Consider the three points P (3,0,0), Q (0,0,-9), and R (0, -6,0). (a) Find a non-zero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the parallelogram with sides PQ and PR.

In mathematics, an expression is a combination of numbers, variables, and/or operators that represents a mathematical phrase or equation. Therefore, when b = -3, f(b) = -15.

An expression can contain constants, variables, functions, and/or mathematical operators such as addition, subtraction, multiplication, division, exponentiation, and logarithms.

To find f(b), we need to substitute b for a in the expression for f(a):

f(b) = 15b^2 + 40b - 30

To find the value of f when b = -3, we substitute -3 for b in the expression above:

f(-3) = 15(-3)^2 + 40(-3) - 30

f(-3) = 135 - 120 - 30

f(-3) = -15

Therefore, when b = -3, f(b) = -15.

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The inequalities for which the ordered pair (-1,-9) is a solution are a and b

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

The inequality expression y> -5/4x-3 and the list of options

To determine the ordered pairs of the inequality expression, we set x = -1 and then calculate the value of y

Using the above as a guide, we have the following:

y > -5/4(-1) -3

Evauate

y > -1.75 -- this is false because -9 < -1.75

For the list of options, we have

Graph (a) True

Graph (b) True

Hence, the inequalities for which the ordered pair (-1,-9) is a solution are a and b

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Answer: Therefore, the tip of the pendulum rotated through an angle of approximately 0.31 radians.

Step-by-step explanation:

The length of the arc traveled by the tip of the pendulum is 8 centimeters, and the radius of the pendulum is 26 centimeters. We can use the formula for the length of an arc of a circle to find the radian angle rotated through:

Length of arc = radius * angle in radians

Solving for the angle in radians, we get:

Angle in radians = Length of arc / radius

Plugging in the given values, we get:

Angle in radians = 8 / 26

Simplifying this expression, we get:

Angle in radians = 0.30769...

Rounding this value to the nearest hundredth, we get:

Angle in radians = 0.31

Therefore, the tip of the pendulum rotated through an angle of approximately 0.31 radians.

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Answer:

Step-by-step explanation:

A. Sales Budget:

To prepare the sales budget, we need to multiply the unit sales by the sales price per unit for each month. The sales budget for July, August, September, and the total quarter is as follows:

Jones Corporation Sales Budget

Month Unit Sales Sales price Total sales dollars

July 20,000 $180 $3,600,000

August 35,000 $180 $6,300,000

Sept 25,000 $180 $4,500,000

Total 80,000 $180 $14,400,000

B. Production Budget:

To prepare the production budget, we need to calculate the number of units to be produced each month to meet the sales demand and maintain the desired ending inventory level. The production budget for July, August, September, and the total quarter is as follows:

Jones Corporation Production Budget

Month Unit Sales Add: Desired Ending Inventory Total Units Needed Less: Beginning Inventory Units to be Produced

July 20,000 4,000 24,000 - 24,000

August 35,000 5,000 40,250 20,000 20,250

Sept 25,000 7,000 28,750 15,250 13,500

Total 80,000 16,000 93,000 35,250 57,750

Note: The desired ending inventory for finished goods for each month is calculated as 20% of the unit sales for the next month. For materials, the desired ending inventory for September is given as 25,200 pounds.

Therefore, we can calculate the total materials needed for September and subtract the desired ending inventory to find the materials to be purchased for September.

The production budget takes into account the inventory levels for both finished goods and materials.

We can now calculate the total direct materials needed, direct labor hours needed, and total manufacturing overhead costs for the quarter.

C. Direct Materials Budget:

To prepare the direct materials budget, we need to calculate the total materials needed for production and deduct the beginning inventory and desired ending inventory levels to determine the materials to be purchased each month.

The direct materials budget for July, August, September, and the total quarter is as follows:

Jones Corporation Direct Materials Budget

Month Units to be Produced Materials required per unit Total Materials Needed Add: Desired Ending Inventory Total Materials Required Less: Beginning Inventory Materials to be Purchased

July 24,000 3 72,000 - 72,000 20,700 51,300

August 20,250 3 60,750 7,500 68,250 51,300 16,950

Sept 13,500 3 40,500 25,200 65,700 36,300 29,400

Total      

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Answer:

(1/2)(6.5 + 12) = x + 4

(1/2)(18.5) = x + 4

9.25 = x + 4

x = 5.25 cm

Jerome will need approximately 138.72 square meters of grass seed to cover his lawn.

