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11. Find the Taylor polynomial of degree 2 for the given function, centered at the given number a: a f(x)=e^{-2x} at a=-1. b. S(x) = cos(5x) at a = 2Pi.

Answer:

|6-8|=2

Step-by-step explanation:

You see, absolute value makes any number positive. It doesn't matter if the number was already positive or negative. |x|>=0. If that makes sense. So, 6-8 would be -2. But -2 in absolute value would be 2.

Answer: not spend anything

Step-by-step explanation:

not spend anything :) YOUR WELCOME

The absolute minimum value of f(x, y) is -16, occurring at the points (7, 0) and (7, 10). Therefore, the minimum value is -16.

To find the absolute minimum and absolute maximum of the function f(x, y) = 6 - 4x + 7y on the closed triangular region with vertices (0, 0), (7, 0), and (7, 10), we need to evaluate the function at the critical points and the boundary of the region.

Critical points: To find critical points, we need to take the partial derivatives of f(x, y) with respect to x and y and set them equal to zero.

∂f/∂x = -4 = 0

∂f/∂y = 7 = 0

Since there are no solutions to these equations, there are no critical points within the region.

Boundary of the region: We need to evaluate the function at the vertices and on the sides of the triangle.

Vertices:

f(0, 0) = 6 - 4(0) + 7(0) = 6

f(7, 0) = 6 - 4(7) + 7(0) = -16

f(7, 10) = 6 - 4(7) + 7(10) = 60

Sides:

Side 1: From (0, 0) to (7, 0)

y = 0

f(x, 0) = 6 - 4x + 7(0) = 6 - 4x

The minimum occurs at x = 7 with a value of -16.

Side 2: From (0, 0) to (7, 10)

y = (10/7)x

f(x, (10/7)x) = 6 - 4x + 7((10/7)x) = 6 - 4x + 10x = 6 + 6x

The minimum occurs at x = 0 with a value of 6.

Side 3: From (7, 0) to (7, 10)

x = 7

f(7, y) = 6 - 4(7) + 7y = -22 + 7y

The minimum occurs at y = 0 with a value of -22.

From the above evaluations, we can conclude:

The absolute minimum value of f(x, y) is -16, occurring at the points (7, 0) and (7, 10).

The absolute maximum value of f(x, y) is 60, occurring at the point (7, 10).

Therefore, the minimum value is -16.

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True. In a pairwise scatter plot matrix, each scatterplot represents the relationship between two variables.

Since the scatterplot between variable X and variable Y is the same as the scatterplot between variable Y and variable X, the matrix is perfectly symmetric.

The scatterplot at the lower-left corner is indeed identical to the one at the upper-right corner. This symmetry is a result of the fact that the relationship between X and Y is the same as the relationship between Y and X.

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The number of volunteers who worked more than 15 hours can be found by summing up the frequencies

of the bars in the histogram that represent the groups with more than 15 hours of community service.

To determine how many volunteers worked more than 15 hours using the given histogram.

Identify the section of the histogram that represents volunteers who worked more than 15 hours.

Read the height (frequency) of the bars representing the groups of volunteers with more than 15 hours of community

service.

Add the frequencies of these bars to get the total number of volunteers who worked more than 15 hours.

In conclusion, the number of volunteers who worked more than 15 hours can be found by summing up the frequencies

of the bars in the histogram that represent the groups with more than 15 hours of community service.

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Answer:

Graph C.

The question asks for the graph that consists of:

Non-negative values

Values that are, at most, 80

This means that any graphs where a value goes below 0 or above 80 do not work. C is the only graph that does not go below 0 or above 80.

Answer:

Step-by-step explanation:

Petra

Answer:

Lin

Step-by-step explanation

(Plz listen to other awnser if right) I need coins plz ignore answer thx

The area of the triangle is 13 square units.

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According to the given information the line integral is 8(1+125\(\sqrt{110}\)) / 15 .

