What is the end behavior of the graph?

The calculated value of the integral [tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx[/tex] is 0.7358

From the question, we have the following parameters that can be used in our computation:

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx[/tex]

The above expression can be integrated using integration by parts method

When integrated, we have

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = -\left(x+1\right)\mathrm{e}^{-x}[/tex]

Recall that the x values are from 1 to ∝

This means that

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = -\left(\infty +1\right)\mathrm{e}^{-\infty} + \left(1+1\right)\mathrm{e}^{-1}[/tex]

So, we have

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = 0 + \frac{2}{e}[/tex]

Solving further, we get

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = 0 + 0.7358[/tex]

Evaluate

[tex]\int\limits^{\infty}_1 {(xe^{-x}) \, dx = 0.7358[/tex]

Hence, the value of the integral is 0.7358

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The coordinates of A' and B' include the following:

A' (4, 7).

B' (10, 9).

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 2 centered at the point (6, 3) by using the following mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate A', we have;

Coordinate A' = (5, 5)  →  (2(5 - 6) + 6, 2(5 - 3) + 3)

Coordinate A' = (5, 5)  →  (2(-1) + 6, 2(2) + 3)

Coordinate A' = (5, 5)  →  (-2 + 6, 4 + 3)

Coordinate A' = (5, 5)  →  (4, 7)

For coordinate B', we have;

Coordinate B' = (8, 6)  →  (2(8 - 6) + 6, 2(6 - 3) + 3)

Coordinate B' = (5, 5)  →  (2(2) + 6, 2(3) + 3)

Coordinate B' = (5, 5)  →  (4 + 6, 6 + 3)

Coordinate B' = (5, 5)  →  (10, 9)

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The graphed velocity function ​v(t)=ds/dt=f'(t) and the acceleration function ​ is attached.

we start by  Plotting  the position function

Choosing a set of time values within the given interval [0, 9.5] and find the corresponding position values by substituting each time value into the position function s(t) = 152t - 16t².

We then plot the points (t, s) on a coordinate system.

We go ahead to Plot the velocity function by calculating  the derivative of the position function to obtain the velocity function v(t) = ds/dt = f'(t).

Plot the acceleration function by calculating the second derivative of the position function to obtain the acceleration function a(t) = d²s/dt² = f''(t).

We then connect the points representing the various function to create the needed graph.

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∠LMN is an obtuse angle.

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

Explanation

Let's go through the answer choices to see which are true, and which are false.

The given sequence does not follow a simple arithmetic or geometric pattern, making it challenging to determine an explicit rule based on the given terms.

To identify the type of sequence and write the explicit rule, we need to examine the pattern of the given sequence: -39, -45, 51, 57, ...

By observing the differences between consecutive terms, we can determine if it follows an arithmetic or geometric pattern.

Arithmetic sequences have a common difference between each term, meaning that by adding (or subtracting) the same value repeatedly, we can generate the sequence. Geometric sequences, on the other hand, have a common ratio between each term, meaning that by multiplying (or dividing) by the same value repeatedly, we can generate the sequence.

Let's calculate the differences between consecutive terms:

-45 - (-39) = -6

51 - (-45) = 96

57 - 51 = 6

From the differences, we can see that the sequence is not arithmetic since the differences are not constant. However, the differences alternate between -6 and 6, indicating a possible geometric pattern.

Let's calculate the ratios between consecutive terms:

-45 / (-39) ≈ 1.1538

51 / (-45) ≈ -1.1333

57 / 51 ≈ 1.1176

The ratios are not constant, indicating that the sequence is neither geometric nor arithmetic.

Therefore, the given sequence does not follow a simple arithmetic or geometric pattern, and it is difficult to determine the explicit rule based on the given terms. It is possible that the sequence follows a more complex pattern or rule that is not apparent from the given terms.

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The equation of a line is not unique to its graph; this means that multiple lines can have the same slope and y-intercept. Therefore, this equation is a possible match, making option D the correct answer.

The equation of the graph shown below could be `y = 3x - 2`.

We are given an equation of the line that can fit the graph shown.

To determine which equation it is, we can compare the graph to each of the answer choices:

A. y = -10:

This is the equation of a horizontal line that is 10 units below the x-axis.