To find the area that the grass seed needs to cover, we first need to find the area of the entire lawn. Let's assume that the lawn is rectangular in shape.

Jerome hasn't given us the dimensions of the lawn, so let's say that it measures 10 meters by 15 meters. Therefore, the area of the entire lawn would be:

10 meters x 15 meters = 150 square meters

Now we need to subtract the area of the pool from the area of the entire lawn.

The pool measures 4 5/6 meters by 2 1/3 meters, which we can convert to improper fractions:

4 5/6 = (4 x 6 + 5) / 6 = 29 / 6
2 1/3 = (2 x 3 + 1) / 3 = 7 / 3

So the area of the pool would be:

29/6 meters x 7/3 meters = 203/18 square meters

To find the area that the grass seed needs to cover, we subtract the area of the pool from the area of the entire lawn:

150 square meters - 203/18 square meters

To subtract these two values, we need to get a common denominator:

150 square meters = (150 x 18) / 18 = 2700/18 square meters
203/18 square meters = 203/18 square meters

So the area that the grass seed needs to cover would be:

2700/18 square meters - 203/18 square meters = 2497/18 square meters

We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 1:

2497/18 square meters ≈ 138.72 square meters

Therefore, Jerome will need approximately 138.72 square meters of grass seed to cover his lawn, excluding the area around the pool.

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The answer would be

A = $8,650

P = $5,000

t = 5 years

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the amount of money after t years

P = the principal (initial deposit)

r = the annual interest rate

n = the number of times the interest is compounded per year

t = the number of years

We know that Allen opened a retirement savings account with an initial deposit of $5,000 and made annual contributions. After 5 years, the account grew to $8,650. We don't know the annual interest rate or how the interest is compounded, so we can use the formula to find out.

Let's assume that Allen made no additional contributions to the account after the initial deposit. Then:

A = $8,650

P = $5,000

t = 5 years

We can rearrange the formula to solve for r:

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Answer:

The value of 1/4 (-4^3+10^2) is 9

Corresponding Angles Theorem: If a transversal intersects two parallel lines, then the corresponding angles formed are congruent.

Statements Reasons

1. ∠1 and ∠3 are corresponding angles Given

2. m//n Given

3. ∠1 and ∠2 are congruent Alternate Interior Angles Theorem

4. ∠2 and ∠3 are congruent Alternate Interior Angles Theorem

5. ∠1 ≅ ∠2 and ∠2 ≅ ∠3 Substitution (from statements 3 and 4)

6. ∠1 ≅ ∠3 Transitive Property of Congruence

In this proof, we start by stating that ∠1 and ∠3 are corresponding angles, which is given in the problem statement. We also know that m and n are parallel lines, which is also given.

Then, we apply the Alternate Interior Angles Theorem to show that ∠1 and ∠2, as well as ∠2 and ∠3, are congruent.

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The numbers that are less than 3/7 are 1/8 and 3/10, while the numbers that are greater than 3/7 are 1/2 and 2/3. The decimal 0.102, which is equivalent to 51/500 as a fraction, is also less than 3/7.

To determine which of the given numbers are less than 3/7, we can convert them to fractions and compare them to 3/7.

12.5% is equivalent to 0.125 as a decimal or 1/8 as a fraction. To compare 1/8 and 3/7, we can convert them to a common denominator. The least common multiple of 8 and 7 is 56, so we can rewrite 1/8 as 7/56 and 3/7 as 24/56. Therefore, 1/8 is less than 3/7.

0.3 is equivalent to 3/10 as a fraction. To compare 3/10 and 3/7, we can also convert them to a common denominator. The least common multiple of 10 and 7 is 70, so we can rewrite 3/10 as 21/70 and 3/7 as 30/70. Therefore, 3/10 is less than 3/7.

50% is equivalent to 0.5 as a decimal or 1/2 as a fraction. To compare 1/2 and 3/7, we can convert 3/7 to a fraction with a denominator of 2. Multiplying the numerator and denominator of 3/7 by 2 gives us 6/14. Therefore, 1/2 is greater than 3/7.

