the square from the area of the rectangle:
= 973.44 - 144
= 829.44 ft²
You intend to conduct a goodness-of-fit test for a multinomial distribution with 5 categories. You collect data from 55 subjects. What are the degrees of freedom for the xa distribution for this test?
For the goodness-of-fit test with data collected from 55 subjects, the degrees of freedom for the chi-square distribution will be 4.
In a goodness-of-fit test, the degrees of freedom for the chi-square distribution determine the critical values and the interpretation of the test statistic. For a multinomial distribution with k categories, the degrees of freedom are calculated as (k - 1).
In this specific case, we have a multinomial distribution with 5 categories. Therefore, the degrees of freedom for the chi-square distribution will be (5 - 1) = 4.
Having 4 degrees of freedom means that the chi-square test statistic will be evaluated against the chi-square distribution with 4 degrees of freedom to determine the p-value and assess the significance of the test. The critical values at the chosen significance level will also depend on these degrees of freedom.
In summary, when conducting a goodness-of-fit test for a multinomial distribution with 5 categories and collecting data from 55 subjects, the chi-square test will have 4 degrees of freedom. These degrees of freedom play a crucial role in determining the validity and interpretation of the test results.
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find the slope of the two points: 4,-3 and 8,-3
Answer:
0 slope
Step-by-step explanation:
flat horizantal line
no increase in y-value
Reading Improvement Program To help students improve their reading, a school district decides to implement a reading program. It is to be administered to the bottom 14% of the students in the district, based on the scores on a reading achievement exam. If the average score for the students in the district is 124.5, find the cutoff score that will make a student eligible for the program. The standard deviation is 15. Assume the variable is normally distributed. Round 2-value calculations to 2 decimal places and the final answer to the nearest whole number.
Rounding the cutoff score to the nearest whole number, the cutoff score that will make a student eligible for the reading program is approximately 108.
To find the cutoff score that will make a student eligible for the reading program, we need to determine the score below which the bottom 14% of students fall.
Since the variable is normally distributed and we know the average score and standard deviation, we can use the Z-score formula to find the cutoff score.
The Z-score formula is:
[tex]\[Z = \frac{X - \mu}{\sigma}\][/tex]
Where:
Z is the Z-score,
X is the raw score,
[tex]\mu[/tex] (mu) is the mean, and
[tex]\sigma[/tex] (Sigma) is the standard deviation.
We want to find the Z-score that corresponds to the bottom 14% of students, which means the area to the left of the Z-score is 0.14.
Using a standard normal distribution table or calculator, we can find the Z-score that corresponds to an area of 0.14, which is approximately -1.08.
Now we can rearrange the Z-score formula to solve for X, the cutoff score:
[tex]\[X = Z \cdot \sigma + \mu\][/tex]
Substituting the values we have:
[tex]\[X = -1.08 \cdot 15 + 124.5\][/tex]
Calculating the expression:
[tex]\[X = -16.2 + 124.5\]\\X = 108.3[/tex]
Rounding the cutoff score to the nearest whole number, the cutoff score that will make a student eligible for the reading program is approximately 108.
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When rolling a die why is the probability of rolling a 2 or 3
Answer:
1/3
Step-by-step explanation:
If you're talking about a 6-sided die, then there are 6 sides. Rolling a 2 or a 3 would be a 2/6 chance. To simplify if from there, you can also say that there is a 1/3 chance.
Matt bought 7 shirts for a total of $38. Tee shirts cost $5 and long sleeve shirts cost $6. How many of each type of shirt did he buy? HELP PLZ 100 POINTS
Answer:
tee shirt:4
sleeve shirt:3
Step-by-step explanation:
we are given two conditions
Matt bought 7 shirts for a total of $38Tee shirts cost 5 dollars and long sleeve shirts cost 6 dollarswe want to figure out how many each type of shirt he bought
let tee and sleeve shirts be t and s respectively
according to the first condition
[tex] \displaystyle t + s = 7[/tex]
according to the second condition
[tex] \displaystyle5t + 6s = 38[/tex]
therefore
our system of linear equation is
[tex] \displaystyle\begin{cases}t + s = 7 \\ 5t + 6s = 38 \end{cases}[/tex]
so
now we need our algebra skills to figure out t and s
to do so we can use substitution method
cancel s from both sides of the first equation:
[tex] \displaystyle t = 7 - s \: \cdots \: i[/tex]
now substitute the value of i equation to the second equation:
[tex] \displaystyle 5(7 - s) + 6s = 38[/tex]
distribute:
[tex] \displaystyle 35 - 5s+ 6s = 38[/tex]
collect like terms:
[tex] \displaystyle s + 35 = 38[/tex]
cancel 35 to both sides:
[tex] \displaystyle \therefore s = 3[/tex]
now substitute the value of s to the i equation:
[tex] \displaystyle t = 7 - 3 \\ \therefore \: t = 4[/tex]
hence,
he bought tee shirt 4 and sleeve shirt 3
Can someone help me you’re correct me it only let me type one number plz
Answer:
9
Step-by-step explanation:
Hello There!
