There exists a function with continuous second-order partial derivatives such that (x,y) = 1 + 2 and fy(x, ) = - yo True False Reset selection

Answer:

The numerator (a*c) is the product of two integers ( a and c) and the denominator (b*d) is also ( b and d). This is why multiplying rational numbers is like multiplying integers.

Step-by-step explanation:

Answer:

f(x)=2x+x2

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

2x→1

x^2→2

The largest exponent is the degree of the polynomial.

2

Step-by-step explanation:

if it helped you please mark me a brainliest :))

Answer:

triangle

Step-by-step explanation:

The advantages may be of using the method of completing the square to solve quadratic equations to estimate the values of x and y roots without calculating them.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Using Completing the square.

1. First of all we can find the minimum or maximum of the equation immediately.

2. Second is to cuts out the need to use the given ones (a, b, c) in the quadratic formula.

3. It allows estimating the values of x and y roots without calculating them.

Then Estimating on a test is a very valuable asset.

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The equation can be rewritten into the following form

(x + 6)²

To rewrite the equation x² + 12x + 5 = 3 so that the left side of the equation is in the form (x + a)², we need to complete the square. By manipulating the equation, we can transform it into the desired form.

First, let's subtract 3 from both sides of the equation:

x² + 12x + 5 - 3 = 0

Simplifying:

x² + 12x + 2 = 0

Now, to complete the square, we take half of the coefficient of x (which is 12) and square it, which gives us 36. We add this value to both sides of the equation:

x² + 12x + 36 + 2 = 36

Simplifying further:

(x + 6)² + 2 = 36

Thus, the rewritten equation in the desired form (x + a)² is (x + 6)² + 2 = 36.

In the given equation, we start by subtracting 3 from both sides to isolate the quadratic terms on the left side. This yields x² + 12x + 2 = 0. To complete the square, we consider the coefficient of x, which is 12. We divide it by 2 to obtain 6 and then square it to get 36. We add 36 to both sides of the equation, resulting in (x + 6)² + 2 = 36. This form aligns with the desired format (x + a)², where a = 6.

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Answer:

15min : 4 3/4 laps

30min : 9 2/4 laps

45min: 14 1/4 laps

60min: 20 laps

Step-by-step explanation:

A positively skewed distribution is due to an extremely large number.

A positively skewed distribution is a type of distribution in which the majority of the data values are clustered towards the left side of the distribution, with a tail extending to the right. This means that there are relatively more smaller values in the dataset than larger values. In a positively skewed distribution, the mean of the dataset is typically larger than the median, and the mode may not be a good representation of the central tendency of the data. This is because the presence of a long tail on the right-hand side of the distribution pulls the mean towards the higher values, while the median remains closer to the center of the dataset. Some common examples of positively skewed distributions include income distributions, where there are a few extremely high earners that skew the data towards the right, and test scores, where there may be a few students who perform extremely well and pull the average higher than the median.

Here,

A positively skewed distribution occurs when the tail of the distribution extends to the right, and the majority of the data is clustered towards the left side of the graph. This means that there are relatively more smaller values in the dataset than larger values. One common cause of positive skewness is the presence of extremely large values, also called outliers, in the dataset. These large values pull the mean of the dataset towards the right, resulting in the tail of the distribution stretching in that direction.

Therefore, out of the options provided, the correct answer is "an extremely large number."

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The surface area of a cylinder using 3.14 with a radius 15 and hight of 72 is 8195.4 square unit.

Given that

Radius of cylinder = 15

Height of cylinder = 72

We have calculate the surface area of cylinder

Since we know that

A cylinder's surface area is the area occupied by its surface in three dimensions.
A cylinder is a three-dimensional structure with circular bases that are parallel. It is devoid of vertices. In most cases, the area of three-dimensional shapes refers to the surface area.

Surface area is measured in square units. For instance, cm², m², and so on.

A cylinder is made up of circular discs that are placed on top of one another.  Because the cylinder is a three-dimensional solid, it contains both surface area and volume.

Surface area of cylinder = 2πrh + 2πr²

Here r represents radius of cylinder

And h represents height of cylinder

Now put the values we get

= 2x3.14x15x72  + 2x3.14x15x15

= 6782.4 + 1413

= 8195.4

Hence the surface area of the given cylinder = 8195.4

square unit.

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Answer:

I. 56 cubic feet of water.

II. 5 feet

Step-by-step explanation:

Answer:  4

Step-by-step explanation:

10 + 4 + 4 +2 = 20/4 = 4

probability that exactly 5  customers pay in cash  is 0.178863

Total number of customer = 20

probability of payment in cash = 0.3

probability of payments via other methods  = 1 - 0.3 =0.7

let probability of payment in cash be p

and probability of payments via other methods be q

To find the probability that exactly y customers pay in cash

p [ x = y ] =  \(n_c__x p^x q ^(n-x)\)

here value of y= 5 and n=20 , p =0.3 , q= 0.7

putting the values in above equations we get:

p [ x =5 ] = \(20_c__5 * 0.3 ^5 * 0.7 ^15\)

p [ x =5 ] = (15504) * (0.00243) * (0.0047475615)

p [ x =5 ] = 0.178863

so the probability that exactly 5  customers pay in cash  is 0.178863

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Recall the formula for compound interest

Using the formula, rearrange the equation and solve in terms of time t

Substitute the given values and we get

A = $2700, P = $1100, n = 12 (12 months in a year), r = 0.045 (from 4.5%)

Rounding the answer to the nearest tenth, the time it takes is 20 years.

not sure if this is your answer because you didnt show a picture but

Step-by-step explanation:

both 8, 15, 17 and 15, 20, 25 will form a right triangle.