2/3 is already a fraction, and we can compare it directly to 3/7. Multiplying the numerator and denominator of 3/7 by 3 gives us 9/21, and we can see that 2/3 is greater than 3/7.

0.102 is a decimal that is less than 1, but it can also be written as a fraction. To do so, we can place the decimal over 1 followed by the appropriate number of zeros. This gives us 102/1000, which can be simplified to 51/500. To compare 51/500 and 3/7, we can convert them to a common denominator. The least common multiple of 500 and 7 is 3500, so we can rewrite 51/500 as 357/3500 and 3/7 as 1500/3500. Therefore, 51/500 is less than 3/7.

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The unit rate of the linear equation y = 8x is 8.

A linear equation of a function illustrates the straight line on a coordinate plane. It can be expressed in a slope intercept form y = mx + b, where:

The slope shows steep the gradient is and it is the change in the rise over the run. For a unit rate which is usually the ratio between two different quantities. We can say in the linear equation, the unit rate represents the slope of the function.

Given that:
y = 8x

To find the unit rate(slope) which is the change in the y-axis(rise) over the change in the x-axis(run) by using slope-intercept form. Then, we can conclude that the unit rate is 8.

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The force between the two charges is 1.69 x[tex]10^-^1^5[/tex] N

The force between two electric charges can be calculated using Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:

F = k * (q1 * q2) / d²

where F is the force, k is Coulomb's constant (9 x 10⁹ N m² / C²), q1 and q2 are the magnitudes of the two charges, and d is the distance between them.

Substituting the given values, we get:

F = (9 x [tex]10^9[/tex] N m² / C²) * (0.000003 C) * (0.0000009 C) / (0.06 m)²

Simplifying this expression gives:

F = 1.69 x[tex]10^-^1^5[/tex] N

Therefore, the force between the two charges is 1.69 x [tex]10^-^1^5[/tex] N.

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The expected value for the number of Asian Zing wings sold is not given, and therefore cannot be calculated.

The expected value is a statistical measure that represents the average outcome of a random variable. It is calculated by multiplying each possible outcome by its probability, and then summing the products. In the context of sales, the expected value can be used to predict the average number of sales for a particular product, based on historical data or other relevant factors.

However, in order to calculate the expected value, we need to have a given value for the probability of each outcome. Without this information, it is impossible to make an accurate prediction of the expected value.

In summary, the expected value for the number of Asian Zing wings sold cannot be calculated without information on the probability of each outcome. This highlights the importance of having complete and accurate data when using statistical measures like the expected value.

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Once we apply one of these tests and determine whether the series converges or diverges, we can then further analyze the series to find its sum, if it exists.

To test the convergence of a series, we typically use one of several tests, depending on the nature of the series. Some of the commonly used tests are:

Divergence test: If the terms of a series do not approach zero, the series must diverge. The test states that if lim(n->inf) an != 0, then the series diverges.

Comparison test: If the terms of a series are positive and can be compared with a known convergent or divergent series, we can determine the convergence or divergence of the given series. If an <= bn for all n and the series sum of bn converges, then the series sum of an also converges. If an >= bn for all n and the series sum of bn diverges, then the series sum of an also diverges.

Limit comparison test: If the terms of a series are positive, we can compare the given series with a known convergent series, using the limit comparison test. If lim(n->inf) (an/bn) = L, where L is a positive finite number, then both series either converge or diverge.

Ratio test: If the terms of a series approach zero and the ratio of consecutive terms approaches a limit L, then the series converges if L < 1 and diverges if L > 1. If L = 1, the test is inconclusive.

Root test: If the terms of a series approach zero and the nth root of the absolute value of the nth term approaches a limit L, then the series converges if L < 1 and diverges if L > 1. If L = 1, the test is inconclusive.

Alternating series test: If the terms of a series alternate in sign and decrease in magnitude, then the series converges.

There are also other tests, such as integral test, p-series test, and Dirichlet test, among others, which can be used to test the convergence of certain types of series.

Once we apply one of these tests and determine whether the series converges or diverges, we can then further analyze the series to find its sum, if it exists.

