Write the equation of a line with slope of 5/6 , and x-intercept of −8 in point-slope form.

D. Poisson distribution most frequently describes the arrival rate in queuing​ theory.

The study of how people, things, or information move in a line is known as queuing theory. It is possible to develop services and systems that are more effective and economical by researching congestion and its causes.

Waiting lines in healthcare settings may be analysed using the queueing theory. Queuing analysis can be utilised for short-term solutions or for facility and resource planning because the majority of healthcare systems have extra capacity to tolerate random changes.

Because it offers the tools for queue optimization and helps to define queue characteristics like the average wait time, queueing theory is crucial. Queuing theory provides guidance for the design of successful and affordable workflow systems from a commercial perspective.

Correct option: D

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Answer:

yes

Step-by-step explanation:

Since there is one value of y for every value of x, this relation is a function.

The relation is a function.

The first four terms of the sequence are:

a1 = 2

a2 = 2 - 3 = -1

a3 = -1 - 3 = -4

a4 = -4 - 3 = -7

The sequence defined by the rule an = 2, if n = 1; an-1-3, if n > 1, starts with the first term being 2. For all subsequent terms, the value of the previous term is subtracted by 3. Therefore, the second term of the sequence is -1 (2-3), the third term is -4 (-1-3) and fourth term is -7 (-4-3). This pattern of subtracting 3 from the previous term will continue for all subsequent terms in the sequence. The sequence can be represented by the function an = 2 - 3(n-1) for any natural number n.

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Answer:

M = 6

N= 7

Step-by-step explanation:

M + 7 = 3

M= 6

6 + 7 = 13, so we get 3 and carry 1

Now 1 + 4 + N = 12

1 + 4 + 7  = 12

So N = 7

Therefore,

46 + 77 = 123

Answer:

In a general point (x, y) the horizontal component is the x-component, and the vertical component is the y-component.

then if we have the points (a, b) and (c, d)

The vertical distance or change between these points will be the difference between the y-components, and the horizontal distance or change is the difference between the x-components.

Then the vertical change between the points (2.5 , 1) and (5, 2) is:

2 - 1 = 1 unit.

The horizontal change between the points (2.5, 1) and (5, 2) is:

5 - 2.5 = 2.5 units.

Answer:

60%

Step-by-step explanation:

he gave away 2/5 which is 40%. 100%-40% is 60%

Answer:

Step-by-step explanation:

Left over chocolate = 3/5

Percentage = \(\frac{3}{5}*100=3*20 =\) 60%

Answer:

99cm^3

Step-by-step explanation:

Volume = Base x Height

Base = 9cm

Height = 11cm

9 x 11 = 99cm^3

The volume of the prism is V = 792 cm³

Given data:

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

So, the value of h = 8 cm

The base area is B = 9 x 11

B = 99 cm²

The volume of prism V = Bh

V = 99 x 8

V = 792 cm³

Hence, the volume of the prism is V = 792 cm³

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The value of length ER rounded to the nearest tenth is 17.9 units (Option C)

The trigonometric ratios which has been proven as regarding right angle triangles are given below:

Sine θ = Opposite / Hypothenus

Cos θ = Adjacent / Hypothenus

Tan θ = Opposite / Adjacent

With above information in mind, we can easily determine the length of ER in the question. This is illustrated below:

From the question given above, which is summarized in the diagram (see attached photo) the following data were obtained:

Since we looking for the Adjacent (ER), the best trig ratio to use is the Cos θ ratio. This can be obtained as illustrated below:

Cos θ = Adjacent / Hypothenus

Cos 61 = ER / 37

Cross multiply

ER = 37 × Cos 61

ER = 37 × 0.4848

ER = 17.9 units

Thus, the length of ER to the nearest tenth is 17.9 units

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Answer:

the answer will be 6 if am wrong please tell me

Answer:

f(6) = 30

Step-by-step explanation:

f(x) = x^2 - x is the function, correctly written.