Answer:

The correct answer is True

Answer:

True

Step-by-step explanation:

Each branch of a tree diagram is the likelihood of that outcome happening. You multiply as you go along the branch.

a) 0.bar(36) expressed as a fraction in simplest form is 4/11. b) 0.3bar(6) expressed as a fraction in simplest form is 0.4. c) 0.36 expressed as a fraction in simplest form is 9/25.

(a)  To express 0.bar(36) as a fraction in simplest form, we can use the concept of repeating decimals. Let x = 0.bar(36). Multiplying x by 100 gives:

100x = 36.bar(36)

Subtracting the original equation from the multiplied equation eliminates the repeating part:

100x - x = 36.bar(36) - 0.bar(36)

99x = 36

x = 36/99

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9:

x = (36/9) / (99/9) = 4/11

Therefore, 0.bar(36) expressed as a fraction in simplest form is 4/11.

(b) o express 0.3bar(6) as a fraction in simplest form, let's call it x. Multiplying x by 10 gives:

10x = 3.6bar(6)

Subtracting the original equation from the multiplied equation eliminates the repeating part:

10x - x = 3.6bar(6) - 0.3bar(6)

9x = 3.6

x = 3.6/9

x = 0.4

Therefore, 0.3bar(6) expressed as a fraction in simplest form is 0.4.

(c) To express 0.36 as a fraction in simplest form, we can write it as 36/100 and simplify it. Both the numerator and denominator have a common factor of 4, so we can divide both by 4:

36/100 = 9/25

Therefore, 0.36 expressed as a fraction in simplest form is 9/25.

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The predicted number of runs for the player with only 86 hits can be calculated using the equation Runs = Hits + Walks - Home Runs. Plugging in the values given, we get: Runs = 86 + Walks - Home Runs. Therefore, the predicted number of runs for the player is dependent on the number of walks and home runs they have.

To solve for the predicted number of runs, we can use the following steps:

Therefore, the predicted number of runs for the player with only 86 hits can be calculated by plugging in the values of the number of walks and home runs into the equation Runs = Hits + Walks - Home Runs.

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Answer:

fraction- 1/4

Answer:

slope: -1/3

you find the slope by taking one point (0,2) and then finding the change in y over the change in x from it to another point (3,1) :

1-2/(3-0) = -1/3

According to algebra property of power of a power, the following results are listed below:

Case 1: (x⁵)³ = x¹⁵ (Correct choice: 1)

Case 2: (x⁸)⁷ = x⁵⁶ (Correct choice: 4)

Case 3: (x⁷)¹⁰ = x⁷⁰ (Correct choice: 2)

Case 4: (x¹⁴)³ = x⁴² (Correct choice: 3)

In this question we find four cases of power of a power, whose solution is described by the following algebra property:

(xᵃ)ᵇ = xᵃᵇ, where x, a and b are real numbers.

Now we proceed to determine the solution to each case:

Case 1

(x⁵)³ = x¹⁵

Case 2

(x⁸)⁷ = x⁵⁶

Case 3

(x⁷)¹⁰ = x⁷⁰

Case 4

(x¹⁴)³ = x⁴²

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Answer

The answer to this equation would be 64. '^' just means multiplied by. It has the same mathematical definition as the multiplication sign.

Step-by-step explanation:

USING PEMDAS (NO PARENTHESES)

4 x 2 x 2 x 4

8 x 2 x 4

16 x 4

64

USING PEMDAS (WITH PARENTHESES)

(4 x 2) x (2 x 4)

(8) x (2 x 4)

(8) x (8)

64

If every individual in a population has an equal chance of being selected for a sample, the sample is said to be a "random sample" or a "simple random sample."

A random sample is a sampling technique used in statistics to gather data from a population. It is considered one of the most unbiased and reliable methods for selecting a sample. In a random sample, each individual in the population has an equal probability of being selected, regardless of their characteristics or attributes.

This equal chance of selection eliminates any systematic bias and ensures that the sample is representative of the population.

The process of obtaining a random sample involves assigning a unique identifier to each individual in the population and using a randomization method to select the desired number of individuals.

Random sampling can be conducted through various techniques, such as simple random sampling, where individuals are selected directly from the population using a random number generator or a randomization table.

The goal of a random sample is to reduce the potential for selection bias and increase the generalizability of the findings to the larger population. By giving every individual an equal opportunity to be included in the sample, researchers can make more accurate inferences and draw conclusions about the population as a whole.

