determine the average number of planes that will stack up, waiting to land. 2. (2) find the average time a plane must wait in line before it can land. 3. (2) calculate the average time it takes a plane to clear the runway once it has notified the airport that it is in the vicinity and wants to land.

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Answer:

B, 2I + 3 = 39

Step-by-step explanation:

work backwards first, so 39 minus 3 is 36, divided by two is 13.

The value of the expression a + 4 when a = 7 is 11.

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.

We are given that;

Function= a+4

Now,

By algebra

If a = 7, then we can substitute this value into the expression a + 4 to get:

=a + 4

= 7 + 4

= 11

Therefore, by algebra the answer will be 11.

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The complete question is;

Evaluate the expression a+4 when a=7?

The sequence {an} = {\(8n^4 + n + 1\)} is not convergent. It diverges to infinity as n approaches infinity.

To determine whether the sequence {an} = {\(8n^4 + n + 1\)} is convergent, we need to examine the behavior of the terms as n approaches infinity.

The sequence {an} is said to be convergent if there exists a real number L such that the terms of the sequence get arbitrarily close to L as n approaches infinity.

To investigate convergence, we can calculate the limit of the sequence as n approaches infinity.

lim(n→∞) \((8n^4 + n + 1)\)

To evaluate this limit, we can look at the highest power of n in the sequence, which is \(n^4.\) As n approaches infinity, the other terms (n and 1) become insignificant compared to n^4.

Taking the limit as n approaches infinity:

lim(n→∞) \(8n^4 + n + 1\)

= lim(n→∞) \(8n^4\)

Here, we can clearly see that the limit goes to infinity as n approaches infinity.

Therefore, the sequence {an} = {\(8n^4 + n + 1\)} is not convergent. It diverges to infinity as n approaches infinity.

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The trigonometric values for a right triangle can be obtained through the measurements of the different sides,

this can be found in a triangle like this,

then, identify the measurements in the given triangle

then,

Answer: n=90

Step-by-step explanation:

(n-2) 180

(n-2) = 2n

2n/180 =90

you find a number that both 2 and 180 go into which is 2

Answer:

18.288

Step-by-step explanation:

Answer: 7th Graders

Explanation:

Several people have gotten this question and 7th graders are the right choice

Answer:7th grade should be awarded !

Step-by-step explanation:

Answer:

w = -12

Step-by-step explanation:

I think because you make the positive a negative so -6+-6 which is -12

The nonzero vector orthogonal to the plane through the points P, Q, and R is [-8/13, -8/13, -12/13].

To find a nonzero vector orthogonal to the plane through the points P, Q, and R, we can use the cross product of two vectors that lie in the plane.

Let's find the vectors PQ and PR, which can be found by subtracting the coordinates of P from the coordinates of Q and R:

PQ = Q - P = (-2, 1, 3) - (1, 0, 1) = (-3, 1, 2)

PR = R - P = (4, 2, 5) - (1, 0, 1) = (3, 2, 4)

Next, we'll take the cross product of these two vectors to find a vector orthogonal to the plane:

n = PQ x PR =

[(1)(4) - (2)(2), (2)(-3) - (3)(1), (3)(3) - (2)(-2)]

= [-8, -8, -12]

This vector is orthogonal to the plane through the points P, Q, and R. To make it a nonzero vector, we can scale it to have magnitude 1:

n = [-8, -8, -12] / sqrt((-8)^2 + (-8)^2 + (-12)^2) = [-8/13, -8/13, -12/13]

So, the nonzero vector orthogonal to the plane through the points P, Q, and R is [-8/13, -8/13, -12/13].

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In the equation\(`x = sin^-1(1/u)`,\) the letter x represents the angle while the letter u represents the value of the trigonometric function.

The inverse sine function is defined as the arc or angle whose sine is equivalent to the value of the input argument.

It's also known as the arcsine function. In trigonometry, it is commonly represented as \(sin^-1\) or arcsin.

In trigonometry, the sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse of a right-angled triangle.

It is often abbreviated as sin.

The sine of an angle x is denoted by

sin(x) = Opposite side / Hypotenuse.

For any angle x, the sine function returns a value between -1 and 1.

In summary, x represents the angle in the equation \(x = sin^-1(1/u)\)while u represents the value of the trigonometric function, which is equal to 1/sin(x).

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The solution for given inequality is - 30 and 18. So the answer is option c. x < −30 and x < 18.

In mathematics, an inequality is an unequal comparison between 2 algebraic terms or algebraic expressions. The signs we used in inequality are Lessthan (<), greater than (>) or Less than or equal to(≤), greater than or equal to (≥).  

To solve an inequality we can add or subtract the same integer on both sides or we can multiply or divide the same integer on both sides. which doesn't change the condition of inequality.

Here we have an inequality that is

The inequality is three-fourths times the absolute value of the quantity third times x plus 2 end quantity is less than 6.  

