find the indicated partial derivative. f(x, y) = y sin−1(xy); fy 4, 1 8

Answer:

£200

Step-by-step explanation:

To determine how many pounds Jenny got back, we first need to calculate the exchange rate between pounds (£) and dollars ($).

Jenny initially changed £480 into $744, so £480 = $744.

To find the exchange rate in terms of pounds (£) to dollars ($), divide both quantities by 480:

[tex]\dfrac{480}{480}=\dfrac{744}{480}[/tex]

[tex]\£1=\$1.55[/tex]

Therefore, the exchange rate was £1 = $1.55.  

This means that for every £1 Jenny exchanged, she received $1.55.

To convert the $310 Jenny had left back into pounds (£), divide the dollar amount by 1.55:

[tex]\dfrac{310}{1.55}=200[/tex]

Therefore, if the exchange rate stayed the same, Jenny got back £200.

The probability that exactly 12 out of 22 pitches are strikes is approximately 0.18 (rounded to two decimal places).

To find the probability that exactly 12 out of 22 pitches are strikes, we can use the binomial probability formula. In this case, the probability of throwing a strike for each pitch is 0.431, and we want to calculate the probability of getting exactly 12 strikes out of 22 pitches.

Using the binomial probability formula, the probability of getting exactly 12 strikes out of 22 pitches is:

P(X = 12) = C(22, 12) * (0.431)^12 * (1 - 0.431)^(22 - 12)

where C(22, 12) represents the number of ways to choose 12 strikes out of 22 pitches.

Calculating this probability, we find:

P(X = 12) = 22! / (12! * (22 - 12)!) * (0.431)^12 * (1 - 0.431)^(22 - 12)

P(X = 12) ≈ 0.1832

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The measure of angles ∠1 and ∠2 is 72 and 54.

Option C is the correct answer.

We have,

The total angle of a polygon can be found using the formula:

total angle = (n - 2) x 180 degrees

So,

The given polygon is a pentagon (5 sides).

n = 5

Now,

Total angle.

= (5 -2) x 180

= 3 x 180

= 540

Now,

There are 5 angles that make 540.

So,

1 angle = 540/5 = 108

And,

One angle is split into two where one is ∠2.

So,

∠2 = 108/2

∠2 = 54

Now,

We can see that ∠2 and ∠1 form a triangle.

Where the other angle is equal to ∠2.

So,

∠2 + ∠2 + ∠1 = 180

∠1 = 180 - (54 + 54)

∠1 = 180 - 108

∠1 = 72

Thus,

The measure of angles ∠1 and ∠2 is 72 and 54.

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The height of the new pasta box designed by Kevin is 9 in and the area of the base is 9 in². Kevin’s boss has said that there must be at least 2 in of space between the top of the pasta and the top of the box. Will the pasta fit in the new box with enough space at the top.

Kevin's boss has indicated that there should be at least 2 inches of space between the top of the pasta and the top of the box. This indicates that the maximum capacity of the box will be reduced by this amount.The volume of the pasta box can be calculated as the product of the height and the area of the base. Here's how:Volume of the box = Height × Area of the base Given that the height of the box is 9 inches and the area of the base is 9 square inches.

Thus, the volume of the box is:V = Height × Area of the baseV = 9 × 9V = 81 cubic inchesHowever, the boss has said that at least 2 inches of space must be left between the top of the pasta and the top of the box. This implies that the pasta must occupy a volume that is less than or equal to 81 − 2 = 79 cubic inches.Therefore, the pasta will fit into the new box with enough space at the top since 79 cubic inches are greater than or equal to the volume of pasta in the box.

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Answer:

15 + c ≤ 345

Step-by-step explanation:

Inequality is a mathematical statement that compares two algebraic expressions using the symbols < , > , ≠ ,≤ or ≥.

          'c' is the total cost of all the items sold. The total order should not exceed 345. This 345 includes the total cost and the shipping fee.

