Encuentre la derivada de f(x)=eˣ(x²+2)

To find the determinant of the given matrix, we use the formula for a 2x2 matrix, Therefore, the determinant of the given matrix is 3/40.

Determinant = (a * d) - (b * c)

Here, a = 3/10, b = 1/5, c = 1/8, and d = 1/3

Determinant = (3/10 * 1/3) - (1/5 * 1/8)

Determinant = 1/10 - 1/40

Determinant = 4/40 - 1/40

Determinant = 3/40

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Answer:

The cost of one-month gameplay is $39.33 or 39.

Step-by-step explanation:

Let the cost of one month = x

The cost of software = $50

The total amount that can be spent = $218

Therefore, we have to find the cost of one month of game play. Here is the following equation.

218 = (50 + x) + (50 + 2x)

218 = 100 + 3x

218 – 100 = 3x

118 = 3x

x = 118 / 3

x = 39.33 or 39

thus, the cost of one-month gameplay is $39.33 or 39.

Answer:

80 degrees

Step-by-step explanation:

What we see in this drawing is a triangle formed by three lines. In order to solve this problem, we need to know that when two lines intersect, the two angles formed are supplementary (meaning they add up to 180 degrees). For example, the 150-degree angle, and the angle right next to it (the angle on the left side of the triangle) add up to 180 degrees. This means that the left-most angle of the triangle is 180-150, which is 30 degrees

We can figure out the topmost angle of the triangle using the same method. We know that the angle outside the triangle is 130 degrees, so the angle right next to it (in this case, right below it), is 180-130, or 50 degrees.

Next, we use the fact that triangles are 180 degrees on the inside to figure out the third angle (the one on the right, right next to angle 1). We know that the other two angles are 30 and 50 degrees, and if you add that up, you get 80 degrees. The last angle, then, is 180-80, or 100 degrees.

Lastly, we know that the rightmost angle of the triangle and angle 1 add up to 180 degrees. In other words, 100+Angle1=180. Therefore, Angle 1 is 180-100 or 80 degrees.

Answer:

ab=42

Step-by-step explanation:

42-6=36

36/4=9

7x9=63+15=78

78+42=120

4x9=36+6=42

To graph a rational function example, start by writing the equation in the form y = (ax + b)/(cx + d).

Then, plot the points where the denominator equals zero (when x = -d/c). These points are called vertical asymptotes.Next, plot the points where the numerator equals zero (when x = -b/a). These are called horizontal asymptotes.Finally, plot points between the vertical and horizontal asymptotes to graph the rational function.Plotting the points between the vertical and horizontal asymptotes will allow you to see the shape of the graph. Start by plotting points on either side of the vertical and horizontal asymptotes. Then, plot points at evenly spaced x-values between the vertical and horizontal asymptotes. For example, if the vertical asymptote is at x=-d/c, and the horizontal asymptote is at x=-b/a, you can plot points at x=-1.5d/c, x=-0.5d/c, x=-1.5b/a, and x=-0.5b/a. By plotting these points and connecting them with a smooth curve, you can graph the rational function.

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Comparing the bookmarks, it is calculated that Mateo can make more 9/10 more orange bookmarks than aqua bookmarks

The number of bookmark each color can make is solved using division

If each bookmark is 1/6 yard then

aqua will make 3/4 / 1/6 = 9/2 bookmarks

Orange will make 9/10 / 1/6 = 27/5 bookmarks

The number of more orange bookmarks than aqua bookmarks

= 27/5 bookmarks - 9/2 bookmarks

= 9/10

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The given scenario of rolling a fair die repeatedly until we see the number four appear, and then we stop, is an example of a geometric distribution. The probability that we need at most 3 rolls is 91/216

This can be calculated as follows:

Given that we roll a fair die repeatedly until we see the number four appear and then we stop.

Let X be the number of times the die is rolled until we see the number four. Then X is a geometric random variable with the parameter p = 1/6.