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Question 1: The probability of picking 1 almond cookie followed by another almond cookie is 1/5.

Question 2: The probability of drawing 2 blue marbles in a row is 1/4.

Question 3: The probability of Chang wearing the white shirt and tan pants is 1/4.

In the problem, the chef draws two cookies without replacement from a box containing six cookies of three different types. The probability of picking one almond cookie followed by another almond cookie can be found by using the multiplication rule of probability.

The probability of picking the first almond cookie is 3/6, and since the first cookie is not replaced, there are now only 2 almond cookies left in the box out of a total of 5 cookies. Therefore, the probability of picking another almond cookie is 2/5. Using the multiplication rule, we multiply these probabilities together to get:

P(almond, then almond) = (3/6) x (2/5) = 1/5

In the problem, Peter draws two marbles randomly from a bag containing three different colors of marbles. The probability of drawing two blue marbles in a row can be found by using the multiplication rule of probability again.

The probability of drawing a blue marble on the first draw is 4/8, and since the marble is replaced, there are still 4 blue marbles left out of a total of 8 marbles. Therefore, the probability of drawing another blue marble on the second draw is also 4/8. Using the multiplication rule, we multiply these probabilities together to get:

P(blue, then blue) = (4/8) x (4/8) = 1/4

In the problem, Chang has two shirts and two pairs of pants, and he chooses one of each at random to wear.

The probability of him choosing the white shirt is 1/2, and the probability of him choosing the tan pants is also 1/2. Using the multiplication rule, we multiply these probabilities together to get:

P(white shirt and tan pants) = (1/2) x (1/2) = 1/4

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One way Olivia might have achieved this is by performing a translation followed by a rotation.

One way Olivia might have achieved the transformation of ABCD onto A" B" C" D" is by performing a translation followed by a rotation. Here's a possible approach:

By combining these two transformations, Olivia could have successfully moved ABCD onto A" B" C" D" and achieved the desired configuration. It's important to note that there could be other valid combinations of transformations as well.

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It will take 8 weeks to save up for $40 pair of trousers.

Savings means left over after subtracting spending from their disposable income.

We will calculate how money saved each week which is:

= 10% *  $50

=  $5.

So, this means we have $45 left after saving for a week.

To save up $40, we need to save for:

= 40/5

= 8 weeks.

Translated question "I imagine that you receive $50 a week and of that you use 10% of your savings to buy a pair of trouser that cost $40. How many weeks will you have to save?"

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Answer:is 230

Step-by-step explanation:

230 i hoped i helped

The amount of magnesium sulfate produced from the given reaction cannot be determined solely from the energy absorbed by the reaction.

The given reaction is: Al2(SO4)3 + 3 MgI2 → 2 AlI3 + 3 Mg(SO4) and the enthalpy change for the reaction is ΔH = +722 kJ. The enthalpy change indicates that the reaction is endothermic, meaning that energy is absorbed by the reaction. The question asks about the amount of magnesium sulfate produced, which is not directly related to the energy absorbed by the reaction.

The balanced chemical equation shows that the reaction produces 3 moles of magnesium sulfate for every 3 moles of magnesium iodide consumed. Therefore, the amount of magnesium sulfate produced depends on the amount of magnesium iodide consumed.

To determine the amount of magnesium sulfate produced, we would need information about the amount of magnesium iodide consumed. The energy absorbed by the reaction does not provide enough information to determine the amount of magnesium sulfate produced.

In summary, the amount of magnesium sulfate produced from the given reaction cannot be determined solely from the energy absorbed by the reaction.

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The average rate of change of DVD sales is 723.1 billion dollars.

The average rate of change of an equation can be determine by using the formula below:

average rate of change = (f(x₂)- f(x₁)) / [x₂- x₁]

From the given information of the DVD sales:

f(x) = -158.8x² + 2469.9x + 3010.5

x₁ = 2001 - 1999 = 2

x₂ = 2008 - 1999 = 9

average rate of change =  ([-158.8(9)² + 2469.9(9) + 3010.5] - [-158.8(2)² + 2469.9(2) + 3010.5]) / (9-2)

                                      = (12376.8 - 7315.1)/(7)

                                      = 723.1 billion dollars

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Complete Question

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Answer:

The speed of the ship =21 km/h

Speed of the current = 3 km/h

Step-by-step explanation:

Let's denote the speed of the ship in still water as s and the speed of the current as c.

