Answer: 4096
Step-by-step explanation: 2^3=8, 8^4=4096.
Answer:
4096
Step-by-step explanation:
2 cubed=8
8^4=4096
How do you do this question?
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.
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?
Answer:
6
Step-by-step explanation:
i had this same problem :)
help asap!! answer
solve system equation
1/2m+3/4n=13 5/6m-2/9n=4
Answer:
.
21
Step-by-step explanation:
linear equations to Standard Form y=10x-4
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
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?
Answer:
2,750
Step-by-step explanation:
2x1,125=2,250, 5,000-2,250=2,750
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?
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
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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
Answer:
It is 3
Step-by-step explanation:
Answer:
It is 3
Step-by-step explanation:
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.
Answer:
f h f
Step-by-step explanation:
jikdmj n
5x + 2 = 3x + 4(2x - 1) solve the following equation for x.
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
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.
How can you do a story from this equation:3+(4x12)
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!
gcmf of 25x²y³+55xy³
Answer: the answer is 5xy^3
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?
Answer:
5643
Step-by-step explanation:
you add them together then you divide
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
g Regression is a functional relationship between two or more correlated variables, where one or more variables are used to predict a single variable of interest. Group of answer choices True False
Answer:
True
Step-by-step explanation:
In regression analysis, it tries to infer that there is a supposed relationship between two or more variables.
Now it has a couple of functions such as;
It allows us to directly estimate the parameters in linear functions only, although there are some other ways in which it would allow many non - linear functional forms to get estimated indirectly.
Regression also allows us to test and find out if there is a functional relationship between two or more variables. This is done by testing the hypothesis whether each of the slopes have a value of zero.
Thus, from the definitions given, we can see that regression is a basically a functional relationship between two or more variables, where one or more variables are used to predict a single variable of interest.
Thus, the given statement is true.
13 - (-4) it won’t answer my question
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. ❤️
find the domain of 5x-2
w(−4+z)=mz+17
solve for z
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?
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
Express the percent as a decimal.
154%
Answer:
1.54 as a decimal
154 divided by 100 to get 1.54
Step-by-step explanation:
Your brother won 7 packages of colored candies with 24 pieces each. According to manufacture. For each 1 blue piece produced. The company makes 3 brown. 2 yellow. 2 red. 1 orange and 1 green. How many of each color do you expect to find in your brothers candy?
Answer:
16.8 or 17 blue
50.4 or 50 brown
33.6 or 34 yellow
33.6 or 34 red
16.8 or 17 orange
16.8 or 17 green
Step-by-step explanation:
7 x 24 = 168 candies
blue = b
brown = w
yellow = y
red = r
orange = o
green = g
1b = 3w + 2y + 2r + 1o + 1g
1 +3 + 2 + 2 + 1 + 1 = 10
168/10 = 16.8
1(16.8) +3(16.8) + 2(16.8) + 2(16.8) + 1(16.8) + 1(16.8) =
16.8 blue
50.4 brown
33.6 yellow
33.6 red
16.8 orange
16.8 green
What is this expression equivalent to? Will Give Brainliest! Image is below.
Answer:
the correct answer is 4
An application of the Monte Carlo method to find the area Ac inside a circle uses a random sample of points Ns in a square area As surrounding the circle and counts the number of points that are found inside the circle Nc. Which expression describes the estimate for the area inside the circle
Answer:
As*Nc/Ns
Step-by-step explanation:
The square has Ns discrete points. The points are quite large and are close around each other
As = Area of square
Nc = number of points inside square
Ns = total number of points inside square
Ac = area of circle
Such that
Nc/Ns = Ac/As
We cross multiply
AcNs = NcAs
Dividing through by Ns will give:
Ac = NcAs/Na
Which Is also
= As *Nc/Na
I also added an attachment to help you!
Express the percent as a decimal. { 98% }
Answer:
98.
Step-by-step explanation:
Answer:
0.98 would be the 98% as a decimal
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 )
Answer:
420
140 x 4 = 420
Step-by-step explanation:
Nicole used 3/8 of her ribbon to wrap a present. If she used 6 feet of ribbon for the present, how much ribbon did Nicole have at first?
Answer:
She had 16 feet of ribbon
Step-by-step explanation:
Answer:
16 ft of ribon
Step-by-step explanation:
divide 6 by 3 and get 2. there is 2 ft for every 8th of the ribbon so 2×8=16
hope it helped
honestly what is better being happy or making other people happy?
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:
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.
Answer:
You cant make this..
Step-by-step explanation:
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
Answer:b and e
Step-by-step explanation:I took the test