Find the inverse of f(x)

∂g/∂u is equal to 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v)).

To find the indicated derivative, we need to use the chain rule. Let's differentiate step by step:

Given:

g(u, v) = f(x(u, v), y(u, v))

f(x, y) = 7x³y³

x(u, v) = ucos(v)

y(u, v) = usin(v)

To find ∂g/∂u, we differentiate g(u, v) with respect to u while treating v as a constant:

∂g/∂u = (∂f/∂x) * (∂x/∂u) + (∂f/∂y) * (∂y/∂u)

To find ∂f/∂x, we differentiate f(x, y) with respect to x:

∂f/∂x = 21x²y³

To find ∂x/∂u, we differentiate x(u, v) with respect to u:

∂x/∂u = cos(v)

To find ∂f/∂y, we differentiate f(x, y) with respect to y:

∂f/∂y = 21x³y²

To find ∂y/∂u, we differentiate y(u, v) with respect to u:

∂y/∂u = sin(v)

Now, we can substitute these partial derivatives into the equation for ∂g/∂u:

∂g/∂u = (21x²y³) * (cos(v)) + (21x³y²) * (sin(v))

To find the simplified form, we substitute the given values of x(u, v) and y(u, v) into the equation:

x(u, v) = ucos(v) = u * cos(v)

y(u, v) = usin(v) = u * sin(v)

∂g/∂u = (21(u * cos(v))²(u * sin(v))³) * (cos(v)) + (21(u * cos(v))³(u * sin(v))²) * (sin(v))

Simplifying further, we get:

∂g/∂u = 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v))

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According to the given formula, the percentage of voters using electronic voting systems in the county is represented by P = 2.9x + 20.3, where x is the number of years after 2001. To find the year when the percentage first exceeds 40.6%, we need to solve the equation 2.9x + 20.3 = 40.6.

To determine the year when the percentage of voters using electronic systems exceeds 40.6%, we can solve the equation 2.9x + 20.3 = 40.6. Subtracting 20.3 from both sides of the equation, we get 2.9x = 20.3. Dividing both sides by 2.9, we find that x is approximately 7.

Therefore, the number of years after 2001 when the percentage first exceeds 40.6% is 7. Adding 7 years to 2001, we get the year 2008. Therefore, in the year 2008, the percentage of voters in the county using electronic voting systems will first exceed 40.6%.

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We need to know about test statistic to solve the problem. The formula we will need to calculate test statistic is  (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Test statistic is a number calculated by a statistical test. It describes how far the observed data is from the null hypothesis of no relationship between variables or no difference among sample groups. The test statistic can be calculated using the sample mean, the population mean and population standard deviation.

test statistic= (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Therefore the formula to calculate the test statistic will be (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

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Answer:

\( - x - 3\)

Step-by-step explanation:

1) regroup term.

\( - \frac{1}{2} (8x - 4) + 3x - 5\)

2) Simplify 1/2 ( 8x - 4 ) to 8x - 4/2.

\( - \frac{8x - 4}{2} + 3x - 5\)

3) Factor out the common term 4.

\( - \frac{4(2x - 1)}{2} + 3x - 5\)

4) Simplify 4( 2x - 1 ) / 2 to 2( 2x - 1).

\( - 2(2x - 1) + 3x - 5\)

5) Expand by distributing terms.

\( - (4x - 2) + 3x - 5\)

6) Remove parentheses.

\( - 4x + 2 + 3x - 5\)

6) Collect like terms.

\(( - 4x + 3x) + (2 - 5)\)

8) Simplify.

\( - x - 3\)

Therefor, the answer is -x - 3.

Answer:

there isn't enough info

Step-by-step explanation:

..................

Answer:

The area would be doubled also

The perimeter will be increased in a factor of 1.4

Step-by-step explanation:

Originally the area of new crate = L * B = 1.2 * 0.8 = 0.96 m^2

perimeter is 2(L+ B) = 2(1.2 + 0.8) = 4 m

Now let’s double the width , it becomes 0.8 * 2 = 1.6 m

Area would be 1.6 * 1.2 = 1.92 m^2 which is two times the previous area

The increased perimeter will be 2(1.6 + 1.2) = 5.6 m

This is an increase in factor of 1.4

the sample is truly representative of all horses in the state, and that there are no biases or confounding factors that might affect the proportion of stallions in the sample.