When the ship is traveling with the current, the effective speed is (s + c). (we have to sum up both the speeds) Therefore, in 3 hours, the ship can travel a distance of:

distance = speed × time = (s + c) × 3

We know that this distance is 72 km, so we can write:

(s + c) × 3 = 72

Simplifying this equation, we get:

s + c = 24

Similarly, when the ship is traveling against the current, the effective speed is (s - c). (The difference between the speeds). Therefore, in 4 hours, the ship can travel a distance of:

distance = speed × time = (s - c) × 4

We know that this distance is also 72 km, so we can write:

(s - c) × 4 = 72

Simplifying this equation, we get:

s - c = 18

We now have two equations:

s + c = 24 ; s - c = 18

We can solve for s and c by adding these two equations:

2s = 42

Therefore, s = 21 km/h.

Substituting this value of s into one of the equations above, we can solve for c:

s + c = 24

21 + c = 24

c = 3 km/h.

Therefore, the speed of the ship in still water is 21 km/h, and the speed of the current is 3 km/hs

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The equation that can be used to find t, the number of minutes that Luis rode his bike last week, is t = 875/3, which represents the total time in minutes for his 25-mile ride based on the average time it took him to ride 3 miles.

We can use proportions to find the number of minutes Luis rode his bike last week. Since Luis took 35 minutes to ride 3 miles, we can set up a proportion to relate the time and distance for his entire ride: 35 minutes / 3 miles = t minutes / 25 miles

To solve for t, we cross-multiply and simplify: 35 * 25 = 3 * t, 875 = 3t, t = 875 / 3, t ≈ 291.67 minutes

Therefore, the equation that can be used to find t, the number of minutes that Luis rode his bike last week, is t = 875/3, which represents the total time in minutes for his 25-mile ride based on the average time it took him to ride 3 miles.

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The value of x and y in the right triangle are 11.31 units and 8 units respectively.

The tangential ratio of ∠P and ∠Q are 16 / 12 and 12 / 16 respectively.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios as follows:

tan 45 = opposite / adjacent

tan 45 = 8 / y

cross multiply

y = 8 / tan 45

y = 8  /1

y = 8 units

Therefore,

sin 45 = opposite / hypotenuse

sin 45 = 8 / x

cross multiply

x = 8 / sin 45

x = 11.313816999

x = 11.31 units

Let's find the tangent ratio of ∠p and ∠q.

Hence,

tan ∠P = 16 / 12

tan ∠Q = 12 / 16

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The probability of drawing a shape that is red or a circle is 7/16 from the bag that contains 4 red circles, 3 blue circles, and 9 yellow triangles.

Number of red circles = 4

Number of blue circles = 3

Number of yellow triangles = 9

Total number of all items = 4+3+9 = 16

Thus, the total number of possible outcomes is 16.

The probability of getting a red shape  = 4/16

The probability of getting a circle   = 4/16 + 3/16 = 7/16

To calculate the probability of drawing an item circle or red color,

P(red or circle) = P(red) + P(circle) - P(red and circle)

P(red or circle) = 4/16 + 7/16 - 4/16

P(red or circle) = 7/16

Therefore, we can conclude that the probability of drawing a shape that is red or a circle is 7/16.

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The correct answer is "Translated to the left 10 and down 3 and then reflected about the y-axis."

Transformation is a process that changes the position, orientation, size, or shape of a geometric object. Transformations are often described using matrices, vectors, or other mathematical operations.

Types of Transformations

From the problem statement, to move the center from (15,-2) to (-5,-5), we need to translate the circle to the left by 10 units and down by 3 units. So the first transformation is a translation to the left 10 units and down 3 units.

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Measurement is closest to the length of the ramp in feet is 33 feet

Let AB = 26 ft and BC = 19.5 ft

Let AC be the length of the ramp

Let's use the Pythagorean theorem to find the length of the ramp:

AC² = AB² + BC²

where AC is the hypotenuse (the unknown side), and AB and BC are the other two sides given.

