Answers
Answer:
C, A, D, B
Step-by-step explanation:
(a) We need to compare the sum of this series to 3/4 and 31/36. So we just need to find the sum within 1/36.
1 / (n + 1 + 1)² ≤ 1/36
(n + 2)² ≥ 36
n + 2 ≥ 6
n ≥ 4
So we just need to find the partial sum of the terms from n=0 to n=4.
1 − 1/4 + 1/9 − 1/16 + 1/25 ≈ 0.839
We can use this to approximate the actual sum within 1/64.
(b) 1 − 1/7 + 1/49 − 1/343 + ...
We can rearrange this as the difference between two geometric series:
(1 + 1/49 + 1/2401 + ...) − (1/7 + 1/343 + 1/16807)
∑₀°° (1/49)ⁿ − ∑₀°° 1/7 (1/49)ⁿ
1 / (1 − 1/49) − (1/7) / (1 − 1/49)
(6/7) / (48/49)
7/8
So from smallest to largest, the answer is C, A, D, B.
Related Questions
Alabama has 140 state legislators representing its population of 4 million people. Pennsylvania has 12 million people. How many legislators should it have for representing that is proportional to Alabama?
A) Pennsylvania should have 1,680 legislators
B) Pennsylvania should have 560 legislators
C) Pennsylvania should have 140 legislators
D) Pennsylvania should have 420 legislators
Someone Please Help Me ( It’s Not A )
Answers
Answer:
420
140 x 4 = 420
Step-by-step explanation:
Express the percent as a decimal.
154%
Answers
Answer:
1.54 as a decimal
154 divided by 100 to get 1.54
Step-by-step explanation:
The shapes below are similar. What does x have to be?
Answers
if 8 is divided by 4, you get two since they are the same shape, 14 should be divided by 4 as well which is 3.5
How can you do a story from this equation:3+(4x12)
Answers
Answer:
A car dealership has a special on rentals. They charge a one time fee of $3 and then $4 per day for the rental. If John gets a rental from this dealership, how much will his total be after 12 days?
Step-by-step explanation:
Hope this helps!
13 - (-4) it won’t answer my question
Answers
Hi! I believe your answer is 17 because when two negative signs are next to each other, they make a positive sign, except if the expression has absolute value. Ex: 13- |-4|. So, 13+4=17. I hope this helps you! Good luck and have a great day. ❤️
Terrell sells clay pots. He sells 2 clay pots for $6, 3 clay pots for $9, and 4 clay pots for $12. What is the unit rate of dollars per clay pot?
A
1
B
2
C
3
D
4
Answers
Laura red 312 page book in 13 hours if she read the same number of pages each hour how many pages did she read i
Answers
Answer:
24 pg per hour
Step-by-step explanation:
Divide 312 by 13, and the result will be 24. Hope it helps!
Answer:
24
Step-by-step explanation:
Melanie needs 5,000 chocolates for an event. So far, she has bought 2cases of 1,125 chocolates each. How many more does she need?
Answers
Answer:
2,750
Step-by-step explanation:
2x1,125=2,250, 5,000-2,250=2,750
QUESTION:
An airplane flies with a constant speed of 660 miles per hour. How long will it
take to travel a distance of 2475 miles?
Answers
Answer:
5643
Step-by-step explanation:
you add them together then you divide
find the domain of 5x-2
Answers
Use long division to find the quotient below.
(16x3 + 40x2 + 72) - (2x+6)
A. 8x2 + 3x + 12
O B. 8x2 - 4x + 12
C. 8x2 + 5x + 12
D. 8x2 - 6x + 12
Answers
Answer-
B. 8x2-4x+12
PLSSSSSS 15 POINTS
create a discount booklet using
actual advertisements available right
now. Use newspaper or flyers. Must
have actual ads for the work. You
must show your calculations for each
ad.
Answers
It's supposed to represent half of what the people who answer are getting but in total you ow 15 or 16 so it takes that amount
Answer:
You cant make this..
Step-by-step explanation:
Express the percent as a decimal. { 98% }
Answers
Answer:
98.
Step-by-step explanation:
Answer:
0.98 would be the 98% as a decimal
5
10
Joe borrowed $7,000 from the bank at a rate of 7% simple interest per year. How much interest did he pay
in 3 years?
