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Answer:
y equals 5x + 20
Related Questions
How do you do this question?
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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.
I only have 30 minutes left
Answers
Answer:
what is the question?
Step-by-step explanation:
U only posted a picture of a half paragraph
I can’t see the whole thing
is this correct or not
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Answer:
yes it is u did a good job
The length of a rectangle is 4 more than the width. The area is 357 square centimeters.
Find the length and width of the rectangle
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Answer:
17*21 = 357
Step-by-step explanation:
Firstly, set up your equation.
x*(x+4)=357
Multiply X by (x+4)
x^2+4x=357
You then subtract 357 from both sides
x^2+4x-357=0
Simplify using the quadratic formula shown, if you need assistance on solving this equation put it into a online calculator, or photomath as it shows the steps taken to solve it.
[tex]\frac{-4+\sqrt{4^2-4\cdot \:1\cdot \left(-357\right)}}{2\cdot \:1}\\[/tex]
3.A normal bus carries x passengers.
A large bus will carry twice as many passengers than the normal bus
A small bus will carry 8 passengers less than the normal bus.
Altogether the buses carry 128 passengers.
(a) Form a simplified equation in terms of x
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Answer: A) 4x -8 = 128
Step-by-step explanation:
We will represent the amount that the normal bus carries by n= x
We will represent the amount that the large bus carries by l = 2x
We will also represent the amount that the small bus carries by s = x-8
Now add them to equal to 128.
x + 2x + x -8 = 128
4x -8 = 128
Mr. Clopu buys an 18-month CD that pays 434% simple interest for $5,000. Find the value of the CD at the end of its term.
Answers
Answer:
FV= $5,325.8
Step-by-step explanation:
Giving the following information:
Mr. Clopu buys an 18-month CD that pays 4.34% simple interest for $5,000.
To calculate the future value, we need to use the following formula:
FV= (P*r*t) + P
P= $5,000
r= 0.0434/12= 0.00362
t= 18
FV= [(5,000*0.00362)*18] + 5,000
FV= $5,325.8
The value of the CD at the end of its term is $39,060
Given:
Time = 18 month
Principal = $5000
Interest rate = 434%
Future value = ?
Future value = Principal × Rate × Time
= 5,000 × 434% × 18
= 5000 × 434/100 × 18
= 5000 × 4.34 × 18
= 39,060
Therefore, the value of the CD at the end of its term is $39,060
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Calculate the vertices
(x+3, y + 1)
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Answer:
A' (4,4), B' (5,7), C' (9,7)
Step-by-step explanation:
I don’t understand what this means
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Answer:
This means that if you have that amount of those and you do whatever the rest of the question is.
Step-by-step explanation:
Answer:
120 different ways
Step-by-step explanation:
So Fundamental Counting Principle helps understand probability. So for this question, they are asking how many different ways there are.
To do that, we have to split into sets.
Set A: 4 Theme Parks
Set B: 6 Passes
Set C: 5 Food Options
Now we have to multiply the sets.
4 x 6 x 5 = 120
Therefore, the answer is 120 different ways.
Shelley and her friend are working together on a group homework assignment. Shelley has
completed 2/12 of the problems and her friend has completed another 9/12 of them.
Together, what fraction of the problems have they completed so far?
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Answer: The answer is 11/12 problems
Step-by-step explanation:
You add 2/12 + 9/12 which gives you a result of 11/12
Which of the following cities does NOT rely on lumber for its economy?
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PLSSSS HELLPPPP MEEEEEEE ASAPPPP I WIILL GIVE BRAINLIEST!!!!!!!!! PLS SHOW WORK STEP BY STEP
Answers
Answer:
y = -3x + 3
Step-by-step explanation:
Slope = -3
y-intercept = 3
Substitute values into slope intercept form :
y=mx + b
Where :
m= Slope
b = y-intercept
[tex]y = - 3x + 3[/tex]
plssssssssssssssssssssssss help for test
Your math class is collecting canned food for a local food drive. The goal is to collect at least 130 cans but no more than 250 cans due to space limitations. There are 24 students in your math class and your teacher has promised to bring in 10 cans. Select which inequalities represent the possible numbers n of cans that each student should bring in.
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the first thing we must do is define variables.
We have then:
n: number of cans that each student must bring.
We know that:
The teacher will bring 5 cans
There are 20 students in the class
At least 105 cans must be brought, but no more than 205 cans
Therefore the inequation of the problem is given by:
105 < 20n + 5 <205
Answer:
the possible numbers n of cans that each student should bring in is: 105 < 20n + 5 < 205
There are 16 boys and 20 girls in a class. What part of the class is boys? What part girls?
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Answer:
girls 4/9 or (Decimal: 0.444444) percent is 44.4%
boys 5/9 or (Decimal: 0.555556) percent is 55.5%
Given a 45-45-90 triangle with the hypotenuse measuring 5√7 feet. Which is the exact measure of each leg?
Answers
Which number line shows 1/3 and its opposite
Answers
Classify the following triangle. Check all that apply.