It is not the equation of the graph shown.B. 2x - 3y = -9:

To convert this equation to slope-intercept form, we need to solve for y:

2x - 3y = -93y = 2x + 9y

= (2/3)x + 3

This is the equation of a line with a slope of 2/3, meaning it has a positive slope.

The graph shown has a negative slope, so this equation is not a match.C.

-4x + 2y = -6:

To convert this equation to slope-intercept form, we need to solve for y:

-4x + 2y = -62y

= 4x - 6y

= 2x - 3

This is the equation of a line with a slope of 2, meaning it is steeper than the graph shown.

This equation is not a match.D. y = 3x - 2:

This equation is already in slope-intercept form, meaning it has a slope of 3 and a y-intercept of -2.

The graph shown has a slope of -3 and a y-intercept of -2.

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This introduces some bias as it excludes individuals who haven't attended, potentially influencing the overall popularity of the tricks.

We can evaluate the sampling method used for the magician's survey.

Voluntary: The survey was sent out to people who had previously attended the magician's programs. It suggests that participation in the survey is optional, meaning respondents can choose whether or not to participate. Therefore, the survey can be considered voluntary.

Ranking Preference: The survey asks participants to rank their three favorite tricks. This allows respondents to express their preferences in a specific order. It provides a clear structure for respondents to indicate their choices, making it easier for the magician to analyze the data and determine the most popular tricks.

Email Survey: The survey was conducted through email, which can be an effective method for reaching a targeted audience. However, it's important to note that the sample is limited to people who have attended the magician's programs in the past. This may introduce some bias as it excludes individuals who haven't attended, potentially influencing the overall popularity of the tricks.

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Answer:

19m75

Step-by-step explanation:

Solution:

To evaluate the expression 7×2+(7+3×(5-2)÷4×2), we need to follow the order of operations (PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Step 1: First, we need to simplify the expression inside the parentheses.

5-2 = 3

3÷4 = 0.75

3×0.75 = 2.25

7+2.25 = 9.25

Step 2: Next, we need to simplify the multiplication and division from left to right.

3×2 = 6

0.75×2 = 1.5

Step 3: Finally, we need to simplify the addition and subtraction from left to right.

7×2+9.25+6-1.5 = 19.75

Therefore, the value of the expression 7×2+(7+3×(5-2)÷4×2) is 19.75.

Answer:

[tex] \sqrt{ {( - 3 - 0)}^{2} + {( - 3 - 1)}^{2} } = [/tex]

[tex] \sqrt{ {( - 3)}^{2} + {( - 4)}^{2} } = \sqrt{9 + 16} = \sqrt{25} = 5[/tex]

The trigonometric identity cos a(2sec a + tan a)(sec a - 2tan a) = 2cos a - 3tan a

Trigonometric identities are equations that contain trigonometric ratios.

Given the trigonometric identity cos a(2sec a + tan a)(sec a - 2tan a) = 2cos a - 3tan a, we need to show that Left hand side (L.H.S) equals Right hand side (R.H.S). We proceed as follows

L.H.S =  cos a(2sec a + tan a)(sec a - 2tan a)

Expanding the brackets, we have that

cos a(2sec a + tan a)(sec a - 2tan a) =  cos a(2sec² a -  4tan asec a + tan a sec a - 2tan² a)

= cos a(2sec² a -  3tan a sec a - 2tan² a)

Now using the trigonometric identity 1 + tan² a = sec² a, we have that

cos a(2sec² a -  3tan a sec a - 2tan² a) = cos a(2(1 + tan² a) -  3tan a sec a - 2tan² a)

= cos a(2 + 2tan² a -  3tan a sec a - 2tan² a)

Collecting like terms in the equation, we have that

= cos a(2 + 2tan² a - 2tan² a -  3tan a sec a)

= cos a(2 + 0 -  3tan a sec a)

= cos a(2 -  3tan a sec a)

Expanding the bracket, we have that

= 2cos a -  cos a × 3tan a sec a

=  2cos a -  cos a × 3tan a/cos a  (since sec a = 1/cos a)

= 2cos a - 1 × 3tan a

= 2cos a - 3tan a

= R.H.S

So, since L.H.S = R.H.S,

cos a(2sec a + tan a)(sec a - 2tan a) = 2cos a - 3tan a

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Therefore, the missing angle = (1080° - 947°) = 133°

