Consider the functions
f: R2→R2 given by f (x,y) = ( 5y−3x, x2) and
g: R2→R2 given by g (v,w) = (−2v2, w3+7)
Find Df and Dg. Use the chain rule to find D(g(f)) at the point (x,y) = (1,2)

Answer: Option (1)

Step-by-step explanation:

\(\angle DMA\) is another name for angle 3, but not \(\angle DME\).

Answer:

I think its C (I think..im doing the test so ill tell u if its right or wrong)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Blake should not include the outlier because it overstates the effect of rainfall on temperature.

Answer:  A) SAS  and   B) ASA  and   (D) LA

Step-by-step explanation:

A) AC = XZ  Sides are congruent

   ∠C = ∠Z   Angles are congruent

   BC = YZ   Sides are congruent  

                  Side-Angle-Side

B) ∠A = ∠X   Angles are congruent

    AC = XZ   Sides are congruent

   ∠C = ∠Z   Angles are congruent  

                  Angle-Side-Angle

C) AB = XY is not given. We can use Pythagorean Theorem to discover that they are the same but since it is not given we cannot use Side-Side-Side.

D) AC = XZ   Legs are congruent

    ∠A = ∠X   acute Angles are congruent  

                     Leg-Angle

This is the true statement  ΔABC≅ΔXYZ due to SAS, ASA, and LA, which are correct options (A) SAS, (B) ASA, and (D) LA

Two triangles are said to be congruent if their corresponding sides and angles are equal.

In ΔABC and ΔXYZ,

Side BC = Side YZ

∠C = ∠Z = 90°

Side AC = Side XZ

According to SAS, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

In ΔABC and ΔXYZ,

∠A = ∠X

Side AC = Side XZ

∠C = ∠Z

According to ASA, two triangles are congruent if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle.

AB = XY is not given. The Pythagorean Theorem can be used to determine that they are equivalent, however, Side-Side-Side cannot be used because it is not a given.

In ΔABC and ΔXYZ,

AC = XZ  

∠A = ∠X

Legs and acute Angles are congruent  

Hence,  ΔADB ≅ ΔBDC due to SAS, ASA, and LA

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Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.

Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):

AC² = AB² + BC²

Substituting the given values, we have:

(AC)² = (AB)² + (BC)²

(AC)² = 16² + (BC)²

(AC)² = 256 + (BC)²

Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.

AC = 2 * radius

To find the radius, we can use the formula for the area of a circle:

Area = π * radius²

Given that the area of the circle is 2897 units², we can solve for the radius:

2897 = π * radius²

radius² = 2897 / π

radius = √(2897 / π)

Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:

(2 * radius)² = 256 + (BC)²

4 * radius² = 256 + (BC)²

Substituting the value of radius, we have:

4 * (√(2897 / π))² = 256 + (BC)²

4 * (2897 / π) = 256 + (BC)²

Simplifying the equation gives:

(4 * 2897) / π = 256 + (BC)²

BC² = (4 * 2897) / π - 256

Now we can solve for BC by taking the square root of both sides:

BC = √((4 * 2897) / π - 256)

To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.

In summary:

BC = √((4 * 2897) / π - 256)

mBC = 90 degrees

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Explanation:

From the properties of a parallelogramgiven in the image below, we will have that

From the parallelogram, we were given the opposite sides to be

Hence,

Since the property of a parallelogram states that opposite sides are equal, we will have that

Answer:

i think its c person :)

Step-by-step explanation:

Answer:

The correct answer is A! :)

We know that our bag has n white tiles and 5 black tiles.

So, the total number of tiles in the bag is n + 5.

We know that a tile is drawn at random and is replaced, then a second tile is drawn.

a) We want to find the probability that the first tile is white.

Because all the tiles have the same probability of being randomly drawn, the probability of drawing a white tile is just the quotient between the number of white tiles and the total number of tiles in the bag.

\(P = n/(n + 5)\)

And for the second draw, we do not have any restrictions, so the probability is the above one.

\(P = n/(n + 5)\)

b) Now we want both tiles to be white.

For the first one we already know the probability, which is:

\(P = n/(n + 5)\)

And because the tile is replaced, the probability of drawing a white tile again is exactly the same:

\(Q =n/(n + 5)\)

The joint probability (the probability of both of these outcomes to happen together) is the product of the individual probabilities.

Probability = \(P*Q = (n/(n + 5))^2\)

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Answer:

Step-by-step explanation:

Remark

The ratios are certainly correct but that doesn't mean that they show similarity. SSA is a very dangerous proposition to use. Redraw triangle DEF of that DF is going to upwards to your right hand side. Make E as it was before. Why isn't this right?

It isn't right because E has gone from being an acute angle to an obtuse angle (an angle larger than 90 but less than 180).

The ratios are still true, but the angles do not match. So the whole answer is incorrect.

Answer:

Step-by-step explanation:

Polynomial with a degree of 3 (due to 3 intersection points). Since the end of the graph is approaching positive infinity, we also know the equation of this graph has a positive coefficient.

(I don't know if you're in calculus yet, but...) We also know that there is a local min and local max, as well as inflection points as the graph changes concavity.

This is an example of a polynomial funciton because the graph of a polynomial function is a smooth continuous curve. Also, I had to graph a polynomial function in one of my past assignments, so I know its appearance.

Answer:

The area of circle 1 is 9 times greater than area of circle 2.

Step-by-step explanation:

Given that:

Radius of circle 1 = 12

Area of circle 1 = πr²

Area of circle 1 = \(3.14*(12)^2 = 3.14*144\)

Area of circle 1 = 452.16

Radius of circle 2 = 4

Area of circle 2 = \(3.14*(4)^2 = 3.14*16\)

Area of circle 2 = 50.24

Let,

x be the number of times circle 1 is bigger than circle 2.

Area circle 1 = x * Area circle 2

\(\frac{452.16}{50.24}=\frac{50.24x}{50.24}\\\\x=9\)

Hence,

The area of circle 1 is 9 times greater than area of circle 2.

since a year has 12 months total, 6 months will be 6/12 of a year, thus

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$15000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\to \frac{6}{12}\dotfill &\frac{1}{2} \end{cases}\)

\(A=15000\left(1+\frac{0.07}{1}\right)^{1\cdot \frac{1}{2}}\implies A=15000(1.07)^{\frac{1}{2}}\implies A\approx 15516.12 \\\\\\ \stackrel{\textit{interest yielded}}{~~ \approx ~~ 15516.12~~ - ~~15000} ~~ \approx ~~ 516.12\)

Answer:

The value of x is 10 because 44-4=40 and divide by 4 will equal 10 which is the answer.

The score assigned by the logistic regression classifier to the positive class is 8.

In logistic regression, the score assigned to a class is calculated by taking the dot product of the weight vector and the feature vector, and adding the bias term. Here, the weight vector is [2, 5, -10, 0, -1], the feature vector is [0, 1, 1, 3, -5], and the bias term is 0.

To calculate the score for the positive class, we multiply each corresponding element of the weight vector and feature vector, and sum up the results.

(2 * 0) + (5 * 1) + (-10 * 1) + (0 * 3) + (-1 * -5) + 0 = 8

Therefore, the score assigned by the classifier to the positive class is 8.

The cross-entropy loss is a measure of how well the classifier is performing. It quantifies the difference between the predicted class probabilities and the true class labels. In logistic regression, the cross-entropy loss is given by the formula:

-1 * (y_true * log(y_pred) + (1 - y_true) * log(1 - y_pred))

Where y_true is the true label (0 for NEG and 1 for POS) and y_pred is the predicted probability for the positive class.

If the correct label for the example is POS, the cross-entropy loss would be calculated using y_true = 1 and y_pred = sigmoid(score). In this case, the score is 8, and the sigmoid function squashes the score between 0 and 1.

If we assume the correct label is NEG, then the cross-entropy loss would be calculated using y_true = 0 and y_pred = sigmoid(score).

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In one sweep, the area covered by the sprinkler is 77.19 sq ft (approx). The area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).

We know that a rotating sprinkler can reach up to 14 feet through a 300-degree angle. Area covered by the sprinkler in one sweep = area of the sector whose radius = 14 feet and angle = 300°Area of sector = (θ / 360) × πr²Where θ = 300°, r = 14 ftArea of sector = (300/360)× π(14)²= 77.19 sq ft (approx) Therefore, the area covered by the sprinkler in one sweep is 77.19 sq ft (approx).

We need to find the total area of the lawn that receives water from this sprinkler. The sprinkler rotates 360 degrees, so it will cover a full circle whose radius is 14 feet. Area of a circle = πr²= π(14)²= 615.752 sq ft (approx) Therefore, the area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).

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The difference in the area of the square 'a' and 'b' as per given side-length is equal to 8 ( x + 1 ) square meters.