A. Right
B. Isosceles
C. Obtuse
D. Acute
E. Equilateral
F. Scalene
Answers
Answer:
is there a chart to this question?
because I can't tell the answer just by looking at it
Step-by-step explanation:
it's a b c d and f are all the correct answers
The grandpapa car traffic function is shown check although following statements are true of the function
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Determine wheather the given lines are parallel or not. Write the reasons .
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Answer:
yes it is parallel because the alternate interior angles are equal
Solve the literal equation xy - 4xz = 5 for x.
X=
Answers
Answer:
x = 5/(-4 z + y)
Step-by-step explanation:
Solve for x:
x y - 4 x z = 5
Hint: | Write the linear polynomial on the left-hand side in standard form.
Collect in terms of x:
x (-4 z + y) = 5
Hint: | Solve for x.
Divide both sides by -4 z + y:
Answer: x = 5/(-4 z + y)
A taxi cab in Myrtle Beach charges $2 per mile and $1 for every person. If a taxi cab ride for two people costs $12 how far will the cab travel?
Answers
Answer:
5 miles
Subtract the 1 dollar for each person from 12. You get ten, and divide ten by two, which is 5
2 points 5. What property is used to get from Step 1 to Step 2? * Step 1 : 28x + 10 = 66 Step 2: 28x = 56
Answers
Answer: subtraction property of equality
Step-by-step explanation:
Deandre pays $15.20 for a pack of 8 towels.
Find the unit price in dollars per towel.
If necessary, round your answer to the nearest cent.
Please help
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Answer: Each towel costs $1.90
Step-by-step explanation:
$15.20 divided by 8 = $1.90
Which of the following statements describes the value of the expression 35 – 2x, when x = 6?
Answers
Answer:
35-2(6)
= 23
Prime number
Step-by-step explanation:
Answer:
23 . It is a prime number.
Step-by-step explanation:
[tex]35 - 2x \\ x = 6 \\ \\ 35 - 2(6) \\ = 35 - 12 \\ [/tex]
Simplify
[tex]23[/tex]
if you can help i’d appreciate it
Answers
Answer:
B- 44
Step-by-step explanation:
87.5 divided by 2 is 43.75. Since it's a square wall, the length and height are both the same, and since length times height is area, if you divide the area by two, you can get a length of one of the sides. Out of all the answers, 44 is the closest to 43.75.
hope this helped! -brooke :))
Ethan bought 4 packages of pencils. After he gave 8 pencils to his friends, he had 40 pencils
left over. How many pencils were in each package? Use the drop-down menus to solve the
problem arithmetically and algebraically.
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He had 40 pencils left after he gave away 8, so originally he had 40 + 8 pencils, which is 48.
Now, he bought 4 packages, which had a total of 48 pencils, so divide 48 by 4, which is 12. He had 12 pencils in each package.
To determine the solution arithmetically, first add 8 to 40, then divide 48 by 4.
To determine the solution algebraically, set up and solve the equation 40 = 4x - 8.
Each package contained 12 pencils.
Hope this helps
Find the distance between each pair of points in the coordinate plane.
(3,-2) and (2,-1)
Answers
Answer:
1.41
Step-by-step explanation:
Explain the phrase conservation of energy and provide an example.
Answers
Answer:
Conservation of energy, principle of physics according to which the energy of interacting bodies or particles in a closed system remains constant. ... For example, when a pendulum swings upward, kinetic energy is converted to potential energy.
Step-by-step explanation:
Jared bought a cell phone for $42, Juanita spent 1 1/2 times as much how much did she spend
Answers
answer:
Juanita spent 1 1/2 times as much as Jared, how much did she spend?
$63
explanation:
one and a half of 42 is: 63
so,
the answer is Juanita spent $63!
Juanita paid $63 for the phone, which is equal to 3/2 of what Jared paid while buying the phone.
What is the definition of a mixed fraction?A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.How are mixed fractions written?Follow these procedures to convert an incorrect fraction to a mixed number:
Subtract the denominator from the numerator. The quotient's whole number component should be written down. Write the leftover amount on top of the original denominator.Given: Jared spent $42 on a cell phone.
We need to determine 1 and 1/2 which is 3/2 of total amount spent by Juanita.
So,
42(3/2) = $63
Therefore, Juanita spent $63 which is 3/2 amount spent by Jared in buying the cell phone.
Learn more about mixed fraction here:
https://brainly.com/question/414559
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15 men can dig a ditch in 10 days, how many day
Will 10men take working at the same rate
Answers
Answer:
If 10 men dig a ditch in 12 days .
Total man-days required to dig the ditch
= 10 men × 12 days
= 120 man-days
how long would 15 men take to dig it?
No of days required to finish the job by 15 men
= 120 men-days / 15 men
= 8 days
Answer: 8 days will be required to finish the job by 15 men
Step-by-step explanation:
Hope this helps u
Crown me as brainliest:)
How many solutions does this equation have
2x + 1 = 2x – 1