To find f(6), substitute 6 for each occurrence of x:

f(6) = 6^2 - 6, or

f(6) = 36 - 6, or

f(6) = 30

The fraction 36/8 represents the lowest amount.

The given fractions are 5 1/4, 36/8, 46/9, 35/7.

We can compare fractions with unlike denominators by finding the least common denominator, or the smallest multiple the denominators share. Then we make equivalent fractions or fractions that represent the same part of the whole.

Now, 21/4, 36/8, 46/9, 35/7.

Here LCM of denominators is 504.

Thus, 2646/504, 2268/504, 2576/504, and 2520/504.

Therefore, the fraction 36/8 represents the lowest amount.

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The area of the circle is 452.16 square inches

Area is the the total surface that is occupied by a two dimensional shape

The radius of the circle = 12 inch

The radius of a circle is the distance between the center and any point on the circumference of the circle

The area of the circle A = π×\(r^2\)

Where A is the area of the circle

r is the radius of the circle

π = 3.14

substitute the values in the equation

The area of the circle = 3.14 × \(12^2\)

= 3.14 × 144

= 452.16 square inches

Hence, the area of the circle is 452.16 square inches

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Answer:

D

Step-by-step explanation:

the "<" (or "smaller") symbol tells us that the solution must have empty dots at the interval ends, as these values are not included in the solution.

otherwise, we would have a "<=" ("smaller or equal") symbol.

let's start for the first limit to calculate without the absolute value :

-2 + (x - 3) < 7

-5 + x < 7

x < 12

the other end we get by multiplying only the left side (still without the absolute value) by -1 and do it again :

-1×(-2 + (x - 3)) < 7

2 - (x - 3) < 7

2 - x + 3 < 7

-x + 5 < 7

-x < 2

x > -2 (remember, when we multiply the whole inequality, left and right side, by a negative value, we need to flip the inequality symbol).

The volume of the larger cylinder is (25/8)πR³.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically measured in units of cubic meters, cubic centimeters, cubic feet.

Let's denote the radius and height of the smaller cylinder as r and h, respectively, and the radius and height of the larger cylinder as R and H, respectively.

We know that the lateral area of a cylinder is given by the formula:

Lateral area = 2πrh

Using this formula for the smaller and larger cylinders, we get:

25π = 2πrh

64π = 2πRH

Dividing both sides of the first equation by 2π, we get:

rh = 25/2π

We also know that the following formula determines a cylinder's volume:

Volume = πr²h

Using this formula for the smaller cylinder, we get:

150π = πr²h

Substituting rh = 25/2π from above, we get:

150π = πr²(25/2π)

r² = 12

Taking the square root of both sides, we get:

r = √12 = 2√3

Substituting this value into rh = 25/2π, we get:

h = 25/(2πr) = 25/(4π√3)

Now, we can use the ratio of the lateral areas to find the ratio of the heights:

25π/64π = (2πrh)/(2πRH)

25/64 = rh/RH

25/64 = (2√3)(25)/(4πR)(H)

H = 2hR/r

Finally, we can use the formula for the volume of the larger cylinder to find its volume:

Volume = πR²H

Volume = πR²(2hR/r)

Volume = 2πR³h/r

Substituting the values we found for r, h, and H, we get:

Volume = 2π(R³)(25/(4π√3))/(2√3)

Volume = (25/8)πR³

Therefore, the volume of the larger cylinder is (25/8)πR³.

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a) The Corresponding minimum UGPA = 3.70

b) The range of middle 50% values will be: (3.28, 3.52).

