Find the sum of the convergent series. sigma^infinity _n = 1 8/(9n^2 +3n-2)
______

Answer:

2000

Step-by-step explanation:

440 customers are 22% of total meaning there is 78% left.

440*100=44,000     44,000/22=2,000

The equation of the line passing through the point (7, -8) with a slope of 2/7 is y = (2/7)x - (58/7).

To find the equation of a line, we can use the slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope (m) is given as 2/7, and we have a point (7, -8) on the line.

We can substitute the values of the slope (2/7) and the coordinates of the point (7, -8) into the slope-intercept form equation. Let's start by finding the value of b, the y-intercept:

-8 = (2/7)(7) + b

Simplifying the equation:

-8 = 2 - (14/7) + b

-8 = 2 - 2 + b

-8 = b

Now that we have the y-intercept (b = -8), we can write the equation of the line:

y = (2/7)x - 8

Therefore, the equation of the line passing through the point (7, -8) with a slope of 2/7 is y = (2/7)x - (58/7).

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Answer:

14:8 = 7:4 =28:16

Step-by-step explanation:

equivalent ratio:

14:8 = 7:4 =28:16

Answer: 0.01090566037

Answer: The short answer to this is 0.0109

The third term and fourth term has a sum of 108.

Let's use the formula for the nth term of an exponential sequence:

\(a_n = a_1 * r^{(n-1)}\)

where \(a_1\) is the first term, r is the common ratio, and n is the term number.

We're given that the second term is 9, so we know:

\(a_2 = a_1 * r = 9\)

We're also given that the fourth term is 81, so we know:

\(a_4 = a_1 * r^3 = 81\)

We can use the equation for \(a_2\) to solve for \(a_1\):

\(a_1 * r = 9\\a_1 = 9 / r\)

Substituting this expression for \(a_1\) into the equation for \(a_4\), we get:

\((9 / r) * r^3 = 81\\r^2 = 9\\\)

r = 3 or r = -3

Since we have a common ratio, we can find the third term using either value of r:

\(a_3 = a_2 * r = 9 * 3 = 27\)

Now we can find the sum of the third and fourth terms:

\(a_3 + a_4 = 27 + 81 = 108\)

Therefore, the sum of the third term and fourth term is 108.

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X=4

Please mark brainliest

Answer: s = p - 0.25p; $30

Step-by-step explanation:

      First, we need to know that a percent divided by 100 becomes a decimal.

          25% / 100 = 0.25.

      Next, we will use this equation because it takes 25% off of the original price (p) by subtracting 0.25p from p.

          s = p - 0.25p

      Lastly, we will substitute 40 in for 0 and solve.

          s = ($40) - 0.25($40)

          s = $30

Answer:

the angle is 80° ,, for sure .

Answer:

Angle SRT is equal to 79 degrees

Step-by-step explanation:

The reason this is so is because for every single triangle all the angles must add up to 180 degrees. So take 180 minus angle T, and then minus angle S and you get 79.

Answer:

B

Step-by-step explanation:

just need to keep my streak up

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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The net present value of the machine is rounded to the nearest dollar is $-76,447.56.

Net gift fee is the prevailing fee of after-tax coins flows from an funding much less the quantity invested.

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Answer:

I just graphed it in desmos for you UvU

The second answer is false. The vertex is not (-3, 11). The vertex is (3, 11). I can see that the parabola has a point of (1, 19), and the parabola opens upward, as well as has an axis of symmetry; x = 3.

Hope that helps

Using f -statistic value relationship with population variation , the ratio of population variance lie in interval [0.1008,2.021].

0.1008 <σ₁²/σ₂²< 2.021

So, the correct option is option( d).

A professor wants to compare the variances of scores between two sections of classess.

we have

sample size for first class score (n₁) = 13

sample size for second class score (n₂) = 16

confidence interval is 99%

sample variance of first sample (s₁²) = 203.25

sample variance of second sample (s₂²)= 474.42

Using the relationship

( s₁² /s₂² )/F₁₋ₐ/₂ < σ₁²/σ₂²< ( s₁²/s₂²)/Fₐ/₂

a = 0.005

F at (1- a/2) or F₀.₉₉₅, ₁₃,₁₆= 4.249

F at a/2 or F₀.₀₀₅,₁₃, ₁₆ = 0.2118

plugging all known values in above formula

=> ( 203.25/474.42)/4.249<σ₁²/σ₂²< (203.25/474.42)/0.2118

=> 0.1008 <σ₁²/σ₂²< 2.021

=> σ₁²/σ₂² ∈[0.1008,2.021]

Hence, the ratio of population variance lies between interval [0.1008,2.021].