This type of sampling method ensures that each member of the population has an equal opportunity to be included in the sample, making it a representative subset of the population.

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Answer:

\(\frac{333}{1000}\) ≠ 0.3 because it is 0.333, not 0.3 .

0.3 is defined by \(\frac{3}{10}\).

Hope this helps!

Answer:

\( \$ 4.68 \times 10^7\)

Step-by-step explanation:

\( monthly \: payment = \$ 1.3 \times {10}^{6} \\ 3 \: years = 3 \times 12 = 36months \\ money \: made \: by \: athelete \: at \: the \: end \: of \: \\3 \: years \\ = \$ 1.3 \times {10}^{6} \times 36 \\ = 46.8\times {10}^{6} \\ = \$4.68\times {10}^{7} \)

Answer:

We have the function y = k(x).

We want to define a new function p(x), such that is equal to k(x) but translated down 3 units.

When we have a general case of a function y = f(x), the function g(x) = f(x) + A is a translation of A units up (if A is positive) or A units down (if A is negative).

Then if we want to go 3 units up, we should have:

p(x) = k(x) + 3.

So now our points are:

(x, y) = (x, p(x)) = (x, k(x) + 3)

So for all the points the y-coordinate has ben mooved 3 units up.

\(\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill\)

\(\log_3\left( \cfrac{18}{25} \right)\implies \log_3(18)~~ - ~~\log_3(25)\implies \log_3(2\cdot 3\cdot 3)~~ - ~~\log_3(5^2) \\\\\\\ [\log_3(2)+\log_3(3)+\log_3(3)]~~ - ~~2\log_3(5) \\\\\\\ [\log_3(2)+1+1]~~ - ~~2\log_3(5)\implies 2+\log_3(2)-2\log_3(5)\)

The monthly rate for the given loan is 1.0118%.The annual rate for this loan is 12.1423%.

Given loan: $150,000

Payment per month: $1,770

Duration of loan: 10 years

Interest = ?

The formula for monthly payment is given by:

\(PV = pmt x (1 - (1 + r)^-n) / r\)

Where, PV is the present value, pmt is the payment per period, r is the interest rate per period and n is the total number of periods.Solving the above formula for r will give us the monthly rate for the loan.

r = 1.0118%The monthly rate for the given loan is 1.0118%.The annual rate can be calculated using the following formula:

Annual rate = \((1 + Monthly rate)^12 - 1\)

Annual rate = 12.1423%

The annual rate for this loan is 12.1423%.The effective annual rate can be calculated using the following formula:

Effective annual rate =\((1 + r/n)^n - 1\)

Where, r is the annual interest rate and n is the number of times interest is compounded per year.If interest is compounded monthly, then n = 12

Effective annual rate = (1 + 1.0118%/12)^12 - 1

Effective annual rate = 12.6801%

The effective annual rate for this loan is 12.6801%.

Total amount paid after 10 years = Monthly payment x Number of payments

Total amount paid after 10 years = $1,770 x 120

Total amount paid after 10 years = $212,400

The total amount paid after 10 years is $212,400.

The future value for this loan can be calculated using the following formula:

FV = PV x (1 + r)^n

Where, PV is the present value, r is the interest rate per period and n is the total number of periods.If the loan is paid off in 10 years, then n = 120 (12 payments per year x 10 years)

FV = $150,000 x (1 + 1.0118%)^120

FV = $259,554.50

The future value for this loan is $259,554.50.

Thus, the monthly rate for the loan is 1.0118%, the annual rate for this loan is 12.1423%, the effective annual rate for this loan is 12.6801%, the total amount paid after 10 years is $212,400 and the future value for this loan is $259,554.50.

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The entries of the table, denoted as T(i, j), represent the length of the longest nicely spaced subsequence ending at index i, with the difference between the last element and the element at index j.

The recurrence relation for the entries of the table can be defined as follows:

  T(i, j) = max(T(j, k) + 1), where 0 <= k < j and |S(i) - S(j)| <= 5.

  This means that we consider all previous elements (j) that have a difference of at most 5 with the current element (i), and we update the maximum length of the nicely spaced subsequence by adding 1 to the length of the subsequence ending at index j (T(j, k)).

  The base case is T(i, j) = 1, where there are no previous elements that satisfy the nicely spaced condition.

Pseudocode for the algorithm:

  Initialize an array T with length n, where n is the length of the input sequence S.

  Set all values in T to 1.

  Initialize a variable max_length to 1.

  for i = 1 to n:

      for j = 1 to i-1:

          if |S[i] - S[j]| <= 5:

              T[i] = max(T[i], T[j] + 1)

              max_length = max(max_length, T[i])

  Return max_length as the length of the longest nicely spaced subsequence of S.

The running time of this algorithm can be analyzed as follows:

  - The outer loop iterates through each element of the sequence, so it takes O(n) time.

  - The inner loop iterates through all previous elements for each element, so it takes a total of O(n^2) time in the worst case.

  - Therefore, the overall time complexity of the algorithm is O(n^2).

  Since we only use an array of size n (T) to store the lengths of subproblems, the space complexity is O(n).

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