What distinguishes a line integral from a definite integral?

Line integrals include several integrals across a curve, but definite integrals only entail a single integral over a specified interval. This is the primary distinction between the two types of integrals.

\(\int\limits_c {xy} \, ds\),  C : x = t^2 , y = 2t,  0 ≤ t ≤ 3

x' = 2t , y' = 2

ds = \(\sqrt{(x')^2 + (y')^2}\)

\(\sqrt{4(t)^2 + 4}\)

\(\int\limits C {xy} \, ds\) = \(\int\limits^3_0 {2.2t.2\sqrt{1+t^2}} \, dt\)

t = tanθ

dt = (1+\(tan^{2}\)θ)dθ = (\(sec^{2}\)θ)dθ

= \(\int\limits^3_0 {4t^3\sqrt{1+t^2} } \, dt\)

= 8(1+125\(\sqrt{110}\)) / 15

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The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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The correct option is c) Easier interpretation. One of the main advantages of simple models is their ease of interpretation. Simple models tend to have fewer parameters and less complex mathematical equations, making it easier to understand and interpret how the model is making predictions.

This interpretability can be valuable in various domains, such as medicine, finance, or legal systems, where it is important to have transparent and understandable decision-making processes.

Complex models, on the other hand, often involve intricate relationships and numerous parameters, which can make it challenging to comprehend the underlying reasoning behind their predictions. While complex models can sometimes offer higher accuracy or make more detailed predictions, they often sacrifice interpretability in the process.

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The translation of the polygon 3 units down and 4 units left is;

A''(-2, -4)

B"(-3, -7)

C"(-1, -8)

D"(1, -6)

We are given the coordinates of the polygon as;

A(2, -1), B(1, -4), C(3, -5), D(5, -3)

Now, we are told that all points are translated 3 units down and 4 units left. Thus, the new coordinates are;

A'(2, -1 - 3) = A'(2, -4)

B(1, -4 - 3) = B'(1, -7)

C(3, -5 - 3) = C'(3, -8)

D(5 , -3 - 3) = D'(5, -6)

Translation of 4 units left is now;

A''(2 - 4, -4) = A''(-2, -4)

B"(1 - 4, -7) = B"(-3, -7)

C"(3 - 4, -8) = C"(-1, -8)

D"(5 - 4, -6) = D"(1, -6)

The translation of the polygon 3 units down and 4 units left is;

A''(-2, -4)

B"(-3, -7)

C"(-1, -8)

D"(1, -6)

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The number of ways to arrange the 11 donors in line is 11!. 11! = 39,916,800.

The donors can be in line in different ways.

To calculate the number of distinguishable ways, we can use the concept of permutations. Since all the donors are distinct (different blood types), we need to find the total number of permutations of these donors.

The total number of donors is 4 (type O+), 4 (type A+), and 3 (type B+), giving a total of 11 donors.

The number of ways to arrange these donors in line can be calculated using the formula for permutations. The formula for permutations of n objects taken all at a time is n!.

Therefore, the number of ways to arrange the 11 donors in line is 11!.

Calculating 11!, we get:

11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 39,916,800.

Hence, the donors can be in line in 39,916,800 different ways.

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1. The mean of a dataset represents the average value of the entire set of numbers. It is calculated by adding up all the values and dividing by the number of values in the dataset. Knowing the standard deviation of a dataset adds information about how much the values deviate from the mean.

A high standard deviation indicates that the values are more spread out from the mean, while a low standard deviation indicates that the values are closer to the mean. It can help to identify outliers and the overall variability of the dataset.

2. A p-value is a statistical measure that helps to determine whether the null hypothesis (there is no significant difference between two groups) is true or false.

It is the probability of obtaining a result as extreme or more extreme than the observed result, assuming that the null hypothesis is true. A p-value of less than 0.05 (typically) is considered statistically significant, which means that there is strong evidence to reject the null hypothesis and accept the alternative hypothesis (there is a significant difference between the two groups).