Side length of square 'a' = (2x + 1) meters

Side length of square 'b' = ( 2x + 1 + 2 ) meters

                                         = ( 2x + 3 ) meters

Area of a square 'a' = ( side length )²

                                = ( 2x + 1 )²

Area of a square 'b' = ( side length )²

                                = ( 2x +3 )²

Difference in the area of the squares = ( 2x +3 )² - ( 2x +1 )²

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

                                                             = ( 2 ) ( 4x + 4 )

                                                             = 8 ( x + 1 )

Therefore, the difference in the area of the given squares is equal to    8 ( x + 1 ) square meters.

The side length of square 'a' is (2x + 1) meters. The side length of square 'b' is 2 meters longer than that of square a. find the difference in the area of the squares.

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Answer:

\(c=-2\)

Step-by-step explanation:

We are given the function:

\(f(x) = -2c + cx - x^2\)

And that:

\(\displaystyle f^{-1} (5) = -1\)

And we want to determine the value of c.

Recall that by definition of inverse functions:

\(\displaystyle \text{If } f(a) = b, \text{ then } f^{-1}(b) = a\)

So, since f⁻¹(5) = -1, then f(-1) = 5.

Substitute:

\(f(-1) = 5 = -2c + c(-1) - (-1)^2\)

Simplify:

\(5 = -2c - c - (1)\)

Combine like terms:

\(6 = -3c\)

And divide. Hence:

\(c = -2\)

In conclusion, the value of c is -2.

So, there are 52 ways to draw two cards such that the first card is a spade and the second card is a queen.

In a standard 52-card deck, there are 13 cards of each suit: spades, hearts, diamonds, and clubs. Each suit has 4 face cards (Jack, Queen, King, and Ace) and 9 numbered cards (2 through 10).

To find the number of ways to draw two cards such that the first card is a spade and the second card is a queen, we first need to determine the number of spades in the deck, and then the number of queens.

There are 13 spades in a standard 52-card deck, so there are 13 ways to draw a spade as the first card.

There are 4 queens in a standard 52-card deck (one from each suit), so there are 4 ways to draw a queen as the second card.

To find the total number of ways to draw two cards such that the first card is a spade and the second card is a queen, we multiply the number of ways to draw each card: 13 * 4 = 52 ways.

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The area between the curves f(x) = 3 - \(x^{2}\) and g(x) = \(x^{2}\) - 1 can be determined by calculating the definite integral of the absolute difference between the two functions. This can be done using the Fundamental Theorem of Calculus (FTC). The resulting area, denoted by A, can be found by integrating the absolute difference of the functions over a specific interval.

To sketch the area A between the functions f(x) = 3 -\(x^{2}\) and g(x) =\(x^{2}\) - 1, we first need to find the x-values where the two curves intersect.

Setting f(x) equal to g(x), we have:

3 - \(x^{2}\) = \(x^{2}\) - 1

Rearranging the equation, we get:

2\(x^{2}\) = 4

Dividing by 2, we find:

\(x^{2}\) = 2

Taking the square root, we have:

x = ±√2

Now let's plot the functions and shade the area A on a graph:

     |            __________

 3  |         /                            \

     |       /                                \

     |     /                                   \

     |    /                                     \

 1   |_/__________________\_____

    -√2      -1   0    √2   1    2

The area A is the shaded region between the curves f(x) and g(x) from x = -√2 to x = √2.

To express A as a definite integral, we need to determine which curve is on top in different parts of the interval.

For x values between -√2 and √2, the curve g(x) = \(x^{2}\) - 1 is on top.

Therefore, we can express A as the following definite integral:

A = ∫[-√2, √2] (g(x) - f(x)) dx

Now, we can calculate the area A using the Fundamental Theorem of Calculus (FTC).

The indefinite integral of (g(x) - f(x)) with respect to x is:

∫ (g(x) - f(x)) dx = ∫ ((\(x^{2}\)- 1) - (3 - \(x^{2}\))) dx

= ∫ (2\(x^{2}\) - 4) dx

= (2/3)\(x^3\) - 4x + C

To evaluate the definite integral, we substitute the limits of integration:

A = [(2/3)\(x^3\) - 4x] [-√2, √2]

= [(2/3)\((\sqrt{2})^{3}\) - 4√2] - [(2/3)\((-\sqrt{2})^{3}\)- 4(-√2)]

= [(2/3)(2√2) - 4√2] - [(2/3)(-2√2) + 4√2]

= (4/3)√2 - 4√2 + (4/3)√2 + 4√2

= (8/3)√2

Therefore, the area A between the curves f(x) = 3 - \(x^{2}\) and g(x) = \(x^{2}\) - 1 is (8/3)√2.

