Alberto is training for a race. He begins his training by running 5 miles this week. He increases his distance by 2 miles each week. Which equation can be used to find the number of miles, ww, Alberto is running after training for w weeks? A. W= 271 +- 5 O B. M= 2w + 5 Oc m= 5w+2 OD. W = 501 + 2​

Answer: She is using the counting-on technique.

Step-by-step explanation:

Upper Control Limit (UCL) for R chart = D4 x Rbar = 2.282 x 0.347 = 0.792 and Lower Control Limit (LCL) for R chart = D3 x Rbar = 0 x 0.347 = 0.

To determine the trial central line and control limits for the X and R control charts, we need to first calculate the average and range of each subgroup.
Average (Xbar):
Subgroup 1: 20.35
Subgroup 2: 20.40
Subgroup 3: 20.36
Subgroup 4: 20.65
Subgroup 5: 20.20
Subgroup 6: 20.40
Subgroup 7: 20.43
Subgroup 8: 20.37
Subgroup 9: 20.48
Subgroup 10: 20.42
Subgroup 11: 20.39
Subgroup 12: 20.38
Subgroup 13: 20.40
Subgroup 14: 20.41
Subgroup 15: 20.45
Subgroup 16: 20.34
Subgroup 17: 20.36
Subgroup 18: 20.42
Subgroup 19: 20.50
Subgroup 20: 20.31
Subgroup 21: 20.39
Subgroup 22: 20.39
Subgroup 23: 20.40
Subgroup 24: 20.41
Subgroup 25: 20.40

Average (Xbar) = (20.35 + 20.40 + 20.36 + 20.65 + 20.20 + 20.40 + 20.43 + 20.37 + 20.48 + 20.42 + 20.39 + 20.38 + 20.40 + 20.41 + 20.45 + 20.34 + 20.36 + 20.42 + 20.50 + 20.31 + 20.39 + 20.39 + 20.40 + 20.41 + 20.40)/25 = 20.408
Range (R):
Subgroup 1: 0.34
Subgroup 2: 0.36
Subgroup 3: 0.32
Subgroup 4: 0.36
Subgroup 5: 0.36
Subgroup 6: 0.35
Subgroup 7: 0.31
Subgroup 8: 0.34
Subgroup 9: 0.30
Subgroup 10: 0.37
Subgroup 11: 0.29
Subgroup 12: 0.30
Subgroup 13: 0.33
Subgroup 14: 0.36
Subgroup 15: 0.34
Subgroup 16: 0.36
Subgroup 17: 0.37
Subgroup 18: 0.73
Subgroup 19: 0.38
Subgroup 20: 0.35
Subgroup 21: 0.33
Subgroup 22: 0.33
Subgroup 23: 0.30
Subgroup 24: 0.34
Subgroup 25: 0.30

Range (R) = max(Range of each subgroup) - min(Range of each subgroup) = 0.73 - 0.29 = 0.44
Using these values, we can now calculate the trial central line and control limits:
Central line (CL) for X chart = Xbar = 20.408
Upper Control Limit (UCL) for X chart = CL + (A2 x Rbar) = 20.408 + (0.577 x 0.44) = 20.672
Lower Control Limit (LCL) for X chart = CL - (A2 x Rbar) = 20.408 - (0.577 x 0.44) = 20.144
Central line (CL) for R chart = Rbar = (0.34 + 0.36 + 0.32 + 0.36 + 0.36 + 0.35 + 0.31 + 0.34 + 0.30 + 0.37 + 0.29 + 0.30 + 0.33 + 0.36 + 0.34 + 0.36 + 0.37 + 0.73 + 0.38 + 0.35 + 0.33 + 0.33 + 0.30 + 0.34 + 0.30)/25 = 0.347
Upper Control Limit (UCL) for R chart = D4 x Rbar = 2.282 x 0.347 = 0.792
Lower Control Limit (LCL) for R chart = D3 x Rbar = 0 x 0.347 = 0
If any points fall outside of these control limits, it suggests that the process is out of control and requires investigation for assignable causes. Upon investigating, any assignable causes should be removed and the control chart revised accordingly.

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True. The scope of a variable refers to the segment or portion of a program where it can be accessed and utilized.

