I need help finding the values of x and y!!

As n increases, 3^n becomes larger, making the fraction 30/3^n approach zero. Therefore, the sequence {A_n} is convergent, and the limit of convergence is 0. (a) Σ(A_n) is convergent and (b) {A_n} is convergent with the limit of convergence equal to 0.

(a) To determine whether sigma _n = 1^infinity (A_n) is convergent, we need to take the sum of the sequence A_n from n=1 to infinity:
sigma _n = 1^infinity (A_n) = A_1 + A_2 + A_3 + ...
Substituting A_n = 30/3^n, we get:
sigma _n = 1^infinity (A_n) = 30/3^1 + 30/3^2 + 30/3^3 + ...
To simplify this, we can factor out a common factor of 30/3 from each term:
sigma _n = 1^infinity (A_n) = 30/3 * (1/3^0 + 1/3^1 + 1/3^2 + ...)
Now, we recognize that the expression in parentheses is a geometric series with first term a=1 and common ratio r=1/3. The sum of an infinite geometric series with first term a and common ratio r is:
sum = a / (1 - r)
Applying this formula to our series, we get:
sigma _n = 1^infinity (A_n) = 30/3 * (1/ (1 - 1/3)) = 30/2 = 15
Therefore, sigma _n = 1^infinity (A_n) is convergent, with a limit of 15.
(b) To determine whether {An} is convergent, we need to take the limit of the sequence A_n as n approaches infinity:
lim n->infinity (A_n) = lim n->infinity (30/3^n) = 0
Therefore, {An} is convergent, with a limit of 0.
(a) To determine if the series Σ(A_n) from n=1 to infinity is convergent, we can use the ratio test. The ratio test states that if the limit as n approaches infinity of the absolute value of the ratio A_(n+1)/A_n is less than 1, the series converges.
For A_n = 30/3^n, we have:
A_(n+1) = 30/3^(n+1)
Now let's find the limit as n approaches infinity of |A_(n+1)/A_n|:
lim(n→∞) |(30/3^(n+1))/(30/3^n)| = lim(n→∞) |(3^n)/(3^(n+1))| = lim(n→∞) |1/3|
Since the limit is 1/3, which is less than 1, the series Σ(A_n) converges.
(b) To determine if the sequence {A_n} is convergent, we need to find the limit as n approaches infinity:
lim(n→∞) (30/3^n)
As n increases, 3^n becomes larger, making the fraction 30/3^n approach zero. Therefore, the sequence {A_n} is convergent, and the limit of convergence is 0.


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Answer:

1,4

Step-by-step explanation:

The survey is an example of non-probability sampling

A survey is a technique for acquiring data from a sample of people by asking pertinent questions with the goal of comprehending populations as a whole. Everyone involved in the information economy, from corporations to the media to the government and academia, relies on surveys as a vital source of information and insights.

There are four modes of surveys that are commonly used.

The survey is an example of non-probability sampling.

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Answer:

5y=10-2x

y=(10-2x)/5

2x=10-5y

X=(10-5y)/2

Answer: x + 30.25 > 50

Step-by-step explanation: X is the amount need to reach 50 dollars or more.

1 - According to the conjugate zeros theorem if a complex number is the root of a polynomial its conjugate is a root as well.

2 - So the conjugates of i, -7i would be

-i, 7i, so

-i , 7i would ALSO be roots of the polynomial according to the conjugates zeros theorem and those are the two roots we were missing.

The shorter side of the rectangle is approximately 237.25 millimeters, and the diagonal makes angles of approximately 41 degrees and 49 degrees with the longer and shorter sides, respectively.

Let us denote the shorter side of the rectangle as x. We can use the Pythagorean theorem to relate the length of the diagonal to the two sides of the rectangle:

diagonal^2 = longer side^2 + shorter side^2

Substituting in the given values, we get:

450^2 = 393^2 + x^2

Solving for x, we get:

x = √(450^2 - 393^2) ≈ 237.25 mm

To find the angles that the diagonal makes with each side of the rectangle, we can use trigonometry. Let θ be the angle between the diagonal and the longer side, and let φ be the angle between the diagonal and the shorter side. Then we have:

sin(θ) = shorter side / diagonal

sin(φ) = longer side / diagonal

Substituting in the given values and solving for θ and φ, we get:

θ ≈ 41 degrees

φ ≈ 49 degrees

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Answer:

$80

Step-by-step explanation:

Answer:

d= negative 16

Step-by-step explanation:

Answer:

0.1(d-6)=0.15d+2.5-1.5+0.05d

Step-by-step explanation:

Answer: 3.19 feet.