The above statement can be converted as follows

=> \(\frac{3}{4} | \frac{x}{3} +2| < 6\)    

The equation can be solved as follows

=> \(3 | \frac{x}{3} +2| < 24\)    [  Multiplied by 4 on both sides ]

=> \(3 | \frac{x+6}{3} | < 24\)    

=> \(| x+6 | < 24\)    

=> \(x+6 < \pm24\)    

Take \(x+6 < 24\)  

=> x + 6 - 6 < 24 - 6     [ Subtract - 6 on both sides ]

=> x < 18

Take x + 6 < - 24

=> x + 6 - 6 < - 24 - 6   [ Subtract - 6 on both sides ]

=> x < - 30  

Therefore,

The solution for given inequality is - 30 and 18. So the answer is option c. x < −30 and x < 18.

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The answer to (c) is ||4v — 4w|| ≈ 27.07.

Given that || v || = 3, || w || = 3, and the angle between v and w is 2.8 radians. We can calculate the following:(a) v. w = ?The dot product of two vectors is defined as the product of their magnitudes and the cosine of the angle between them.

Therefore, v.w = ||v|| ||w|| cos θWhere, θ is the angle between v and w. So, v.w = 3×3 cos(2.8) ≈ -3.20 Therefore, v.w ≈ -3.20.(b) ||1v + 4w|| = ?

The magnitude of the vector ||1v + 4w|| can be calculated as follows:||1v + 4w|| = √((1v + 4w).(1v + 4w))= √(1v.1v + 8v.w + 16w.w) Substitute the value of v.w we obtained above and calculate||1v + 4w|| = √(9 + 8×(-3.20) + 16×9)≈ 9.97

Therefore, ||1v + 4w|| ≈ 9.97.(c) ||4v — 4w|| =Similarly, the magnitude of the vector ||4v — 4w|| can be calculated as follows:

||4v — 4w|| = √((4v — 4w).(4v — 4w))= √(16v.v — 32v.w + 16w.w) Substitute the values of v.w and ||v|| we obtained above and calculate||4v — 4w|| = √(16×9 — 32×(-3.20) + 16×9)≈ 27.07 Therefore, ||4v — 4w|| ≈ 27.07.

The answer to (a) is v.w ≈ -3.20. The answer to (b) is ||1v + 4w|| ≈ 9.97. The answer to (c) is ||4v — 4w|| ≈ 27.07.

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Answer: -4x²z²y + 12xz²y

Step-by-step explanation:-------------

Answer:

10 sides.

Step-by-step explanation:

The sum of the exterior angles pf all polygons is 360 so the sum of the interior angles in this one = 4*360 = 1440 degrees.

Sum of interior angles = 180(n - 2) where n = number of sides. So 1440 = 180(n-2). 180n - 360 = 1440 ; 180n = 1440+360 = 1800, So n = 1800/180= 10.

The probability that the first winner lives in Gaston and the second lives in Pike is (1/36).

What is Probability?

A number that reflects the chance or likelihood that a particular event will occur is called probability.

There are 9 customers in total, so there are 9 choices for the first winner.

According to question 2 of these customers live in Gaston

So, there are 2 choices for the first winner to live in Gaston.

After the first winner is chosen, there are only 8 customers remaining.

Now there are 8 choices for the second winner and one of the winners has already been chosen from Gaston, there are only 2 customers left in Gaston, and one of them is from Pike. Therefore, there is only 1 choice for the second winner to live in Pike.

So the probability that the first winner lives in Gaston and the second lives in Pike is (2/9) × (1/8) = 1/36

Therefore, the probability is 1/36, which is the final answer in its simplest form.

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Answer:

C

Step-by-step explanation:

I think because there is no space or a sign in-between the f and 5, which means you multiply.

Average waiting time for FCFS: 8.75

Average waiting time for SJF: 4.75

To solve this scheduling problem using FCFS (First-Come, First-Served) and SJF (Shortest Job First) algorithms, let's go step by step:

Schedule order for FCFS:

The FCFS algorithm schedules processes based on their arrival time. So, the schedule order for FCFS is as follows:

Pl -> P2 -> P3 -> P4

Average waiting time for FCFS:

To compute the average waiting time for FCFS, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P2 | 3 | 10 | 3

P3 | 4 | 6 | 13

P4 | 5 | 1 | 19

Average waiting time = (0 + 3 + 13 + 19) / 4 = 8.75

Therefore, the average waiting time for FCFS is 8.75.

Schedule order for SJF:

The SJF algorithm schedules processes based on their running time. The process with the shortest running time gets executed first. If multiple processes have the same running time, the process with the earliest arrival time is selected first. The schedule order for SJF is as follows:

Pl -> P4 -> P3 -> P2

Average waiting time for SJF:

To compute the average waiting time for SJF, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P4 | 5 | 1 | 3

P3 | 4 | 6 | 6

P2 | 3 | 10 | 10

Average waiting time = (0 + 3 + 6 + 10) / 4 = 4.75

Therefore, the average waiting time for SJF is 4.75.