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Answer:

The place value of 5 in 4.053 is Hundredth

The place value of 5 in the given number 4.053 is, hundredths

In mathematics, we have assigned a name for each digit in a number, which are known as place values. Place values are Ones, Tens, Hundreds, Thousands.

Given number,

⇒  4.053

we can write it as,

⇒   4 ≡ at ones

⇒   0 ≡ at tenths

⇒   5 ≡ at hundredths

⇒   3 ≡ at  thousandths

So, the place value of 5 is hundredths

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The probability that tails appears on the next toss is 0.5

Given,

In the question:

If I toss a fair coin five times and the outcomes are TTTTT,

To find the probability that tails appears on the next toss is.

Now, According to the question:

The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation.

A sequence of five fair coin flips has a sample space that contains all potential outcomes. \(2^3\) {H, T}  is the sample of a fair coin toss. {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH,...…TTTTT} .

The probability of a tails result on the next flip is always equal to 0.5 It makes no difference if previous outcomes were {TTTTT} , {HHHHH}  or {THTHT} In each of these and all other circumstances, the probability of the next being tails is still 0.5

Hence,  the probability that tails appears on the next toss is 0.5

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Answer:

  120 customers per hour

Step-by-step explanation:

You want to know the processing rate in customers per hour if there are an average of 6 customers waiting, and the average service time is 3 minutes.

Little's law relates the average queue depth to the response time and the average throughput:

  mean response time = mean number in system / mean throughput

Solving for the throughput, we find ...

  throughput = (number in the system)/(response time)

  throughput = (6 customers)/(3/60 hours) = 120 customers/hour

The average rate of processing is 120 customers per hour.

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The length of the protein molecule, in meters, is 208 × 10⁻⁹m.

To find the length of the protein molecule:

Diameter of hydrogen atom = 104 × 10⁻¹⁰m

We are given that A protein molecule has an overall length of 2000 times (or 2 cross times 10 cubed times) the diameter of a hydrogen atom.

Therefore, the length of the protein molecule, in meters, is 208 × 10⁻⁹m.

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The correct question is given below:

The diameter of a hydrogen atom is about 1.04 cross times 10 to the power of negative 10 end exponent meters. A protein molecule has an overall length of 2000 times (or 2 cross times 10 cubed times) the diameter of a hydrogen atom. What is the length of the protein molecule, in meters, if it were written in scientific notation?

Answer:

\(\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)

\(sum \: of \: angles\: of \: a \: polygon \: = \\(n - 2) \times 180\degree\)

in the question , we've been given a five sided figure , i.e. , a pentagon.

sum of angles of a pentagon = ( 5 - 2 ) × 180°

\(\implies \: 3 \times 180\degree \\ \implies \: 540\degree\)

thus we can say that ,

angle sum property of pentagon states that the sum of all the angles of a pentagon equals 540°.

therefore ,

Step-by-step explanation:

\(125\degree + 117\degree + (x + 6)\degree + x + (x - 44)\degree = 540\degree \\ \\ 125\degree + 117\degree + x + 6\degree + x + x - 44\degree = 540\degree \\ \\ 204\degree + 3x = 540\degree \\ \\ 3x = 540\degree - 204\degree \\ \\ 3x = 336\degree \\ \\ x = \cancel\frac{336}{3} \\ \\ x = 112\degree\)

hope helpful ~

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To find :-

The value of x in the angles of Pentagon

Given :-

Here we have been provided 5 angles in Pentagon

x°, (x - 44)°, (x + 6)°, 125°, and 117°

Solution :-

We will find the value of x with the angle sum property.

Now, we will find the sum of angles of Pentagon

there is a formula

(n - 2) × 180°

n = no. of sides of above shape

here n = 5

(5 - 2) × 180°

3 × 180° = 540°

Now will add the above given angle in the diagram and put equal to 540°.

x° + (x - 44)° + (x + 6)° + 125° + 117° = 540° (angle sum property)

\(3x + 204{\degree} = 540{\degree} \\ 3x = 540{\degree} -204{\degree} \\ 3x = 336{\degree} \\ x = \frac{336{\degree}}{3} \\ x = 112{\degree}\)

x = 112°

further we will find further 2 angles related to x.

x - 44 = 112 - 44 = 68°

x + 6 = 112 + 6 = 118°

Result :-

The all angles of Pentagon are

125°, 117°, 118°, 112°, and 68°.

The space C1(S1) is a Banach space, which means it is a complete normed vector space, equipped with the norm ||f|| = sup{|f(θ)| + |f'(θ)| : θ ∈ S1}.

The space C1(S1) is the space of continuously differentiable real-valued functions defined on the unit circle S1, which is a subset of the complex plane given by the equation |z| = 1, where z is a complex number.