If we assume that the horses constitute a random sample of all horses in the state, then we can estimate the probability that a randomly selected horse is a stallion by calculating the proportion of horses in the sample that are stallions. Let's assume that we have a sample of n horses, and that x of these horses are stallions. Then the estimated probability of selecting a stallion is:

x/n

For example, if we had a sample of 100 horses and 25 of them were stallions, the estimated probability of selecting a stallion would be:

25/100 = 0.25 or 25%

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In statistics, p represents the true proportion p hat represents the sample proportion

p represents population that has a certain characteristic or falls into a certain category. It is a fixed, unknown value that we are trying to estimate.

p hat represents the sample proportion, which is an estimate of the true proportion based on a sample of the population. It is calculated by dividing the number of individuals in the sample with the characteristic or in the category by the total sample size.

For example, if we want to estimate the proportion of students who prefer chocolate ice cream, we could take a sample of 100 students and find that 60 of them prefer chocolate.

In this case, p hat would be 60/100 or 0.6. This is our estimate of the true proportion, p, of all students who prefer chocolate ice cream.

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Answer:

6960

Step-by-step explanation:

rand() % 6 expression is most appropriate for randomly choosing a day of the week .

Rand generates random number and This number is produced using an algorithm that, each time it is run, outputs a string of numerical values that seem unrelated.

A % B generates the number less than or equal to the B.

Therefore , for randomly choosing a day of the week we can use  rand() % 6 as there are 7 days in a week and  rand() % 6 returns any number between 0 to 6 as Total 7 days.

The best statement for choosing a day of the week at random is rand()% 6.

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Answer:

PT = 17

Step-by-step explanation:

Since T is the midpoint of PQ, then

PT = TQ , substitute values

4x + 5 = 8x - 7 ( subtract 4x from both sides )

5 = 4x - 7 ( add 7 to both sides )

12 = 4x ( divide both sides by 4 )

3 = x

Thus

PT = 4x + 5 = 4(3) + 5 = 12 + 5 = 17

Answer:

17

Step-by-step explanation:

since T is mid point of PQ

PT=TQ

\(4x + 5 = 8x - 7 \\ 5 + 7 = 8x - 4x \\ 12 = 4x \\ x = 12 \div 4 \\ x = 3 \\ \)

so

\(pt = 4x + 5 \\ = 4(3) + 5 \\ = 12 + 5 \\ pt = 17\)

Answer:

\(\boxed{\tt v < 6.8}\)

Step-by-step explanation:

\(\tt 0.5v+0.06 < 3.46\)

Multiply both sides by 100:-

\(\tt 0.5v\times\:100+0.06\times\:100 < 3.46\times\:100\)

\(\tt 50v+6 < 346\)

Subtract 6 from both sides:-

\(\tt 50v < 340\)

Divide both sides by 50:-

\(\tt \cfrac{50v}{50} < \cfrac{340}{50}\)

\(\tt v < \cfrac{34}{5}\)

Or

\(\tt v < 6.8\)

Therefore, your answer is v < 6.8!!! :)

______________________

Hope this helps!

Have a great day!

In a 2 x 3 between subjects ANOVA, there are a total of 6 groups. The first factor, with 2 levels, divides the participants into two distinct groups. The second factor, with 3 levels, further divides each of the two groups into three subgroups. This results in a total of 6 groups.

In this design, each group consists of a unique combination of the two factors, ensuring that each participant is assigned to only one group.

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Answer:

1 & 2

1 & 8

2 & 7

Step-by-step explanation:

Any two angles that add up to 180 degrees (aka a straight line) are supplementary angles.

Answer:

$31.92

Step-by-step explanation:

28.50 x .12 = 3.42

3.42 + 28.50 = $31.92

The total cost is thirty-one dollars and ninety-two cents, which includes a tip of three dollars and forty-two cents. Here’s one way to find these amounts.

Let’s set up a proportion. We can substitute the amounts we know into the proportion.  

Now, we cross multiply. Amount of tip times one hundred equals twenty-eight dollars and fifty cents times twelve.  

Then, we divide both sides of the equation by one hundred. The total cost is the food cost plus the amount of the tip. So, the total cost of the meal is thirty-one dollars and ninety-two cents.

The equation of the line 2x + 3y + 1 = 0 after it has been reflected across y = -1 and rotated about O(2,3) by 180 degrees is -2x + y = 15.

To reflect the line 2x + 3y + 1 = 0 across the line y = -1, we need to subtract twice the y-coordinate of each point on the line from the equation of the line.

