Determine whether the geometric series is convergent or divergent. 8 + 7 + 49/8 + 343/64+... convergent divergent

Answer:

\((2 \times {10}^{4} )(5.4 \times{10}^{6} ) \\ = 2 \times 5.4 \times {10}^{(4 + 6)} \\ = \boxed{ 10.8 \times {10}^{10} }\)

9514 1404 393

Answer:

Step-by-step explanation:

These "special" right triangles have side length ratios that it is useful to remember.

45°-45°-90° triangle

Sides have the ratios 1 : 1 : √2. That is, x is √2 times as long as the side length shown as 18.

  x = 18√2

30°-60°-90° triangle

Shortest to longest, sides have the ratios ...

  1 : √3 : 2

That is, y is √3 times the length of the side marked 18, and z is 2 times the length of the side marked 18.

  y = 18√3

  z = 2·18 = 36

Therefore

TheThe positive even numbers less than 10 are 2, 4, 6, and 8, providing multiple solutions to the problem as there are multiple even numbers within the given range.

To find all the positive even numbers less than 10, we consider numbers that are divisible by 2 and greater than zero. Starting from 2, the smallest positive even number, we increment by 2 until we reach a number less than 10.

By following this process, we find the positive even numbers 2, 4, 6, and 8. These numbers satisfy the conditions of being even (divisible by 2) and less than 10. Therefore, the list of positive even numbers less than 10 is 2, 4, 6, and 8. These numbers provide multiple solutions to the problem, as there are multiple positive even numbers within the given range.

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Answer:

\((xy+1)(xy-1)\)

Step-by-step explanation:

x²y²-1

=(xy)²-(1)²

=(xy+1)(xy-1)

Answer:

5

Step-by-step explanation:

Answer:

multiplying by 2.3 is the opposite

The area of the triangle is 31.54 square units

From the question, we have the following parameters that can be used in our computation:

We have the following values

a = 7 units

c = 11 units

B = 55 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 7 * 11 * sin(55 degrees)

Evaluate

Area = 31.54

Hence, the area is 31.54 square units

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Answer:

Hats cost $15, T-Shirts cost $25, Jackets cost $45

If this was helpful please mark brainliest, have a great day!

Answer:

45\

Step-by-step explanation:

it will be 8 units

hope it helps

x+2 x 2x+3

2x+x= 3x

2+3=5

So final answer is 3x+5

Answer:

1,000

Step-by-step explanation:

First, there are 10,000 cents in $100.

So divide 10,000 by 10. (because 1 pencil is 10 cents)

1,000.

I hope this helps!

pls ❤ and mark brainliest pls

The arc length is D) 3.14 meters.

What is arc length?

In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.

It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.

The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.

                                      \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

Here the give circle Radius PR = 3m and θ=60°.

Now using arc length formula then,

=> Arc length \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

=> \(A_L=\frac{60}{360} \times2\times3.14\times3\)

=> \(A_L=\frac{1}{6}\times2\times3.14\times3\)

=> \(A_L\) = 3.14 m.

Hence the arc length is D) 3.14 meters.

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Answer:

The equation would be:

Y=-3/4 + 9

Step-by-step explanation:

Hope it helps.

Answer:

  9.80 m

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between sides of a right triangle and its angles.

__

The geometry of this problem can be modeled by a right triangle, so these relations apply. We are given an angle and adjacent side, and asked for the opposite side, so the relation of interest is ...

  Tan = Opposite/Adjacent

Using the given values, we have ...

  tan(24°) = AC/AB = (tree height)/(distance from tree)

  tan(24°) = AC/(22 m)

Multiplying by 22 m gives ...

  tree height = AC = (22 m)·tan(24°) ≈ 9.79503 m

The height of the tree is about 9.80 meters.

Answer:

d

Step-by-step explanation:

No, the residual plot does not show random scatter around the residual = 0.

No, the residual plot does not show random scatter around the residual = 0.

A residual plot is a type of plot that has residuals on the vertical axis, while the horizontal axis displays the independent variables.

A residual plot shows random scatter around the residual = 0.

Thus, based on the residual plot, the power model will be inappropriate if the residual plot does not show random scatter around the residual = 0.

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Answer:

Here's the exponential equation to model the card's value:

y = 98.70 * 2^x

where x is the number of years after Mr. Olsen purchased the card.

To find the value of the card after 5 years:

x = 5

y = 98.70 * 2^5 = 98.70 * 32 = $3162.40

So, Mr. Olsen can expect the card's value to be $3162.40 5 years after he purchased it.

Step-by-step explanation:

Answer:

Step-by-step explanation:

m

Answer:

The answer's are down below.

