If American Airlines selects randomly a set of 40 flights on a given day, and then selects randomly a gr

Answer:

250

Step-by-step explanation:

Answer:

\( \frac{7}{4} \pi\)

or

\( \frac{3}{4} \pi\)

Step-by-step explanation:

See attached. I know (very haphazard). But the basic method is to inverse the trig function. This gives you the position of the terminal angle. -45 degrees means that you turned 45 degrees clockwise and are in quadrant 4. This corresponds to an angle of rotation of 315 degrees counter clockwise which is what we are looking for since the specified domain is betwern 0 and 360 degrees or 0 and 2 pi.

The next thing to remember is that Tan is also negative in Quadrant 2 (using the ASTC rule). This corresponds to an angle of rotation of 180 - 45 = 135 degrees.

Hope that helps.

question 3: -2

question 4: 0

Ordered pairs in a graph go in the sequence of (x, y)

The longest poster that can fit in the box must have dimensions of 10 inches (height) by 20 inches (length) by 12 inches (width).

To find the longest poster that can fit in the box, we need to determine the longest dimension of the box itself. Since the box is 10 inches high, the longest poster that can fit in the box must have a height of no more than 10 inches.

Now, we need to consider the other two dimensions of the box. The box is 20 inches long and 12 inches wide, so the longest poster that can fit in the box must have a length of no more than 20 inches and a width of no more than 12 inches.

As for why we can only fit one maximum-length poster in the box but we can fit multiple 22-inch posters in the same box, it's because the length and width of the box are larger than the length and width of the 22-inch poster.

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Fans of X-Men movies have been debating the best X-Men movie on an online forum. To see what the overall opinion is, visitors to the site were able to rank the four films in order of preference.

The result of the preference schedule is essential in finding the best movie according to the majority's opinion.

It is important to note that the preference schedule shows that the best X-Men movie can be determined through visitors ranking the four films in order of preference.

To determine the best X-Men film, you can start by looking at the film that received the most first-place rankings. This film is likely to be the favorite among the voters. If there is a tie for the most first-place rankings, you can consider the film that received the most second-place rankings, and so on.

By analyzing the preference schedule and considering the rankings for each film, you can identify the film that received the highest overall ranking and declare it as the best X-Men film according to the preferences of the voters.

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The z-score for a person who received a score of 77 is approximately 1.90 (rounded to two decimal places).

To calculate the z-score for a person who received a score of 77, we need to use the formula:

z = (x - μ) / σ

where:

x is the individual score,

μ is the mean of the distribution, and

σ is the standard deviation of the distribution.

Given that the class mean (μ) is 73 and the standard deviation (σ) is 2.1, and the individual score (x) is 77, we can substitute these values into the formula:

z = (77 - 73) / 2.1

z = 4 / 2.1

z ≈ 1.90

Therefore, the z-score for a person who received a score of 77 is approximately 1.90 (rounded to two decimal places).

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Answer:

54.7

Step-by-step explanation:

16.7 + 11 + 11 + 8 + 8 = 54.7

Note

I don't know how you are wrong but I showed my work and I got the same answer which is weird.

===========================================

Explanation:

x = amount (in inches) the spring is stretched

y = force applied (in pounds)

y = kx for some constant k, since x and y vary directly

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

Plug in the given info that x = 5 and y = 150 pair up together

Solve for k

150 = k*5

150/5 = k

k = 30

The equation goes from y = kx to y = 30x. Whatever the stretching distance (x) is, you multiply by 30 to get the force needed (y) to pull the spring.

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

Plug in y = 180 to solve for x

y = 30x

180 = 30x

30x = 180

x = 180/30

x = 6

The spring will be stretched 6 inches if you apply a force of 180 pounds.

Unicode value of 66, which is the letter "B". Therefore, the correct answer to this question is option B: "B".

The terms you mentioned are related to the Unicode character encoding standard and the concept of evaluating expressions. When discussing the expression "A" + 1, it's essential to note that the Unicode value for the character "A" is 65.

The expression "A" + 1 is attempting to add a numerical value (1) to a character ("A"). In many programming languages, this operation is allowed, and the result would be based on the Unicode values of the characters involved. Since the Unicode value for "A" is 65, adding 1 to it would result in a new Unicode value of 66. Consequently, the evaluated expression would correspond to the character with the Unicode value of 66, which is the letter "B". Therefore, the correct answer to this question is option B: "B".

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The given function is y = 2/x + x. We can find the length of the curve from x = 1 to x = 3 by using the formula of the arc length of a curve. Let's have a look at the formula of the arc length of a curve:

L = ∫ [a, b]√[1 + (dy/dx)^2]dx Where a and b are the two limits of x, and dy/dx is the first derivative of the function with respect to x. Now, we will find the first derivative of the function y = 2/x + x. dy/dx = -2/x^2 + 1On simplifying it, we get; dy/dx = (x^2 - 2)/x^2Now, we will put this value of dy/dx in the formula of the arc length of a curve. L = ∫ [1, 3] √[1 + (dy/dx)^2] dxL = ∫ [1, 3] √[1 + (x^2 - 2)^2/x^4] dx.

