suppose the length of time (in minutes) going through customs at u.s. airports with global entry (goes) is normally distributed with a population mean of 40 minutes and a population standard deviation of 12 minutes. what is the approximate wait time for the fastest 4% of passengers?

The series 1/n^2 from n=1 to infinity converges. To determine whether the series converges or diverges, we can use the p-series test.

The p-series test states that a series of the form 1/n^p converges if p > 1 and diverges if p <= 1. In our case, the series is 1/n^2, where the exponent is p = 2. Since p = 2 is greater than 1, the p-series test tells us that the series converges.

Additionally, we can examine the behavior of the terms in the series as n approaches infinity. As n increases, the denominator n^2 becomes larger, resulting in smaller values for each term in the series. In other words, as n grows, the individual terms in the series approach zero. This behavior suggests convergence.

Furthermore, we can apply the integral test to further confirm the convergence. The integral of 1/n^2 with respect to n is -1/n. Evaluating the integral from 1 to infinity gives us the limit as n approaches infinity of (-1/n) - (-1/1), which simplifies to 0 - (-1), or 1. Since the integral converges to a finite value, the series also converges.

Based on both the p-series test and the behavior of the terms as n approaches infinity, we can conclude that the series 1/n^2 converges.

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Answer: A

Step-by-step explanation:

4^3=64.

Option:-

\( \: \)

Given:-

\( \: \)

To prove:-

\( \: \)

Solution:-

\( \: \)

put the value of x = 3

\( \: \)

\( \: \)

━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

Answer:

Option D

Step-by-step explanation:

Fractions are considered to be rational numbers because they are decimals that can be written as a fraction and since it's already wrote as a fraction but can be converted back to a decimal it is a rational number. The fraction is considered to be a real number because all rational numbers are real numbers and since we just proved that 5/8 is a rational number it is therefore a real number. Which means your answer is option D or "rational numbers, real numbers."

Hope this helps.

•given that is smallest angle of rotational symmetry for a regular polygon is 30

•we have to find the number of side does the regular polygon have

•if we can rotate of figure around a center point be fewer than 360° and the figure appears and change then the figure has the rotation symmetry

no. of side= 360/ smallest angle at centre=12

I hope it's help

Answer:

the answer is D

Step-by-step explanation:

Answer:

x < − 33 4  or  x > − 27/4

The equation

Is in point intercept form

The general equation of point intercept form is given as

Comparing the two equations

This implies

Hence, the slope in the equation is -2

Also, by comparing the equations

Thus the point in the equation is (2, 1)

Step-by-step explanation:

A body at rest accelerates to 2.5 meters in 1 second, it then maintains a constant speed for 2 seconds and accelerate 2.5 meters in 2 seconds. It then maintains a constant speed for 2 seconds and finally decelerates for the next eight seconds.

scale = 1cm : 1 unit.

distance axis : 1 to 7.5 meters

Time axis : 1 to 15 seconds

Answer:

x=7

Step-by-step explanation:

As seen from the higher two numbers, there is a distinct ratio between the shorter side and the longer side. To find the ratio we simply get the given two without the x and we get 8:12 which simplifies to 2:3 or 1: 1.5

This means in order to find 3x-6, we need to multiply 10 by 1.5 which means:

3x-6=15

3x=21

x=7

Hope this helped!

In order for Janet's investment to increase to $10,000 in five years at a 4% yearly interest rate compounded monthly, she needs to put aside about $8,079.90 now.

For instance, if you put $1,000 in a bank account that offers 1% yearly interest, after a year you would have received $10 in interest. Compound interest allowed you to make 1 percent on $1,010 in Year Two, which amounted to $10.10 in interest payments for the year.

We can use the formula for compound interest to find how much Janet needs to invest now:

\(A=P\left(1+\frac{r}{n}\right)^{n t}\)

where:

A = the amount of money after the specified time period

P = the principal (the amount of money Janet needs to invest now)

r = the annual interest rate (4% = 0.04)

n = the number of times the interest is compounded per year (12, since it is compounded monthly)

t = the time period, in years (5)

Plugging in the values we get:

10,000 = P(1 + 0.04/12)⁽¹²*⁵⁾

Solving for P, we get:

P = 10,000 / (1 + 0.04/12)⁽¹²*⁵⁾

P ≈ $8,079.90

Therefore, Janet needs to invest about $8,079.90 now to grow to $10,000 in 5 years at a 4% annual interest rate compounded monthly.

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Answer:

y = 10

Step-by-step explanation:

\(\displaystyle \frac{6+9+18}{3}=\frac{12+y}{2}\\ \\\frac{33}{3}=\frac{12+y}{2}\\ \\11=\frac{12+y}{2}\\ \\22=12+y\\\\10=y\)

3

6+9+18

=

2

12+y

3

33

=

2

12+y

11=

2

12+y

22=12+y

10=y

answer: 10=y

The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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The statement (a) is true. For any positive real number x, we can always find a positive real number y such that xy < y^2.

The statement (b) is false. There is no positive real number x that satisfies the condition for all y.

The statement (b) ∃x such that ∀y, xy < y^2 is true. It asserts the existence of a positive real number x such that for any positive real number y, the inequality xy < y^2 holds. This can be proven by considering the case where x = 0. Since x is a positive real number, we know that x < y for any positive y. By multiplying both sides of this inequality by y, we get xy < y^2, which satisfies the given statement.

In other words, there exists at least one positive real number x that satisfies the inequality for all positive real numbers y. This can be demonstrated by taking x = 0 as an example. For any positive y, multiplying x = 0 by y results in 0, which is less than y^2. Therefore, the statement (b) is true.

It is important to note that the statement (a) ∀x, ∃y such that xy < y^2 is not true. This statement claims that for every positive real number x, there exists a positive real number y such that xy < y^2. However, this is not the case as we can find values of x for which no such y exists. For instance, if we consider x = 0, no positive value of y can satisfy the inequality since multiplying 0 by any positive y would always result in 0, which is not less than y^2.

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Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

The angle of elevation from the stake up to the tent pole is, 54.55°.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, A 19 ft rope is tied from the top of a tent pole, It is the hypotenuse length.

Also, The state is 11 feet away and it is the adjacent length.

We know, cos = adjacent/hypotenuse.

cos = 11/19.

Ф = cos⁻¹(0.58).

Ф = 54.55°.

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Answer:

Step-by-step explanation:

answer B

since for all real positive r,  r^x >0

The unique function who give a negative answer is f(x)=-3* 2^x

The dimensions of the rectangle are width = 20 centimeters and length = 1 centimeter.

Let's denote the width of the rectangle as "w" centimeters. According to the problem, the length of the rectangle is 19 centimeters less than its width, so the length can be expressed as "w - 19" centimeters.

The formula for the area of a rectangle is length multiplied by width. In this case, the area is given as 20 square centimeter

Area = Length × Width

20 = (w - 19) × w

To solve this equation, we can expand it:

20 = \(w^2\) - 19w

Rearranging the equation to bring everything to one side:

\(w^2\) - 19w - 20 = 0

Now, we can factor the quadratic equation:

(w - 20)(w + 1) = 0

Setting each factor equal to zero and solving for "w":

w - 20 = 0 --> w = 20

w + 1 = 0 --> w = -1

Since a negative width doesn't make sense in this context, we discard w = -1.

Therefore, the width of the rectangle is 20 centimeters (w = 20).

To find the length, we substitute this value back into the expression for length:

Length = w - 19

Length = 20 - 19

Length = 1 centimeter

So, the dimensions of the rectangle are width = 20 centimeters and length = 1 centimeter.

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Using a graphing calculator with the given parametric equations, we can determine the location of the graph when –1.5 ≤ t ≤ 1.5. The graph covers Quadrants I and II as t varies from -1.5 to 1.5.

The graph will be located in Quadrants I and II because the values of x and y will both be positive for t in this range. As t increases from -1.5 to 0, x decreases from 8 to -8 while y increases from 0 to approximately 5.7, resulting in the graph moving from Quadrant I towards the positive y-axis. As t increases from 0 to 1.5, x increases from -8 to 8 while y decreases from approximately 5.7 to 0, resulting in the graph moving from Quadrant II towards the positive x-axis.

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The function's value at x = 1, y = - 1 Or f(1) = -1.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

The x-coordinate represents the input and the y-coordinate represents the output.

From the given points in the graph, we can conclude that when x = 1, y = -1.

Therefore, The value of the function f(1) = -1.

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The marginal cost of producing one more unit of the product when x = 100 is $150 per unit. To find the instantaneous rate of change (or the marginal cost) of c with respect to x when x = 100, we need to calculate the derivative of the cost function c(x) with respect to x and evaluate it at x = 100.

Let's assume that we have the cost function c(x) = 0.5x^2 + 50x + 1000, where x is the number of units produced. To find the derivative of this function, we need to use the power rule of differentiation, which states that if f(x) = x^n, then f'(x) = nx^(n-1). Applying this rule to our cost function, we get:

c'(x) = d/dx (0.5x^2 + 50x + 1000)
     = 1x^(2-1) + 50x^(1-1) + 0
     = x + 50

Now, we can evaluate this derivative at x = 100 to find the marginal cost:

c'(100) = 100 + 50
       = 150

Therefore, the marginal cost of producing one more unit of the product when x = 100 is $150 per unit. This means that if the company produces one more unit of the product, it will cost them $150 more than the cost of producing the previous unit. The significance of the marginal cost will be explained in a future chapter, but for now, it is important to understand that it is a crucial concept in economics and business decision-making.

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Answer:

p = 8

Step-by-step explanation:

\(\frac{p+4}{3} = 4\)

\(p + 4 = 4 * 3\)

\(p + 4 = 12\)

\(p = 12 - 4\)

\(p = 8\)

8 additional workers need to be added for the remaining 6 days to complete the graduation task. The remaining work to be done is 7/12.

Let's solve the problem step by step:

We are given that 15 workers can complete the graduation task in 12 days. On the morning of the 5th day, the task is already partly completed.

To determine the progress made by the morning of the 5th day, we can calculate the total work done up to that point. Since the workers are equally efficient, we can assume that the work is distributed evenly over the days.

From day 1 to day 5, a total of 5 days have passed. Since the workers are completing the task in 12 days, the progress made by the morning of the 5th day is 5/12 or 5/12th of the total work.

Therefore, the remaining work to be done is 1 - (5/12) = 7/12.

To complete the remaining work in the remaining 6 days, x workers are added.

Since we have established that the 15 workers can complete the task in 12 days, we can set up a proportion to determine the relationship between the number of workers and the number of days.

15 workers / 12 days = x workers / 6 days

By cross-multiplying, we get:

15 * 6 = 12 * x

90 = 12x

Dividing both sides by 12, we find:

x = 90 / 12

x = 7.5

Since the number of workers must be a whole number, we cannot have 7.5 workers. Therefore, we round up to the nearest whole number.

Therefore, x is rounded up to 8 workers.

In conclusion, 8 additional workers need to be added for the remaining 6 days to complete the graduation task.

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The correct answer is C. The Mode.

Data is the collection of data term that is organized and formatted in a specific way it's typically contains fact observation or statistics that are collected through a process of measurement or research data set can be used to answer question and help make informed decision they can be used in a variety of ways such as to identify trends on cover patterns and make prediction.

This measure of centre is most meaningful when the data is qualitative because it shows the value that appears most frequently in the data set. The mode can be used to identify the most popular item or most commonly occurring outcome. It is the only measure of centre that can be used for qualitative data, as the other measures (mean, median, and range) require numerical data.

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The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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The profit of the company if the company has 1800 customers is 649124 dollars

What is profit ?

A monetary gain, specifically the sum remaining after expenses for purchasing, running, or producing an item have been deducted.

P = 8.5√c³  ------->(1)

c = 1800 customers = 18 hundreds

(1) => P = 8.5√(18)³

           = 8.5 √5832 ( cube of 18=5832

          = 8.5 * 76.3675

          = 649.124 thousands of dollars

( convert into dollars by multiplying by 1000)

          = 649124.025 dollars  

          ≈ 649124 dollars

The profit of the company if the company has 1800 customers is 649124 dollars

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Answer: 48148

Step-by-step explanation:

The environment will no longer be able to support the population after 24 years

The proper representation of the table is given as:

y   1   2    3  4

n 55 60 67 75

An exponential function is represented as:

\(n = ab^y\)

Where:

Next, we determine the function equation using a statistical calculator.

From the statistical calculator, we have:

a = 49.19 and b = 1.11

Substitute these values in \(n = ab^y\).

So, we have:

\(n = 49.19 * 1.11^y\)

From the question, the maximum is 600.

So, we have:

\(49.19 * 1.11^y = 600\)

Divide both sides by 49.19

\(1.11^y = 12.20\)

Take the logarithm of both sides

\(y\log(1.11) = \log(12.20)\)

Divide both sides by log(1.11)

y = 23.97

Approximate

y = 24

Hence, the environment will no longer be able to support the population after 24 years

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Answer:

a

Step-by-step explanation:

just did it

The expectation values ⟨x2⟩ and ⟨p2⟩ as a function of σ are given by,⟨x2⟩ = πσ and ⟨p2⟩ = π/2σ.

The given wave function is ψ(x) = \([2\pi \sigma](-1/4) e^{-x_2/(4\sigma)}\).

To confirm that this wave function is normalized, we need to perform the following steps:

i) ∫ψ(x)*ψ(x) dx from -infinity to +infinity.

ii) Solve the above integral and check if the result is equal to 1.

After performing the above steps, we get the following results

As per the given problem, the wave function is given by,ψ(x) = \([2\pi \sigma](-1/4) e^{-x_2/(4\sigma)}\).

We need to confirm that this wave function is normalized.

For that, we need to perform the following steps:

i) ∫ψ(x)*ψ(x) dx from -infinity to +infinity.

ii) Solve the above integral and check if the result is equal to 1.

Substituting the wave function, we get,

\(\int\limits^\infty_{-\infty} {2\pi\sigma(-1/4)e^{-x_2/4\sigma} \times 2\pi\sigma(-1/4)e^{-x_2/4\sigma} \, dx\)

Now, ∫exp[-x2/(2σ)]dx from -infinity to +infinity can be solved as follows:

Let y = x/(√2σ)

Substituting the limits, we get,

\(∫exp[-x2/(2σ)]dx from -infinity to +infinity = √(2σ) * ∫exp(-y2) dy from -infinity to +infinity\)

= √(2πσ).

∴ \(∫[2πσ](-1/4) exp[-x2/(4σ)]*[2πσ](-1/4) exp[-x2/(4σ)] dx from -infinity to +infinity = ∫[2πσ](-1/2) exp[-x2/(2σ)] dx from -infinity to +infinity= 1, which is equal to 1.\)

Hence, the given wave function is normalized.

Now, we need to calculate the expectation values ⟨x2⟩ and ⟨p2⟩ as a function of σ.

⟨x2⟩ = ∫x2 |ψ(x)|2 dx from -infinity to +infinity.

Substituting the wave function, we get,

⟨x2⟩ = ∫x2 [2πσ](-1/2) exp[-x2/(2σ)] dx from -infinity to +infinity.

Using the relation,

∫x2 exp(-ax2) dx = √(π/2a3)⟨x2⟩ = √(2σ) * ∫x2 exp[-x2/(2σ)] dx from -infinity to +infinity

= 1/2 * σ * √(2σ) * ∫[2σ](-3/2) exp(-u) du from -infinity to +infinity

= 1/2 * σ * √(2σ) * Γ(3/2), where Γ is the Gamma function.

Using the value of Γ(3/2) = √π, we get,⟨x2⟩ = (1/2) * (2σ) * π = πσ.

Conversely, ⟨p2⟩ = ∫p2 |ψ(p)|2 dp from -infinity to +infinity.

Substituting the wave function, we get,

⟨p2⟩ = ∫[2πσ](-1/2) p2 \(e^{-p2\sigma/2}\) dp from -infinity to +infinity.

Integrating by parts twice, we get,

⟨p2⟩ = (2σ) *\(∫[2πσ](-1/2) exp[-p2σ/2] dp from -infinity to +infinity= (2σ) * √(π/(2σ3))\)= π/2σ.

Hence, the expectation values ⟨x2⟩ and ⟨p2⟩ as a function of σ are given by,⟨x2⟩ = πσ and ⟨p2⟩ = π/2σ.

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Answer: m=-18

Step-by-step

9*-2=-18 to get m, as 4/-2 = -2

The slope y-intercept form of a linear equation is given as y = mx +c so for 13,14,15,16 the equations are y = 2x - 5,y = -x - 5,y = -x/2 + 1, and y = 3x/4 - 2 respectively.

A linear function is a function that varies linearly with respect to the changing variable.

A linear function always has the same and constant slope.

In the 13 figure,

The linear equation of a line is ,

y = mx + c where m is the slope while c is the y-intercept.

The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope(m) = (y₂ - y₁)/(x₂ - x₁)

So, the slope associated with points (3,1) and (1,-3) is,

m = (-3 - 1)/(1 - 3) = 2

So, y = 2x + c

Now substitute,(3,1)

1 = 2(3) + c

c = -5

So the b becomes, y = 2x - 5.

With the same approaches, the equations for the 14,15, and 16 figures are y = -x - 5,y = -x/2 + 1, and y = 3x/4 - 2 respectively.

Hence "The slope y-intercept form of a linear equation is given as y = mx +c so for 13,14,15,16 the equations are y = 2x - 5,y = -x - 5,y = -x/2 + 1, and y = 3x/4 - 2 respectively".

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Answer:

  A. 1/2

  D. -1/3

Step-by-step explanation:

You want to know the solutions to 6x² -x -1 = 0.

We can factor the equation as ...

  6x² -3x +2x -1 = 0

  3x(2x -1) +1(2x -1) = 0

  (3x +1)(2x -1) = 0

The solutions will make the factors zero:

  3x +1 = 0   ⇒   x = -1/3

  2x -1 = 0   ⇒   x = 1/2

The solutions are 1/2 and -1/3.

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Answer:

D

Step-by-step explanation:

Step 1: (3)^2*6pi

Step2: 54 pi cm^3 Ans

Answer:

169.71

Step-by-step explanation:

FIRST PUT THE VALUES IN THE FORMULA OF VOLUME OF CYLINDER i.e.  V= πr^2 h  then evaluate the values as V=22/7(3)^2(6)  =169.71cm^3