The prove of converges is shown below.
And, The limit of the sequence is,
L = 1/2 (1-√{5}-a)
Now, First, we notice that all the terms of the sequence are non-negative, since we are subtracting the square root of a non-negative number from 1.
Therefore, we can use the Monotone Convergence Theorem to show that the sequence converges if it is bounded.
To this end, we observe that for 0<a<1, we have 0 < a₀ = a < 1, and so ,
0<1-√{1-a}<1.
This implies that 0<a₁<1.
Similarly, we can show that 0<a₂<1, and so on.
In general, we have 0<a{n+1}<1 if 0<a(n)<1.
Therefore, the sequence is bounded above by 1 and bounded below by 0.
Next, we prove that the sequence is decreasing. We have:
a_{n+1} = 1 - √{1-a(n)} < 1 - √{1-0} = 0
where we used the fact that an is non-negative.
Therefore, a{n+1} < a(n) for all n, which means that the sequence is decreasing.
Since the sequence is decreasing and bounded below by 0, it must converge.
Let L be its limit. Then, we have:
L = 1 - √{1-L}.
Solving for L, we get ;
L = 1/2 (1-√{5}-a), where we used the quadratic formula.
Since 0<a<1, we have -√{5}+1}/{2} < L < 1.
Therefore, the limit of the sequence is,
L = 1/2 (1-√{5}-a)
Read more about Limit in Calculus
brainly.com/question/23935467
#SPJ4
what is 0.571 as a fraction
ANSWER ASAP PLEASE! (PICTURE INCLUDED)
Answer:
12
Step-by-step explanation:
please help
30 points
The baker can decorate 1.4 or 1 1/3 of cupcakes in a minute.Step-by-step explanation: 42 cupcakes in 30 minutes so if you divide 42 cupcakes in 30 groups you get 1 in each group and 12 left so if make 30 in 3 it makes 4 in each group but it is 30 so you make the four in to a 0.4 or 1/3 which is 1.4.You can also multiply if you make 1.4 into 14 x 3 = 42 same as 1.4 x 30 = 42 so the answer is 1.4.
-2(0)+2y=6
please help now I need to get this done please thank you
Answer:
y=3
Step-by-step explanation:
Multiply -2 by 0 to get 0. Now to get y alone, divide 6 by 2 to get the answer y=3.
Brenton is a phone sales specialist who makes $33,000 per year plus an $8 fee for each sale he makes. If Brenton makes 15 sales per week, what are his annual earnings?
Answer:
Brenton's annual earnings are $39,240.
b) A prize is divided between three people
X, Y and Z. If the ratio of X's share to Y's
share is 3:1 and Y's share to Z's share
is 2:5, calculate the ratio of X's share
to Z's share.
Answer:
X : Z = 6 : 5
Step-by-step explanation:
X : Y = 3 : 1
Double both sides
X : Y = 6 : 2
Y : Z= 2 : 5
Combined
X : Y : Z = 6 : 2 : 5
Therefor
X : Z = 6 : 5
Miranda is conducting a poll to determine how many students would attend a students-only school dance if one was held. Which sample is most likely to yield a representative sample for the poll? twenty names from each grade pulled blindly from a container filled with the names of the entire student body written on slips of paper every tenth person walking down Main Street in town at different times of the day all of the students who write into the school newspaper every student from all of Miranda’s classes
The sample that is most likely to yield a representative sample for the poll is "twenty names from each grade pulled blindly from a container filled with the names of the entire student body written on slips of paper."
A representative sample is one that accurately reflects the characteristics of the population from which it is drawn. In this case, Miranda wants to determine how many students would attend a students-only school dance. To achieve this, she needs a sample that represents the entire student body.
The option of selecting twenty names from each grade ensures that the sample includes students from all grades, which is important to capture the diversity of the student body.
By pulling the names blindly from a container filled with the names of the entire student body, the selection process is unbiased and random, minimizing any potential biases that could arise from alternative methods.
The other options have certain limitations that may result in a non-representative sample. For example, selecting every tenth person walking down Main Street may introduce a bias towards students who live or frequent that particular area.
Students who write into the school newspaper may have different interests or characteristics compared to the general student body, leading to a biased sample. Similarly, selecting all the students from Miranda's classes would not represent the entire student body, as it would only include students from those specific classes.
For more such question on sample visit:
https://brainly.com/question/24466382
#SPJ8
What is the probability that you will randomly land on a BLUE section?