Specifically, a function f: S1→R belongs to C1(S1) if it has a continuous first derivative f': S1→R that also belongs to C(S1), the space of continuous real-valued functions defined on S1.

Formally, we can define the space C1(S1) as follows:

C1(S1) = {f: S1→R | f is continuously differentiable on S1 and f' belongs to C(S1)}

Here, f' denotes the first derivative of f, which is defined as the limit:

f'(θ) = lim [f (θ + h) - f(θ)]/h

h→0

for all θ in S1

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Answer: QPR must be congruent to SPT

Step-by-step explanation:

Answer:

Step-by-step explanation:

The correct option that describes the set being linearly dependent is option A: f2(x) = c1 f1(x) + c2 f3(x) + c3 f4(x).

If one of the functions in the set can be expressed as a linear combination of the other functions, it implies that the set is linearly dependent. In option A, f2(x) can be written as a linear combination of f1(x), f3(x), and f4(x), indicating that the set is linearly dependent.

Option B does not necessarily imply linear dependence, as it represents a specific linear combination of the functions rather than one function being a linear combination of the others.

Option C refers to the Wronskian, which is a concept used to test linear independence of functions, but its value not being zero does not necessarily imply linear dependence.

Option D, stating that the functions are not multiples of each other, does not provide enough information to determine linear dependence or independence.

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The number of days it would take for a news story to reach 1,500,000 shares include the following: B. 6 days.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x) = a(b)^x\)

Where:

Based on the information provided above, the number of shares this news story can be modeled by the following exponential function;

\(y = 5(7)^x\\\\1500000=5(7)^x\\\\300000=(7)^x\)

By taking the natural log (ln) of both sides of the equation, we have:

Time, x = 6.4 ≈ 6 days.

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a university student is selecting courses for his next semester. he can choose from humanities courses and science courses. the number of ways in which he can  choose courses if or more must be humanities courses can be found using combinations

C(h, r) + C(h, r+1) + C(h, r+2) + ... + C(h, h)

To determine the number of ways a university student can choose courses for the next semester with a requirement of at least "r" humanities courses, we can use combinatorial techniques.

Let's assume there are "n" total courses available, "h" of which are humanities courses, and "s" of which are science courses.

The student needs to select "r" or more humanities courses. We can calculate the number of ways to choose "r" or more humanities courses by summing the combinations for "r" to "h" humanities courses.

The formula to calculate the number of ways to choose "k" items from a set of "n" items is given by the combination formula: C(n, k) = n! / (k! * (n - k)!)

Using this formula, the calculation for the number of ways to choose "r" or more humanities courses can be expressed as:

Number of ways = C(h, r) + C(h, r+1) + C(h, r+2) + ... + C(h, h)

Now, let's substitute the values and calculate the number of ways:

Number of ways = C(h, r) + C(h, r+1) + C(h, r+2) + ... + C(h, h)

In conclusion, the number of ways the university student can choose courses, with a requirement of at least "r" humanities courses, is obtained by summing the combinations for "r" to "h" humanities courses using the combination formula.

the number of ways in which he can  choose courses if or more must be humanities courses can be found using combinations

C(h, r) + C(h, r+1) + C(h, r+2) + ... + C(h, h)

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Answer:

$67,680

Step-by-step explanation:

average is calculated as

average = \(\frac{sum}{count}\)

Denver

\(\frac{sum}{137}\) = 67,013 ( multiply both sides by 137 )

sum = 9,180,781

Anchorage

\(\frac{sum}{25}\) = 71,332 ( multiply both sides by 25 )

sum = 1,783,300

total sum for both = $9,180,781 + $1,783,300 = $10,964,081

then average salary across both companies is

average = \(\frac{10,964,081}{162}\) = $67,680 ( to the nearest dollar )

Thus, the area of the rectangular playground is found as 1500 sq. ft.

A parallelogram with four opposing, parallel, congruent sides is referred to as a rectangle. The rectangle's corners are at a right angle. The fact that a rectangle's sides are not all equal is the only distinction between it and a square.

A two-dimensional shape's area is the interior blank space. The quantity of space that a shape occupies is another way to define area. When calculating a rectangle's area, we multiply the length by the width of a rectangle.

Given that-

P = 2(l + w)

160 = 2 (50 + w)

80 = 50 +w

w = 80 - 50

w = 30 feet

area = length* width

area = 50*30

area = 1500 sq. ft

Thus, the area of the rectangular playground is found as 1500 sq. ft.

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Correct question-

The perimeter of the playground shown is 160 feet. Find the area.

Length is 50 ft.

Answer:

Step-by-step explanation: