Given the following table of values for a one-to-one function g −1(x), determine the graph of g(x).


x 0 one half 1 3 over 2 2
g−1(x) −2 −1 1 5 13



power function increasing from the left in quadrant 3 asymptotic to the line y equals negative 3 passing through the points 0 comma negative 2 and 1 comma 1
power function increasing from the left in quadrant 2 asymptotic to the line y equals 3 passing through the points 0 comma 4 and 1 comma 7
logarithmic function increasing from the left in quadrant 3 asymptotic to the line x equals negative 3 passing through the points negative 2 comma 0 and 1 comma 1
logarithmic function increasing from the left in quadrant 4 asymptotic to the line x equals 3 passing through the points 4 comma 0 and 7 comma 1

The nonlinear regression model that specifies the given shape is option (d): yi = exp(β0 + β1x1i + β2x2i + ui).


Option (d) represents a nonlinear regression model where yi (the dependent variable) is equal to the exponential function of the sum of β0 (intercept), β1x1i (the coefficient of the first independent variable x1i), β2x2i (the coefficient of the second independent variable x2i), and ui (the error term).

The exponential function introduces nonlinearity into the model, allowing for curved or nonlinear relationships between the dependent variable and the independent variables. This form is suitable for capturing complex nonlinear shapes in the data. The other options either lack the necessary components (coefficients or nonlinearity) or provide a linear specification.

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Using the properties of the median, the area of quadrilateral BFGE is 210 square units.

Let's take ΔABC by drawing diagonal AC. The area ΔABC is 1/2 the area of the rectangle.

Segment CF is the median of that triangle and the median of a triangle divides the "big" triangle into two triangles of equal area

So Area of ΔFBC =  1/2 (1/2) (1260) = 315 1260 square units

Segment AE is a 2nd median for ΔABC and another theorem (property) for medians says that the 2nd median divides the areas of the two triangles created by one median in the ratio 2:1.

So, area of quadrilateral BFGE = 2(area of ΔGEC)

If x =  area of ΔGEC

Then 2x + x = 315

       3x = 315

         x = 105

Hence, area of quadrilateral BFGE = 2 x 105 = 210 square units

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Using proportions, it is found that the scale of dilation is of \(\frac{3}{4}\).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The length of LM changed from 12 to 9, hence:

\(\frac{9}{12} = \frac{3}{4}\).

The length of MN changed from 8 to 6, hence:

\(\frac{6}{8} = \frac{3}{4}\).

Thus, the scale of dilation is of \(\frac{3}{4}\).

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Answer:

21 glasses of water.

Step-by-step explanation:

You can do a proportion.

\(\fraction{1 glass}{1/6 of a bottle)\) or

1 glass/1/6 of a bottle.

x glasses/3.5 bottles.

You can cross multiply.

1/6 times x is 1/6x

1 times 3.5 is 3.5/

1/6x=3.5.

do the reciprocal of 1/6 which is 6.

So, 6 times 3.5 is 21.

Therefore, you have 21 glasses of water.

Emily needs  to have a score of 92 on the next quiz have an overall average of 84

What is the mean of exam scores?

The mean of exam quizzes is the sum of the scores divided by the number of quizzes taken, more like an average of all scores

Initially, average score on 4 quizzes is 82

average=total score/number of quizzes

average score on 4 exams=82

total score =unknown=assumed as x

number of exams=4

82=x/4

x=4*82

x=328

In order to have an overall average score of 84, we would sum the total score of 4 exams and the fifth exam and divide by 5 quizzes

84=(328+y)/5

84*5=328+y

420=328+y

y=420-328

y=92

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Average waiting time for FCFS: 8.75

Average waiting time for SJF: 4.75

To solve this scheduling problem using FCFS (First-Come, First-Served) and SJF (Shortest Job First) algorithms, let's go step by step:

Schedule order for FCFS:

The FCFS algorithm schedules processes based on their arrival time. So, the schedule order for FCFS is as follows:

Pl -> P2 -> P3 -> P4

Average waiting time for FCFS:

To compute the average waiting time for FCFS, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P2 | 3 | 10 | 3

P3 | 4 | 6 | 13

P4 | 5 | 1 | 19

Average waiting time = (0 + 3 + 13 + 19) / 4 = 8.75

Therefore, the average waiting time for FCFS is 8.75.

Schedule order for SJF:

The SJF algorithm schedules processes based on their running time. The process with the shortest running time gets executed first. If multiple processes have the same running time, the process with the earliest arrival time is selected first. The schedule order for SJF is as follows:

Pl -> P4 -> P3 -> P2

Average waiting time for SJF:

To compute the average waiting time for SJF, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P4 | 5 | 1 | 3

P3 | 4 | 6 | 6

P2 | 3 | 10 | 10

Average waiting time = (0 + 3 + 6 + 10) / 4 = 4.75

Therefore, the average waiting time for SJF is 4.75.

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In order to simplify and verify trig identities, one needs to use the rules of trigonometry and algebra to manipulate the equation until it is in a simplified form.