Variable scope is essential in programming because it helps maintain well-structured, organized code and prevents unintended modifications or collisions between variables with the same name in different parts of the program.

There are two primary types of variable scope: local scope and global scope. A local variable is defined within a specific function or block of code, and it can only be accessed within that particular area. Once the function or block of code is exited, the local variable ceases to exist, and its memory is freed up.

On the other hand, a global variable is accessible throughout the entire program. It is typically declared outside of any function or code block, making it available for use by any part of the code. However, using global variables can lead to potential issues, such as unintentional changes to their values and increased complexity in managing the flow of information within the program.

Understanding the scope of variables is crucial for efficient and effective programming. Proper management of variable scope promotes clean, maintainable code, and reduces the likelihood of bugs or errors resulting from variable conflicts or unintended modifications.

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Complete Question

The scope of a variable is the segment of the program in which the variable can be accessed. State whether True or False.

In Lesson 7.06 the reader is asked to open the eBook and read pgs. 4-9. In this

reading it introduces Badminton and describes how a player must be able to move

quickly as the "shuttle" or "birdie" and fly at speeds of up to 200 mph. The speed they reference is option D. 200 mph

The object of the game is to hit buckets (also known as birds) over the net with the racket and hit them back and forth to score points. Success in badminton requires stamina, speed, agility and strategy. It is also a popular Olympic sport. The speed of a badminton shuttlecock can reach up to 200 mph when hit by professional players.

Therefore, the correct answer is as given above. It could then be concluded that option D. 200mph is the speed they reference.

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Therefore, there are 230,300 ways we can select a set of four microprocessors from the set of 50, given that four of them are defective.

To find the number of ways we can select a set of four microprocessors from a set of 50 microprocessors, we can use the combination formula. The formula for combination is:

nCk = n! / (k! * (n-k)!)

where n is the total number of items in the set and k is the number of items we want to select. In this case, n = 50 and k = 4.

So, the number of ways we can select a set of four microprocessors from the set of 50 is:

50C4 = 50! / (4! * (50-4)!)
= 50! / (4! * 46!)
= (50 * 49 * 48 * 47) / (4 * 3 * 2 * 1)
= 230,300

Therefore, there are 230,300 ways we can select a set of four microprocessors from the set of 50, given that four of them are defective.

To answer your question, you can use the combination formula, which is used to calculate the number of ways to choose a specific number of items from a larger set without regard to their order.

The combination formula is: C(n, k) = n! / (k!(n-k)!)

In this case, you have a set of 50 microprocessors (n = 50) and you want to select a set of 4 microprocessors (k = 4). Plugging these values into the formula, you get:

C(50, 4) = 50! / (4!(50-4)!) = 50! / (4! * 46!)

Calculating this, you'll find there are 230,300 ways to select a set of four microprocessors from the given set of 50.

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U+W satisfies these three conditions, it is a subspace of V.

If V = R^3, U = x-axis, and W = y-axis, then U+W represents the set of all vectors formed by the addition of vectors from U and W.

To prove that U+W is a subspace of V, we must show the following:

1. U+W contains the zero vector: Since both U and W contain the zero vector (0,0,0), their sum, which is (0,0,0), is also in U+W.

2. U+W is closed under vector addition: Let x, y ∈ U+W. Then, we can write x = u1 + w1 and y = u2 + w2, where u1, u2 ∈ U and w1, w2 ∈ W. Now, x + y = (u1 + w1) + (u2 + w2) = (u1 + u2) + (w1 + w2). This is in U+W because u1 + u2 ∈ U and w1 + w2 ∈ W.

3. U+W is closed under scalar multiplication: Let x ∈ U+W and c be a scalar. Then, we can write x = u + w, where u ∈ U and w ∈ W. Now, cx = c(u + w) = cu + cw. This is in U+W because cu ∈ U and cw ∈ W.

Since U+W satisfies these three conditions, it is a subspace of V.

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The values of dy and δy for the function y = (x²)⁴, given x = 1 and δx = dx = 0.02, are dy = 0.16 and δy = 0.16, respectively.

Let's compute the values of dy and δy for the function y = (x²)⁴, given x = 1 and δx = dx = 0.02.

