use implicit differentiation to find ∂z/∂x and ∂z/∂y. e4z = xyz

The quotient is 2x² + 10x − 5, and the remainder is 0.

What is synthetic division?

Synthetic division is a method in algebra for manually performing Euclidean division of polynomials that requires less writing and fewer calculations than long division. It is typically taught for division by linear monic polynomials, but the method can be applied to any polynomial.

The given polynomial is (2x³ + 4x² - 35x + 15) and we have to divide this polynomial by (x - 3).

By using synthetic division

   2x³ + 4x² - 35x + 15

Take the constant term of the divisor with the opposite sign and write it to the left

     3 |   [tex]x^3[/tex]    [tex]x^2[/tex]     [tex]x^1[/tex]      [tex]x^0[/tex]

        |   2     4     -35     15

   ----|----------------------------

Write down the first coefficient as it is

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

   3 |   2            4     -35     15

      |         3.2 = 6

 ----|----------------------------

         2           10    

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

 3 |   2      4     -35     15

    |           6       30

-----|----------------------------

         2    10       -5

Again, we get

3 |   2      4     -35     15

    |           6      30   -15

-----|----------------------------

         2    10     -5      0

We have completed the table and have obtained the following resulting coefficients: 2,10,−5,0.

Thus, the quotient is 2x² + 10x − 5, and the remainder is 0.

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The statements that are True about the Correlations is , "Correlations are a measure used to determine the degree to which two variables are related" , the correct option is (c) .

In the question,

few statements about Correlation is given ,

we need to find the statement that is True .

we know that , Correlation is the term that is used to measure the degree of relationship between two variable ,

the correlation can be negative , positive or 0 ,

and the negative correlation implies that if one variable increases then other variable decreases and vice a versa .

So , from the above information about Correlation ,

we conclude that , the True statement is "Correlations are a measure used to determine the degree to which two variables are related. "

Therefore , the statement in option (c) is True  .

The given question is incomplete , the complete question is

Select the statement below that is true about correlations.

(a) Correlations can only be negative

(b) Correlations are a measure of how much one variable changes as the other variable changes

(c) Correlations are a measure used to determine the degree to which two variables are related.

(d) Correlations are a measure of causation between two variables

(e) A negative correlation implies no relationship between variables

(f) Correlations can only be positive .

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What is this question I don't understand

System A: (1, -1)

System B: No solution

Answer:

System A

The system has a unique solution: x=1, y=-1

System B

The system has no solution

Step-by-step explanation:

System A

Use simultaneous equations to see if we can solve the system by multiplying the second equation by -1 and adding them together:

5x + 3y = 2

-4x - 3y = -1

We get (5-4)x+(3-3)y=(2-1), which simplifies to x=1

If x=1:

5+3y=2

3y=-3

y=-1

Since we have specific answers for x and y, we can say the system has a unique solution.

System B

If y is equal to both 5x+8 and 5x+5, that means

5x+8=5x+5

Subtracting 5x from both sides we get 8=5, which is illogical.

Therefore the system has no solution

Given two calculations are different.

What is a square of a number?

The square of any number can be calculated by multiplying the number by itself twice.

Let 'a' be any number then the square of this number 'a' will be

                        a² = a × a

Now  - 3² = - (3) × (3)

               = -9  ----------(I)

and (-3)² = (-3) × (-3)

              = 9 ----------(II)

By observing (I) and (II) we can say that in the second case just because of the scope of brackets the square of -3 would result in 9.

But in the first case square of 3 would give 9 and because of the minus sign, it gave -9.

Hence, These two calculations are different.

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In the discrete distribution the probability that x equals 5 is 0.51

A discrete probability distribution counts occurrences that have countable or finite outcomes. This is in contrast to a continuous distribution, where outcomes can fall anywhere on a continuum

The summation of the discrete probabilities must be always equal 1,

The probaility of 2 is 0.16

The probaility of 6 is 0.30

The probaility of 8 is 0.21

We need to find The probaility of 5

To find the probaility of 5, we can subtract the probaility of all other numbers from 5.