This is because the reflection of a point across a line is obtained by reflecting it across the line's perpendicular bisector, which is also the line with the same x-coordinates and twice the distance from the point to the line.

Subtracting twice the y-coordinate, we get:

2x + 3(-2y - 1) + 1 = 0

Simplifying the equation, we get:

2x - 6y - 5 = 0

Now, to rotate the line about the point O(2,3) by 180 degrees, we can use the rotation formula:

x' = 2a - x

y' = 2b - y

where (x,y) are the coordinates of a point on the original line, and (x',y') are the coordinates of the same point after rotation about the point (a,b).

Substituting the coordinates of two points on the line, we get:

(0,-1) → x' = 2(2) - 0 = 4, y' = 2(3) - (-1) = 7

(-1/2,0) → x' = 2(2) - (-1/2) = 4 1/2, y' = 2(3) - 0 = 6

Now, we can use the two points (4,7) and (4 1/2,6) to find the equation of the rotated line using point-slope form:

slope = (6-7) / (4 1/2 - 4) = -2

y - 7 = -2(x - 4)

y = -2x + 15

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Answer:2 i think im not sure

Step-by-step explanation:

1. Maximum value: The maximum value of the function P = 20x - 5y + 64 is 184.00.

2. Minimum value: The minimum value of the function P = 20x - 5y + 64 is 44.00.

3. Values of x and y: The maximum value occurs at x = 6.00 and y = 0, while the minimum value occurs at x = 0 and y = 4.00.

To find the maximum and minimum values of the function P = 20x - 5y + 64, we need to consider the given constraints: 6x + 7y ≤ 42, 0 ≤ y ≤ 4, and 0 ≤ x ≤ 6.

These constraints represent a feasible region in the x-y plane.

To find the maximum value, we optimize the objective function P within this feasible region.

By evaluating the objective function at each corner point of the feasible region, we determine that the maximum value of P is 184.00, which occurs at x = 6.00 and y = 0.

Similarly, to find the minimum value, we evaluate the objective function at each corner point of the feasible region.

The minimum value of P is 44.00, which occurs at x = 0 and y = 4.00.

By considering the given constraints and evaluating the objective function at the corner points of the feasible region, we can determine the maximum and minimum values of the function P and the corresponding values of x and y.

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The probability that the sample mean differs from the population mean by 1.8mm and is rounded off to 4 decimal places is 0.8220

According to the given problem the mean diameter μ= 140 mm (population mean) and the standard deviation is σ=8mm

random sample size, n= 49 steel bolts is selected

Let the random variable that represents the diameter of steel bolts be denoted by x and from the problem we have x = 1.8mm

Let z = (x-μ) / (σ/√n )         (1)

using formula (1) and when the sample mean differs from the population mean by more than 1.8mm

z = 1.8/(8/√49 )

⇒z = 63/40 = 1.575

The probability that the sample mean will differ from the population mean by more than 1.8 mm

P( z > 1.575) = 1 - P(z< 1.575) = 1 - 0.178 = 0.822

The probability that the sample mean will differ from the population mean by more than 1.8 mm = 0.8220

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It follows that the anticipated value of the biassed coin game is zero if the expected earnings from playing it are $0. The chance of each occurrence is multiplied by the associated payout, and the result is added to determine the expected value.

Let's say that in this scenario, the prizes for a head would be $x and the winnings for a tail would be -$y (because it would result in a loss). The odds of getting a head are 0.8 to 1 and getting a tail are 0.2 to 0.8.

We can construct the equation to determine the relationship between x and y:

(0.8 * x) + (0.2 * (-y)) = 0

If we simplify this equation, we get:

0.8x - 0.2y = 0

Rearranging results in:

0.8x = 0.2y

This suggests that x equals

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Answer:

70

You got it correct :)

Step-by-step explanation:

\(\frac{28}{y} =\frac{40}{100}\)

y × 40 = 100 × 28

40y = 2800

40y ÷ 40 = 2800 ÷ 40

y = 70

Answer:

\(\huge{\boxed{\sf{ -20i^{2} + 48i - 16}}}\)

Step-by-step explanation:

( 8 - 4i ) ( 5i - 2 )

Use the distributive property to multiply each term of the first binomial by each term of the second binomial.

⇒\(8 ( 5i - 2 ) - 4i ( 5i - 2 )\)

⇒\(40i - 16 - 20i^{2} + 8i\)

Combine like terms.

Like terms are those which have the same base.