First, we can compute dy, which represents the change in y due to a change in x.

dy = dy/dx * dx

To find dy/dx, we can first differentiate y with respect to x using the chain rule:

dy/dx = 4 * (x²)³ * 2x

Now, plugging in x = 1, we get:

dy/dx = 4 * (1²)³ * 2(1)

= 4 * 1⁶ * 2

= 8

So, dy = dy/dx * dx = 8 * 0.02 = 0.16

Next, we can compute δy, which represents the change in y due to δx.

δy = dy/dx * δx

Plugging in dy/dx = 8 and δx = 0.02, we get:

δy = 8 * 0.02 = 0.16

Therefore, the values of dy and δy for the function y = (x²)⁴, given x = 1 and δx = dx = 0.02, are dy = 0.16 and δy = 0.16, respectively.

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now, by radius of a polygon, we're referring to the distance from its center to a corner where two sides meet, or namely the radius of the circle that surrounds it or namely the circumcircle.

[tex]\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=\cfrac{nR^2}{2}\cdot \sin(\frac{360}{n}) ~~ \begin{cases} n=sides\\ R=\stackrel{\textit{radius of}}{circumcircle}\\[-0.5em] \hrulefill\\ n=20\\ R=6 \end{cases}\implies A=\cfrac{(20)(6)^2}{2}\cdot \sin(\frac{360}{20}) \\\\\\ A=360\sin(18^o)\implies A\approx 111.25~mm^2[/tex]

Make sure your calculator is in Degree mode.

Once you have the sample mean, sample standard deviation, and sample size, plug those values into the formulas above to calculate the confidence interval. The upper bound of the confidence interval will be the result of the addition (Sample mean + 1.96 * Standard error).

To construct a 95% confidence interval for the population mean weight of the candies, we need to first collect a sample of candy weights and calculate the sample mean and standard deviation. Let's assume we have a sample of 50 candies and the sample mean weight is 20 grams with a standard deviation of 3 grams.

Using a t-distribution with 49 degrees of freedom (n-1), we can find the margin of error for a 95% confidence interval, which is given by:

Margin of Error = t(0.025,49) x (s / sqrt(n))
where t(0.025,49) is the critical value of t with a significance level of 0.025 and 49 degrees of freedom (from a t-table or calculator), s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

Margin of Error = 2.009 x (3 / sqrt(50)) ≈ 0.85 grams

To find the confidence interval, we simply add and subtract the margin of error from the sample mean:

95% Confidence Interval = (20 - 0.85, 20 + 0.85) = (19.15, 20.85) grams

Therefore, the upper bound of the confidence interval is 20.85 grams.
To construct a 95% confidence interval for the population mean weight of the candies, we need to use the following formula:

Confidence interval = Sample mean ± (Z-score * Standard error)

Here, the Z-score for a 95% confidence interval is 1.96. The standard error can be calculated using the formula:

Standard error = Sample standard deviation / √(Sample size)

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Lin's method yields an area of 54 √(3) square inches, and Andre's method yields an area of 18 √(10) square inches.

We have,

Using Lin's method, the hexagon can be decomposed into 6 identical equilateral triangles, each with a side length of 6 inches.

The area of one such triangle.

= (√(3)/4) x (6)²

= 9 √(3) square inches.

The area of the hexagon is 6 times this value, or 54 √(3) square inches.

Using Andre's method,

The hexagon can be decomposed into a rectangle and two identical triangles.

The rectangle has dimensions of 6 inches by 2 √(10) inches

(since each side of the hexagon is 6 inches, the rectangle's width is also 6 inches, and its length can be calculated using the Pythagorean Theorem). Therefore, the area of the rectangle.

= 6 x 2 √(10)

= 12 √(10) square inches.

Each triangle has a base of 6 inches and a height √10 inches, so the area of each triangle.

= (1/2) x 6 x √ (10)

= 3 √(10) square inches.

Therefore, the total area of the hexagon is the sum of the area of the rectangle and two triangles.

= 12 √(10) + 6 √(10)

= 18 √(10) square inches.

Thus,

Lin's method yields an area of 54 √(3) square inches, and Andre's method yields an area of 18 √(10) square inches.

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The given geometric series is convergent. We can see that the common ratio (r) is 1/√3, which has an absolute value less than 1. So, the sum of this convergent geometric series is √3 / (√3 - 1).