The circumference is equal to the diameter times π
The diameter given is 9m
NOTE: it says "leave answer in terms of π" meaning that we do not apply π to the diameter
So the answer would be just 9π
Answer:
9
Step by step:
C= 2 x pi x r
c = 2 x pi x 4.5
c= 9 x pi
S5=7+7x^(5)+7x5^(2)+7x5^(3)+7x5^(4)
Answer:7
+
7
(
5
)
+
7
5
(
2
)
+
7
5
(
3
)
+
7
5
(
4
)
Step-by-step explanation:
Answer: 5473+7x^5
Step-by-step explanation:
Try Photo Math! Gives step by step explanations!
Hope this helps!!
ANSWER NO LINKS!!!! OKAY
Answer:
50
Step-by-step explanation:
180-(65+65)
Answer:
<C = 50
Step-by-step explanation:
<c = x
x + 65 + 65 = 180
x + 130 = 180
x = 50
Sydney is building a doghouse. The house will be 3 and one-half feet tall. How
many inches tall will the house be?
Answer:
42 inches
Step-by-step explanation:
1 FT=12 inches
One half FT=6 inches
12×3=36
36+6=42
Answer:
42 inches
Step-by-step explanation:
The question is basically asking you to convert 3 1/2 ft into inches. Since there are 12 inches in a feet you have to multiply 3 1/2 by 12. It easier to do it when you turn 3 1/2 into a decimal, which would be 3.5. So then, you multiply 3.5 by 12, to get 42 inches.
12 inches = 1 feet
3 1/2 = 3.5
3.5 x 12 = 42
The house will be 42 inches tall.
The table shows the transactions for one week for Tasha and Jamal Who was the greater account balance at the end of the week How Much greater?
______ has the greater balance at the end of the week. This balance is $_______ greater than the other balance
Answer:
Tasha has the greater balance at the end of the week.This balance is $381
The account balance is the remaining amount after the deduction of withdrawals from the deposits.
Tasha has the greater balance at the end of the week. This balance is $1 greater than the other balance.
What is account balance?It is the remaining amount after the deduction of withdrawals from the deposits.
We have,
Tasha:
Initial deposits = $250
Withdrawals = $20
Deposits = $65
Debit card purchases = $46
Balance = $250 - $20 + $65 - $46 = $249
Jamal:
Initial deposits = $200
Withdrawals = $60
Deposits = $135
Debit card purchases = $27
Balance = $200 - $60 + $135 - $27 = $248
We see that Tasha has a greater balance than Jamal and Tasha's balance is greater than Jamal's by $1.
Thus,
Tasha has the greater balance at the end of the week. This balance is $1 greater than the other balance.
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A square dance floor has a perimeter of 120 yards.
What is the length of a diagonal of the dance floor?
O 38.3 yd
O 30 yd
O 60 yd
O 42.4 yd
How did Clay and Webster fight against Jackson’s dislike for the bank?
Answer:
Jackson's opponents planned to use the bank to defeat him in the 1832 presidential campaign. Senators Henry Clay and Daniel Webster were friends of Biddle. ... They thought that if Jackson tried to veto, or reject, the renewal of the charter, he would lose support.
Step-by-step explanation:
Problem 6. Miss Ang buys a dozen of eggs (12 eggs in an egg tray) from HS Farm every day, starting at Day 1. For each egg produced by HS Farm, there is a 0.001 chance that it is spoiled.