Step-by-step explanation:

Given: Octagon

7 Interior Angles: 122°, 143°, 152°, 107°, 128°, 130° & 165°

Find: The measure of the missing angle:

Plan: Determine total sum of an octagons interior angles and subtract the total of the given angles

Sum of the Interior Angles of an Octagon:S = (n-2) 180°

S = (8 - 2)180° = 6 x 180° = 1080°

Sum of 7 Given Angles: S7IA = 947°

Answer:

16 months

Step-by-step explanation:

In order to find the number of months it will take for Alma's bank account to reach $145, we can plug in 145 for y and solve for x:

Step 1:  Subtract 577 from both sides:

(145 = -27x + 577) - 577

-432 = -27x

Step 2:  Divide both sides by -27 to solve for x:

(-432 = -27x) / -27

16 = x

Thus, it will take 16 months for Alma's account to reach $145.

Answer: My guess is 0

Step-by-step explanation:

Checked with my math teacher

The angles of the triangle formed by the towns can be determined using the law of cosines with the given side lengths.

We may apply the rule of cosines to get the angles of the triangle the towns create. Assume that the towns are identified as A, B, and C and that their relative distances are 80 km, 90 km, and 100 km. These sides' opposing angles shall be designated as,, and, respectively.

We may determine the angles by using the law of cosines to calculate: cos() = (2bc)/(b2 + c2 - a2)

cos() is equal to (c2 + a2 - b2) / (2ca).

cos() is equal to (2ab) / (a2 + b2 - c2).

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Angle J is equal to 90°.Hence, the measure of Angle J is 90°.

Kayla can see that the measure of Angle I and Angle J form a straight line. Since Kayla knows that a straight line has an angle measure of 180°, what is the measure (in degrees) of Angle J

Given,The angle formed by angle I and J is a straight line which measures 180°.We need to find the measure of angle J.To find the measure of angle J, we need to find out the angle measure of angle I.

From the above information, we know that the angle formed by angle I and J is a straight line that measures 180°.So,Angle I + Angle J = 180°Substitute Angle I in terms of Angle J. We know that the angles are supplementary and they add up to 180 degrees.

If we know the measure of one of the angles, we can find the measure of the other angle as well.So ,Angle I = 180° - Angle JNow, substitute the value of Angle I in the above equation.Angle I + Angle J = 180°(180° - Angle J) + Angle J = 180°180° - Angle J + Angle J = 180°

Thus, Angle J is equal to 90°.Hence, the measure of Angle J is 90°.

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the number of physics textbooks sold is 240 and the number of math textbooks sold is 182.

Let's suppose the number of math textbooks sold is "m".

'Therefore, the number of physics textbooks sold will be "m+58".According to the problem, the total number of textbooks sold is 422. Therefore, we can write an equation for this situation as:

m + (m + 58) = 422Simplifying this equation, we get:2m + 58 = 4222m = 364m = 182So, 182 math textbooks were sold. The number of physics textbooks sold is 182+58 = 240.

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Hello!

The sum of an interior angle and its adjacent exterior angle is 180°

The answer is:

C) 180°

Work/explanation:

The sum of an interior angle and its adjacent exterior angle is [tex]\sf{180^o}[/tex], which means that an interior angles and its adjacent exterior angle form a linear pair.

This also means that the angles are supplementary, because they add up to [tex]\sf{180^o}[/tex].

The value of the integral is [tex]\int\limits^{10}_4 {f(x)} \, dx = 6[/tex]

The average rate of change over the interval [4, 10] is 3/2

From the question, we have the following parameters that can be used in our computation:

[tex]f(x) = \left\{ \begin{array}{lr} -4, & \text{if } 4 \le x < 7\\ 5, & \text{if } 7 \le x < 10 \end{array}[/tex]

The integral expression is given as

[tex]\int\limits^{10}_4 {f(x)} \, dx[/tex]

So, we have

[tex]\int\limits^{10}_4 {f(x)} \, dx = \int\limits^{10}_4 {[5 - 4]} \, dx[/tex]

Evaluate the difference

[tex]\int\limits^{10}_4 {f(x)} \, dx = \int\limits^{10}_4 {[1]} \, dx[/tex]