Probability (X = 5) = 1 - (0.25+0.16+0.08) = 0.51

Therefore, in the discrete probability distribution the probability that x equals 5 is 0.51

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Answer:9/10

Step-by-step explanation:

make 3/4 equal to 3/20 by multiplying by 5

15/20 + 3/20 = 18/20

18/20 = 9/10

Answer:

y+5 = -2(x+3)

Step-by-step explanation:

y-(-5) = -2(x-(-3)

y+5 = -2(x+3)

y +5 = -2x - 6

y = -2x - 6 - 5

y = -2x - 11

Step-by-step explanation:

b.) 8/7≈ 1.1

Final.) and then using the exponential decay formula, 18.1 will be left after

The exact value of tan(θ ) in simplest radical form is 1/9 .

What is the trigonometric ratio?

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.

(-9,-1), is a point with x= -9 = adjacent side, y= -1 = opposite side

tan(θ ) = opposite side/adjacent side = -1/-9  = 1/9

1/9 can't be simplified further

So, the exact value of tan(θ ) in simplest radical form is 1/9 .

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Ordered triplet (-2, -6, 3) is the solution of the system of equations

3x+4y-z = 5

5x-y + 3z = -7

9x + 5y + 7z = -21

How to determine if an ordered triplet is solution to system of equations?

To determine if an ordered triplet is a solution to a system of three equations, we substitute the values of the variables into each equation. If the ordered triple makes all three equations true, it is a solution to the system.

According to the given question:

System of equations are

3x+4y-z = 5

5x-y + 3z = -7

9x + 5y + 7z = -21

Now, substituting (-1, 2, 0) in every equation to check if LHS = RHS for each.

1. 3x + 4y - z = 5

    LHS = 3(-1) + 4(2) - 0 = -3 + 8 = 5 = RHS

2. 5x-y + 3z = -7

   LHS = 5(-1) - 2 + 0 = - 5 -2 = -7 = RHS

3. 9x + 5y + 7z = -21

   LHS = 9(-1) + 5(2) + 0 = -9 + 10 = 1 ≠ RHS

Therefore (-1, 2, 0) is not the solution for the system of equations.

Similarly substituting (-2, -6, 3) in every equation.

Clearly (-2, -6, 3) satisfies the system of equations.

Hence (-2, -6, 3) is the solution to the system of equations.

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Answer: First number is 16, second number is 17.

Step-by-step explanation
16 + 17 = 33

16 x 7 = 112
17 x 5 = 85

112 + 85 = 197

Answer:

129723

Explanation:

[tex]1800(1+0.13)^{35} \approx 129723[/tex]

Answer:

About 2.1 pounds a month.

Step-by-step explanation:

In this question, we know the amount of weight gained and the time it took, 20 pounds and 9.5 months.

to find the rate, we can do:

20/9.5

about 2.1

So, the answer will be:

about 2.1 pounds / month

There may be an association, but not a correlation unless the variables are quantitative. There could be a correlation between the average number of hours of TV watched per person and number of crimes committed per year. Even if there is a relationship, one does not cause the other.

Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate).

What are qualitative and quantitative variables?

The variables are classified as qualitative or quantitative as follows:

Qualitative variables assume labels as values.

Quantitative variables assume numbers as values.

The relevance of the variables according to association and correlation are given as follows:

Qualitative variables can have association.

Quantitative variables can have correlation.

The variables in this problem are given as follows:

Television watching -> yes/no -> qualitative.

Crimes committed -> yes/no -> qualitative.

As they are qualitative variables, they can have association, and thus there is no correlation between the two variables

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Answer:

A,B, C is the answer

Step-by-step explanation:

35 +25 +15 +25= 100

I hope this helps

The value of the quotient of the polynomial is 2x^2 + 2x + 10 and the remainder is 28

A method for solving a rational number that represents a polynomial divided by a monomial or another polynomial is called "dividing polynomials." In order to divide normally, we place the dividend and the divisor in the exact same manner.