The probability that we need at most 3 rolls is the probability that we get a four on the first, second, or third roll.

P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

The probability of getting a four on the first roll is:

P(X = 1) = (1 - p)^(1-1) * p = (5/6)^0 * 1/6 = 1/6

The probability of getting a four on the second roll is:

P(X = 2) = (1 - p)^(2-1) * p = (5/6)^1 * 1/6 = 5/36

The probability of getting a four on the third roll is:

P(X = 3) = (1 - p)^(3-1) * p = (5/6)^2 * 1/6 = 25/216

Therefore, P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3) = 1/6 + 5/36 + 25/216 = 91/216

The probability that we need at most 3 rolls is 91/216.

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Answer:

down

Step-by-step explanation:

In mathematics a when dealing with graphs a translation is basically just moving points left/right and up/down but it does not change the shape of the original figure in any way just moves its position. In this scenario, the down arrow's tip will be moved from point (2,0) to (-3,1) but the arrow will still be the same size and still be pointing downward.

the equation \(2/3(x+6)=2/3x+4\) has infinitely many solutions, and we can write the solution set as {x | x ∈ ℝ}.

To determine if the equation  \(2/3(x+6)=2/3x+4\) has one solution, we need to simplify the equation and then solve for x.

First, we can simplify the left side of the equation by distributing the 2/3:

\(2/3(x+6) = 2/3x + 4\)

\(2/3x + 4 = 2/3x + 4\)

As we can see, the equation simplifies to  \(2/3x + 4 = 2/3x + 4\) , which means that the left and right sides of the equation are identical. This tells us that the equation has infinitely many solutions.

To understand why the equation has infinitely many solutions, we can rearrange the equation as follows:

\(2/3x + 4 = 2/3x + 4\)

\(2/3x - 2/3x = 4 - 4\)

\(0 = 0\)

As we can see, when we subtract 2/3x from both sides of the equation, we end up with   \(0 = 0,\) which is always true. This means that any value of x will satisfy the equation.

Therefore, the equation  \(2/3(x+6)=2/3x+4\) has infinitely many solutions, and we can write the solution set as {x | x ∈ ℝ}.

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Using empirical rule and z-score formula, approximately 95% of the data falls within two standard deviations of the mean. Therefore, the percentage of scores between 69 and 85 is approximately 95%.

The Empirical Rule, also known as the 68-95-99.7 Rule, is a statistical rule that states that for a bell-shaped distribution:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

To find the percentage of scores between 69 and 85, we need to determine how many standard deviations away from the mean these values are.

The z-score formula is:

z = (x - μ) / σ

where:

x is the score we want to convert to a z-score

μ is the mean of the distribution

σ is the standard deviation of the distribution

For x = 69:

z = (69 - 77) / 4 = -2

For x = 85:

z = (85 - 77) / 4 = 2

This means that 69 is 2 standard deviations below the mean, and 85 is 2 standard deviations above the mean. According to the Empirical Rule, approximately 95% of the data falls within two standard deviations of the mean. Therefore, the percentage of scores between 69 and 85 is approximately 95%.

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As per the given 4 x 5 matrix, the reduced row echelon form of A is \(\left[\begin{array}{ccc}1&2&0\\0&0&1\\0&0&0\end{array}\right]\)

The term matrix in math refers a set of numbers arranged in rows and columns so as to form a rectangular array.

Here we have the 4 x 5 matrix.

And here we also know that a1,a2,a4 are linearly independent and the value of a3=a1+2a² and a5=2a1-a²+3a⁴.

Now, we have to apply the value of

a1 = 1, a2 = 0, a3 = 0, a4 = 0, a5 = 1, a6 = 0, a7 = 0, a8 = 0, and a9 = 1.

Then we get the matrix of 3 x 3 looks like the following,

\(\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\)

Now, we have to do the following steps in order to get the reduced row echelon form of A,

The first and foremost steps is to take the non-zero number in the first row is the number 1.