A measure of how many standard deviations below or above the population mean a raw score is called z score. It will be positive if the value lies above the mean and negative if it lies below the mean. It is also known as standard score. It indicates how many standard deviations an entity is, from the mean. In order to use a z-score, the mean μ and also the population standard deviation σ should be known. A z score helps to calculate the probability of a score occurring within a standard normal distribution. It also enables us to compare two scores that are from different samples.

a) z score corresponding to top 5% area = 1.645

Hence, Corresponding minimum UGPA = 3.40 + 1.645*0.18 = 3.70

b) z score corresponding to middle 50% area = -0.67, 0.67

Hence, The range of middle 50% values will be:

(3.40 - 0.67*0.18, 3.40 + 0.67*0.18)

(3.28, 3.52)

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Answer:

Step-by-step explanation:

Answer:

Let x be the number of songs downloaded.

Each song is $1.29; the total cost would be found by multiplying the cost by the number of songs, or 1.29x.

This cannot be more than 20, so we set this less than or equal to 20:

1.29x ≤ 20.

To solve this, we divide both sides by 1.29:

≤ ;

x ≤15.5.

We cannot download half of a song, so we round this down to 15 (although the number rounds up mathematically, he would not have enough money to download 16 songs). This means he can download at most 15 songs.

Step-by-step explanation:

if you want the sample response then here: If x represents the number of downloads, you can write the inequality 1.29x ≤ 20. Solving the inequality, you find that x is less than or equal to about 15.5. Since he can’t download part of a song, Joseph can download 15 or fewer songs.

The given sequence an = sin(√n)/√n converges to limit 0 as n approaches infinity

The mentioned nth term of the sequence is an = sin(√n)/√n. To determine the convergence or divergence of the sequence and find its limit, we can use the limit comparison test, which is based on comparing the given sequence with a known sequence whose convergence or divergence is already known.Suppose bn is a known sequence whose convergence or divergence is already known. Then, by the limit comparison test, the given sequence converges or diverges according as the sequence bn converges or diverges.

To apply the limit comparison test, we need to find a suitable sequence bn whose convergence or divergence is known. For this, we observe that sin x ≤ x for all x > 0. Hence, we have 0 ≤ sin(√n)/√n ≤ 1/√n, where the inequality follows by dividing both sides of sin x ≤ x by √n and substituting x = √n. Also, we know that the sequence bn = 1/√n converges to 0 as n approaches infinity. Therefore, by the limit comparison test, the given sequence an = sin(√n)/√n also converges to 0 as n approaches infinity.

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The minimum sample size required to ensure that the estimate has an error of at most 0.15 at the 99% level of confidence = 426

Here, the population variance is σ² = 1.44

The mean is \(\bar{x}\) = 6

And the margin of error is  E = 0.15

The standard deviation is given by,

⇒ σ = \(\sqrt{1.44}\)

⇒ σ = 1.2

Here, the confidence level is 99%

So, the level of signoficance would be,

⇒ α = (100 - 99)%

⇒ α = 0.01

From the normal distribution table the critical value would be,

\(z_{\alpha /2}\) = 2.58

Now we find the sample size :

\(n=(\frac{z_{\alpha /2}\times \sigma}{E} )^2\\\\n=(\frac{2.58 \times 1.2}{0.15} )^2\)

n = 426

Therefore, the sample size is 426

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Answer:

$1500

Step-by-step explanation:

Let's start by converting 80% to a decimal. 80% means 80/100, or 0.8. Let's call the full budget b.

0.8b=1200

Divide both sides by 0.8 to isolate b:

b=1200/0.8=$1500

Hope this helps!

The mean and standard deviation of a sampling distribution of sample means with sample size n=36 are 72,3

The act of deciding on the number of observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study that seeks to draw conclusions about a population from a sample. In practice, the sample size employed in a study is frequently dictated by the cost, time, or convenience of gathering the data, as well as the necessity for statistical power. In complex research, sample sizes may vary: for example, in a stratified survey, sample sizes may fluctuate for each strata. Because data for an entire population is sought in a census, the targeted sample size is the population. During the experimental design process.