The geometric series in question is given by the formula:

Σ (1/√3)^n from n=0 to infinity.

To determine if this geometric series is convergent or divergent, we need to examine the common ratio, which is 1/√3. The geometric series converges if the absolute value of the common ratio is less than 1, i.e., |r| < 1, and diverges otherwise.

In this case, the common ratio r is 1/√3, and its absolute value is also 1/√3 since it's already positive. Since 0 < 1/√3 < 1, the series is convergent.

To find the sum of this convergent geometric series, we can use the formula:

Sum = a / (1 - r),

where a is the first term of the series and r is the common ratio. For this series, a = (1/√3)^0 = 1, and r = 1/√3.

Sum = 1 / (1 - 1/√3) = 1 / ( (√3 - 1) / √3 ) = √3 / (√3 - 1).

So, the sum of this convergent geometric series is √3 / (√3 - 1).

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Based on the information provided, we can use hypothesis testing to determine whether or not the economist's claim is true.

The null hypothesis (H0) would be that the proportion of US adults with a great deal of confidence in banks is 12% or less. The alternative hypothesis (Ha) would be that the proportion is greater than 12%. To test this, we would use a one-tailed z-test with a significance level of 0.05. First, we need to calculate the sample proportion of adults with a great deal of confidence in banks:
156/1220 = 0.1279
Next, we need to calculate the test statistic (z-score):
z = (0.1279 - 0.12) / sqrt(0.12 * 0.88 / 1220)
z = 1.45
Finally, we compare the test statistic to the critical value at a significance level of 0.05. Since this is a one-tailed test, the critical value is 1.645.
Since our test statistic (1.45) is less than the critical value (1.645), we fail to reject the null hypothesis. This means that we do not have enough evidence to support the claim that greater than 12% of US adults have a great deal of confidence in banks.
Therefore, based on this analysis, we cannot conclude that the economist's claim is true.

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Q1. The value of lim f(x) as x approaches 17 is 3.

Q2. The value of lim f(x) as x approaches infinity does not exist.

Q1. To find the value of lim f(x) as x approaches 17, we substitute 17 for x in the expression f(x) = x(2-x)/(sqr(11x)+1). This gives us:

lim f(x) = lim [x(2-x)/(sqr(11x)+1)] as x approaches 17

= 17(2-17)/(sqr(11*17)+1)

= -15/2(187)+1

= 3

Q2. To find the value of lim f(x) as x approaches infinity, we can use L'Hopital's rule. Taking the derivative of the numerator and denominator with respect to x, we get:

lim f(x) = lim [(2-x)/(2sqr(11x)+x)] as x approaches infinity

= lim [-(1)/(22sqr(11x)+1)] as x approaches infinity (by applying L'Hopital's rule again)

As x approaches infinity, the denominator approaches infinity, so the limit of the expression is 0. Therefore, the limit of f(x) as x approaches infinity does not exist.

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Answer:

3, 11 and 1312

Step-by-step explanation:

To find the three integers, you need to use the given information about the mean, median and range. The mean is the average of all the numbers in the set, and is found by adding all the numbers and dividing by the number of numbers. The median is the middle number in the set, and is found by ordering the numbers from smallest to largest and picking the middle one. The range is the difference between the highest and lowest numbers in the set12

Let x, y and z be the three integers, such that x ≤ y ≤ z. Then, we have:

Mean = 9 Median = 11 Range = 10

Using these facts, we can write three equations:

(x + y + z) / 3 = 9 y = 11 z - x = 10

Solving for x and z, we get:

x + y + z = 27 x + 11 + z = 27 x + z = 16

z = x + 10 x + (x + 10) = 16 2x = 6 x = 3

z = x + 10 z = 3 + 10 z = 13

Therefore, the three integers are 3, 11 and 1312

The criteria included in the response for determining congruence are;

First, it is important to know the difference between congruence and similarity in shapes and figures. The term congruence implies that the figures in discuss have the same shape and size while Similarity implies that the figures have the same shape but not necessarily the same size.

Consequently, for congruence, the corresponding sides have equal lengths and the corresponding angle measures are equal.

