Consider f = x41 + x42, with x1 and x2 real. To minimize f, I set ∇f = 0 which yields x∗ = (0, 0)T . I claim that this is the global minimum. Explain my reasoning.

Time taken by Adam to complete his seventh lap of the circular track as per given data is equal to 1minute 28seconds.

As given in the question,

Time taken by Adam to complete hi first lap of circular track = 1 min 58 sec

First term t₁ = 1 minute 58seconds

Time taken by each successive lap is 5seconds less then the previous lap

Common difference 'd' = -5seconds

let time taken to complete the seventh lap be t₇

t₇ = t₁ + ( 7 - 1 ) d

⇒ t₇ = 1 minute 58 seconds + ( 6 ) (- 5seconds)

       =  1 minute 58 seconds - 30seconds

      = 1 minute 28 seconds

Therefore, the time taken by Adam to complete his seventh lap is equal to

1 minute 28 seconds.

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Answer:

\(x = 14ft\)

Step-by-step explanation:

Given

\(Actual\ Length = 21ft\)

Model:

\(3\ ft = 2\ in\)

Required

Determine the length of the replica

Represent the model as a ratio:

\(Ratio = 3\ in:2\ ft\)

Convert to fraction

\(Ratio = \frac{3\ in}{2\ ft}\)

Represent the actual lengths as a ratio

\(Ratio = 21\ ft : x\)

Where x is the length of the replica

Convert to fraction

\(Ratio = \frac{21\ in}{x}\)

Equate both ratios (because they are in proportion)

\(\frac{3\ in}{2\ ft} = \frac{21\ in}{x}\)

\(\frac{3}{2\ ft} = \frac{21}{x}\)

Cross Multiply:

\(3 * x = 21 * 2\ ft\)

\(3x = 42\ ft\)

Solve for x

\(x = \frac{42ft}{3}\)

\(x = 14ft\)

Hence, the length of the replica is 14ft

Answer:

0.87 inches (or if it meant after 3.5 more hours, 4.37 inches)

Step-by-step explanation:

15/3.5 is 4.29(rounded to the nearest hundredth)

3.75/4.29= 0.87 inches

(or if it meant after 3.5 more hours)

3.5+0.87= 4.37

Answer: Answer on the bottom below

Step-by-step explanation: And p.s this is worth 18 points because it needed to divide the points in two.- Have a brilliant day mate ^_^

The answer to the given question is as follows:

The given information is to be analyzed and observed. The findings are as follows: Most students prefer to learn English because it is a global language and used worldwide, making it the most popular international language among the students. The increasing importance of China and its economy may be the reason why students are taking up Chinese courses. Due to this, Chinese is the second most studied international language after English. A few students are interested in taking up French courses as compared to other courses. Italian is the least preferred international language among the students.

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Answer:

45 yards

Step-by-step explanation:

Formula to find area of rectangle: Length * Width

Given:

Length = 70 yards

Area = 3,150 yards

Width = 3,150/70

        ==> 45 yards

Width = 45 yards

Answer:

one side is 16, the other is 8\(\sqrt{3}\)

Step-by-step explanation:

30-60-90 angle triangle always give the following sides

1-\(\sqrt{3}\)-2 , which is a-b-c

to label your triangle as such

8= a

other leg =b

hypotenuse = c

so. if a =8, then

c = 8*2 =16

b=8\(\sqrt{3}\)

Answer: No it’s not.

Step-by-step explanation: So if to find the next number, you add five, then all of the numbers in the sequence will either end with 8 or 3. (5+3 or 0+3). Therefore 97 is not a term in the sequence.

The average rate of change of y with respect to x over the interval [1, 5] for function \(y=4x^{2}\) is 24.

To find the average rate, follow these steps:

Therefore, the average rate of change of y with respect to x over the interval [1, 5] for the function \(y=4x^{2}\)  is 24.

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Answer: 34

Step-by-step explanation:

The probability that the student receives a grade above C is 0.75

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that the student receives a grade above C be P ( C )

And , the equation will be

Let the probability you will get an A in this class is P ( A ) = 0.25

Let the probability you will get a B in this class is P ( B ) = 0.50

Now , the events P ( A ) and P ( B ) are mutually exclusive events

So , P ( A ∩ B ) = 0

And , P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B )

On simplifying the equation , we get

P ( A ∪ B ) = P ( C )

And , probability that the student receives a grade above C = P ( A ) + P ( B )

The probability that the student receives a grade above C = 0.25 + 0.50

The probability that the student receives a grade above C = 0.75

Hence , the probability is 0.75

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The equation to represent the time taken by piper to walk and skate is  x + 2x = 21. The correct option is (A).

A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.

Suppose the number of times piper walked be x.

Then, the number of times he skated is 2x.

Now, as the total time spent on walking and skating is 21 minutes, the equation can be written as,

Total time = Time for walking + time for skating

⇒ 21 = x + 2x

⇒ 3x = 21

⇒ x = 7

Thus, the solution of the equation is x = 7 which is equivalent to the time for walking in minutes.

