How do you divide 8 out of 5

Using the cosine rule, the distance the plane has flown during Jack's phone call can be calculated by taking the square root of the sum of the squares of the initial and final distances, minus twice their product, multiplied by the cosine of the angle difference.

To determine the distance the plane has flown during Jack's phone call, we can use the cosine rule in trigonometry.

The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Let's denote the initial distance from Jack to the plane as d1 and the final distance as d2.

We know that the altitude of the plane remains constant at 2400 meters.

According to the cosine rule:

\(d^2 = a^2 + b^2 - 2ab \times cos(C)\)

Where d is the side opposite to the angle C, and a and b are the other two sides of the triangle.

For the initial angle of elevation (70°), we have the equation:

\(d1^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \timescos(70)\)

Similarly, for the final angle of elevation (50°), we have:

\(d2^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \times cos(50)\)

To find the distance the plane has flown, we subtract the two equations:

\(d2^2 - d1^2 = 2 \times 2400 \times a \times (cos(70) - cos(50))\)

Now we can solve this equation to find the value of a, which represents the distance the plane has flown.

Finally, we calculate the square root of \(a^2\) to find the distance in meters.

It's important to note that the angle of elevation assumes a straight-line path for the plane's movement and does not account for any changes in altitude or course adjustments that might occur during the phone call.

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Ella's Grade: 15

Minh's Grade: 16

Step-by-step explanation:

If each grade has 20 girls in the grade, then that implies effectively that the ratios would apply via fractions, which are 3:4 and 4:5. As such, take both Fractions and increase them both to 20: 15:20 and 16:20.

Answer:

Number of quarters with Pablo = 4

Number of quarters with Laqueta = 12

Step-by-step explanation:

Given that:

Laqueta has three times as many quarters as Pablo.

They both spend $0.50.

After that Laqueta will have 5 times as many quarters as Pablo.

To find:

Number of quarters with Laqueta and Pablo now?

Solution:

Let number of quarters with Laqueta = \(x\)

Let number of quarters with Pablo = \(y\)

As per given statement:

\(x=3y ..... (1)\)

In $0.50, there are 2 quarters:

After spending $0.50, number of quarters left with both of them:

Number of quarters left with Laqueta = \(x\) - 2 =  \(3y-2\)

Money left with Pablo = \(y\) - 2

As per given statement:

\(3y-2 = 5(y-2)\\\Rightarrow 3y-2 = 5y-10\\\Rightarrow 2y = 8\\\Rightarrow y = 4\)

Therefore, the answer is:

Number of quarters with Pablo = 4

Number of quarters with Laqueta = \(3 \times 4\) = 12

The domain and the range of a graph are the set of input and output values  on the graph

On the graph, the x values starts at x = -3  (with a closed circle), and it ends at x = 2 (with an open circle)

This means that, the domain of the graph is [-3,2)

On the graph, the y values starts at y = -5, and it ends at y = 4 (with an open circle)

This means that, the range of the graph is (-5,4)

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The absolute maximum and minimum for the function f(x) = x^4 - 4x^3 - 10 are as follows: (A) on the interval [-1,1], there is no absolute maximum; (B) on the interval [0,4], the absolute maximum occurs at x = 2; (C) on the interval [-1,2], the absolute maximum occurs at x = 2.

To find the absolute maximum and minimum of the function, we need to analyze the critical points and the endpoints of the given intervals.
(A) On the interval [-1,1], we first find the critical points by taking the derivative of f(x) and setting it equal to zero: f'(x) = 4x^3 - 12x^2 = 0. Solving this equation, we get x = 0 and x = 3. However, since 3 is not within the interval [-1,1], there are no critical points in the interval. Therefore, we check the endpoints of the interval, which are f(-1) = -14 and f(1) = -12. The function does not have an absolute maximum in this interval.
(B) On the interval [0,4], we find the critical points by setting f'(x) = 0: 4x^3 - 12x^2 = 0. Solving this equation, we find x = 0 and x = 3. However, 0 is not within the interval [0,4]. Therefore, we check the endpoints: f(0) = -10 and f(4) = 26. The absolute maximum occurs at x = 2, where f(2) = 2^4 - 4(2)^3 - 10 = 2.
(C) On the interval [-1,2], we find the critical points by setting f'(x) = 0: 4x^3 - 12x^2 = 0. Solving this equation, we get x = 0 and x = 3. However, 3 is not within the interval [-1,2]. We check the endpoints: f(-1) = -14 and f(2) = -10. The absolute maximum occurs at x = 2, where f(2) = 2^4 - 4(2)^3 - 10 = 2.
Therefore, the answers are: (A) No absolute maximum, (B) Absolute maximum at x = 2, and (C) Absolute maximum at x = 2.

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Answer:or point  A (-2, 3) is (-8,12).

Step-by-step explanation:

The missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x is step 6: The division property of inequality: x > -9

The missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x is step 6: The division property of inequality.

After step 4, which is -2x < 18, we need to divide both sides of the inequality by -2 to solve for x.

However, since we are dividing by a negative number, the direction of the inequality sign needs to be reversed.

Dividing both sides by -2:

-2x / -2 > 18 / -2

This simplifies to:

x > -9

Therefore, the correct answer is x > -9.

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The independent variable, denoted by "t" or any other variable, represents the variable with respect to which the differentiation is performed.To find the general solution to the system of linear differential equations, we need to know the specific equations and the given eigenvalue and eigenvector.

To solve the system, follow these steps:
1. Write down the system of linear differential equations, which should include the derivatives of the variables involved.
2. Find the eigenvalue λ given in the problem.
3. Use the eigenvalue to find the corresponding eigenvector v.
4. Plug the eigenvector into the system of equations and set it equal to λ times the eigenvector.
5. Solve the resulting system of linear equations for the variables involved.
6. Express the variables in terms of the eigenvalue and other constants if necessary.
7. Combine the solutions for the variables to form the general solution.
Without the specific equations and the given eigenvalue and eigenvector, it is not possible to provide a concrete solution. Make sure to provide the necessary information for a more accurate answer.

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Linear differential equations involve derivatives with respect to an independent variable. Eigenvalues and eigenvectors play a crucial role in solving these equations and determining their behavior.

Linear differential equations are equations that involve derivatives of an unknown function with respect to an independent variable. The order of a linear differential equation is determined by the highest derivative present in the equation.  The independent variable is the variable with respect to which the derivative is taken. For example, in the equation dy/dx + 2y = 0, x is the independent variable.

An eigenvalue is a scalar value λ that satisfies the equation Ax = λx, where A is a square matrix and x is a non-zero vector. In the context of linear differential equations, eigenvalues play a crucial role in finding solutions.
An eigenvector is a non-zero vector x that satisfies the equation Ax = λx, where A is a square matrix and λ is an eigenvalue. Eigenvectors correspond to the eigenvalues and help determine the behavior of the system.

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Complete Question:

Explain linear differential equations, independent variable, eigenvalue and eigenvector.

Answer:

7743 caught you again lolllll

Answer:

\(\theta=65.82^{\circ}\)

Step-by-step explanation:

Given that,

Perpendicular = 49 ft

Base = 22 ft

We need to find the angle of elevation of the sun. It can be calculated using trigonometry as follows :

\(\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{49}{22}\\\\\theta=65.82^{\circ}\)

So, the required angle of elevation is \(65.82^{\circ}\).

Answer:

(2x+5)(x+4)

Step-by-step explanation:

After factoring we can find that it equals

(2x+5)(x+4)

Answer:

(2x +5) (x+4)

Step-by-step explanation:

2x*2+13x+20

(2x +   )(x+  )

Factoring 20 into 4 and 5  so we can get 13 in the middle

(2x +5) (x+4)

2*4 +5 = 13 for the middle term

Answer:

The answer is option B.

A = pi • 8^2

Step-by-step explanation:

The formula for area of a circle as A = pi • r^2. Radius is half the diameter, and the given diameter is 16 - therefore, the radius is 8. You then have to raise it to the second power and multiply it by pi to get the area of the circle. Hope this helped! Best of luck.

Answer:

The ameliorated retort, concerning the contemporaneous presented interrogate, is equated to an equation equivalence of B. A= π * 8^2

Step-by-step explanation:

To convey the ideology and retort proposed, the imminent is evaluated.

- To commence, the beginning of the interrogate states the figure obtains a diameter configuration of 16 inches.

- In addition, the radius, given which the diameter is equivalent to such, is obligated to equal 8 inches (r = 1/2(d)).

Furthermore, the precedent may be equated as the following:

A=πr^2

A= π * 8^2, whom is expressed to the unit of A = π * 64

Alas, in conclusion, the voracious retort, subject to the interrogate is equivalent to A = π * 8^2, A = π * 64, or "B."

I hope this helps.

Yes, there is sufficient evidence to refute the publisher's claim that 20% of their readers own a Rolls Royce at the 0.01 level.

The hypothesis test result indicates that the p-value is less than 0.01, which means the null hypothesis can be rejected at a 0.01 level of significance. Therefore, there is evidence to suggest that the true percentage of Rolls Royce owners among the newsletter publisher's readers is less than 20%. This could have implications for the publisher's advertising strategy and target audience.

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Answer: 2/3

Step-by-step explanation:

Slope is rise over run. From red point to first blue point you go up 2 and over 3.

Answer:

Step-by-step explanation:

Answer: 2.074

can also be written as a fraction 2  37/500

There are 1023 ways a person can toss a coin 11 times so that the number of tails is between 6 and 10 inclusive.

To determine the number of ways a person can toss a coin 11 times with the number of tails between 6 and 10 inclusive, we need to sum up the number of ways for each possible number of tails within that range.

Number of ways to get 6 tails:

This can be calculated using the binomial coefficient formula: C(n, k), where n is the total number of tosses (11) and k is the number of tails (6).

C(11, 6) = 462

Number of ways to get 7 tails:

C(11, 7) = 330

Number of ways to get 8 tails:

C(11, 8) = 165

Number of ways to get 9 tails:

C(11, 9) = 55

Number of ways to get 10 tails:

C(11, 10) = 11

To find the total number of ways, we sum up the individual counts:

462 + 330 + 165 + 55 + 11 = 1023

Therefore, there are 1023 ways a person can toss a coin 11 times so that the number of tails is between 6 and 10 inclusive.

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To find f(-8) and f(6), all that we need to do is plug in each of the numbers for x.

f(-8) = -8 - 1 = -9

f(-8) = -9

f(6) = 6 - 1 = 5

f(6) = 5

Hope this helps!

If f(-x) = x - 1, then f(x) = - x - 1. So

f(-8) = 8 - 1 = 7

and

f(6) = - 6 - 1 = -7

(-4 + 7i)² = 9 + 56i ; Where x + iy is complex form.

To find the square of (-4 + 7i), we can use the formula for squaring a complex number, which states that (a + bi)² = a² + 2abi - b².

In this case, a = -4 and b = 7. Applying the formula, we have:

(-4 + 7i)² = (-4)² + 2(-4)(7i) - (7i)²

= 16 - 56i - 49i²

Since i² is equal to -1, we can substitute -1 for i²:

(-4 + 7i)² = 16 - 56i - 49(-1)

= 16 - 56i + 49

= 65 - 56i

So, (-4 + 7i)² simplifies to 65 - 56i.

If we multiply the result by 4, we get:

4(-4 + 7i)² = 4(65 - 56i)

= 260 - 224i

Therefore, 4(-4 + 7i)² is equal to 260 - 224i.

The square of (-4 + 7i) is 65 - 56i. Multiplying that result by 4 gives us 260 - 224i.

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find dy/dx

x= t sin(t); (Given in the question)

y= t²+8t; (Given in the question)

then, x= t sin(t)

dx/dt = sin t + t cos t ;

y= t²+8t

dy/dt = 2t + 8;

then, dy/dx = dy/dt x dx/dt

dy/dx = (2t+8)/(sin t + t cos t)

dy/dx = 2(t+4)/(sin t + t cos t)

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Answer

• a) Range: (-∞, –1)

• b) Horizontal asymptote when x ≤ 2: y = –3. Vertical asymptote when x > 2: x= 2. Horizontal asymptote when x > 2: y = –1.