Divide the first term of the dividend by the highest term of the divisor, which in this case is x (i.e., the term with the highest power of x).

Divide the divisor by the outcome you just got (the first term of the eventual quotient).

By following the above rules where

2x3-4x2+3x+2 is divided by the x-3, We get the following equation

where

quotient is 2x2+2x+10

and the remainder is 28

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0.0721 proportion of the students in the class have a height less than Ikue's height.

Here, we are given that a set of elementary school student heights are normally distributed with a mean of 105 cm ⇒ μ = 105 and standard deviation 10 cm ⇒ σ = 10

The z score can be calculated using the formula-

Z = (X - μ) / σ

X is the observed value, here, X = 90.4

Since we need the proportion of student heights are lower than ikue's height, we look at the negative z score only.

Substituting the values in the z score formula we get-

Z = ( 90.4 - 105) / 10

Z = - 1.46

Now, from the z score tables, we see that the value of Z < -1.46 is 0.0721.

Thus, 0.0721 proportion of the students in the class have a height less than Ikue's height.

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Using the binomial distribution, it is found that the probability of getting 3 heads from an biased coin is of 8/125

The probability that a variable would take one of two independent values under a certain set of constraints or assumptions is summarised by the binomial distribution, a probability distribution in statistics.

The basic assumptions of binomial distribution are that each trial has just one result, that each trial has the same chance of success, and that each trial is mutually exclusive or independent of the others.

The binomial distribution is a typical discrete distribution used in statistics, as opposed to a continuous distribution such as the normal distribution.

The formula is:

P(X=x)Cn,x.p^x.(1-p)^n-x

Cn,x = n!/z!(n-x)!

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem, we have that when n = 3,P(X=3)=27/125 , hence:

p^3 =27/125

p=3/5

The probability of 3 heads is P(X = 0), hence:

P(X=x)=Cn,x.p^x.(1-p)^n-x = C3,0.(3/5)^0.(2/5)^3= 8/125

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The Division Equation that has solution of -9/14 will be [tex]\frac{-18x}{28x}[/tex].

What is Division Equation?

Mathematical equations involving the division operator are referred to as division equations. An equals sign appears in a division equation in its entirety.

For given solution i.e. -9/14, we can write division equation as follows,

           [tex]\frac{-9* 2x}{14*2x}[/tex]

    i.e.   [tex]\frac{-18x}{28x}[/tex]

Hence, The division equation that has solution of -9/14 will be [tex]\frac{-18x}{28x}[/tex].

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The final answer to this Problem is 32000 pesos.

What is Company?

A company is an organization that provides goods or services to its customers in exchange for money. Companies are typically formed by entrepreneurs or business owners who have a vision for a product or service they want to offer. The company is responsible for producing the product or service, marketing it, and then distributing and selling it to the public. Companies must also manage their finances and comply with any legal or regulatory requirements. Companies are typically owned by shareholders who reap the profits of the business. Successful companies often have a strong corporate culture that is reflected in their mission and values.

Pesos that initially was available = 15000 pesos

During year Pesos purchased by company = 25000 pesos

Total pesos at end of the year = 15000 + 25000 pesos = 40000 pesos

Total pesos remaining at end of year = 8000 pesos

Hence pesos consumed in the complete year = 40000 - 8000= 32000 pesos

Hence 32000 pesos are left in the company

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The object continues to roll without slipping, and the actual force of static friction stays constant.

A force that holds an object at rest is called static friction.

The definition of static friction is: The resistance people feel when they attempt to move a stationary object across a surface without actually causing any relative motion between their body and the surface they are moving the object across.

The range of static friction is 0 to the minimum force required to initiate motion.

The following is the formula to determine static friction: Normal Force x Static Friction Coefficient = Static Friction.