Write your answer in a simplified fraction, using a "/" to separate the numerator and denominator.
Answer:
2/8. or simplified= 1/4
Step-by-step explanation:
This equation has one solution. 5(x – 1) 3x = 7(x 1) what is the solution?
Answer:
send the complete question . there are some missing signs .
PLEASE HELP!!! It’s due soon!!!
Answer:
you have to add all the cups she needs and then times that by 3.
Step-by-step explanation:
so, 3 + 1 + 2 = 6
times that by 3 and thats how many batches she can make.
Answer:
Do the same thing but 2 more times.
Step-by-step explanation:
9 yellow, 3 red, 6 ivory
The shop sold a Home Entertainment system to Leslie for $46 480. The shop made a profit of 12%
on the price it paid for the system.
Calculate how much the shop paid for the system.
Answer:
41 500
Step-by-step explanation:
100+12=112
112/100 * x = 46480
41500
convert into foot?
809meter,7cm
Answer: 2,654.429659
Is this the answer you were looking for? Comment below if it was helpful!
Answer:
2654.4291 foot, but rounded off is 2654 foot
Step-by-step explanation:
(x + 3)(x^2 - 5x + 7)
write in standard form once you find answer.
Five pounds is equal to 2.268 kilograms. How many kilograms is 2 pounds?
0.4536
O 0.9072
0 1.8144
4.536
Given:
5 pounds = 2.268 kilograms
To find:
The number of kilograms in 2 pounds.
Solution:
We have,
5 pounds = 2.268 kilograms
Divide both sides by 5.
1 pounds = \(\dfrac{2.268}{5}\) kilograms
1 pounds = 0.4536 kilograms
Multiply both sides by 2.
2 pounds = 2×0.4536 kilograms
2 pounds = 0.9072 kilograms
Therefore, the correct option is B.
Answer: b
Step-by-step explanation:
Where did Hip-Hop get its start?
A. Sunderland
B. New York
C. Atlanta
D. Hendersonville
Answer:
New York
Step-by-step explanation:
we define a uniform random variable between 5 and 15. what is the value of the probability density function (pdf) at 0?
The value of the probability density function (pdf) at 0 for a uniform random variable between 5 and 15 is 0, because the pdf for a uniform distribution is constant between its minimum and maximum values, and is 0 elsewhere.
To explain further, a uniform distribution is a continuous probability distribution where every value within a certain range has an equal chance of being selected. In this case, the range is between 5 and 15. The pdf for a uniform distribution is constant within the range of the distribution and is 0 outside of it.
Since 0 is not within the range of the uniform distribution, the pdf at 0 is 0. This means that the probability of selecting a value of 0 from this uniform distribution is 0. The area under the pdf curve between 5 and 15 is equal to 1, which means that the probability of selecting a value within this range is 1.
For more questions like Probability visit the link below:
https://brainly.com/question/30831431
#SPJ11
Write each polynomial in standard form. Then classify it by degree and by number of terms. 7x³ - 10x³ + x³.
Step-by-step explanation:
now,you can solve this question.
The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the maximum error in the calculated surface area. (Round your answer to the nearest integer.) cm2 What is the relative error
The maximum error in the calculated surface area is 24.19cm² and the relative error is 0.0132.
Given that the circumference of a sphere is 76cm and error is 0.5cm.
The formula of the surface area of a sphere is A=4πr².
Differentiate both sides with respect to r and get
dA÷dr=2×4πr
dA÷dr=8πr
dA=8πr×dr
The circumference of a sphere is C=2πr.
From above the find the value of r is
r=C÷(2π)
By using the error in circumference relation to error in radius by:
Differentiate both sides with respect to r as
dr÷dr=dC÷(2πdr)
1=dC÷(2πdr)
dr=dC÷(2π)
The maximum error in surface area is simplified as:
Substitute the value of dr in dA as
dA=8πr×(dC÷(2π))
Cancel π from both numerator and denominator and simplify it
dA=4rdC
Substitute the value of r=C÷(2π) in above and get
dA=4dC×(C÷2π)
dA=(2CdC)÷π
Here, C=76cm and dC=0.5cm.
Substitute this in above as
dA=(2×76×0.5)÷π
dA=76÷π
dA=24.19cm².