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Answer:

did

Step-by-step explanation:

Answer:

104.4 yd²

Step-by-step explanation:

17.4 x 6 = 104.4 yd²

Expression involving a definite integral that equals s(x) s(x) = ∫√(1 + (1/(1 + x^2))^2) dx from 0 to x. s′(x) = √(1 + (1/(1 + x^2))^2) is the derivative of the arc length function s(x) with respect to x.

(a) To find an expression for the arc length function s(x), we need to integrate the square root of the sum of squares of the derivatives of y with respect to x. For the curve y = arctan x, the derivative is:
dy/dx = 1/(1 + x^2)
Now we can use the arc length formula:
s(x) = ∫√(1 + (dy/dx)^2) dx from 0 to x
s(x) = ∫√(1 + (1/(1 + x^2))^2) dx from 0 to x

(b) To find s′(x), we can differentiate the arc length function with respect to x. Since s(x) is defined as an integral, we can use the Fundamental Theorem of Calculus to find its derivative:
s′(x) = √(1 + (1/(1 + x^2))^2)
This is the derivative of the arc length function s(x) with respect to x.

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Enlarging the shape by scale factor 1/2 using P as the centre of enlargement

let's start from bottom left point is given.

We have to calculate position from P to that point as below

it is 2 units up and 11 units left

so as scale factor is 1/2

We have to shift that point to 1 unit up and 5.5 units left

Pink point corresponding to it is denoted below

We have to do the same process for all the five points to cover the total figure

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Complete question

Enlarge the shape by scale factor 1/2 using P as the centre of enlargement

The statistical measure of the linear association between two variables where both have been measured using ordinal scales is called the Spearman's rank correlation coefficient.

This coefficient is used to measure the strength and direction of the relationship between the two variables.

Ordinal scales are used to measure variables that have a natural order, but the distance between values is not known.

For example, a Likert scale where respondents rate their agreement or disagreement with a statement using categories such as "strongly agree," "agree," "neutral," "disagree," or "strongly disagree" is an example of an ordinal scale.

Spearman's rank correlation coefficient is a non-parametric test, which means it does not rely on any assumptions about the distribution of the data. Instead, it ranks the values of each variable and then calculates the correlation between the ranks.

The resulting coefficient ranges from -1 to +1, where -1 represents a perfect negative correlation, 0 represents no correlation, and +1 represents a perfect positive correlation.

In summary, the Spearman's rank correlation coefficient is a useful statistical measure to determine the strength and direction of the linear relationship between two variables measured on an ordinal scale.

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The absolute maximum of f(x, y) on the region D is 36, which occurs at the points (0, 6) and (0, -6).

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

To find the absolute maximum of f(x, y) on the region D, we need to consider the values of f(x, y) at the critical points and on the boundary of D.

First, we find the critical points by setting the partial derivatives of f(x, y) equal to zero:

fx = 2x - 6 = 0

fy = 2y = 0

Solving these equations, we get the critical point (3, 0).

Next, we need to evaluate f(x, y) at the vertices of the triangular region D:

f(6, 0) = 0 + 0 - 6(6) = -36

f(0, 6) = 0 + 36 - 6(0) = 36

f(0, -6) = 0 + 36 - 6(0) = 36

Now, we need to evaluate f(x, y) along the boundary of D. The boundary consists of three line segments:

The line segment from (6, 0) to (0, 6):

y = 6 - x

f(x, 6 - x) = x² + (6 - x)² - 6x = 2x² - 12x + 36

The line segment from (0, 6) to (0, -6):

f(0, y) = y²

The line segment from (0, -6) to (6, 0):

y = -x - 6

f(x, -x - 6) = x² + (-x - 6)² - 6x = 2x² + 12x + 72

To find the absolute maximum of f(x, y) on the region D, we need to compare the values of f(x, y) at the critical point, the vertices, and along the boundary. We have:

f(3, 0) = 9 + 0 - 6(3) = -9

f(6, 0) = 0 + 0 - 6(6) = -36

f(0, 6) = 0 + 36 - 6(0) = 36

f(0, -6) = 0 + 36 - 6(0) = 36

f(x, 6 - x) = 2x² - 12x + 36

f(x, -x - 6) = 2x² + 12x + 72

f(0, y) = y²

To find the maximum along the line segment from (6, 0) to (0, 6), we need to find the critical point of f(x, 6 - x):

f(x, 6 - x) = 2x² - 12x + 36

fx = 4x - 12 = 0

x = 3/2

f(3/2, 9/2) = 2(3/2)² - 12(3/2) + 36 = -9/2

Therefore, the absolute maximum of f(x, y) on the region D is 36, which occurs at the points (0, 6) and (0, -6).