Hence, the required equation is  x + 2x = 21 and its solution is 7.

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The correct option is: (i) and (iii) are correct statements but not (ii).

The correct answer is:

(i) The uniform probability distribution's shape is a rectangle.

(ii) The uniform probability distribution is symmetric about the mode.

(iii) In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values.

Therefore, the correct option is: (i) and (iii) are correct statements but not (ii).

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Hello !

Answer:

\(\boxed{\sf V{cone} \approx 2408.55 m^3}\)

Step-by-step explanation:

To find the volume of a cone with the radius of its base and its height, we will apply the following formula:

\( \sf V{cone} = \dfrac{\pi \times r^2 \times h}{3} \)

Where r is the radius of its base and h is its height.

Given:

Let's substitute our values into the formula:

\(\sf V{cone} = \dfrac{\pi (10)^2(23)}{3} = \dfrac{2300\pi}{3} \ \ \\\boxed{\sf V{cone} \approx 2408.55 m^3}\)

Have a nice day ;)

We can always find a monochromatic rectangle by reducing the problem to finding a monochromatic rectangle in a smaller area by moving the bottom of the rectangle up by one unit method.

What is rectangle?

A rectangle is a quadrilateral (a 2-dimensional shape with four sides) with four right angles. This means that opposite sides of a rectangle are parallel and congruent, and all four angles are equal to 90 degrees.

Let us consider a rectangle with sides parallel to the coordinate axes. Such a rectangle can be uniquely determined by two pairs of points that define its opposite corners. If all four of these points are the same color, then we have found a monochromatic rectangle. Otherwise, there are three cases to consider:

The two points at the top of the rectangle are the same color, and the two points at the bottom are the other color. In this case, we can reduce the problem to finding a monochromatic rectangle in a smaller area by moving the bottom of the rectangle up by one unit.

The two points on the left side of the rectangle are the same color, and the two points on the right side are the other color. In this case, we can reduce the problem to finding a monochromatic rectangle in a smaller area by moving the left side of the rectangle to the right by one unit.

Both pairs of points are of mixed color. In this case, we can reduce the problem to finding a monochromatic rectangle in two smaller areas by dividing the rectangle into four equal parts with a vertical or horizontal line.

By repeating this process on the smaller rectangles obtained in each case, we can eventually find a monochromatic rectangle. Since the rectangles we consider at each step have half the area of the previous ones, this process terminates after at most log_2(A) steps, where A is the area of the original rectangle.

Therefore, we can always find a monochromatic rectangle with this method.

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Complete question:

Each point in the x-y plane colored red or blue. show that there is a rectangle whose corners are all the same color.

In a course of 12 weeks, Perry will be able to play a total of 25 pieces of the piano Leon.

A total of 18 pieces of piano are learnt by Perry in a course of 9 weeks.

By using simple algebra, we can find the number of pieces that will be played by Perry in one week,

So, we can write, The learing speed,

Number of piano pieces learnt = Weeks

19 pieces = 9 weeks

Learning speed = 19/9 Pieces per week

So, the number of pieces learnt in 12 weeks is,

Number of pieces learnt = 19/9 x 12

Number of pieces learnt = 25.22

Number of pieces learnt = 25

So, Perry will be able to play 25 pieces.

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Answer:

\(a_{62}=-107\)

Step-by-step explanation:

This is an arithmetic sequence:

\(a_n=a_1+(n-1)d\)

where d is the common difference and n is the index of any given term.

The common difference of the given sequence is -2:

\(13-15=-2\\11-13=-2\)

Using the first term and the common difference, you can write the equation for this sequence:

\(a_n=15+(n-1)(-2)\)

And using that equation, you can find the 62nd term:

\(a_{62}=15+(62-1)(-2)\\a_{62}=15+(61)(-2)\\a_{62}=15-122\\a_{62}=-107\)

The volume of a silo cylinder with radius of 8 feet and height of 36 feet is 7235 feet cube.

The volume of a cylinder can be calculated as follows;

Volume = πr²h

where

Therefore,

r = 8 ft

h = 36 ft

volume = 3.14 × 8² × 36

volume = 3.14 × 64 × 36

volume of the silo = 7234.56

Therefore, the volume of the cylindrical silo is 7235 ft³

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The required computations are: G(-1) = -3 and G(G(-1)) = -9

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The Figure that can be transformed into Figure K by a reflection across the x-axis, and a dilation of 1/2 is given as follows:

A. Figure J.

The first transformation is a reflection across the x-axis, which has the rule defined as follows:

(x,y) -> (x, -y).

Meaning that the orientation of the rotated figure is rotated upside down compared to the original figure.

Then the second transformation is a dilation by a scale factor of 1/2, meaning that each vertex of the figure is multiplied by 1/2, and thus the image size is half the original image.

Figure K is in the third quadrant, hence:

Hence Figure J is the original figure, meaning that option A is correct.

The options are given by the image shown at the end of the answer.