Integrate

[tex]\int\limits^{10}_4 {f(x)} \, dx = [x]\limits^{10}_4[/tex]

Expand

[tex]\int\limits^{10}_4 {f(x)} \, dx = 10 - 4[/tex]

Evaluate the difference

[tex]\int\limits^{10}_4 {f(x)} \, dx = 6[/tex]

Here, we have

[tex]f(x) = \left\{ \begin{array}{lr} -4, & \text{if } 4 \le x < 7\\ 5, & \text{if } 7 \le x < 10 \end{array}[/tex]

The interval is [4, 10]

So, we have

Average rate = (5 + 4)/(10 - 4)

Evaluate

Average rate = 3/2

Hence, the average rate of change is 3/2

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The statistical analysis of the data using a two-sample t-test indicates;

(a) B. Yes, the Meters On data appears to have higher speeds

A. No, there does not appear to be any outlier

(b) H₀; [tex]\mu_{on}[/tex] = [tex]\mu_{off}[/tex]

H₁; [tex]\mu_{on}[/tex] > [tex]\mu_{off}[/tex]

The P-value for the test is about 0.037

A two-sample t-test is used to determine if there is a difference between the means of two independent groups of data.

(a) The average of the data values are;

Ramp meters on;

[tex]\mu_{on}[/tex] = (29+47+55+38+32+25+42+47+51+36+55+41+43+25+47)/15 ≈ 40.87

[tex]\mu_{off}[/tex] = (25+25+43+35+36+31+48+37+19+29+22+40+36+50+40)/15 ≈ 34.4

The higher average value for the speed with the Ramp meters on indicates;

B. Yes, the Meters On data appears to have higher speeds

The five number summary are;

Ramp Meters On

Min = 25, Max = 55, Q₁ = 32, Q₂ = 42, Q₃ = 47

IQR = 47 - 32 = 15

Outlier = 47 + 1.5 × 15 = 69.5

32 - 1.5 × 15 = 9.5

Therefore, there are no outliers for the Ramp Meters On

Ramp Meters Off

Min = 19, Max = 50, Q₁ = 25, Q₂ = 36, Q₃ = 40

IQR = 40 - 25 = 15

Outlier = 40 + 1.5 × 15 = 62.5

25 - 1.5 × 15 = 2.5

Therefore, there are no outliers for the Ramp Meters Off data

(b) The null hypothesis is; H₀; [tex]\mu_{on}[/tex] = [tex]\mu_{off}[/tex]

The alternative hypothesis is; H₁; [tex]\mu_{on}[/tex] > [tex]\mu_{off}[/tex]

(c) The two sample t-test, can be obtained using the formula;

[tex]t_{cal} = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} ) } }[/tex]

Where; [tex]\bar{x}_1[/tex] = 40.87

[tex]\bar{x}_2[/tex] = 34.40

s₁ = 9.91

s₂ = 9.20

n₁ = n₂ = 15

Therefore; [tex]t_{cal}[/tex] = 1.8516. The degrees of 15 + 15 - 2 = 28, and the one-tailed hypothesis, indicates, using an online tool;

The p-value is less than 0.05, therefore, the result is significant.

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The correct option is C, ON is the normal to the surface.

Remember that when we have an incident ray on a surface, a reflected ray will be emmited such that the angle with respect to the normal is the same one for the incident ray.

For any plane surface, this normal is perpendicular to the surface.

Here, we can see that ON is normal to the sruface of reflection, thus, the correct option is C, segment ON is the normal.

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Answer:

Ximena can use 1 gigabytes of data

Step-by-step explanation:

The first thing you want to do is subtract

51.10 - 44.50 =  5.6

5.6 is the amount of money she will have to spend on data

With each gigabyte costing 4 dollars and only 5 dollars to spend

she can only use one gigabyte

Answer:

Set your calculator to degree mode.

x/sin(120°) = 5/sin(23°)

x = 5sin(120°)/sin(23°) = about 11.08

11.08 belongs in the green box.

Answer:

No

Step-by-step explanation:

3 x 5 is 15 because is multiplying 3 x 5

3^5 is 3 x 3 x 3 x 3 x 3 and gives a bigger result.

The total art exhibit attendance at the end of 5 years would be approximately 5186 people.

To find the total art exhibit attendance at the end of 5 years, we need to calculate the attendance for each year and sum them up.