• c) When x decreases, it approaches –3, and when x increases, it approaches –1.

Explanation

• Part A: Graph the piecewise function f (x) and determine the range.

Using a graphing tool we can get the following graph:

As the range is all the y-values included in the function, we can see that in this case, the range is:

• Part B: Determine the asymptotes of f (x). Show all necessary calculations.

We have to get the asymptotes from the part where x ≤ 2 and x > 2.

In x ≤ 2 we do not have a vertical asymptote as it is not a rational function, but we do have a horizontal asymptote, which is y = k when we have the function:

Thus, in our case y = –3.

In x > 2, we do have a vertical and horizontal asymptote. We can get the vertical asymptote by setting the denominator of the function to 0:

If we solve the expression by factoring we get two solutions:

Based on our function we can see that the vertical asymptote is x = 2 when x > 2. Then, the horizontal asymptote can be calculated with the limit:

Thus, our horizontal asymptote is y = –1 when x > 2.

• Part C: Describe the end behavior of f (x).

The end behavior of a function is how the function acts when x increases or decreases. Based on our graph we can see that when x decreases, it approaches –3, and when x increases, it approaches –1.

Answer:

x = 3

Step-by-step explanation:

Simplify both sides of the equation, then isolate the variable.

Answer:

i love uuuuuuuuuuuuuuuuuuuuuuuu

Step-by-step explanation:

The statement "D. Given any two distinct lines in the Cartesian plane, the two lines will either be parallel or perpendicular" is NOT true.

A. The statement is true. The ratios of the vertical rise to the horizontal run, also known as the slopes, of any two distinct nonvertical parallel lines are equal. This is one of the properties of parallel lines.

B. The statement is true. If two distinct nonvertical lines are parallel, then they have the same slope. Parallel lines have the same steepness or rate of change.

C. The statement is true. Given two distinct lines in the Cartesian plane, the two lines will either intersect at a point or they will be parallel and never intersect. These are the two possible scenarios for distinct lines in the Cartesian plane.

D. The statement is NOT true. Given any two distinct lines in the Cartesian plane, they may or may not be parallel or perpendicular. It is possible for two distinct lines to have neither parallel nor perpendicular relationship. For example, two lines that have different slopes and do not intersect or two lines that intersect but are not perpendicular to each other.

Therefore, the statement "D. Given any two distinct lines in the Cartesian plane, the two lines will either be parallel or perpendicular" is the one that is NOT true.

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\(3\sqrt{2} - 4 * (\sqrt{2})^2 = 3\sqrt{2} - 8\)

Answer = \(3\sqrt{2} - 8\)

The 95% upper bound represents the value below which 95% of the data falls. In this case, we have X ~ N(70,38), which means that X follows a normal distribution with a mean of 70 and a standard deviation of 38.

To find the 95% upper bound, we need to find the z-score associated with the 95th percentile.

The z-score can be calculated using the formula:
z = (x - μ) / σ

Where:
x is the value we want to find the z-score for,
μ is the mean of the distribution, and
σ is the standard deviation of the distribution.

In this case, we want to find the z-score corresponding to the 95th percentile, which is 1.645. However, the critical value given is 1.69, which is slightly higher than 1.645. Therefore, we will use the critical value of 1.69 instead.

Now, we can rearrange the formula to solve for x:
x = z * σ + μ

Plugging in the values, we have:
x = 1.69 * 38 + 70

Calculating this, we find that the 95% upper bound is approximately 135.1.
Therefore, we can say with 95% confidence that X will be less than approximately 135.1.

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The magnitude and direction of the initial magnetic force acting on the bar as it slides to the right

Magnetic force, attraction or repulsion that arises between electrically charged particles because of their motion. It is the basic force responsible for such effects as the action of electric motors and the attraction of magnets for iron.                                                                        Can be calculated using the equation F = qvB sinθ, where F is the magnitude of the magnetic force, q is the charge, v is the velocity, B is the magnetic field, θ is the angle between the velocity and the magnetic field. Therefore, the magnitude of the magnetic force is qvB sinθ, and the direction is in the same direction as the magnetic field vector.