Step-by-step explanation: 319 divided by 100 is 3.19

Answer:

(M/7) - 4

Step-by-step explanation:

Divide M by 7

M/7

subtract 4 from the quotient

(M/7) - 4

The required expression will be M/7 - 4 which represents dividing M by 7, and then subtracting 4 from the quotient.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

To divide M by 7 and then subtract 4 from the quotient, you can follow these steps:

Divide M by 7 to find the quotient. This is written as M/7 = quotient.

Subtract 4 from the quotient. This is written as quotient - 4 = result.

For example, if M = 35, you would do the following:

Divide 35 by 7 to get a quotient of 5. This is written as 35/7 = 5.

Subtract 4 from the quotient of 5 to get a result of 1. This is written as 5 - 4 = 1.

Therefore, if you divide M by 7 and then subtract 4 from the quotient, the result is 1 when M = 35.

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Answer:

$7.08

Step-by-step explanation:

I'm pretty sure it correct but if not sorry

Answer:

12 cans  = $49.56

bc

12 cans x 4.13 = $49.56

Step-by-step explanation:

The congruent angles are:

Congruent angles are angles that have the same degree measurement. In other words, they are equal in size or angle measure. For instance, if one angle measures 45 degrees and another angle also measures 45 degrees, these two angles are congruent.

The symbol for congruence is ≅. So, if angle A is congruent to angle B, it is written as ∠A ≅ ∠B.

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Answer:

Elimination , $1.79

Step-by-step explanation:

You were correct with elimination! Good job , now to find the cost of fries we have to put elimination in practice. Elimination is subtracting one equation from the other to get the equation of one variable.

4x + 5y = 24.11

-4x + 3y = 20.53

        2y = 3.58

     2y/2 = 3.58/2

           y = 1.79

In one sweep, the area covered by the sprinkler is 77.19 sq ft (approx). The area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).

We know that a rotating sprinkler can reach up to 14 feet through a 300-degree angle. Area covered by the sprinkler in one sweep = area of the sector whose radius = 14 feet and angle = 300°Area of sector = (θ / 360) × πr²Where θ = 300°, r = 14 ftArea of sector = (300/360)× π(14)²= 77.19 sq ft (approx) Therefore, the area covered by the sprinkler in one sweep is 77.19 sq ft (approx).

We need to find the total area of the lawn that receives water from this sprinkler. The sprinkler rotates 360 degrees, so it will cover a full circle whose radius is 14 feet. Area of a circle = πr²= π(14)²= 615.752 sq ft (approx) Therefore, the area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).

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Step-by-step explanation:

3*85 <= 83+91+x <= 3*90  

255 <= 174+x <= 270  

81 <= x <= 96

Answer:

81 ≤ x ≤ 96

Step-by-step explanation:

85 ≤ (x + 83 + 91)/3 ≤ 90

85 ≤ (174 + x)/3, (174 + x)/3 ≤ 90

81 ≤ x ≤ 96

Answer:

वि स्कुल माध्यामिक विद्यालय निम्न माध्यामिक विद्यालय व्यवस्थापन समिति सम्पादन र प्रकाशनमा बुटवलबाट निस्कने एक्सरे साप्ताहिकमा एक पटक साप्ताहिकमा छापिएको थियो। प्रकाशित

The slοpe οf the line that gοes thrοugh (-3,-5) and (-3,-6) is undefined.

Slοpe is a measure οf the steepness οr incline οf a line. It represents the rate at which the line is rising οr falling, and is defined as the change in the y-cοοrdinate (vertical change) divided by the change in the x-cοοrdinate (hοrizοntal change) between twο pοints οn the line.

The slope of the line that goes through (-3,-5) and (-3,-6) is:

\($ \rm m = \frac{y_2 - y_1}{x_2 - x_1}\)

y2 - y1 = m(x2 - x1)

-6 - (-5)= m(-3 - (-3))

-6 + 5 = m(-3 + 3)

-1 = m0

m = -1/0

Thus, The slope of the line that goes through (-3,-5) and (-3,-6) is undefined.

This is because the x-coordinates of the two points are the same, which means that the line is vertical and has no defined slope. In other words, the line is parallel to the y-axis and does not have a rate of change with respect to x.

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Answer:

Step-by-step explanation:

Find b first:

Find 1/b:

Accoding to the information, the equation would be: Weight = 48.411 + 70.870 * Fuel Capacity and the predicted weight of a small motorcycle would be 618.66 pounds.