Given,

Mean μ=72

Standard deviation σ=18

Sample size n=36

The mean of the sample distribution is defined as:

E(\(\bar{x}\))=μ

E(\(\bar{x}\))=72

Standard deviation of a sample mean is,

SE(\(\bar{x}\))=σ/√n

SE(\(\bar{x}\))=18/√36

SE(\(\bar{x}\))=3

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Answer:

n = 10

Step-by-step explanation:

let the number be n , then

45 - 3n = n + 5 ( subtract n from both sides )

45 - 4n = 5 ( subtract 45 from both sides )

- 4n = - 40 ( divide both sides by - 4 )

n = 10

The solution of equation is x=-3

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given

The equation;√x+3=-6

Now,

√x=-6-3

√x=-9

x=-3

Therefore the answer of the given equation will be -3

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The length of the curve y = 4(x − 1)³/² from x=1 to x=4 is approximately 18.42 units.

This can be found using the formula for arc length: ∫(1 to 4)√(1 + (dy/dx)²) dx. After taking the derivative of y, we get dy/dx = 6(x-1)½. Plugging this into the formula and simplifying gives us ∫(1 to 4)6(x-1)dx = 18(3/2) = 27. Therefore, the length of the curve is approximately 18.42 units.

To find the length of a curve, we use the formula for arc length which involves taking the integral of the square root of 1 + (dy/dx)². In this case, we first take the derivative of y to get dy/dx = 6(x-1)½.

We then plug this into the formula for arc length and simplify the integral. After integrating from x=1 to x=4, we get the length of the curve to be approximately 18.42 units.

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The potential difference and the electric field strength of Two 2.40cm X 2.40cm plates that form a parallel-plate capacitor can be calculated by applying various formulae.

A. The potential difference across a capacitor can be calculated using the formula V = Q/C, where V is the potential difference, Q is the charge stored on the capacitor, and C is the capacitance. Given that the charge on the capacitor is +/- 0.708nC and the spacing between the plates is 1.30mm, we need to calculate the capacitance first. The capacitance of a parallel-plate capacitor is given by the formula C = ε0 * A / d, where ε0 is the permittivity of free space, A is the area of the plates, and d is the spacing between the plates. By substituting the given values, we can calculate the capacitance. Once we have the capacitance, we can use the formula V = Q/C to find the potential difference across the capacitor.

B. The electric field strength inside a capacitor can be calculated using the formula E = V/d, where E is the electric field strength, V is the potential difference, and d is the spacing between the plates. Given that the spacing between the plates is 2.60mm, and we already calculated the potential difference in part A, we can substitute these values into the formula to find the electric field strength inside the capacitor.

C. To find the potential difference across the capacitor if the spacing between the plates is 2.60mm, we can use the formula V = Q/C, where Q is the charge stored on the capacitor and C is the capacitance. We can use the previously calculated capacitance and the given charge to find the potential difference across the capacitor.

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Answer: 68 Miles

Work: 8*8.5=68

Answer:

At, x=-5

Step-by-step explanation:

(2-4)(x+5)=-2×0

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

By solving the generated equation, Calvin caught 16 smallmouth bass and 9 largemouth bass.

What is meant by equation?

An equation states that the two expressions have the same value or are equivalent to each other. Equations are used in various areas of mathematics, science, engineering, and everyday life to describe relationships and solve problems.

Let x represent the number of smallmouth bass that Calvin caught, and y represent the number of largemouth bass that he caught.

From the problem, we know that the total number of fish that Calvin caught is 25:

x + y = 25

We also know that the number of smallmouth bass that Calvin caught is 2 less than double the number of largemouth bass that he caught:

x = 2y - 2

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y:

y = 25 - x

Substituting this into the second equation, we get:

x = 2(25 - x) - 2

Simplifying this equation, we get:

x = 48 - 2x

Solving for x, we get:

3x = 48

x = 16

Substituting this value of x back into either of the original equations, we can solve for y:

y = 25 - x = 25 - 16 = 9

Therefore, Calvin caught 16 smallmouth bass and 9 largemouth bass.

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Answer:

Step-by-step explanation:

mkk