(a) Find the probability of that in one week, Miss Ang bought at most (≤) 2 trays of eggs with each having at least one spoiled egg. Write your answer (applying to (b) and (c) as well) up to 3 decimal point.
(b) Let N be the first day (counted from Day 1) that Miss Ang bought a tray of eggs containing at least one spoiled. Find the expected value of N.
(c) Suppose Day 1 is Sunday. Compute the probability that Day N is also Sunday.
a) The probability that in one week, Miss Ang bought at most (≤) 2 trays of eggs with each having at least one spoiled egg=0.016
b) The expected value of N=86.6
c) The probability that Day N is also Sunday=1/7.
Explanation:
a)
For 1 day, 1 tray must contain no spoiled eggs: 0.999^12,
1 tray must have at least 1 spoiled egg: 1 - 0.999^12,
and the probability that Miss Ang has 2 trays, each containing at least 1 spoiled egg in one day:
(1 - 0.999^12) * (1 - (0.999^12 + 11 * 0.001 * 0.999^11)) = 0.00245
For 7 days, the probability that Miss Ang has at most 2 trays, each containing at least 1 spoiled egg:
= 0.00245 * C(7,0) * 1^0 * (1 - 1)^7 + 0.00245 * C(7,1) * 1^1 * (1 - 1)^6 + 0.00245 * C(7,2) * 1^2 * (1 - 1)^5
= 0.01622 ≈ 0.016
b)
Let X be the number of trays that Miss Ang has to buy to get the first tray containing at least 1 spoiled egg. Then X follows a geometric distribution with parameter
p = 1 - 0.999^12 and
E(X) = 1/p = 1/0.011543 ≈ 86.6 (rounded to the nearest 0.1).
c)
Since Miss Ang buys one tray of eggs a day, the probability that Day N is Sunday is 1/7. Therefore, the probability that Day N is Sunday given that it is the first day that Miss Ang bought a tray of eggs containing at least one spoiled is also 1/7.
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a) The probability of that in one week, Miss Ang bought at most (≤) 2 trays of eggs with each having at least one spoiled egg:
P(X ≤ 2) = 0.2966763801
b) The expected value of N = 83.8059327318 days
c) The probability that Day N is also Sunday= 0.1406909760
(a)
For each egg produced by HS Farm, there is a 0.001 chance that it is spoiled. Therefore, the probability that an egg is not spoiled is
1-0.001 = 0.999.
Since Miss Ang buys one dozen eggs every day, the probability that all 12 eggs in a tray are not spoiled is
(0.999)¹² = 0.98806738389.
Therefore, the probability that there is at least one spoiled egg in a tray is
1 - 0.98806738389 = 0.01193261611.
The probability that Miss Ang buys at most 2 trays of eggs with each having at least one spoiled egg in one week (7 days) can be found using the Poisson distribution with a mean of λ = 1.19574793916.
Therefore,
P(X ≤ 2) = 0.2966763801
(b)
Let N be the first day that Miss Ang bought a tray of eggs containing at least one spoiled.
Since Miss Ang buys one tray of eggs every day, the probability that N = n is the probability that the tray she buys on day n has at least one spoiled egg, and all the trays she buys on days 1, 2, ..., n - 1 have no spoiled eggs.
This probability is given by
[tex]P(N = n) = (0.98806738389)ⁿ⁻¹(0.01193261611)[/tex]
The expected value of N can then be found by taking the sum of nP(N = n) over all possible values of n.
This gives
[tex]E(N) = Σn=1∞nP(N = n)[/tex]
[tex]= Σn=1∞(0.98806738389)ⁿ⁻¹(0.01193261611)[/tex]
n= 83.8059327318 days.
(c)
Suppose Day 1 is Sunday. Since Miss Ang buys one tray of eggs every day, Day N is also Sunday if and only if N ≡ 1 (mod 7).
Using the same method as in part (b), we get
[tex]P(N ≡ 1 (mod 7)) = Σk=0∞P(N = 7k + 1)[/tex]
=[tex]Σk=0∞(0.98806738389)ⁿ⁻¹(0.01193261611)[/tex]
= 0.1406909760
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HELP ASAP!!
Rewrite the function by completing the square
f(x) = x^2 - 6x - 60
f(x) = (x+ ___)^2 + ___
Answer:
-3 for the first box and -69 for the second one.
Step-by-step explanation: