I need a step-by-step explanation.
(x+y)/(2x-y)-(2x)/(y-2x)
(3x)/(x^2+x-12)-(x)/(x^2-16)

Answer:

3

Step-by-step explanation:

The distance traveled in the first 2 seconds is 48 units, given the units of the velocity function.

To calculate the distance traveled during the time interval [0, 2] seconds, we need to integrate the velocity function over that interval. From part (d), we have the velocity function: v(t) = -16t + 40. To find the distance traveled, we integrate the absolute value of the velocity function over the interval [0, 2]: Distance = ∫[0, 2] |v(t)| dt. Using the given velocity function, we have: Distance = ∫[0, 2] |-16t + 40| dt.

To evaluate this integral, we need to split it into two parts based on the different intervals of the absolute value function: Distance = ∫[0, 2] (16t - 40) dt for 0 ≤ t ≤ 2. Integrating this expression, we get: Distance = [8t^2 - 40t] evaluated from 0 to 2. Plugging in the limits of integration, we have: Distance = [8(2)^2 - 40(2)] - [8(0)^2 - 40(0)]. Simplifying, we find: Distance = [32 - 80] - [0 - 0];Distance = -48. Therefore, the distance traveled in the first 2 seconds is 48 units, given the units of the velocity function.

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Answer:

Step-by-step explanation:

It's right

Answer:

x=-4.5 x=-0.5

y=-1

vertex=-2

Answer:

\( \sqrt{44} \)

Answer:

44

Step-by-step explanation:

\(7\frac{1}{2}\implies 7.5\hspace{5em}1\frac{1}{4}\implies 1.25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Monday through Friday} }{\stackrel{ days }{(5)}\stackrel{ rate }{(10.80)}\stackrel{ hours }{(7.5)}}~~ + ~~\stackrel{ Saturday }{\stackrel{ days }{(1)}\stackrel{ rate }{(10.80)(1.25)}\stackrel{ hours }{(7.5)}} \\\\\\ 405~~ + ~~101.25\implies \text{\LARGE 506.25}\)

Markov chain model with periodic classes of states can be exemplified by a weather model and ergodic system in a Markov chain is the game of Monopoly.

Example of Markov chain with periodic classes of states:

One example of a Markov chain model with periodic classes of states is a weather model that includes seasonal variations. Let's consider a simplified model with three states: sunny, cloudy, and rainy. In this model, the weather is observed over a long period of time, and it is known that the weather tends to follow a cyclic pattern, transitioning from one season to another. The stochastic matrix representing this Markov chain will have non-zero probabilities for transitions between states within the same season (e.g., sunny to sunny, cloudy to cloudy, rainy to rainy), but zero probabilities for transitions between states in different seasons (e.g., sunny to rainy, rainy to cloudy). This creates periodic classes or groups of states that correspond to the different seasons, resulting in a Markov chain with periodic behavior.

Example of ergodic system in a Markov chain:

A common example of an ergodic system in a Markov chain is the game of Monopoly. In Monopoly, players move around the board based on the outcome of rolling dice. The states in this Markov chain correspond to the positions on the board. Each roll of the dice determines the transition probabilities from one state (position) to another. In an ergodic system, it means that it is possible to reach any state from any other state in a finite number of steps. In the context of Monopoly, this means that players can move from any position on the board to any other position by rolling the dice and following the game rules. The stochastic matrix for this Markov chain will have non-zero probabilities for transitions between all states, reflecting the possibility of moving to any position on the board from any other position.

In summary, a Markov chain model with periodic classes of states can be exemplified by a weather model that represents the cyclic nature of seasons, while an example of an ergodic system in a Markov chain is the game of Monopoly, where players can reach any position on the board from any other position through successive dice rolls and gameplay.

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The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.

In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.

The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.

Regarding the other statements:

In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.

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Answer:

What's the context???

Step-by-step explanation:

I don't understand oof

Answer:

The value of x is 8.1

Step-by-step explanation:

We can use SOH CAH TOA to find our answer.

In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse. S is for the SIN function. C is for the COS function. T is for the TAN function.

We can calculate the length of the string by using the COS function.

So we can say the tangent of angle \(\beta\) is the opposite side divided by the adjacent side.

\(tan( \beta)=\frac{O}{A}\)

We are given the angle and the opposite side. We are looking for the adjacent side.

Lets solve for \(A\).

Take the reciprocal of both sides.

\(\frac{1}{tan(\beta)} =\frac{A}{O}\)

Multiply both sides by \(O\).

\(\frac{1}{tan(\beta)} *O=A\)

We are given

\(\beta=56\textdegree \\O=12\)

\(\frac{1}{tan(56)} *12=A\)

\(A=8.0941022\)

Answer:

y = 70x

Step-by-step explanation:

Answer:

Angle 1 is 135 degree

Angle 2 is 45 degree

Angle 3 is 135 degree

negative; The inverse function will have a slope that is the negative reciprocal of the original function.

A linear function is a function that can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept. A linear function with a negative slope will have an inverse function. The inverse function will have a slope that is the negative reciprocal of the original function. For example, if the original linear function has a slope of -2, the inverse function will have a slope of 1/2. The inverse function will also have a y-intercept that is the negative reciprocal of the original function's y-intercept. The inverse function will be of the same form, y = mx + b, but with a different m and b than the original function. The inverse function will have the same x-intercept as the original function. Knowing the slope and y-intercept of the original linear function allows us to calculate the slope and y-intercept of the inverse function.

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Answer:

x = 17.2

Step-by-step explanation:

\(x = 21 \: cos 35 \degree \\ \\ x = 17.20219293 \\ \\ x = 17.2\)

Answer:

17.2

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos = adjacent/ hypotenuse

cos 35 = x/21

21 cos 35 =x

17.2021293=x

Rounding to the nearest tenth

17.2

Answer:

c= sqrt149; 12.2 rounded

Step-by-step explanation:

Pythagorean Theorem to find c(hypotenuse): a^2+b^2=c^2

7^2+10^2=149

sqrt149= 12.2 rounded

a. S is linearly dependent over R.

b. The dimension of Span(S) is 2 since we have a basis with 2 vectors.

c. The basis of R* that contains S is {(1, 0, -1, -1), (1, -1, 1, 2), (1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1)}.

a) To show that S is linearly dependent over R, we need to demonstrate that there exist coefficients c₁, c₂, c₃ such that at least one of them is non-zero and the linear combination c₁v₁ + c₂v₂ + c₃v₃ equals the zero vector.

Let's set up the equation:

c₁(1, 0, -1, -1) + c₂(1, -1, 1, 2) + c₃(5, 2, -9, -11) = (0, 0, 0, 0)

Expanding this equation component-wise, we have:

c₁ + c₂ + 5c₃ = 0 (1)

-c₂ + 2c₃ = 0 (2)

-c₁ + c₂ - 9c₃ = 0 (3)

-c₁ + 2c₂ - 11c₃ = 0 (4)

Now, we can solve this system of linear equations. Adding equation (1) to equation (2) gives:

c₁ + c₂ + 5c₃ - c₂ + 2c₃ = 0

c₁ + 3c₃ = 0

Substituting this result into equation (3), we get:

-(c₁ + 3c₃) + c₂ - 9c₃ = 0

-c₁ + c₂ - 6c₃ = 0

Adding equation (4) to this equation gives:

-(c₁ + 3c₃) + c₂ - 6c₃ + 2c₂ - 11c₃ = 0

3c₂ - 20c₃ = 0

c₂ = (20/3)c₃

Now, substituting c₂ = (20/3)c₃ into equation (1), we have:

c₁ + (20/3)c₃ + 5c₃ = 0

c₁ + (35/3)c₃ = 0

c₁ = -(35/3)c₃

From these equations, we can see that for any value of c₃, c₁ and c₂ are determined accordingly, which means there are infinitely many solutions to the system of equations.

Therefore, S is linearly dependent over R.

b) To determine a basis of Span(S), we need to find a set of vectors in S that spans the entire space of S.

From the equation we obtained in part (a), we can see that the vectors in S are not linearly independent, so we can remove one of them without changing the span. Let's remove one vector, for example, (5, 2, -9, -11).

Now, we have two vectors remaining in S: {(1, 0, -1, -1), (1, -1, 1, 2)}.

We can check that these two vectors are linearly independent. Therefore, they form a basis for Span(S).

The dimension of Span(S) is 2 since we have a basis with 2 vectors.

c) To determine a basis of R* that contains S, we need to find additional vectors that, when combined with the vectors in S, span R*.

One possible basis of R* that contains S is the standard basis for R⁴: {(1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1)}.

Therefore, a basis of R* that contains S is:

{(1, 0, -1, -1), (1, -1, 1, 2), (1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1)}.

Note: R* refers to the vector space R⁴ in this context.

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The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The given road rises 3 yards for every 16 yards measured on the surface of the road. We have to determine how far does a car travel horizontally when it travels 3.5 miles along the road. 1 mile = 1760 yards Therefore, 3.5 miles

= 3.5 × 1760 yards

= 6160 yards

A road rises 3 yards for every 16 yards measured on the surface of the road.We need to find the distance a car travels horizontally

=\((distance\,travelled\,horizontally)^2 + (distance\,travelled\,vertically)^2

= (distance\,travelled)^2\)Let the distance a car travels horizontally

= x

We know, the road rises 3 yards for every 16 yards measured  on the surface of the road. Therefore, the distance a car travels vertically

= \(\frac{3}{16}\) × distance a car travels horizontally

= \(\frac{3x}{16}\)

Using the Pythagorean Theorem,

=\(x^2 + \left(\frac{3x}{16}\right)^2

= (6160)^2\)\(x^2 + \frac{9x^2}{256}

= (6160)^2\)\(\frac{265x^2}{256}

= (6160)^2\)x²

= \(\frac{256 × 6160^2}{265}\)x

= \(\sqrt{\frac{256 × 6160^2}{265}}\)x

= 8926.03 yards

Therefore, the car travels 8926.03 yards horizontally when it travels 3.5 miles along the road. 1 yard = 0.000568182 miles

Therefore, the distance a car travels horizontally = 8926.03 × 0.000568182= 5.0761 miles (rounded to four decimal places) Hence, the car travels 5.0761 miles horizontally when it travels 3.5 miles along the road.

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Answer:

2x-y-4=0

3x+y-6=0

Step-by-step explanation:

I hope it helps you

An compound inequality that describes the acceptable weights for a 20 oz box is 19.25 ≤ x ≤ 20.75.

The absolute value of a number is defined as its magnitude irrespective of the sign of the number. To determine the absolute value of a real number, we consider only the number and remove the sign. It can only be a non-negative value.

We are Given that, cereal manufacturer has a tolerance of 0.75 oz for a box of cereal that is supposed to weigh 20 oz.

Let the weight of cereal box be; w

Now, the inequality is

20-0.75 ≤ x ≤ 20+0.75

Add 20 on both sides of an inequality, we get

19.25 ≤ x ≤ 20.75

Here, 19.25 ≤ x ≤ 20.75

Therefore, an absolute value inequality to find the range of acceptable weights is 19.25 ≤ x ≤ 20.75.

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Answer:

8

Step-by-step explanation:

We know that angles in a triangle add up to 180, so:

5x-60+2x+40+3x-80=180

Simplify

10x-100=180

Solve

Subtract 100 from both sides

10x=80

Divide 80 by 10 to find x

x=8

Answer:

Step-by-step explanation:

The linear function in this case:

We have:

Find the value of b:

The equation is now:

Find the value of y when x = 18:

Answer:

4

Step-by-step explanation:

Answer:2+2 = 4.............

Answer:

16.95%

Step-by-step explanation:

Enjoy your day !

to equal y positions

first you need to equal the equalities that defines y positions

therefore:

\( \frac{ x}{2} + 2 = x + 1\)

this means x = 2 if y positions are equal

so y = 3

(2,3)

you can easily find it by just looking at the graph

Part (a)

Answer: 42

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

Work Shown:

The angle ABC is 90 degrees since AB and BC are perpendicular. The two segments form a right angle. Therefore, the three pieces of the angle must add to 90

24+x+24 = 90

x+48 = 90

x+48-48 = 90-48 ... subtracting 48 from both sides

x = 42

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

Part (b), subpart (i)

Angle q is congruent to the 135 degree angle because they are vertical angles.

Vertical angles are opposite angles formed by the X shape when two lines cross, and vertical angles are always the same measure.

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

Part (b), subpart (ii)

Answer: 225

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

Reasoning:

The four angles p,q,r and the 135 all add to 360, so,

p+q+r+135 = 360

subtract 135 from both sides so we isolate the "p+q+r" and that leads to

p+q+r+135 = 360

p+q+r+135-135 = 360-135

p+q+r = 225

In a curvilinear regression model, the squared term of the predictor variable represents the curvilinear effect.

In a curvilinear regression model, the relationship between the predictor variable and the response variable is not linear but exhibits a curvilinear pattern. To capture this non-linear relationship, the model includes a squared term of the predictor variable.

The squared term of the predictor variable allows the regression model to account for both the linear and curvilinear components of the relationship.

It introduces a curvilinear effect by capturing the curvature or non-linear pattern observed in the data. This squared term enables the model to better fit the data points that deviate from a simple linear relationship.

By including the squared term in the curvilinear regression model, the relationship between the predictor and response variables can be characterized by a more flexible curve, allowing for a better representation of the underlying relationship

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8x - 3 is a factor of the polynomial 48x² - 26x + 3. The correct answer is a

To determine if any of the given options is a factor of the polynomial 48x² - 26x + 3, we can substitute the values of x from each option into the polynomial and check if the result is equal to zero.

a. 8x - 3

Substituting x = 3/8:

48(3/8)² - 26(3/8) + 3 = 27/4 - 39/4 + 3 = 0

b. 12x - 1

Substituting x = 1/12:

48(1/12)² - 26(1/12) + 3 = 1/3 - 13/6 + 3 = 7/6 ≠ 0

c. 4x - 3

Substituting x = 3/4:

48(3/4)² - 26(3/4) + 3 = 27 - 39/2 + 3 = 21/2 ≠ 0

Therefore, 8x - 3 is a factor of the polynomial 48x² - 26x + 3. The correct answer is a

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