solve the following equation for a: -g + 3/4a = y

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.

Answer:

1

Step-by-step explanation:

You could have just used a calculator tard lol

Answer:

1

Step-by-step explanation:

-7 +8=1 cause you have 1 positive left over

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.

The relationship between strategy and written method in mathematics is that;

Strategies can be changed or modified whereas written methods cannot be changed or modified because they have standards upon which such methods are based.

A student wants to perform addition of 19 and 46.

He could add the number straight away by doing 19 + 46 = 65or he can

take away 1 from 46 to become 45 and add that 1 to 19 to become 20 and

then sum 45 and 20 together as 20 + 45 = 65.

So we can see that the two strategies used to add 19 and 46 gave the same result.

For example, we want to use partial products to multiply 13 x 52.

The solution would become (10 × 50) + (10 × 2) + (3 × 50) + (3 × 2) = 676.

In this method, there cannot be another way used as the standard for using partial products is written and fixed.

Read more at; https://brainly.com/question/18884089

Answer:

D x = 1

Step-by-step explanation:

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

Answer:

4a - 22x

Step-by-step explanation:

-13x +14a - 12x + 7x - 4x = 4a - 22x

hope this helps :)

Answer:

y equals 5x + 20

Answer:

The answer is B, I know this because I just took a test with this question lol

If 12 correct answers constitute a passing grade on a 20-item true-false exam, the probability that someone will pass is 1/2 if they are guessing.

Therefore,

Let X denote the number of correctly answered questions out of a total of 20.

Bernoulli trails are formed by repeated coin tosses. Because the "head" on a coin represents the correct answer and the "tail" represents the incorrect answer, the questions that are correctly answered are Bernoulli trials.

[tex]$&\therefore \mathrm{p}=\frac{1}{2} \\[/tex]

[tex]&\therefore \mathrm{q}=1-\mathrm{p}=1-\frac{1}{2}=\frac{1}{2}[/tex]

X follows a binomial distribution with n = 20 and p = 1/2

[tex]&\therefore P(X=x)={ }^n C_x q^{n-x} p^x \\[/tex]

[tex]&={ }^{20} C_x\left(\frac{1}{2}\right)^{20-x} \cdot\left(\frac{1}{2}\right)^x \\[/tex]

[tex]&={ }^{20} C_x\left(\frac{1}{2}\right)^{20}[/tex]

P ( at least 12 questions answered correctly )= P (X ≥ 12)

[tex]&=\mathrm{P}(\mathrm{X}=12)+\mathrm{P}[/tex][tex](\mathrm{X}=13)+\ldots+\mathrm{P}(\mathrm{X}=20) \\[/tex]

[tex]&={ }^{20} \mathrm{C}_{12}\left(\frac{1}{2}\right)^{20}+{ }^{20}[/tex][tex]\mathrm{C}_{13}\left(\frac{1}{2}\right)^{20}+\ldots+{ }^{20}[/tex][tex]\mathrm{C}_{20}\left(\frac{1}{2}\right)^{20} \\[/tex]

[tex]&=\left(\frac{1}{2}\right)^{20} \cdot\left[{ }^{20} \mathrm{C}_{12}+{ }^{20} \mathrm{C}_{13}+\ldots+{ }^{20} \mathrm{C}_{20}\right][/tex]

Hence, If 12 correct answers constitute a passing grade on a 20-item true-false exam, the probability that someone will pass is 1/2 if they are guessing.

The complete question is:

In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers 'true', if it falls tails, he answers 'false'. Find the probability that he answers at least 12 questions correctly.

To learn more about probability, refer to:

https://brainly.com/question/24756209

#SPJ2

Answer:

4 chocolates

Step-by-step explanation:

n-c

brother-5n

5n-n=4

=4

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

Answer:1.7 x 10 ^ -5

Step-by-step explanation:

Answer:1.7 x 10-5

hope this helps

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)

Answer:

3         8

18       48

22.5   60

27       72

Step-by-step explanation:

3:8 ratio

18/3=6

8*6=48

Answer:

48

60

72

Step-by-step explanation:

1. Find the number of times x or the first column numbers are multiplied to get y or the second column numbers.

2. Equation: 3*?=8, ? = 8/3

3. Multiply all of the other numbers by 8/3 to get the answers.

4. 3*8/3=8, 18*8/3=48, 22.5*8/3=60, 27*8/3=72.

Answers: 48, 60, 72

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]

Answer: Each towel costs $1.90

Step-by-step explanation:

$15.20 divided by 8 = $1.90

Answer:

A' (4,4), B' (5,7), C' (9,7)

Step-by-step explanation:

9514 1404 393

Answer:

  If x-y is a natural number, then x and y are natural numbers.

Step-by-step explanation:

The converse of ...

  If P, then Q.

is ...

  If Q, then P.

__

Here, we have ...

  P = "x and y are natural numbers"

  Q = "x-y is a natural number"

So, the converse is ...

  If x-y is a natural number, then x and y are natural numbers.

_____

In this case, the converse is false.

Answer:

C.

Step-by-step explanation:

f(3) is referring to 3 on the left side and it is beside 1 which is on the left so it's 1.

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  

Answer:

the correct answer is: C. The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.

Step-by-step explanation:

A straight line passing through the points (1, 2), (3, 4), (5, 6) and (7, 8) does not pass through the origin, as shown on the graph below.

Therefore, the line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.

Answer:

The line that passes through the given coordinates represents a proportional relationship because the line passes through the origin--the correct answer is B.

Step-by-step explanation:

You first graph the coordinates shown, then you repeat the same pattern until the answer is revealed which is shown in the column above. Also, a reminder to all a proportional line is a line that goes through the origin ((0,0)).

Answer:

I don’t think the question makes sense

Answer: If 2 log x + 3 log y = 0, find y in terms of x.

sorry for my messy handwriting!!!

Step-by-step explanation:

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]

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

Answer:

23

Step-by-step explanation:

Answer:

the answer is 2,3,and 5

Step-by-step explanation:

Answer:

2, 3, and 5

Step-by-step explanation:

Answer:

yes it is u did a good job