So, in the given situation the object keeps rolling without slipping, and the static friction's actual force remains constant.

Therefore, the object continues to roll without slipping, and the actual force of static friction stays constant.

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The coordinates of a' after scaling factor of 1/3 is a'(1,1).

Given:

points a (3, 3) and b (3, 6) are two vertices of rectangle abcd. the rectangle is dilated by a scale factor of 1/3.

Rectangle:

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel.

Scale factor :

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.

scale factor = 1/3

= (3*1/3 , 3*1/3)

= (3/3 , 3/3)

= (1,3/3)

= (1,3)

Therefore the coordinates of a'(1,1).

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The distance between holes is 11.7m

A diagonal is a line segment that joins one corner (vertex) of a polygon to another but is not an edge (side). In other words, it joins any two non-adjacent vertices of a polygon. So, we form a diagonal in a polygon when we directly join any two vertices which are not joined by any side.

let x be the distance between opposite holes which is the diagonal of the rectangle.

so that,

x^2 = 11^2 + 4^2

x^2 = 121 + 16

x^2 = 137

x = [tex]\sqrt{137}[/tex]

x = 11.7km

In conclusion the distance between holes is 11.7km

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Answer:

-626.8

Step-by-step explanation:

78 -716 + (0.8)(14)

78 - 716 + 11.2

(78 -716) + 11.2

-638 + 11.2

-626.8

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{20})\hspace{10em} \stackrel{slope}{m} ~=~ 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{20}=\stackrel{m}{ 1}(x-\stackrel{x_1}{4}) \\\\\\ y-20=x-4\implies {\Large \begin{array}{llll} y=x+16 \end{array}}[/tex]

If an 80% confidence interval for a proportion is found to be (0.27, 0.33), then the sample proportion would be 0.30

Sampling is frequently used to estimate the proportion of a population that has a given attribute, such as the proportion of all faulty goods coming off an assembly line or the proportion of all individuals visiting a retail store who make a purchase before leaving. The percentages for the population and sample are written as p and p, respectively. Thus, if 43% of individuals visiting a business make a purchase before departing, p = 0.43; if 78 people enter the store and make a transaction, p=78/200=0.39.

The sample proportion is a random variable because it differs from sample to sample in ways that are impossible to anticipate in advance.

How to solve?

For this case the confidence interval is given by:

(0.27; 0.33)

We can find the estimaed proportion in the following way:

p = (0.27 + 0.33)/2 = 0.30

then the sample proportion would be 0.30

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Answer:

  (2n -5)(3n -2)

Step-by-step explanation:

You want to factor 6n² -18n +10.

You want to start by finding factors of the product (6)(10), the first and last coefficients, that have a sum equal to -18, the linear term coefficient.

This sum is negative, but the product is positive, so both factors will be negative. Listing the smallest magnitude first, we have ...

  60 = (-1)(-60) = (-2)(-30) = (-3)(-20) = (-4)(-15) = (-5)(-12) = (-6)(-10)

The sums of these pairs are -61, -32, -23, -19, -17, -16. This identifies the pair of interest as (-4)(-15).

From here, there are a couple of ways you can proceed. One is to write the linear term as a sum using these values:

  6n² -4n -15n +10

Now, you can factor by grouping:

  = (6n² -4n) -(15n -10)

  = 2n(3n -2) -5(3n -2)

  = (2n -5)(3n -2) . . . . . . . . the factorization you want

Another way you can do this is to write binomial factors using the leading coefficient for each one. The product of these must be divided by the leading coefficient for it to remain equal to the original trinomial.

  = (6n -4)(6n -15)/6

The denominator of 6 is used to reduce each of the binomial factors.

  [tex]=\dfrac{(6n-4)(6n-15)}{2\cdot3}=\dfrac{6n-4}{2}\cdot\dfrac{6n-15}{3}[/tex]

  = (3n -2)(2n -5) . . . . . . . the factorization you want