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Answer:

Linear. While all linear equations produce straight lines when graphed, not all linear equations produce linear functions. In order to be a linear function, a graph must be both linear (a straight line) and a function (matching each x-value to only one y-value).

What is the first error Vanessa made in her proof: B. Vanessa only established some of the necessary conditions for a congruence criterion.

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of three (3) pairs of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.

Based on the reflexive property of equality, we can logically deduce the following congruent and similar triangles:

KM ≅ KM

ΔKLM ≅ ΔMNK  (SSS similarity theorem).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

Answer:

$3.71

Step-by-step explanation:

52.99*1.07=56.6993

56.6993-52.99=3.7093

3.7093 rounded to the nearest hundredth is 3.71

So therefore, the sales tax is $3.71

Answer:

ASA

Step-by-step explanation:

this is because both lines that are equal to each other share the same angle D on the triangle. Meanign that the angle between the two congruent sides is also equal, thus ASA

Applying the square root of the variance, the standard deviation of the distribution is of 13.964.

The standard deviation of a distribution is given by the square root of the variance of the distribution.

For this problem, the variance of the distribution is of 195, hence the standard deviation is:

s = sqrt(195) = 13.964.

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Answer:

3) 2\(x^{2}\) + 3x - 1

Step-by-step explanation:

A quadratic expression is an expression involving a squared term

It can be written as y = a\(x^{2}\) + bx + c, where a ≠ 0

// note that here b and c can be equal to 0

1) 6\(x^{4}\) - 5\(x^{3}\)  + 3\(x^{2}\)  - 7x - 8 is simply incorrect because you can't write in the previously mentioned form. It is a quartic function, since the unknown variable x in forth degree. It can be written as y = a\(x^{4}\) +b\(x^{3}\) +c\(x^{2}\) + dx + e, where a before \(x^{4}\) ≠ 0

2) 5\(x^{3}\)  + 3\(x^{2}\)  - 7x - 8 is simply incorrect because you can't write in the previously mentioned form. It is a cubic function, since the unknown variable x in third degree.

3) 2\(x^{2}\) + 3x - 1 is correct

4) 3x - 1 is incorrect because there is no squared term. You could also say that here a = 0 and write it as y = 0 * \(x^{2}\)  + 3x - 1. It is also called a linear function because if you'd draw a graph, it would be a line

Answer:

2x2 + 3x - 1

Step-by-step explanation:

Answer: 30

180 - x = 180 - 2x + 30

x = 30

Answer:

The measure of the unknown angle is 30°.

Step-by-step explanation:

Let the measure of the unknown angle be x°.

Supplementary angles are two angles whose measures sum to 180°.

Complementary angles are two angles whose measures sum to 90°.

Therefore, the supplement of x° is (180 - x)°, and its complement is (90 - x)°.

Given that the supplement is 30° more than twice its complement:

(180 - x)° = 2(90 - x)° + 30°

To find the measure of the angle, solve the equation:

⇒ (180 - x)° = (180 - 2x)° + 30°

⇒ 180° - x° = 180° - 2x° + 30°

⇒ 180° - x° = 210° - 2x°

⇒ 180° - x° + 2x° = 210° - 2x° + 2x°

⇒ 180° + x° = 210°

⇒ 180° + x° - 180° = 210° - 180°

⇒ x° = 30°

Therefore, the measure of the unknown angle is 30°.

lamo thought it said terrorists

Answer:

1000

Step-by-step explanation:

The easiest way to go about this is by turning our number into ABCD.

A will be in the 1000th spot, B 100th, C 10th, and D 1st.

A has to be ≥ 5. So 5, 6, 7, 8, 9.

B has to be a prime number. 2, 3, 5, 7.

C is able to be any number it wants, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Since the number is odd, D has to be 1, 3, 5, 7, 9.

A has 5 different possibilities. B has 4, C has 10, and D has 5.
You'll then multiply all of these numbers for your answer.
5 * 4 * 10 * 5 = 1000

Answer:

x=7     x=-5

Step-by-step explanation:

x^2 – 2x – 35 = 0

Factor

What two numbers multiply to -35 and add to -2

-7*5 = -35

-7+5 = -2

(x-7) (x+5 ) =0

Using the zero product property

x-7 =0   x+5 =0

x=7     x=-5

Answer: {7,-5}

Step-by-step explanation: To solve the equation x² - 2x - 45 = 0, factor the left side of the equation to get (x - 7)(x + 5).

To factor x² - 2x - 35, look for factors of -35 that that add to -2.

These factors are -7 and 5.

So now we have (x - 7)(x + 5) = 0.

So either x - 7 = 0 or x + 5 = 0.

Solving for x in each equation, our answer is {7,-5}.

Answer:

21

Step-by-step explanation:

It landed on 4 and 5 about 37% of the time with 240 rolls. So since 60 is 1/4 of 240, we just divided the number of times it landed on 4 and 5 by 4. So since it landed on 4 or 5 84 times, we divide 84 by 4

84 ÷ 4 = 21

So the number of times the cube will land on 4 or 5 is 21