The arc length of a curve is a concept that we use in mathematics. It is the length of a curve in two dimensions. The arc length is the distance that we have to cover along the curve to go from one point to another. The formula of the arc length of a curve is given by;

L = ∫ [a, b]√[1 + (dy/dx)^2]dx.

Where a and b are the two limits of x, and dy/dx is the first derivative of the function with respect to x. In this question, we were given a function; y = 2/x + x. We were asked to find the length of the curve from x = 1 to x = 3.

Firstly, we found the first derivative of the given function with respect to x. dy/dx = -2/x^2 + 1On simplifying it, we got; dy/dx = (x^2 - 2)/x^2Then we put this value of dy/dx in the formula of the arc length of a curve.

L = ∫ [1, 3] √[1 + (dy/dx)^2] dxL = ∫ [1, 3] √[1 + (x^2 - 2)^2/x^4] dx.

On evaluating the definite integral, we get the length of the curve from x = 1 to x = 3.

In this question, we learned about the arc length of a curve. We learned that the arc length is the distance that we have to cover along the curve to go from one point to another. We also learned the formula of the arc length of a curve.

We used this formula to find the length of the curve from x = 1 to x = 3 for the given function y = 2/x + x. We solved the problem by finding the first derivative of the function and putting its value in the formula of the arc length of a curve.

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Answer:

3 3/2 trust meh

hello

since we're given y and x intercept, we can use it to find the slope of the equation

y-intercept = 2.1

x-intercept = 3.5

what this implies that in a given graph, y-axis is (0, 2.1) and x-axis (3.5, 0)

now we can use this co-ordinate to find our slope

so our odered pair are (3.5, 0) and (0, 2.1)

y2 = 2.1

y1 = 0

x2 = 0

x 1 = 3.5

now we know our slope as 3/5

we can use this slope to find the equation of the line

remember our y-intercept = 2.1

equation of staright line is given as y = mx + c

m = slope

c = y-intercept

now, the equation of this line is

y = 3/5x + 2.1

b.

we have one point (1.2, 5.1) and an x-intercept of 3.7

let the first point (1.2, 5.1) be A and the second point as B

A = (1.2, 5.1)

B = (3.7, 0)

y2 = 0

x2 = 3.7

y1 = 5.1

x1 = 1.2

y = mx + c

m = slope

c = y-intercept

let's use co-ordinate B to find our y-intercept

we can now re-write our equation with the standard form of y = mx + c

y = -2.04x + 7.548

Answer:

D 37.64

Step-by-step explanation:

C=2πr

so 2✘3.14 ✘6

A.68

Linear pair of angles:

If Non common arms of two adjacent angles form a line, then these angles are called linear pair of angles.

Axiom- 1

If a ray stands on a line, then the sum of two adjacent angles so formed is 180°i.e, the sum of the linear pair is 180°.

Axiom-2

If the sum of two adjacent angles is 180° then the two non common arms of the angles form a line.

The two axioms given above together are called the linear pair axioms.

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

Solution:

Given,

∠PQR = ∠PRQ

To prove:

∠PQS = ∠PRT

Proof:

∠PQR +∠PQS =180° (by Linear Pair axiom)

∠PQS =180°– ∠PQR — (i)

∠PRQ +∠PRT = 180° (by Linear Pair axiom)

∠PRT = 180° – ∠PRQ

∠PRQ=180°– ∠PQR — (ii)

[∠PQR = ∠PRQ]

From (i) and (ii)

∠PQS = ∠PRT = 180°– ∠PQR

∠PQS = ∠PRT

Hence, ∠PQS = ∠PRT

PLEASE MARK THIS AS A BRILLIANT ANSWER

Answer:

2(y-7) = 3

Step-by-step explanation:

Twice means multiply by 2.

The difference of a number and 7 means subtract a number/variable and 7.

Is equal to 3 means = 3.

2(y-7) = 3

Hope that helps.

Evaluating a function means finding the value of the function that corresponds to a given value of x. To do this, simply replace all the x variables with whatever x has been assigned.

Evaluating our function at x = -4 and x = 6, we have:

and those are our answers.

Answer:

i think

Step-by-step explanation:

1/24

The brush B has the larger surface area to paint the room quicker.

Mrs. Warren has 2 different paint brush rollers. Roller A has a radius of 1 inch and a length of 8 inches. Roller B has a radius of 1.5 inches and a length of 6 inches.

Therefore, the roller that has a larger surface area to paint her sons room quicker is as follows:

surface area of the brush  = 2πrh

where

Hence,

Brush A surface area = 2 × π × 1  ×  8

Brush A surface area = 16π inches²

Brush B surface area = 2 × π × 1.5 × 6

Brush B surface area = 18π inches²

Therefore, brush B has the larger surface area.