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Answer:

-1.6, -1.55, -0.4, 1.35, 1.7

Answer:

-1.6,-1.55, -0.4, 1.35, 1.7

Answer:

(x−7,y+5)

A p e x n dat

Answer:

43lb 8oz

Step-by-step explanation:

add 18lb and 25lb which makes 43lb

and then add the oz of 3oz and 5oz which makes 8oz

Answer:

26.019

Step-by-step explanation:

Answer:

26.01

Step-by-step explanation:

As long as the measures of the three angles of a triangle add up to less than 180 degrees, and none of the angles measures more than 90 degrees, the triangle will be acute.

An acute triangle is a triangle that has three acute angles, which are angles that measure less than 90 degrees. All three angles of an acute triangle must be acute, so they must measure less than 90 degrees. The measures of the three angles of an acute triangle can be any combination of angles that add up to less than 180 degrees.

Here are some examples of the measures of the three angles of an acute triangle:

45 degrees, 45 degrees, 90 degrees

30 degrees, 60 degrees, 90 degrees

35 degrees, 40 degrees, 105 degrees

60 degrees, 60 degrees, 60 degrees (this would be an acute equilateral triangle)

As long as the measures of the three angles of a triangle add up to less than 180 degrees, and none of the angles measures more than 90 degrees, the triangle will be acute.

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1) (a) The transformations that occur from the parent function are horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) (-2, -4)

(c) Graph is given below.

1) Given a function,

g(x) = (x + 2)² - 4

(a) Given a parent function p(x) = x².

We can write g(x) as,

g(x) = p(x + 2) - 4

So the transformation is horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) Vertex formula of a parabola is,

y = a (x - h)² + k, where (h, k) is the vertex.

Comparing the given function with vertex form,

Vertex of the parabola = (-2, -4)

(c) Graph of g(x) will be a parabola with vertex at (-2, -4).

It is given below.

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The normal price of each chair is

The percentage off the normal price is

The percentage of the present price of each chair will be

To calculate the present value of one chair, we will use the formula below

By substituting the values, we will have

Since Mr .Krabs bought 4 chairs, the amount he spent will be

By substituting the values, we will have

Therefore,

The amount Mr.Krabs spent is = $6.30

Historical scientists deal with falsification by rigorously analyzing evidence, using peer review and scholarly discourse, and revising hypotheses based on new discoveries and interpretations.



Historical scientists deal with falsification by employing rigorous methodologies and critical analysis of evidence. They strive to gather as much relevant data as possible to test hypotheses and theories. This is done through meticulous research, including the examination of primary sources, archaeological artifacts, historical records, and other forms of evidence. Historical scientists also engage in peer review and scholarly discourse to subject their findings to scrutiny and criticism.

The mechanism used by historical scientists to falsify hypotheses involves a combination of evidence-based reasoning and the application of established principles of historical analysis. They aim to construct coherent and logical explanations that are supported by the available evidence. If a hypothesis fails to withstand scrutiny or is contradicted by new evidence, it is considered falsified or in need of revision. Historical scientists constantly reassess and refine their hypotheses based on new discoveries, reinterpretation of existing evidence, and advancements in research techniques. This iterative process helps to refine our understanding of the past and ensures that historical knowledge remains dynamic and subject to revision.

Therefore, Historical scientists deal with falsification by rigorously analyzing evidence, using peer review and scholarly discourse, and revising hypotheses based on new discoveries and interpretations.

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Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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The height of the flagpole is 12.9 feet to the nearest tenth.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

The boy is 5' 3" tall and his shadow is 4 feet.

The shadow of the flagpole is 17 feet.

The boy is 5.25 feet tall.

Let the height of the flagpole is h feet.

So,

17/h = 5.25/4

h = 68/5.25

h = 12.95

h = 12.9 to one decimal place.

Therefore, h = 12.9 to one decimal place.

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The estimates that is led from the data from a poll conducted by Travelocity , then the percentages are "computed from a sample"  .

The Data from the poll conducted by Travelocity was computed from a sample of travelers and was used to estimate the proportion of travelers

The travelers have certain habits or behaviors, such as checking work email (44%) taking a cell phone (32%) , or bringing a laptop computer on vacation (26%) .

The sample estimates are used to make inferences about the population.

Therefore , the given percentages are that they were  "computed from a sample" .

The given question is incomplete , the complete question is

Data from a poll conducted by Travelocity led to the following estimates:

Approximately 44% of travelers check work email while on vacation, about 32% take cell phones on vacation in order to stay connected with work, and about 26% bring a laptop computer on vacation.

Are the given percentages "population values" or were they "computed from a sample" ?

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