Then we have to place any non-zero rows are placed at the bottom of the matrix.

This steps are repeated until the final row becomes zero.

Then we get the resulting matrix as \(\left[\begin{array}{ccc}1&2&0\\0&0&1\\0&0&0\end{array}\right]\)

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two whose product is a trinomial is (x + 2)(x + 3) = x^2 + 5x + 6.

We are given two binomials: (x + 2) and (x + 3). To find their product, we need to multiply each term in the first binomial by each term in the second binomial. Let's go step by step:

Step 1: Multiply the first terms:

(x + 2) * (x + 3)

= x * x

= x^2

Step 2: Multiply the outer terms:

(x + 2) * (x + 3)

= x * 3

= 3x

Step 3: Multiply the inner terms:

(x + 2) * (x + 3)

= 2 * x

= 2x

Step 4: Multiply the last terms:

(x + 2) * (x + 3)

= 2 * 3

= 6

Step 5: Combine the like terms:

The terms 3x and 2x are like terms since they both have the variable x. To combine them, we add their coefficients:

3x + 2x

= 5x

Step 6: Write the resulting terms together:

Now, we put all the resulting terms together to form the trinomial:

x^2 + 5x + 6

Therefore, the product of (x + 2)(x + 3) is the trinomial x^2 + 5x + 6.

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Answer:

1.5GB or less

Step-by-step explanation:

68 + 5x <= 75.50

5× <= 75.50 - 68

5x <= 7.50

x <= 1.5 GB

Answer:

5x + 68 = 75.50

x = 1.5

Step-by-step explanation:

5x + 68 = 75.50

75.50 - 68 = 7.5

5x = 7.5

x = 1.5

Answer:

Step-by-step explanation:

The required sample size to ensure that the sample mean is within 0.014 of the population mean at a 99% confidence level is 76,166.

To determine the sample size, we use the range rule of thumb which estimates the standard deviation (σ) as one-sixth of the range (R). In this case, R is 6 - 0 = 6. Thus, σ = 1.5.

The formula for the required sample size (n) is given by:

n = (Z * σ / E)^2

Using a 99% confidence level, the corresponding Z-value is approximately 2.576.

Plugging in the values, we get:

n = (2.576 * 1.5 / 0.014)^2 ≈ 76,166

Therefore, the required sample size is 76,166, which is a fairly large number. This sample size is necessary to achieve a high level of precision and confidence in estimating the population mean.

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Answer:

see graph

Step-by-step explanation:

Personally I put into slope intercept form before graphing

y - 3 = 1/2 (x+2)

y -3 = 1/2x + 1

y = 1/2x + 4

4 is y-intercept    

1/2 is slope. \(\frac{Rise= 1}{Run= 2}\)

Answer:

Any fraction with the same number on both the top and bottom

Step-by-step explanation:

example: 1/1 and 2/2

Answer:

2/2, 10/10

Step-by-step explanation: They all equal one

Answer:  b= x²-8

Step-by-step explanation:

Given:

A= 1/2 b h

A= 1/2 ( x³ + 8x² -8x -64)

h= x+8

Solution:

A= 1/2 b h                                                     >substitute what you know

1/2 ( x³ + 8x² -8x -64) = 1/2 b (x+8)              >simplify

b= \(\frac{x^{3} + 8x^{2} -8x -64}{x+8}\)

There are 2 ways to solve this. You can solve by factoring the polynomial or dividing.