The most common trig identities to remember include the Pythagorean identity, reciprocal identities, quotient identities, and sum and difference identities. When simplifying an equation, it is important to remember to include the negative sign when necessary and to factor out any common factors.

After simplifying, it is important to verify the equation. This can be done by plugging in known values for the variables and verifying that the equation is true. By utilizing the rules of trigonometry and algebra, one can simplify and verify trig identities. This process is essential for working with trigonometric functions.

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Answer:

680km

Step-by-step explanation:

2720/4=680

Step-by-step explanation:

x=√(141)

that is the answer

Answer:

x = \(\sqrt{141}\)

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 22² = 25²

x² + 484 = 625 ( subtract 484 from both sides )

x² = 141 ( take square root of both sides )

x = \(\sqrt{141}\)

The IH states that the sum of the angles in convex polygon C(which, by the IH, is (n - 2)·π) and the sum of the angles in triangle B (180°) is the same as the sum of the angles in A.

Using induction all convex polygons with n vertices have angles that add to (n - 2)·π, therefore let P(n) be that. We will demonstrate that P(n), where n≥3, holds for every n ∈ N. We demonstrate P(3), which states that any convex polygon with three vertices has an angle total of 180 degrees. Any triangle formed by such a polygon has angles that add up to 180°.

Assume that P(n) holds for some n ≥ 3 and that all convex polygons with n vertices have angles that add to (n-2) 180° for the inductive step. We demonstrate P(n+1), which states that each convex polygon with n+1 vertices has an angle sum of (n-1)·π. Let A represent any n+1-vertex convex polygon.

The IH states that the sum of the angles in convex polygon C (which, by the IH, is (n - 2)·π) and the sum of the angles in triangle B (180°) is the same as the sum of the angles in A. As a result, the total angle in A is (n-1) 180°. Thus, the induction is complete and P(n + 1) holds.

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Equation of a Line

The slope-intercept form of a line is:

y = mx + b

Where m is the slope.

We are given the equation of a line:

24x - 2y = 38

Subtracting 24x:

-2y = -24x + 38

Dividing by -2:

y = (-24/-2)x + 38/(-2)

Operating:

y = 12x - 19

We can see that b = 12, thus the slope of the graph is 12

Answer:

D. 12

Answer: 1/5 or 20%

Step-by-step explanation:

4 red + 9 blue + 7 white = 20 total

neither blue nor white means it has to be red so 4/20 or 1/5

Answer:

Its B :D

Step-by-step explanation:

Answer:

68 pounds of seed are needed per acre, as it is only a one acre field.

Answer: If it takes 68 pounds to plant a one acre field then it's 68 pounds of seeds per acre.

Unless you messed up the question?

First, multiply the amount of shirts.

9 * 6 = 54

Second, subtract the coupon.

54 - 5 = $49

Best of Luck!

Answer:

49

Step-by-step explanation:

You will buy 6 shirts and 9 dollars each

9*6 = 54

Then take off the coupon

54-5 = 49

Step-by-step explanation:

Area of the big square

Area=L×L

A=7×7

A=49

Area of the inner square(the small square)

A=L×L

A =3×3

A=9

Area of the shaded portion is equal to the difference of area of the big square and that of the inner square

Area of shaded portion=49-9

Area=40 cm

Answer:

25 km

Step-by-step explanation:

Distance covered in 20 min = 5 km

Distance covered in 1 min = 5/20 km or 1/4 km.

Distance covered in 100 min =

1/4 km x 100 = 25 km

Answer:

22.5 cm²

Step-by-step explanation:

Area of Triangle Formula: 1/2bh

Step 1: Define variables

h = 9

b = 5

Step 2: Plug into formula

1/2(9)(5)

1/2(45)

45/2

22.5 cm²

Answer:

22.5 cm^2.

Step-by-step explanation:

Area = 1/2 * base * height

= 1/2 * 9 * 5

= 22.5 cm^2.

Answer:

BC = \(\frac{12}{13}\)

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

BC² + AC² = AB²

BC² + (\(\frac{5}{13}\) )² = 1²

BC² + \(\frac{25}{169}\) = 1 ( subtract \(\frac{25}{169}\) from both sides )

BC² = \(\frac{169}{169}\) - \(\frac{25}{169}\) = \(\frac{144}{169}\) ( take square root of both sides )

BC = \(\sqrt{\frac{144}{169} }\) = \(\frac{12}{13}\)

The parametric equation for the line segment from (−4, 14, 32) to (10, −9, 46), using the parameter t is r(t) = (-4+14t, 14-23t, 32+14t), for 0<= t <=1.

The given points are (-4,14,32) and (10,-9,46).

To find the parametric equations for the line segment we need to follow the below steps.

Step 1: Calculate the direction vector of the line segment. We use the difference of the given points for this purpose.  Let d= direction vector = (10,-9,46)-(-4,14,32)  = (14,-23,14)

Step 2: Choose the initial point on the line segment. We can choose (-4,14,32).

Step 3:  Since there are infinite choices for parameter t, choose any parameter t. We choose t in the range 0<= t <=1, to get the parametric equation for the line segment.