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To choose the addition problems in which you add zeros to align place values in the addends, let's go through each option:

a. 6.23 + 11.01 + 4.99
In this problem, you need to add zeros to align the place values. Let's write it out:

  6.23
+11.01
+ 4.99
_______
 22.23

b. 15.03 + 23.23
In this problem, the place values are already aligned, so you don't need to add any zeros. Let's add the numbers:

  15.03
+ 23.23
_______
  38.26

c. 0.04 + 5 + 3.2
Here, the place values are not aligned. To align them, we need to add a zero to 5 and 3.2. Let's rewrite the problem:

  0.04
+ 5.00
+ 3.20
_______
  8.24

d. 1.2 + 5.75 + 2.8
In this problem, the place values are already aligned, so no need to add any zeros. Let's add the numbers:

  1.20
+ 5.75
+ 2.80
_______
  9.75

e. 18.9 + 0.7
The place values are already aligned, so no need to add any zeros. Let's add the numbers:

  18.90
+  0.70
_______
  19.60

Based on the analysis above, the addition problems in which you add zeros to align place values in the addends are:
a. 6.23 + 11.01 + 4.99
c. 0.04 + 5 + 3.2

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Answer:

The angle between u and v is π/3 and parallel-to u plus v parallel-to = k*(u+v) (where k=const)

Step-by-step explanation:

In this question, one is expected to find the angle between u and v, and to get this angle, I will use the triangle formula.

|u-v|^2 = |u|^2 + |v|^2 - 2*|u|*|v|*cosθ

(2√2)² = (2√2)² + (2√2)² - 2(2√2)*(2√2)*cosθ

Expanding (2√2)² = (2√2)*(2√2) = 2*2*2 = 8

8 = 8 + 8 - 16*cosθ

8 = 16 - 16*cosθ

8 - 16 = -16*cosθ

-8 = -16*cosθ

cosθ = 8/16 = 1/2 = 0.5

θ = cos^(-1) (0.5)

θ = π/3

The angle between u and v is π/3 and parallel-to u plus v parallel-to = k*(u+v) (where k=const)

Using the central limit theorem, for different sample sizes, we find the probabilities Pr(Y < 68) ≈ 0.9439, Pr(68 < Y < 69) ≈ 0.0590, and Pr(Y > 66) ≈ 0.0228.

a) In a random sample of size n = 69, we can approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 69 ≈ 0.7101. To find Pr(Y < 68), we calculate the z-score using the formula z = (x - μ) / σ, where x is the value we want to find the probability for.

z = (68 - 65) / √(0.7101) ≈ 1.5953

Using a standard normal distribution table or a calculator, we find the probability associated with z = 1.5953 to be approximately 0.9439. Therefore, Pr(Y < 68) ≈ 0.9439.

b) In a random sample of size n = 124, we can again approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will still be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 124 ≈ 0.3952. To find Pr(68 < Y < 69), we calculate the z-scores for the lower and upper limits.

Lower z-score: z1 = (68 - 65) / √(0.3952) ≈ 1.5225

Upper z-score: z2 = (69 - 65) / √(0.3952) ≈ 2.5346

Using the standard normal distribution table or a calculator, we find the probability associated with z1 = 1.5225 to be approximately 0.9357 and the probability associated with z2 = 2.5346 to be approximately 0.9947. Therefore, Pr(68 < Y < 69) ≈ 0.9947 - 0.9357 ≈ 0.0590.

c) In a random sample of size n = 196, we can once again approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will still be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 196 ≈ 0.2500. To find Pr(Y > 66), we calculate the z-score.

z = (66 - 65) / √(0.2500) = 2

Using the standard normal distribution table or a calculator, we find the probability associated with z = 2 to be approximately 0.9772. Therefore, Pr(Y > 66) ≈ 1 - 0.9772 ≈ 0.0228.

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