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The feasible region is (3.42, 4.29) and the extreme point is (3.42, 4.29)

For part (b), the feasible region is also (3.42, 4.29) and the extreme point is also (3.42, 4.29)

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

A + 2B ≤ 12

5A + 3B ≤ 30

A, B ≥ 0

Multiply the first by 5

5A + 10B ≤ 60

5A + 3B ≤ 30

Subtract the inequalities

7B ≤ 30

Divide by 7

B ≤ 4.29

The value of A is calculated as

A + 2 * 4.29 ≤ 12

Evaluate

A ≤ 3.42

So, the feasible region is (3.42, 4.29)

In this case, the extreme point is also the feasible region

Here, we have

A + 2B ≤ 12

5A + 3B ≤ 30

A, B ≥ 0

This is the same as the expressions in (a)

This means that the solutions would be the same

So, the extreme point is also the feasible region

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Answer:

True

Step-by-step explanation:

The statement "a ratio that compares a number to 100 is indeed called a percent" is true.

Percentages are used to express proportions or ratios out of 100. They are commonly denoted by the symbol "%."

Percentages provide a convenient way to represent fractions or parts of a whole in a standardized and easily understandable format.

For example, if a student scores 85 out of 100 on a test, it can be expressed as 85%, indicating that the student achieved 85 out of possible 100 marks.

Thus, the statement "a ratio that compares a number to 100 is indeed called a percent" is true.

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Answer:

hmm

Step-by-step explanation:

Answer:

(2, 0) and (6, 0)

Step-by-step explanation:

\(y = x^2 - 8 x + 12\)

To get the x intersept put y = 0

\(x^2 - 8 x + 12 = 0 \\\\x^2 - 6 x - 2 x + 12 = 0 \\\\x(x- 6) - 2(x - 6) = 0 \\\\(x - 2) (x - 6) = 0 \\\\x = 2 and x = 6\)

So, the intersepts are

(2, 0) and (6, 0)

For the equation y = -2/x + 3 - 4, the key points are the x-intercept (-1, 0), the y-intercept (0, -1), and the asymptotes x = 0 and y = -4. The domain is all real numbers except x = 0, and the range is all real numbers except y = -4.

For the equation y = 3x - 2 - 5, the key point is the y-intercept (0, -7), and the graph is a straight line with a slope of 3 and a y-intercept of -7.

For the equation y = -2/x + 3 - 4, we can identify the key points by analyzing the equation. The x-intercept occurs when y = 0, which gives us -2/x + 3 - 4 = 0. Solving this equation, we find x = -1. So the x-intercept is (-1, 0). The y-intercept occurs when x = 0, which gives us y = -2/0 + 3 - 4, which is undefined. The vertical asymptote occurs when the denominator becomes zero, so x = 0 is an asymptote. The horizontal asymptote occurs as x approaches infinity or negative infinity, and in this case, it is y = -4. Therefore, the graph has the key points (-1, 0) and (0, -1), and the asymptotes x = 0 and y = -4. The domain is all real numbers except x = 0, and the range is all real numbers except y = -4.

For the equation y = 3x - 2 - 5, the key point is the y-intercept, which occurs when x = 0. Plugging in x = 0, we find y = -7. So the y-intercept is (0, -7). Since the equation is linear with a slope of 3, we can draw a straight line passing through the y-intercept. Therefore, the graph is a straight line with a slope of 3 and a y-intercept of -7.

Please note that without specific coordinates, it is challenging to accurately sketch the graphs. The provided information gives a general understanding of the key points and characteristics of the graphs.

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Answer:

1/3

Step-by-step explanation:

The left side of Figure A is 6 units long

The left side of Figure B is 2 units long

6 * what = 2

Divide each side by 6

what = 2/6

what = 1/3

The scale factor is 1/3

Answer:

\(\frac{1}{3}\)

Step-by-step explanation:

Figure A has a base of \(6\) units.

Figure B has a base of \(2\) units.

So, 6 * \(x\) (the scaled factor) = 2 which simplified is \(6x=2\).

Now, we divide 6 on both sides giving us \(x = \frac{2}{6}\) which can be further simplified into \(\frac{1}{3}\)

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9514 1404 393

Answer:

  a^4·m^4·n^8

Step-by-step explanation:

The applicable rule of exponents is ...

  (a^b)(a^c) = a^(b+c)

__

m^2n^3 aanm^2a^2n^4

= a^(1+1+2)·m^(2+2)·n^(3+1+4)

= a^4·m^4·n^8

Answer:

A

Step-by-step explanation:

(6-2)/(5+2)

4/7

Answer:

4/7              6 -2/2+5 = 4/7

simple

Answer:

Step-by-step explanation:= 21/4 divided by -5/2

= 21/4 x -2/5. flipped and multiplied

= -21/10

= -2 1/10

Answer:

-2 1/10

Step-by-step explanation:

5 1/4 = 21/4

-2 1/2 = -5/2

21/4 ÷ -5/2=-21/10 = -2 1/10