To find the equation for a linear regression model, we need to find the slope and y-intercept of the line that best fits the data. According to the above, we can infer that the equation is:

On the othe hand, to evaluate how well the linear regression equation fits the model, we have to look at how closely the trendline (represented by the equation) matches the pattern of the data points. So, we can see that the trendline appears to capture the overall trend in the data fairly well, with a positive slope that reflects the general pattern of increasing weight with increasing fuel capacity.

To use the linear regression model to predict the weight of a small motorcycle with a fuel capacity of 6 gallons, we can simply plug in the value of 6 for Fuel Capacity in the equation:

According to this prediction, a small motorcycle with a fuel capacity of 6 gallons would have an estimated weight of approximately 498.84 pounds.

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Answer:

There are 25 students in the class.

Step-by-step explanation:

Let the total number of students in the class= x

No. of students who passed the test = 18 = 72% of x = 72x/100

Therefore, 72x/100=18

=72x=18*100=1800

=x=1800/72= 25 students.

Hence, total number of students in the class= 25 students

Answer:

sample answer for edmentum

Step-by-step explanation:

I do khan academy 2 but sorry the answer

The statement that is if two events are complementary, they must also be mutually exclusive events is False.

Because not all mutually exclusive occurrences are necessarily complimentary, whereas all complementary events are mutually exclusive.  

Mutually excusive events are those events that do not occur at the same time.

Complementary events are those two events which are the only possible events.

Since P(A) + P(B) =1, A and B are possible events.Hence A and B are mutually exclusive and complementary events

Therefore the statement is false.

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The computer equipment was acquired at a cost of $73,700 with an estimated residual value of $34,600 and a useful life of 5 years. The depreciable cost of the equipment is $39,100. The straight-line rate is 20%, and therefore, the annual straight-line depreciation for the computer equipment is $7,820.

a. To determine the depreciable cost, we subtract the estimated residual value from the initial cost: $73,700 - $34,600 = $39,100.

b. The straight-line rate is calculated by dividing 100% by the estimated useful life of the equipment. In this case, the straight-line rate is 100% / 5 = 20% per year.

c. The annual straight-line depreciation is found by multiplying the depreciable cost by the straight-line rate. Thus, the annual depreciation is $39,100 * 20% = $7,820 per year.

By following these calculations, we can determine that the depreciable cost of the computer equipment is $39,100, the straight-line rate is 20%, and the annual straight-line depreciation amounts to $7,820.

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The d) mean is the most affected by an extreme high outlier in a data set.

An extreme high outlier in a data set will have a greater impact on the mean, or average, of the data set.

This is because the mean is calculated by adding up all of the values in the data set and dividing by the number of values. If an extreme high outlier is added to the data set, it will significantly increase the sum of the values and, in turn, increase the mean.

The median (option A) is the middle value of the data set and is not as affected by outliers because it only considers the middle values.

The first quartile (option C) and third quartile (option B) are also not as affected by outliers because they only consider the lower 25% and upper 25% of the data set, respectively.

Hence Option D is correct.

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Answer:

                         a

Step-by-step explanation:

Answer:

Implicit costs

Step-by-step explanation:

Accounting profit is known as the profit during accounting.

The formula given by

Hence implicit cost is wrong

Answer:

apples: 2, 4, 6, 8

oranges: 5, 10, 15, 20

Step-by-step explanation:

what it looks like to me is that they are first counting by 2's, then 5's. hope this helps somehow

Step-by-step explanation:

First, you want to find the change in the top collum, and then the bottom collum.

The top collum seems to go up by 2, so it would be 2,4,6,8

The bottom collum seems to go up by 5 so it would be 5,10,15,20

And boom! there's ur answer!

Answer:

The last one

Step-by-step explanation:

\(x^3+1=0\)

Subtract 1 from both sides

\(x^3+1-1=0-1\)

simplify

\(x^3=-1\)

\(\mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}\)

\(x=\sqrt[3]{-1},\:x=\sqrt[3]{-1}\frac{-1+\sqrt{3}i}{2},\:x=\sqrt[3]{-1}\frac{-1-\sqrt{3}i}{2}\)

simplify

\(x=-1,\:x=\frac{1}{2}-i\frac{\sqrt{3}}{2},\:x=\frac{1}{2}+i\frac{\sqrt{3}}{2}\)

(That's basically the last one but in a different way of writing it)

Answer:

The last one

Step-by-step explanation:

Subtract 1 from both sides

simplify

simplify