In 3 years, Joe pays $
in interest.
Answers
Answer:
f h f
Step-by-step explanation:
jikdmj n
7%=7000/100x7=490
$490 per year.
In 3 years: 490x3=1470
Total=$7000+$1470=$8470
I hope this helped!
Wayne created a dried fruit mix to use on his cereal this week. He
used 7 spoonfuls of raisins for every 3 spoonfuls of dried cherries.
If Wayne used 14 spoonfuls of raisins, how many spoonfuls of dried
cherries did he use?
Answers
Answer:
6
Step-by-step explanation:
i had this same problem :)
Simplify the algebraic expression by combining like (or similar) terms.
5x + 5y - 2x + 5y
Answers
Answer:
3x + 10y
Step-by-step explanation:
(5x - 2x) + (5y + 5y)
= 3x + 10y
Answer:
10y + 3x
Step-by-step explanation:
There are two squares.
The larger square has an area of 1,089 square feet and the smaller square has an area of 121 square inches.
What is the scale factor between the two squares?
(A) 3
B
6
12
D 36
Answers
Answer:
It is 3
Step-by-step explanation:
Answer:
It is 3
Step-by-step explanation:
help asap!! answer
Answers
How do you do this question?
Answers
Answers:
[tex]\displaystyle \lim_{n \to \infty} \frac{a_n}{b_n} = 6[/tex]
Based on the limit comparison test, the series is convergent
========================================================
Explanation:
As n gets really large, the terms [tex]3^n[/tex] and [tex]3^n-2[/tex] are effectively the same. Taking the limit to infinity of the ratio leads to 1.
In other words,
[tex]\displaystyle \lim_{n \to \infty} \frac{3^n}{3^n-2} = \lim_{n \to \infty} \frac{3^n}{3^n} = 1[/tex]
That -2 doesn't really play a role when n gets very large.
This result is then multiplied by the 6 in the [tex]a_n[/tex] sequence, getting 6 as the final limit we want.
So,
[tex]L = \displaystyle \lim_{n \to \infty} \left(a_n \div b_n\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6}{3^n-2} \div \frac{1}{3^n}\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6}{3^n-2} \times \frac{3^n}{1}\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6*3^n}{3^n-2}\right)\\\\\\[/tex]
[tex]L = \displaystyle 6*\lim_{n \to \infty} \left(\frac{3^n}{3^n-2}\right)\\\\\\L = \displaystyle 6*\lim_{n \to \infty} \left(\frac{3^n}{3^n}\right)\\\\\\L = \displaystyle 6*\lim_{n \to \infty} (1)\\\\\\L = \displaystyle 6*1\\\\\\L = \displaystyle 6\\\\\\[/tex]
Since the limiting value is positive and not infinity, this means that both series [tex]\sum a_n[/tex] and [tex]\sum b_n[/tex] converge or they both diverge.
----------------------------
If we plug n = 2 into the [tex]b_n[/tex] sequence, we get
[tex]b_n = \frac{1}{3^n}\\\\b_2 = \frac{1}{3^2}\\\\b_2 = \frac{1}{9}[/tex]
The first term is a = 1/9
If we plugged n = 3, we would get [tex]b_3 = \frac{1}{27}[/tex]
This shows that the common ratio is r = 1/3
Because -1 < r < 1 is true, we know that the infinite geometric series converges. Therefore, [tex]\sum b_n[/tex] converges. We don't need to find the converging value.
Going back to the limit comparison test, we stated that both [tex]\sum a_n[/tex] and [tex]\sum b_n[/tex] either diverge together or converge together.
We've shown that the b series converges, so the 'a' series must converge as well.
Samuel needs to mail a package to his friend in New York. He places an address label with length represented by the function L(w) = 3x³ + 2x² - 4x + 5 and width represented by the function w(x) = x + 2. Which of the following statements is true about the area of the label? Select all that apply.
1. A(x) = L(x) + w(x)
2. The resulting polynomial for a(x) will be a 4th degree polynomial
3. L(x)=A(x) divided by w(x)
4. The resulting polynomial for A(x) will have a leading coefficient of 6
5. A(x) = L(x) * w(x)
I know what the answers are its B,C,D but i need work showing how I got to that conclusion
Answers
Answer:b and e
Step-by-step explanation:I took the test
honestly what is better being happy or making other people happy?