⇒\(- 20i^{2} +40i+ 8i - 16\)

⇒\(-20i^{2} + 48i - 16\)

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The functions when evaluated are

Function (1)

Given that

f(n) = -4n³ - 17n² - 10n + 8 at n = -3

This means that

f(-3) = -4(-3)³ - 17(-3)² - 10(-3) + 8

Expand the brackets

f(-3) = 108 -153 + 30 + 8

Evaluate the like terms

f(-3) = -7

Function (2)

Here, we have

f(n) = -6n⁴ + 38n³ - 16n² + 28n - 29 at n = 6

This means that

f(6) = -6(6)⁴ + 38(6)³ - 16(6)² + 28(6) - 29

Expand the brackets

f(6) = -7776 + 8208 - 576 + 168 - 29

Evaluate the like terms

f(6) = -5

Function (3)

Here, we have

f(a) = 3a³ + 6a² - 15a - 19 at a = -3

This means that

f(-3) = 3(-3)³ + 6(-3)² - 15(-3) - 19

Expand the brackets

f(-3) = -81 + 54 + 45 - 19

Evaluate the like terms

f(-3) = -1

Function (4)

Incomplete

Function (5)

Here, we have

f(a) = a⁴ - 6a³ + 2a² + 25a - 9 at a = 4

This means that

f(4) = (4)⁴ - 6(4)³ + 2(4)² + 25(4) - 9

Expand the brackets

f(4) = 256 - 384 + 32 + 100 - 9

Evaluate the like terms

f(4) = -5

Function (6)

Here, we have

f(x) = x⁴ + 3x³ - x² + 13x + 13 at x = -4

This means that

f(-4) = (-4)⁴ + 3(-4)³ - (-4)² + 13(-4) + 13

Expand the brackets

f(-4) = 256 - 192 -16 - 52 + 13

Evaluate the like terms

f(-4) = 9

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Answer:

x = 6

y = 3

x + y = 9

Step-by-step explanation:

(Step 1)

Isolate one of the variables in one of the equations. This will allow you to solve by substitution in the following steps.

2x + 3y = 21                             <----- Original equation

3y = -2x + 21                            <----- Subtract 2x from both sides

y = (-2/3)x + 7                          <----- Divide all terms by 3

(Step 2)

Substitute the new equation into the untouched equation and isolate the "x" variable.

4x + 3y = 33                                 <----- Original equation

4x + 3((-2/3)x + 7) = 33                <------ Substitute manipulated equation

4x - 2x + 21 = 33                          <------ Multiply 3 by terms in parentheses

2x + 21 = 33                                 <------ Subtract terms with variables

2x = 12                                         <----- Subtract 21 from both sides

x = 6                                             <----- Divide both sides by 2

(Step 3)

Plug the value of "x" into one of the equations to find the value of "y".

4x + 3y = 33                               <----- Original equation

4(6) + 3y = 33                             <----- Plug 6 in for "x"

24 + 3y = 33                               <----- Multiply

3y = 9                                         <----- Subtract 24 from both sides

y = 3                                           <----- Divide both sides by 3

(Step 4)

Since you now know the value of both variables, you can add them together to find your final answer.

x = 6

y = 3

x + y = ?

6 + 3 = ?

9 = ?

The time it takes the ball to strike the ground after it is thrown, found using the kinematic equation, H = -16·t² - 24·t + 200 is approximately 2.86 seconds

A kinematic equation is an equation of the motion of an object moving with a constant acceleration.

The direction in which the ball is thrown = Downwards

Height of the building = 200 foot

Initial velocity of the ball = 24 ft./s

The kinematic equation that indicates the height of the ball after t seconds is, H = -16·t² - 24·t + 200

At ground level, H = 0, therefore;

H = 0 = -16·t² - 24·t + 200

-16·t² - 24·t + 200 = 0

-2·t² - 3·t + 25 = 0

t = (3 ± √((-3)² - 4 × (-2)×25))/(2×(-2))

t = (3 ± √(209))/(-4)

t =  (3 + √(209))/(-4) ≈ -4.36 and t =  (3 - √(209))/(-4)) ≈ 2.86

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Answer:

11%

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

10+x/3=13

(given)

x/3=3

(subtract 3 on both sides)

x=9

(multiply 3 on both sides)

Answer:

Subtract 10 both sides to get x/3 = 3

Then Multiply 3 to both sides,

x = 9

Just use the Order of Operations