Step-by-step explanation:

4 sandwiches and 2 cupcakes are $15.00

5 juices and 4 bagels are $12.50

4 bagels and 5 juices are $11.60

2 bagels and 4 cupcakes are $10.00

a. The medium coffee is the best value for money.

b. The percentage profit is 40%

c The cafe is likely doing this because they know that many people will choose the small coffee because it is the cheapest option.

a) The cost per 100 ml of coffee is:

2.40 / 250 = 0.96p

The cost per 100 ml of coffee for the medium and large sizes is:

2.70 / 330 = 0.82p

3.00 / 500 = 0.60p

Therefore, the medium coffee is the best value for money.

b) The profit on a small coffee is:

2.40 - (0.96 x 250) = 0.96p

The percentage profit is:

(0.96 / 2.40) x 100 = 40%

c) The large coffee is twice the size of the small coffee, but the difference in price is only 60p. This is because the cafe is making a larger profit on the small coffee. The cafe is likely doing this because they know that many people will choose the small coffee because it is the cheapest option.

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Explanation:

Let's find the area of the hexagon. It's composed of two identical (aka congruent) trapezoids.

Each trapezoid has two parallel bases of 4+4 = 8 and 5 units. The height is 3. The area of one trapezoid is

area = height(base1+base2)/2

area = 3*(8+5)/2

area = 19.5

which doubles to 2*19.5 = 39 to represent the area of the entire hexagon

--------------------------------

The volume of any prism is found through this formula

volume = (area of base)*(height of prism)

We just found the area of the base to be 39. The height is unknown, so we'll call it h. The volume is given to be 234.

We end up with this equation

234 = 39h

which solves to h = 6 after dividing both sides by 39. This prism has a height of 6 units.

The height of the prism is 6 units

The hexagonal prism is a prism with hexagonal base.

An isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

Given,

Each hexagon is made from two congruent isosceles trapezoids

Therefore

Area of one isosceles trapezoids = \((a+b).(\frac{h}{2} )\)

where,

a =4+4 = 8 units

b = 5 units

h = 3 units

Area of one isosceles trapezoids =\((8+5)(\frac{3}{2} )\) =19.5 unit square

Area of  the hexagon = Area of two isosceles trapezoids

Area of hexagon = 2× 19.5 = 39 unit square

We know that,

Volume = Base area × Height

Volume = 234 cubic units

234 = 39 × h

h = \(\frac{234}{39}\) = 6 units

Hence, the height of the prism is 6 units

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Answer and Step-by-step explanation:

We see that this is a right angle, which means the entire angle is equal to 90.

We can find what x is by adding this expression and 44 and equaling it to 90.

90 = x + 9 + 44

90 = x + 53

37 = x

The value of x is 37.

I hope this helps!

#teamtrees #PAW (Plant And Water)

Answer:

Step-by-step explanation:

To determine how long it will take for Louise to reach her goal of $30,000, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A is the amount of money Louise will have after "t" years,

P is the initial investment of $20,000,

r is the annual interest rate of 4.28%,

n is the number of times the interest is compounded per year (12 times per year), and

t is the number of years.

We can rearrange this formula to solve for t:

t = (log(A/P)) / (log(1 + r/n))

Plugging in the values:

t = (log(30000/20000)) / (log(1 + (0.0428/12)))

t = 5.97 years

Rounding to the nearest tenth of a year, Louise will need to wait 6.0 years in order to reach her goal of $30,000.

The process capability index for the process is 0.1754.

The first sided specification limit will be:

= (Upper specification limit - mean)/(3 × standard deviation)

= (23.1 - 22.9)/(3 × 0.19)

= 0.2/0.57

= 0.3508

The second sided specification limit will be:

= (22.9 - 22.8)/(3 × 0.19)

= 0.1/0.57

= 0.1754

The process capability index for the process is 0.1754 wine it's the lower value.

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Answer:

7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".

3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".

To solve the equation, we can start by distributing the 3 on the left side:

3(m + 2) = 15

3m + 6 = 15

Then, we can subtract 6 from both sides:

3m + 6 - 6 = 15 - 6

3m = 9

Finally, we can divide both sides by 3:

3m/3 = 9/3

m = 3

Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.

5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".

To simplify the expression, we can use the distributive property to expand the second term:

5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m

Therefore, the simplified expression is m^2 + 3m.

Answer:

√87 and √200

Step-by-step explanation: If a square root is not a perfect square, then it is considered an irrational number. These numbers cannot be written as a fraction because the decimal does not end (non-terminating) and does not repeat a pattern (non-repeating).

Answer:

C. When they're done, José always fills the gas tank.

Hello!

\( \bf 5 \sqrt{37} + \sqrt{98} - 3 \sqrt{147} \)

\( \bf 5 \sqrt{37} + 7 \sqrt{2} - 21 \sqrt{3} \)

I removed the factors from under the radical.

Good luck! :)

Answer:

437.797

Step-by-step explanation:

Answer:

437.797

Step-by-step explanation:

thats the answer