Find relative error as the relative error is between the value of the Area and the maximum error, therefore:
\(\begin{aligned}\frac{dA}{A}&=\frac{8\pi rdr}{4\pi r^2}\\ \frac{dA}{A}&=\frac{2dr}{r}\end\)
As above its found that r=C÷(2π) and r=dC÷(2π).
Substitute this in the above
\(\begin{aligned}\frac{dA}{A}&=\frac{\frac{2dC}{2\pi}}{\frac{C}{2\pi}}\\ &=\frac{2dC}{C}\\ &=\frac{2\times 0.5}{76}\\ &=0.0132\end\)
Hence, the maximum error in the calculated surface area with the circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm is 24.19cm² and the relative error is 0.0132.
Learn about relative error from here brainly.com/question/13106593
#SPJ4
I'd this solved correctly? and if not can u tell me the error and the answer?
You have a mistake in the first step, you should distribute the 2 first, or divide by two, and after that you can follow the procedure as you were doing. Do you understand it?
\(\begin{gathered} 48+w=80-3w \\ w+3w=80-48 \\ 4w=32 \\ w=\frac{32}{4}=8 \end{gathered}\)w=8 is the answer
I can't asnwer more than one question per session, please begin a new session
Have a great day, please begin a ne
if you select a dvd at random, then select another at random (while keeping the first in your hand), what is the probability that both will be harry potter films?
The probability of selecting two Harry Potter DVDs at random, one after the other, is 1/110.
The probability of selecting a Harry Potter DVD at random is dependent on the total number of DVDs and the number of Harry Potter DVDs in the collection. Let's assume there are a total of 100 DVDs and 10 of them are Harry Potter films.
When selecting the first DVD, the probability of picking a Harry Potter film is 10/100 = 1/10.
After selecting the first DVD, there are 99 DVDs left, with 9 Harry Potter films remaining.
When selecting the second DVD, the probability of picking another Harry Potter film, while keeping the first one in hand, is 9/99 = 1/11.
To find the probability of both DVDs being Harry Potter films, we multiply the probabilities: (1/10) * (1/11) = 1/110.
Therefore, the probability that both DVDs will be Harry Potter films is 1/110.
In conclusion, the probability of selecting two Harry Potter DVDs at random, one after the other, is 1/110.
To know more about probability visit:
brainly.com/question/31828911
#SPJ11
Suppose you have a bag of jelly beans: 7 yellow, 3 green, 6 red, 4 purple. All of the
jelly beans are mixed together and all of the jelly beans are the same size. What is
the probability you select a red jelly bean?
1
3/20
O
7/20
4/20
Step-by-step explanation:
There are 20 total jelly jeans.
6 are red.
So 6/20 = 3/10.
I don't see this in your answer list but it's correct!
The population of a city has increased by 28 since it was last measured. if the current population is 80000, what was the previous population?
According to the given statement The preceding population was = 62,500.
In mathematics, what is a percentage?A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is a one-hundred part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.
What is the significance of the term "percentage"?Percent originated from the Latin adverbial phrase per centum, which means "by the hundred." The Latin phrase made its way into English in the 16th century. Later, it was abbreviated to % with a period. The period was eventually eliminated, and the two components amalgamated to form the contemporary one-word form %.
According to the given data:The current population of a city = 80000
A city's population has grown by 28% since the last census.
measured.
We have to calculate the previous population before increasing 28%.
Let the previous population be p
p +(28% × p) = 80000
p + 0.28p = 80000
1.28p = 80000
p = 80000/1.28
p = 62,500
The preceding population was = 62,500.
To know more about Percent visit:
https://brainly.com/question/2884297
#SPJ4
what is the absolute vale of |35|
Answer:
Absolute value of any number is positive. so the absolute value of (-35) is 35.
Step-by-step explanation:
See your levels
➡) Multiply. Write your answer as a fraction or as a whole or mixed number.
X 10 =
E
Submit
Company | Blog | Help center | User guides | Tell us what you think | Testimonials | Contact us | Te
The answer to the expression as a whole or mixed number would be 7 / 8.
How to multiply the fraction ?When given a problem to solve such as 2 ¹ / ₃ x 2 ¹ / ₂ x 1 / 4, the first thing to do is to convert the mixed fractions to improper fractions.