Let the parametric equation for the line segment be r(t).

Then,  r(t) = (-4,14,32) + t(14,-23,14)    

= (-4+14t, 14-23t, 32+14t), for 0<= t <=1.

Thus, the parametric equation for the line segment is r(t) = (-4+14t, 14-23t, 32+14t), for 0<= t <=1.

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To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.

1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.

2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.

3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.

4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.

If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.

It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.

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Answer:

x=2sqrt2

Step-by-step explanation:

The legs are equal, thus the sides are x, x, and hypotenuse is 4. This means that x^2+x^2=4^2. Thus, 2x^2=16 => x^2=8 => x= sqrt8 => x=2sqrt2

The chapter test from maths teacher will contain 15 questions of worth 4 points.

Let the number of questions having weightage of 4 marks be x. Now, we know that problems will only be worth 2 and 4 points. Also we know that some of these problems will be 35. Thus, let us form the equation.

20 + x = 35

Rewriting the equation according to x

x = 35 - 20

Performing subtraction on Right Hand Side of the equation

x = 15

Thus, there will be 15 questions of 4 points.of the maths test to be conducted next week.

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The equation of the circle graphed in this problem is:

(x - 5)² + y² = 16.

The equation of a circle of center \((x_0, y_0)\) and radius r is given by:

\((x - x_0)^2 + (y - y_0)^2 = r^2\)

For the circle graphed, we have that:

Hence the equation of the circle graphed is:

(x - 5)² + y² = 16.

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Answer:

Step-by-step explanation:

x / 12 = 3 / 8

x = 3 / 8 x 12

x = 3 / 94

x = 32

32 / 12 = 3 / 8

In & ΔKPN &Δ AKM

∠KPN =∠ LKMN = 90°

∠ KNP = ∠KNM

KN =KN (Common side)

By A-S-A congruency

Now, MN = MP

=2x+70 = 128

⇒ 2x=58

80 option-(a) is correct:

x = 58 = 29

The identical sign (=) is used in mathematical formulas to indicate that two statements are identical. Mathematical functions are used to show that many academic quantities are equal, and these statements of fact are called assertions. For example, the solution y + 6 = 12 is divided into two parts by the equal symbol, along with the numbers 12 and b + 6. It is feasible to determine how many lines are represented by each portion of a symbol. A symbol's meaning typically runs counter to itself.

Here,

Since O is the center of the circle, we know that OM and OP are radii of the circle, and hence have equal lengths. Therefore, we can write:

OM = OP

128 + 2x + 70 = 2OM (using the fact that MN = 128 and NP = 2x + 70)

198 + 2x = 2OM

We also know that OM is half the length of the diameter of the circle, so:

OM = (1/2)DP (where DP is the diameter of the circle)

Therefore, we can write:

198 + 2x = DP

So,

MN * NP = (NP - MN) * N\(R^2\)

128 * (2x + 70) = (2x + 70 - 128) *\(R^2\)

Simplifying this equation gives:

128 * (2x + 70) = (2x - 58) *\(R^2\)

256x + 12870 = 2xR^2 - 58*\(R^2\)

256x + 128*70 = (2x - 58)*\(R^2\)

Dividing both sides by 2x - 58 gives:

(256x + 128*70) / (2x - 58) = \(R^2\)

We still don't know the value of\(R^2\), but we can simplify the  left hand side of this equation:

(256x + 128*70) / (2x - 58) = 128(x + 70) / (x - 29)

Therefore, we can write:

128(x + 70) / (x - 29) =\(R^2\)

Substituting this expression  \(R^2\) into the equation 198 + 2x = DP gives:

198 + 2x = 128(x + 70) / (x - 29)

Multiplying both sides by (x - 29) gives:

198(x - 29) + 2x(x - 29) = 128(x + 70)

Simplifying this equation gives:

198x - 5760 + 2x² - 58x = 128x + 8960

2x² - 28x - 14720 = 0

Dividing both sides by 2 gives:

x² - 14x - 7360 = 0

We can solve this quadratic equation by using the quadratic formula:

x = (-b ± √b² - 4ac)) / 2a

where a = 1, b = -14, and c = -7360.

Plugging in these values gives:

x = (14 ± √(14)

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Question: In the diagram, MN is tangent to K at M, NP is tangent to K at P, MN = 128, and NP = 2x + 70. Find the value of x.

A. 29

B. 99

C. -9

D. 38

Answer: 17/18

Step-by-step explanation:

4 1/4 is equall to 17/4.

4 1/2 is 9/2.

We can flip 9/2 to get 2/9*17/4.

That simplifies to 17/18.

Answer:

A.

Step-by-step explanation:

<JEK is complementary to <DFH.

From the figure we see that angles DFH and HFG are complementary.

Since angles JEK and HFG are both complementary to <DFH, then

<JEK is congruent to <HFG

<HFG is vertical to <CFL, so angles HFG and CFL are congruent.

That makes angles JEK and CFL complementary.

Answer: A.