Given that the initial attendance is 862, we can use the formula for compound interest to calculate the attendance for each subsequent year. The formula is:

A = P(1 + r/100)^n

Where:

A is the final attendance

P is the initial attendance (862)

r is the annual growth rate (6% or 0.06)

n is the number of years (5)

Let's calculate the attendance for each year:

Year 1:

A1 = 862(1 + 0.06)^1 = 914.92 (rounding to 915)

Year 2:

A2 = 862(1 + 0.06)^2 = 971.09 (rounding to 971)

Year 3:

A3 = 862(1 + 0.06)^3 = 1031.63 (rounding to 1032)

Year 4:

A4 = 862(1 + 0.06)^4 = 1097.85 (rounding to 1098)

Year 5:

A5 = 862(1 + 0.06)^5 = 1169.86 (rounding to 1170)

Finally, we sum up the attendance for each year:

Total attendance = A1 + A2 + A3 + A4 + A5

= 915 + 971 + 1032 + 1098 + 1170

= 5186

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The angle of intersecting chords theorem indicates that the value of x, obtained from the measure of the arc [tex]\widehat{KU}[/tex] is; x = 7

The angle of intersecting chords theorem states that the angle formed at the intersection of two chords is half the sum of the angles of the arcs intercepted by the two chords.

The angle of intersecting chords theorem indicates that we get;

The measure of the arc KU = 6·x + 8

122 = (1/2) × (6·x + 8 + 194)

Therefore; 6·x + 8 + 194 = 2 × 122 = 244

6·x = 244 - (194 + 8) = 42

x = 42/6 = 7

Therefore; m[tex]\widehat{KU}[/tex] = 6 × 7 + 8 = 50°

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Radius: 6√3 inches. Perimeter: 72 inches.

The exact length of the perimeter of regular hexagon ABCDEF:

To find the perimeter of a regular hexagon, we need to multiply the length of one side by 6 since a hexagon has six equal sides. The length of one side can be determined using the formula:

Side length = 2 * apothem * tan(π/6)

Substituting the given apothem length of 6√3 inches, we have:

Side length = 2 * (6√3) * tan(π/6)

Simplifying the equation:

Side length = 12√3 * √3/3

Side length = 12 inches

Now, we can calculate the exact length of the perimeter:

Perimeter = Side length * 6

Perimeter = 12 inches * 6

Perimeter = 72 inches

Therefore, the exact length of the perimeter of regular hexagon ABCDEF is 72 inches.

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Kim's commission was $8140, and her gross pay was $10560 for last month.

Washington Plastic Products pays Kim $2420 monthly salary plus 11% commission each month.

If her sales were $74000 last month, her commission and gross pay can be calculated as follows:

Kim's commission = 11% of $74000

= $8140Kim's gross pay

= $2420 + $8140 = $10560

Therefore, Kim's commission was $8140 and her gross pay was $10560 last month.

In the given problem, Kim's monthly salary is $2420, and she earns an 11% commission on her sales.

Assuming her sales last month were $74000, her commission and gross pay for the month can be found by multiplying her sales by the commission rate and adding her monthly salary.

Commission = 11% of $74000 = $8140Gross Pay = $2420 + $8140 = $10560

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Answer:

BC

Step by step explanation:

opposite

The correct length of side k in triangle JKL is approximately 35.15 units.

The correct answer is option E.

The length of side k in triangle JKL using the correct values for sin(52°) and sin(97°).

Given:

m∠J = 97 degrees

m∠L = 31 degrees

J = 44

According to the Law of Sines, we have:

sin(∠J) / J = sin(∠K) / k

Substituting the given values:

sin(97°) / 44 = sin(∠K) / k

Now, let's solve for k:

k = (44 * sin(∠K)) / sin(97°)

Using a calculator:

k = (44 * sin(52°)) / sin(97°)

k ≈ (44 * 0.79) / 0.99

k ≈ 35.1

Therefore, the correct length of side k in triangle JKL is approximately 35.15 units making option E the correct answer.

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The question probable may be:

Triangle JKL has the following measures :m∠J=97degree, m∠L=31degree, and j=44. What is the length of side k?

A. 46.3

B. 52.0

C. 22.8

D. 34.9

E. 35.1