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The distribution of the total resistance of the two components in series for a randomly selected toaster is also normal, with a mean equal to the sum of the means of the two components, and a standard deviation equal to the square root of the sum of the variances of the two components.

Let's accept that the resistance of each component is regularly conveyed, with implies of μ1 and μ2, and standard deviations of σ1 and σ2, separately. We also assume that the two components are free of each other.

Add up to resistance = R1 + R2

where R1 and R2 are the resistances of the two components.

Concurring to the properties of ordinary dispersions, the entirety of two autonomous ordinary factors is additionally regularly dispersed, with a cruel rise to the entirety of the implies and a change rise to the whole of the changes. Hence, the cruelty of the overall resistance is:

Cruel = μ1 + μ2

and the change is:

Fluctuation = σ1[tex]^{2}[/tex]+ σ2[tex]^{2}[/tex]

The standard deviation of the full resistance is at that point the square root of the change:

Standard deviation = sqrt(σ1[tex]^{2}[/tex] + σ2[tex]^{2}[/tex])

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Answer:

At the given rate, the hot air balloon can travel 9/2 or 4.5 miles in 3/4 of an hour

Step-by-step explanation:

We can solve this problem one of two ways:  

The first ways seems the most straight forward, while the second ways helps you confirm your answer, as I'll show at the end:

[tex]\frac{18}{3}=\frac{d}{3/4} \\\\27/2=3d\\9/2=d\\4.5=d[/tex]

We can check our answer by first finding the rate at which the hot air balloon travelled 18 miles using the distance-rate-time formula, which is

d = rt, where d is the distance, r is the rate, and t is the time:

18 = 3r

6 = r

Now, we can check whether the product of the rate (6 mph) and the second time (3/4 hr) equals the second distance (9/2 mi)

9/2 = 6 * 3/4

9/2 = 9/4

9/2 = 9/2

The solutions to the blanks are below:

a) i) 0.2326

ii) 0.4652

b) i) 7

ii) 14

c) i) 11.3137

ii) 0.4242

To solve these questions we need to find the derivative

a) Let y=tan(4x + 6).

i) when x = 4 and dx = 0.2

dy = sec²(4x + 6) dx

dy = sec²(22) (0.2)

= 0.2326

ii) when x = 4 and dx = 0.4

dy = sec²(4x + 6) dx

dy = sec²(22) (0.4)

= 0.4652

b. Let y = 3x² + 5x +4.

i) when x = 5 and dx = 0.2

dy = (6x + 5) dx

dy = (6(5) + 5) (0.2)

= 7

ii) when x = 5 and dx = 0.4

dy = (6x + 5) dx

dy = (6(5) + 5) (0.4)

= 14

c. Let y=4√x.

i) when x = 2 and ∆x = 0.3

Δy = 4(√2.3) - 4(√2)

= 11.3137

ii) when x = 2 and dx = 0.3

dy = 2/√x dx

dy = 2/(√2) (0.3)

= 0.4242

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Answer:

B. A'B' = 2, measure of A = 37°

There were 385 children and 47 adult.

We have,

The daily prices are $1.50 for children and $2.25 for adults.

let the number of children be x and number of adult be y.

So, x + y = 432

and 1.5x + 2.25y = 683.25

Solving the above equation we get

x= 385 and y = 47.

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[tex]\sf m=\dfrac{y-b}{x}.[/tex]

[tex]\sf y=mx+b[/tex]

[tex]\sf y-b=mx+b-b\\ \\y-b=mx[/tex]

[tex]\sf \dfrac{y-b}{x} =\dfrac{mx}{x} \\ \\ \\\dfrac{y-b}{x} =m\\ \\ \\m=\dfrac{y-b}{x}.[/tex]

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I will break down the question into three parts and answer each one separately.

Part 1: sin 8x lim f(x)
There is no function f(x) provided in the question, so it is not possible to find the limit of f(x). The term "sin 8x" is also not relevant to this part of the question.