2 ¹ / ₃ converted is :
= ( ( 2 x 3 ) + 1 ) / 3
= ( 6 + 1 ) / 3
= 7 / 3
2 ¹ / ₂ converted :
= ( ( 2 x 1 ) + 1 ) / 2
= ( 2 + 1 ) / 2
= 3 / 2
The answer to the expression is:
= 7 / 3 x 3 / 2 x 1 / 4
= 21 / 24
= ( 21 / 3 ) / ( 24 / 3 )
= 7 / 8
Find out more on fractions at https://brainly.com/question/78672
#SPJ1
The full question is:
Multiply. Write your answer as a fraction or as a whole or mixed number.
2 ¹ / ₃ x 2 ¹ / ₂ x 1 / 4 =
A t-shirt decreased in price by
1
4
. After the reduction it was priced at £15. What was the original price of the t-shirt?ILL MARK YOU BRAIEST IF U GIVE ME THE RIGHT ANWSER PLZ I BEGG✌✌✌
Answer:
£20
Step-by-step explanation:
1-1/4=3/4
3/4=15
1
15*1/3/4=
15*4/3=20
A trough in the form of an open rectangular box is 8m long 3m wide and 2. 4m high. It initially contain water of volume 37m cube. Find the depth of water in the trough after 20m cube of water is added to it
To find the depth of water in the trough after adding 20m³ of water, we need to calculate the change in volume and then determine how it affects the water level.
The initial volume of water in the trough is 37m³, and the dimensions of the trough are given as 8m (length), 3m (width), and 2.4m (height).
The volume of a rectangular box is calculated by multiplying its length, width, and height. Therefore, the initial volume of the trough can be represented as:
Volume_initial = length × width × height
Volume_initial = 8m × 3m × 2.4m
Volume_initial = 57.6m³
After adding 20m³ of water, the new volume of water in the trough will be:
Volume_final = Volume_initial + 20m³
Volume_final = 57.6m³ + 20m³
Volume_final = 77.6m³
Now, to find the depth of water in the trough, we need to calculate the new height. Since the length and width of the trough remain the same, we can rearrange the volume formula to solve for the height:
Volume = length × width × height
height = Volume / (length × width)
height = 77.6m³ / (8m × 3m)
height ≈ 3.23m
Therefore, the depth of water in the trough after adding 20m³ of water is approximately 3.23 meters.
Learn more about volume here
https://brainly.com/question/463363
#SPJ11
Assuming that on average there are 100 lightning flashes per second worldwide, calculate the number of lightning flashes per month worldwide. Assume a 30 day month. The number is Group of answer choices a. 269,000,000 flashes per month b. 2.59 x 108 flashes per month c. 25,920,000 flashes per month d. 3.1536 x 109 flashes per month
The number of lightning flashes per month worldwide is 25920000.
A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figures.
Given that,
Average of lightning flashes per second worldwide = 100
Number of days in a month = 30
Total number of seconds in a day = 86400
Total number of lightning flashes in a day = 100* 86400 = 8640000
Therefore, the total number of lightning flashes in a month = 8640000*30 = 25920000
Hence, the number of lightning flashes per month worldwide is 25920000.
To know more about the number system visit: brainly.com/question/17429689
#SPJ4
The number of lightning flashes per month worldwide is 2,59,20,000.
The solution is as follows:-
Average of lightning flashes per second worldwide = 100
Number of days in a month = 30
Total number of seconds in a day = 86400
Total number of lightning flashes in a day = 100* 86400 = 8640000
Therefore, the total number of lightning flashes in a month = 8640000*30 = 25920000
Hence, the number of lightning flashes per month worldwide is 2,59,20,000.
Number system
A number system is a system representing numbers. It is also called the system of numeration and it defines a set of values to represent a quantity. These numbers are used as digits and the most common ones are 0 and 1, that are used to represent binary numbers.
Learn more about number here :-
https://brainly.com/question/17429689
#SPJ4
PLEASE I NEED HELP AND HURRY!
Answer:
95 degrees
Step-by-step explanation:
A and C are acute angles and D is too much
can some on help me of i die
Answer:
Step-by-step explanation:
17 x 100 = 1,700
17 x 10 x 10 = 1,700
(1 ten 7 ones) x 100 = 1,700
All of them go into the thousands column.
Answer: die.
Step-by-step explanation:
Compare using <, >, or =.
23 × 103 ___ 250 × 102
1. =
2. <
3. >
Answer:
b. <
Step-by-step explanation:
2,369 is less than 25,500
23x103=2369
250x102=25500
Answer:
The answer is 3 . Hope you like answer.