Substituting the given values, we get:

AC² = 26² + 19.5²

AC² = 676 + 380.25

AC² = 1056.25

AC = [tex]\sqrt{1056.25}[/tex]

AC = 32.5

Rounding to the nearest feet

AC = 33

Therefore, the measurement closest to the length of the ramp in feet is 33 feet.

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The areas of the sector in the circle are 18π, 3π, 10π and 5π

The orange sector

This is calculated as

Sector area = central angle/360 * πr²

Where

So, we have

Sector area = 180/360 * π * 6²

Sector area = 18π

The yellow sector

This is calculated as

Sector area = central angle/360 * πr²

Where

So, we have

Sector area = 30/360 * π * 6²

Sector area = 3π

The green sector

This is calculated as

Sector area = central angle/360 * πr²

Where

So, we have

Sector area = 100/360 * π * 6²

Sector area = 10π

The purple sector

This is calculated as

Sector area = central angle/360 * πr²

Where

So, we have

Sector area = 50/360 * π * 6²

Sector area = 5π

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The first order partial derivatives of f(x, y) =  ex cos y and the second order partial derivatives are ex sin y = ex cos y.

The given function is f(x, y) = ex sin y. We need to find the first and second order partial derivatives of this function with respect to x and y.
First order partial derivatives:
To find the partial derivative of f(x, y) with respect to x, we treat y as a constant and differentiate ex with respect to x. This gives:
∂f/∂x = ex sin y
To find the partial derivative of f(x, y) with respect to y, we treat x as a constant and differentiate sin y with respect to y. This gives:
∂f/∂y = ex cos y
Second order partial derivatives:
To find the second order partial derivatives, we differentiate the first order partial derivatives we found above. That is, we differentiate ∂f/∂x and ∂f/∂y with respect to x and y, respectively.
∂/∂x (ex sin y) = ex sin y
∂/∂y (ex cos y) = -ex sin y
To find the mixed partial derivatives, we differentiate one of the first order partial derivatives with respect to the other variable. That is,
∂/∂y (ex sin y) = ex cos y
We can also find the mixed partial derivative  by differentiating ∂f/∂y with respect to x, which gives the same result:
∂/∂x (ex cos y) = ex cos y
The first order partial derivatives of f(x, y) = ex sin y are ∂f/∂x = ex sin y and ∂f/∂y = ex cos y and the second order partial derivatives are ex sin y, ∂f/∂[tex]y^2[/tex] = -ex sin y, and ∂f/∂x∂y = ∂f/∂y∂x = ex cos y.

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The survey randomly selected students nationwide if they traveled outside the country for spring break and a 99% confidence interval which is 753 students.

The formula for a confidence interval for a proportion is:

CI = p ± z*sqrt((p*(1-p))/n)

where p is the sample proportion, n is the sample size, and z is the critical value from the standard normal distribution corresponding to the desired confidence level.

In this case, the confidence interval is given as (0.0994, 0.1406), which means:

p = (0.0994 + 0.1406) / 2 = 0.1200

The critical value for a 99% confidence interval is z = 2.576.

Substituting these values into the formula and solving for n, we get:

0.0206 = 2.576*sqrt((0.12*(1-0.12))/n)

Squaring both sides and solving for n, we get:

n = (2.576² * 0.12 * 0.88) / (0.0206²) = 752.3

Rounding up to the nearest integer, we get:

n = 753

Therefore, the survey included 753 students.

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El intervalo correspondiente de millas que Juana puede manejar su nuevo auto está entre 10,000 y 14,000 millas.

Para determinar el intervalo correspondiente de millas que Juana puede manejar su nuevo auto, podemos resolver la fórmula del costo anual en términos de la variable m (millas recorridas por año). Dado que el costo anual está entre $6400 y $7100, podemos establecer la siguiente desigualdad:

6400 ≤ 0.35m + 2200 ≤ 7100

Restando 2200 en los tres lados de la desigualdad, obtenemos:

4200 ≤ 0.35m ≤ 4900

Dividiendo por 0.35 en los tres lados, obtenemos:

12000 ≤ m ≤ 14000

Por lo tanto, Juana puede manejar su nuevo auto en un intervalo de millas que va desde 12000 millas hasta 14000 millas por año.

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