Part 2: find limx tan x
The limit of tan x as x approaches infinity does not exist because the function oscillates between positive and negative infinity. However, the limit of tan x as x approaches pi/2 from the left or right is equal to positive infinity, and the limit of tan x as x approaches -pi/2 from the left or right is equal to negative infinity.

Part 3: find f'(x) given that f(x)= (4x²-8), f(x)- Vox +2), and X-2 f(x) - j) given that 2x +1
To find the derivative of f(x), we need to differentiate each term separately and then combine the results. Using the power rule of differentiation, we have:

f(x) = 4x² - 8
f'(x) = 8x

f(x) = x^2 - Vox + 2
f'(x) = 2x - Vx

f(x) = (x - 2)f(x) - j
f'(x) = (x - 2)f'(x) + f(x) - j
       = (x - 2)(2x - Vx) + (x^2 - Vx + 2) - j
       = 2x^2 - 5x + 2 - Vx - j


a) To find the derivative of sin(8x) with respect to x, use the chain rule:
f'(x) = cos(8x) * 8 = 8cos(8x)

b) To find the derivative of f(x) = (4x^2 - 8) with respect to x, use the power rule:
f'(x) = 8x

c) To find the limit of f(x) = √(x + 2) as x approaches 1, simply substitute x = 1 into the function:
lim(x -> 1) f(x) = √(1 + 2) = √3

d) To find the limit of tan(x)/x as x approaches 0, use L'Hopital's rule. Since tan(x) -> 0 and x -> 0 as x -> 0, the conditions are satisfied:
lim(x -> 0) (tan(x)/x) = lim(x -> 0) (sec^2(x)/1) = sec^2(0) = 1

e) To find the derivative of f(x) = 2x + 1 with respect to x, use the power rule:
f'(x) = 2

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The sum of opposite interior angles of a triangle is equal to the exterior angle.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. The sum of interior angles of a triangle is 180°

The exterior angle theorem states that the sum of opposite interior angle is equal to the exterior angle.

If angle A,B, C are the interior angle of a triangle,and angle D is exterior angle adjascent to C.

Then A+ B + C = 180

C = 180-(A+B)

Also;

C+D = 180

C = 180-D

therefore we can say D = A+B

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For a line plot of data values of a data set present in above figure, the outlier is one of data set value which is equals to the 0.1. So, option(a) is right one.

Outlier is a data value that differ significantly from other values in the dataset. That is, outliers are values that deviate significantly from the mean. In general, outliers affect the mean, but not the median or mode. Therefore, the effect of outliers on the mean is significant. We have a line plot of data set present in above figure. We have to determine the data value would be considered the outlier. From the above discussion about outliers, we can say that outlier is a data value far beyond the meaning of statistical methods. So, after watching the above graph carefully, the data value 0.1 is far away from other data values and mean of values. So, outlier is 0.1.

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Complete question:

The above figure complete the question.

Which data value would be considered the outlier? Enter your answer in the box.

a) 0. 1

b) 0. 2

c) 0. 3

d) 0. 4

e) 0. 5

f) 0. 6

g) 0. 7

The range of values of f(x) that satisfy g(x)≤f(x)≤h(x) for −2 ≤ x ≤ 2 is 0 ≤ f(x) ≤ -26.67. In other words, f(x) must be between 0 and -26.67 for all x in the interval [-2, 2].

To solve this problem, we need to find the range of values of f(x) that satisfy g(x)≤f(x)≤h(x) for −2 ≤ x ≤ 2. First, let's find the maximum and minimum values of g(x) and h(x) over the interval −2 ≤ x ≤ 2.

To find the maximum value of g(x), we need to minimize π/2(x²). Since x² is always nonnegative, the minimum value of π/2(x²) is 0, which occurs at x = 0. Therefore, the maximum value of g(x) is sin(0)³ = 0.

To find the minimum value of h(x), we take the derivative of h(x) and set it equal to 0 to find the critical points:
h'(x) = -3/4x² - 2x - 94 = 0

Solving for x gives x ≈ -4.29 and x ≈ 3.13. We evaluate h(x) at these critical points and at the endpoints of the interval:
h(-2) ≈ -44.33
h(-4.29) ≈ -119.59
h(3.13) ≈ -100.91
h(2) ≈ -26.67

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