Solution by Division:

Synthetic Division is easiest:

-8   |      1         8         -8         -64

      |                -8          0          64

              1        0           -8          0       =>       x²-8 = b

OR

Solution by Factoring:

b= \(\frac{x^{3} + 8x^{2} -8x -64}{x+8}\)            > group first 2 terms on top and 2nd 2 terms on top

b= \(\frac{(x^{3} + 8x^{2} )( -8x -64)}{x+8}\)       >take out gcf of both groupings

b=\(\frac{x^{2} (x + 8 )-8( x +8)}{x+8}\)           > take out x+8 on top as gcf

b=\(\frac{ (x + 8 )( x^{2} -8)}{x+8}\)                 > cancel x+8 from top and bottom

b= x²-8

Answer:

See below

Step-by-step explanation:

3*7

3(3+4)

3*3 + 3*4

9 + 12

21

The antiderivative of 7ex is 7ex, and the antiderivative of 6 sec2(x) is 6 tan(x). Thus, the most general antiderivative is F(x) = 7ex + 6 tan(x) + C, where C represents the constant of integration.

To find the antiderivative of the given function f(x) = 7ex 6 sec2(x), we integrate each term separately. The antiderivative of 7ex is simply 7ex, as the exponential function ex is its own antiderivative.

Next, we consider the antiderivative of 6 sec2(x). The derivative of the tangent function tan(x) is sec2(x), so the antiderivative of sec2(x) is tan(x). However, there is a coefficient of 6 in front of sec2(x), so the antiderivative becomes 6 tan(x).

Combining these results, we have F(x) = 7ex + 6 tan(x) as the antiderivative of the original function f(x) = 7ex 6 sec2(x). The "+ C" at the end represents the constant of integration, as any constant added to the antiderivative remains undetermined. Therefore, the most general antiderivative of f(x) is F(x) = 7ex + 6 tan(x) + C, where C is a constant.

To verify this result, we can differentiate F(x) and confirm that it indeed yields the original function f(x). Taking the derivative of F(x) with respect to x will give us back 7ex 6 sec2(x), thus confirming the correctness of the antiderivative.

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Answer:

(-6,2)

Step-by-step explanation:

for the reflection just go on the opposite side of the y axis and then it would be negative but then going left 2 more would add to 4.

Answer:

is A

Step-by-step explanation:

I hope and this helps you

The amount of work done by pulling the wagon is approximately 11,000 Joules.

3. To find the amount of work done by pulling the wagon, we need to calculate the dot product of the force applied (tension in the rope) and the displacement of the wagon. The dot product is given by:

Work = Force * Displacement * cosθ

where

θ is the angle between the force and displacement vectors.

Given:

Force (tension in the rope) = 2200 N

Displacement = 10 meters

θ = 60°

First, we need to convert the angle to radians:

theta = 60° * (π/180) ≈ 1.047 radians

Next, we can calculate the work done:

Work = 2200 N * 10 m * cos(1.047)

Work ≈ 2200 N * 10 m * 0.5

Work ≈ 11,000 N∙m or 11,000 Joules

Therefore, the amount of work done by pulling the wagon is approximately 11,000 Joules.

4. This question cannot be solved because of invalid variables.

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(3) The work done by pulling the wagon to the desired distance of 10 m is 11,000 J.

(4) The equation of the line parallel to the plane is 2y + 5x  + 41 = 0.

(3) The work done by pulling the wagon to the desired distance of 10 m is calculated by applying the following formula.

W = Fd

where;

The amount of work done by pulling the wagon 10 meters to the right the rope is calculated as;

W = 2200 N x 10 m x cos (60)

W = 11,000 J

(4) The equation of the line parallel to the plane will have the same slope;

point on the line = (y = -2-1, x = -4 - 3) =  (y = -3, x = -7)

The equation;

5x + 2y + 1 = 2

2y = 1 - 5x

y = 1/2 - 5x/2

The slope of the line , m = -5/2

The equation of the line is determined as;

y + 3 = -5/2(x  + 7)

2(y + 3) = -5(x + 7)

2y + 6 = - 5x - 35

2y + 5x  + 41 = 0

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The complete question is below;

(3).  Find the amount of work done by pulling the wagon 10 meters to the right the rope makes an angle of 60' with the horizontal and the tension in the rope 2200N. (4). Find the equation of the plane containing the line  = (y = -2-1, x = -4 - 3) parallel to the plane 5x +2y + 1 = 2.