Answers
Answer:
being happy j
Step-by-step explanation:
step by step explaination
Answer:
well for me it is both because i am only happy when everyone else around me is also happy
Step-by-step explanation:
5x + 2 = 3x + 4(2x - 1) solve the following equation for x.
Answers
x=1
combine like terms and simplify
Answer:
-2
Step-by-step explanation:
just had to answer it :)
3x+15=24 what is the x equal too
Answers
Answer:
x is equal to -1/3
hope this helps
Answer: I'm pretty sure x = 3
Step-by-step explanation: 3 times 3 = 9. 9 + 15 = 24. And when I solve for x it equals 3.
Please Help Me With This Math ;(
Answers
9: 5.96 dollars per year on the interval (0,9)
10: 6.43 dollars per year on the interval (6,12)
You can afford a $1350 per month mortgage payment. You’ve found a 30 year loan at 7% interest.
A) How big of a loan can you afford?
B) How much total money will you pay the loan company?
C) How much of that money is interest?
Answers
B) 1350 because 45 x 30 = 1350
C) 7% because it’s 7% to begin with
A) The loan amount you can afford is, $177,690.52
B) There will be paid a total of $486,000 to the loan company over the course of 30 years.
C) $308,309.48 of the total money you will pay the loan company is interest.
Given that,
You can afford a $1350 per month mortgage payment.
And, found a 30-year loan at 7% interest.
A) Using the formula for calculating the monthly mortgage payment, we can rearrange it to solve for the loan amount:
Loan Amount = [tex]\frac{Monthly Payment }{(Monthly Payment * (1 + (\frac{1}{1+Monthly Payment )^{Number of payments} } }[/tex]
Plugging in the given values:
Monthly Payment = $1350
Monthly Interest = 7% / 12
= 0.00583
Number of Payments = 30 years × 12 months
= 360
Hence,
Loan Amount = [tex]\frac{1350}{(0.00583 (1 + \frac{1}{1+ 0.00583)^{360} } )}[/tex]
By evaluating this expression,
the loan amount you can afford is,
$177,690.52
B) The total money you will pay the loan company,
Total Money Paid = Monthly Payment × Number of Payments
Total Money Paid = $1350 × 360
= $486,000
Therefore, you will pay a total of $486,000 to the loan company over the course of 30 years.
C) the amount of money which is interest,
Interest Paid = Total Money Paid - Loan Amount
Interest Paid = $486,000 - $177,690.52
= $308,309.48
Hence, $308,309.48 of the total money you will pay the loan company is interest.
To learn more about the Interest visit:
https://brainly.com/question/7639734
#SPJ4
gcmf of 25x²y³+55xy³
Answers
Answer: the answer is 5xy^3
HELP PLEASE WILL MARK BRAINLIEST
Answers
Answer:
15
Step-by-step explanation:
What is this expression equivalent to? Will Give Brainliest! Image is below.
Answers
Answer:
the correct answer is 4
the school library had a used book sale. paperbacks were $2 each and hardcover books were $3 each. there were 54 paperbacks and 163 hardcover books sold.
Please help me, I have no idea how to do this we need to use BEDMAS to solve this. Can anyone help?
Answers
Answer:
Total money made is $597, $489 from hardbacks and $108 from paperbacks.
Step-by-step explanation:
$3 x 163= $489
$2 x 54= $108
total $= 3(163)+2(54)
total $= 489 + 108
total $ = 597
linear equations to Standard Form y=10x-4
Answers
Answer:
The standard form of the linear equation is 10x - y = 4
Step-by-step explanation:
The standard form for linear equations in two variables is
Ax + By = C, where A, B, and C are integers
∵ The linear equation is y = 10x - 4
→ Let us move x from the right side to the left side by subtraction
10x from both sides
∴ y - 10x = 10x - 10x - 4
∴ y - 10x = -4
→ Multiply all terms in the two sides by -1
∴ -y + 10x = 4
→ Start the equation by x
∴ 10x - y = 4
∴ The standard form of the linear equation is 10x - y = 4