3. Alpha is the level of significance that is set to determine whether a p-value is statistically significant or not. It is typically set at 0.05, which means that if the p-value is less than 0.05, then the result is considered statistically significant and the null hypothesis is rejected.

If the p-value is greater than 0.05, then the result is not statistically significant and the null hypothesis cannot be rejected. In summary, alpha and p-value are related because alpha sets the threshold for determining whether a p-value is statistically significant or not.

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Step-by-step explanation:

between -5 and -62

-7,-10,-60...so..on

between -1/7 and 1/8

Multiply any number by number with both the numbers but it should be multiplied by both the numbers:

for example:

-1/7×3/3= -3/21 ; 1/8×3/3= 3/24

So,

-2/21,2/24,1/24

hope it helps

Answer:

Pleas find attached the scatter plot of the given data

Step-by-step explanation:

The given data for the chocolate sales are as follows;

Sales ($)                  \({}\)                               Temperature

100                  \({}\)                                            92

213                  \({}\)                                             88

830                  \({}\)                                            54

679                  \({}\)                                            62

209                  \({}\)                                            85

189                  \({}\)                                             16

1110                  \({}\)                                            52

456                  \({}\)                                            65

422                  \({}\)                                            68

235                  \({}\)                                            89

199                  \({}\)                                              91

The scatter plot of the data created with Microsoft Excel is attached.

Answer:

Step-by-step explanation:

If p varies inversely as the square of q and inversely as r if p equals 36 and Q equals to 3 and R equal to 4, then when q = 5 and r = 4, p = 1.

The relationship between p, q, and r can be represented as:

p ∝ 1/q^2 * 1/r

where ∝ means "varies inversely as".

Substituting the given values into this equation, we get:

36 ∝ 1/3^2 * 1/4

36 ∝ 1/36

Multiplying both sides by 36, we get:

p = 1

So, when q = 3 and r = 4, p = 1.

To find p when q = 5 and r = 4, we use the same equation and solve for p:

p ∝ 1/5^2 * 1/4

p ∝ 1/100

Multiplying both sides by 100, we get:

p = 1

So, when q = 5 and r = 4, p = 1.

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Answer:

x = -2/9

Step-by-step explanation:

8x+1=-x-1

8x = -x -2

9x = -2

x = -2/9

Answer:

836 m

Step-by-step explanation:

Given that the tracks are similar, therefore, the ratio of the lenght of all corresponding sides of the inside track to the outside track are equal, and have the same scale factor.

Only 1 side of the inside track is given as 395 m. It corresponds to the side of the outside that measures 553 m. Therefore:

scale factor = 395:553 = \( \frac{395}{553} = 0.7 \)

Find the remaining two sides of the insider tracks by multiplying the lenght of the side of the outside tracks that corresponds to each by the scale factor.

Thus:

280*0.7 = 196 m

350*0.7 = 245 m

The remaining 2 side lengths of the inside tracks are 196 m and 245 m.

If Chang completes 1 lap around the inside tracks, he would have gone: 395 + 196 + 245 = 836 m.

Answer: D. 1277

Step-by-step explanation:

First you divide 553 by 395 : 553/395=1.4

Now that you have 1.4 , you multiply that times both 350 and 280.

280 • 1.4=392

350 • 1.4=490

Add up all the sides: 395+392+490=1277

The gas station serves 16 vehicles per hour, and 72 vehicles arrive in 4 hours. The vehicles will spend 4.50 hours at the gas station.



To find the total time the vehicles will spend at the gas station, we need to calculate the total number of vehicles that arrive and then divide it by the rate at which the gas station serves vehicles.