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Answer:

"Zero and its operation are first defined by [Hindu astronomer and mathematician] Brahmagupta in 628," said Gobets. He developed a symbol for zero: a dot underneath numbers.

The correct statement is: "(0,2) is a solution of the system."

To determine if (0, 2) is an element of the solution set for the system of equations:

Equation 1: x + 3y = 6

Equation 2: -x + 4y = 8

We can substitute the values x = 0 and y = 2 into both equations and check if they hold true.

For Equation 1:

0 + 3(2) = 6

6 = 6

The equation is true.

For Equation 2:

-(0) + 4(2) = 8

8 = 8

The equation is also true.

Since both equations hold true when x = 0 and y = 2, (0, 2) is indeed a solution of the system.

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If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.

What is a logarithmic function?

A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: \(f(x) = log_b(x),\) where b is the base of the logarithm.

To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.

In the case of logarithmic functions, the derivative of \(f(x) = log_b(x)\) is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.

Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.

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If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.

What is a logarithmic function?

A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: \(f(x)=log_b(x)\). where b is the base of the logarithm.

To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.

In the case of logarithmic functions, the derivative of \(f(x)=log_b(x)\). is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.

Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.

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Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in geometry that relates to the three sides of a right-angled triangle. It states that the square of the length of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, it can be expressed as:

                             \(a^2 + b^2 = c^2\)

We can use the Pythagorean theorem to find the distance between the two ships at any given time:

d² = (20t)² + (15(t-4))²

Simplifying this equation, we get:

d² = 400t² + 225(t² - 8t + 16)

d² = 625t² - 1800t + 3600

d = √(625t²- 1800t + 3600)

We want to find the value of t when d = 100 nautical miles, so we can set up the following equation:

100 = √(625t² - 1800t + 3600)

Squaring both sides, we get:

10000 = 625t² - 1800t + 3600

Rearranging, we get:

625t² - 1800t - 6400 = 0

Using the quadratic formula, we get:

t = (1800 ± √(1800² + 46256400)) / (2*625)

t = (1800 ± 3900) / 1250

t = 3.84 or t = 8.16

So the time elapsed for the second ship is:

t2 = t + 4

t2 = 7.84 or t2 = 12.16

We can see that the only solution that works is when t = 8.16 and t2 = 12.16. At that time, the first ship will have sailed for 8.16 hours at 20 knots, or 163.2 nautical miles, and the second ship will have sailed for 8.16 - 4 = 4.16 hours at 15 knots, or 62.4 nautical miles. The distance between the two ships will be:

d = √((163.2)² + (62.4)²) = 174.9 nautical miles

Rounding to the nearest minute, we get that the ships will be 100 nautical miles apart at 8 hours and 10 minutes after the first ship left the harbor.

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Answer:

(x+-6)(x+4)

(x)(x)+(x)(4)+(-6)(x)+(-6)(4)

x^2+4x-6x-24

Answer is x^2-2x-24

Step-by-step explanation:

Answer:

1/2=20/40 19/20=38/40

Step-by-step explanation:

so the first option

a. The number of strings containing at least one pair of adjacent characters that are the same is 4^n - 4 * 3^(n-1), where n is the length of the string. b. The probability that a randomly chosen string of length ten over {a, b, c, d} contains at least one pair of adjacent characters that are the same is approximately 0.6836.

a. To count the number of strings of length n over the set {a, b, c, d} that contain at least one pair of adjacent characters that are the same, we can use the principle of inclusion-exclusion.

Let's denote the set of all strings of length n as S and the set of strings without any adjacent characters that are the same as T. The total number of strings in S is given by 4^n since each character in the string can be chosen from the set {a, b, c, d}.

Now, let's count the number of strings without any adjacent characters that are the same, i.e., the size of T. For the first character, we have 4 choices. For the second character, we have 3 choices (any character except the one chosen for the first character). Similarly, for each subsequent character, we have 3 choices.

Therefore, the number of strings without any adjacent characters that are the same, |T|, is given by |T| = 4 * 3^(n-1).

Finally, the number of strings that contain at least one pair of adjacent characters that are the same, |S - T|, can be obtained using the principle of inclusion-exclusion:

|S - T| = |S| - |T| = 4^n - 4 * 3^(n-1).

b. To find the probability that a randomly chosen string of length ten over {a, b, c, d} contains at least one pair of adjacent characters that are the same, we need to divide the number of such strings by the total number of possible strings.

The total number of possible strings of length ten is 4^10 since each character in the string can be chosen from the set {a, b, c, d}.

Therefore, the probability is given by:

Probability = |S - T| / |S| = (4^n - 4 * 3^(n-1)) / 4^n

For n = 10, the probability would be:

Probability = (4^10 - 4 * 3^9) / 4^10 ≈ 0.6836

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