Answer:

Step-by-step explanation:

The angle bisector theorem states that a triangle's opposite side is divided into two halves by an angle bisector that is proportional to the triangle's other two sides.

A point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects, therefore if mACD = 90°, point D is equidistant from points A and B.

Any point on the perpendicular bisector is simply equal distance from both endpoints of the line segment on which it is drawn, according to the perpendicular bisector theorem.

The answer is that point  is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it makes up. Therefore, if a pillar is stationed at the middle of a bridge at an angle, all the points on the pillar will be equidistant from the end points of the bridge intersects.

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Answer:

(0,-2) is the correct answer.

Step-by-step explanation:

a. The opportunity cost of a goal if the player is a center is 0.5 assists. b. The opportunity cost of a goal if the player is a defenseman is 0.33 assists. c. The opportunity cost of a goal if the player is a center is 0.5 assists. d. The opportunity cost of an assist if the player is a defenseman is 1.5 goals. e. The position of Center has the absolute advantage in goals. f. The position of Center has the absolute advantage in assists. g. The position of Defenseman has the comparative advantage in goals. h. The position of Center has the comparative advantage in assists.

a. The opportunity cost of a goal for a center is 0.5 assists. This means that for every goal scored by the center, they have given up the opportunity to produce 0.5 assists.

b. The opportunity cost of a goal for a defenseman is 0.33 assists. This implies that for every goal scored by the defenseman, they have sacrificed the chance to generate 0.33 assists.

c. The opportunity cost of a goal for a center remains 0.5 assists. This is because the production possibilities for the center indicate that for every goal they score, they could have alternatively produced 0.5 assists.

d. The opportunity cost of an assist for a defenseman is 0.33 goals. This signifies that for every assist made by the defenseman, they have foregone the opportunity to score 0.33 goals.

e. The position of center has the absolute advantage in goals since they can produce 4 goals, which is higher than the defenseman's production of 2 goals.

f. The position of center also has the absolute advantage in assists with 8 assists, surpassing the defenseman's production of 6 assists.

g. The position of defenseman has the comparative advantage in goals since the opportunity cost of a goal for the defenseman (0.33 assists) is lower compared to the center's opportunity cost (0.5 assists).

h. The position of center has the comparative advantage in assists since the opportunity cost of an assist for the center (0.5 goals) is higher compared to the defenseman's opportunity cost (0.33 goals).

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Answer:

the correct answer for the rectangular prisim is 32

The surface are of the rectangular cuboid is 32.

1. Label the length (l), width (w), and height (h) of the prism

2. Use the formula, SA=2lw+2lh+2hw, to find the surface area.

Another option:

- Add the areas of all 6 faces

Answer:

$133

Step-by-step explanation:

$135-$12=

Using line of best fit and correlation coefficient, the correlation coefficient of determination represent the percentage of data that is closest to the lines of best fit.

What is line of best fit?

Line of best fit refers to the "a line through a scatter plot of data points that best expresses relationship between those points". Lines of best fit is used to describe data and predict data where the new data will appear. Examples for lines of best fit is 'Least square method'.

Two variables are said to be correlated or to have a correlation coefficient when "changes in the value of one variable produce changes in the variable of the other variable."

In order to find the correlation between two variables on a graph, the question asks for the line of best fit and correlation coefficient.

Only when there is a linear correlation between the variables—that is, when the relationship between the variables is linear on a graph—does the correlation coefficient hold true.

Variation in "x" on the graph leads to variation in "y." Variation in "y" on the graph results in variation in "x." The variables "x" and "y" are jointly dependent on the graph.

The correlation coefficient between two variables on the graph is calculated in this manner.

Hence, using line of best fit and correlation coefficient, the correlation coefficient of determination represent the percentage of data that is closest to the lines of best fit.

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