Given:

Arrival rate: 18 vehicles per hour

Service rate: 16 vehicles per hour

Time: 4 hours

First, let's calculate the total number of vehicles that arrive during the 4-hour period:

Total number of vehicles = Arrival rate * Time

                      = 18 vehicles/hour * 4 hours

                      = 72 vehicles

Since the gas station can serve 16 vehicles per hour, we can determine the time it takes to serve all the vehicles:

Time to serve all vehicles = Total number of vehicles / Service rate

                         = 72 vehicles / 16 vehicles/hour

                         = 4.5 hours

Therefore, the vehicles will spend 4.5 hours at the gas station. Rounded to 2 decimal places, the answer is 4.50 hours.

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Answer:

B

Step-by-step explanation:

The values of x that will give a range of 55 include 42 and -13.

A range simply means the difference between the highest number that is given and the lowest number that is given.

In this case, the chose numbers include:.

Larger number = 42

Smaller number = -13

Range = Larger number - Small number

= 42 - (-13)

= 42 + 13

= 55

The range of 55 is gotten.

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The two possible values of x given the range are -13 and 58.

Range is used to measure the variation of a dataset. Range is the difference between the highest number in the dataset and the lowest number in the dataset.

Range = highest number - lowest number

x can either be the largest number in the dataset or the smallest number in the dataset.

Value of x if it is the smallest value in the dataset.

42 - x = 55

x = 42 - 55

x = -13

Value of x if it is the largest value in the dataset.

x - 3 = 55

x = 55 + 3

x = 58

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The domain are all of the x-values that are located on the x-axis of a cartesian coordinate while the range all of the y-values that are located on the y-axis of a cartesian coordinate.

In Mathematics, a domain is the set of all real numbers for which a particular function is defined.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

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Answer:

8th generation: 34 relatives

9th generation: 55 relatives

Step-by-step explanation:

Fibonacci sequence is a sequence that is in such a manner that each number will be the sum of the two preceding ones.

Thus, to get how many relatives in the 8th generation, we will need to add the number of relatives in both the 6th and 7th generation.

We are given number of relatives in the 6th and 7th generation as 13 and 21 relatives respectively.

Thus;

No. of relatives in 8th generation = 13 + 21 = 34 relatives

Similarly;

No. of relatives in 9th generation is = no. in 7th generation + no. in 8th generation = 21 + 34 = 55 relatives

The slope-intercept form of the equation can be written as y = -x - 19

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis). Equation of line is the equation that is satisfied by each point that lies on that line.

The equation given is y + 9 = -(x + 10)

Rewriting this equation in y = mx + c format;

y + 9 = -(x + 10)

y + 9 = -x - 10

y = -x - 10 - 9

y = -x - 19

The equation is y = -x - 19

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Answer:

Step-by-step explanation:

To find the boundary of the critical region, given the type I error probability and sample size, we need to calculate the critical value using the standard normal distribution table and the formula for the sample mean.

The critical region is defined by the range of sample means that reject the null hypothesis, based on the given level of significance and the alternative hypothesis.

The critical region is the range of values of the test statistic that leads to rejection of the null hypothesis, based on a predetermined level of significance and the alternative hypothesis. To find the boundary of the critical region, we need to calculate the critical value using the standard normal distribution table and the formula for the sample mean. For a one-tailed test with alpha = 0.01 and n = 10, the critical value is 2.33, and the critical region is defined by the sample mean greater than 181.18. For a one-tailed test with alpha = 0.05 and n = 10, the critical value is 1.645, and the critical region is defined by the sample mean greater than 177.21. For a one-tailed test with alpha = 0.01 and n = 16, the critical value is 2.33, and the critical region is defined by the sample mean greater than 178.82. For a one-tailed test with alpha = 0.05 and n = 16, the critical value is 1.645, and the critical region is defined by the sample mean greater than 177.27. Therefore, the larger the sample size and the smaller the level of significance, the narrower the critical region and the higher the power of t

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Answer: A. 4/3 x

Step-by-step explanation:

x miles in 90 minutes to ? miles in 120 minutes

90 miles to 120 miles is 1.3333 which is equal to 4/3.

Multiply it to x and you have A. 4/3x