     15 + c ≤ 345

Answer: A

Step-by-step explanation: Both distributions are symmetrical, so standard deviation and the mean will be the most useful for comparison because they give more information on the different values in the distribution and their likelihood.

The length of the third side is 4.

Given information:

A right-angled triangle is provided in the diagram.

So, as per the diagram,

The hypotenuse leg = √(97)

Opposite leg = 9

Let the length of the adjacent leg, which is the third side be x. By the Pythagorean theorem, we have:

x² + 9² = √(97)²

Simplifying the right side, we get:

x² + 81 = 97

Subtracting 81 from both sides, we get:

x² = 16

Apply square root property, we get,

x = +/- 4

Since the length of a side of a triangle must be positive, the length of the third side is 4.

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Understanding the truth values and logic behind these statements is important to correctly determine their validity. The questions that are True are B and D, and the questions that are A, C, and E.

a. False. In a conditional statement, if the antecedent (the "if" part) is false, the truth value of the conditional statement depends on the truth value of the consequent (the "then" part). If the consequent is true, the conditional statement is true, but if the consequent is false, the conditional statement is false.

b. True. In a disjunction (logical OR), if at least one of the disjuncts is true, then the entire disjunction is true. It only takes one true statement for the disjunction to be true.

c. False. Similar to statement a, if the consequent of a conditional statement is false, the truth value of the conditional statement depends on the truth value of the antecedent. If the antecedent is true, the conditional statement is true, but if the antecedent is false, the conditional statement is false.

d. True. In a conjunction (logical AND), for the entire conjunction to be true, all conjuncts must be true. If one conjunct is true, it guarantees that the conjunction will be true.

e. False. In a conjunction (logical AND), if at least one conjunct is false, the entire conjunction is false. All conjuncts must be true for the conjunction to be true. If any conjunct is false, the conjunction will be false.

Therefore, it's important to understand the truth values and logic behind these statements to correctly determine their validity.

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The conclusion that "all employees who attend the sales training program and who attend the technical training program are in department B" does not necessarily follow from the given assumptions.

The assumptions state that all employees in department A attend the sales training and employees in department A attend the technical training. It also mentions that employees who attend both training programs are in department B. However, it does not provide any information about employees who only attend one of the training programs.

Based on the given information, we cannot conclude that all employees who attend both training programs are in department B. There could be employees from department A who attend both programs and employees from department B who only attend one of the programs.

Therefore, the conclusion cannot be determined solely based on the given assumptions. Additional information about the distribution of employees across departments and their training program attendance is needed to draw a conclusive statement about the department affiliation of employees attending both training programs.

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The subshell designated by each set of quantum numbers is as follows:

a) n=3, l=1 -> 3p subshell

b) n=4, l=2 -> 4d subshell

c) n=2, l=0 -> 2s subshell

d) n=5, l=3 -> 5f subshell

In the electron configuration of an atom, each electron is described by a set of four quantum numbers, which includes the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (m), and the spin quantum number (s). The second quantum number (l) determines the shape of the subshell, which in turn influences the energy level and chemical behavior of the atom. The letter designation for each subshell is based on the value of the angular momentum quantum number (l): s (l=0), p (l=1), d (l=2), f (l=3), and so on. Therefore, for a given set of quantum numbers, we can determine the subshell designation by identifying the value of l.

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Answer:

The 95% confidence interval for the population proportion of all persons who do not have any health insurance is (0.148, 0.192).

Here is the calculation:

Sample size = 800

Number of persons who do not have any health insurance = 120

Sample proportion = 120 / 800 = 0.15

Confidence level = 95%

Z-critical value for 95% confidence level = 1.96

Confidence interval = (sample proportion - Z-critical value * standard error of the sample proportion, sample proportion + Z-critical value * standard error of the sample proportion)

Standard error of the sample proportion = sqrt(sample proportion * (1 - sample proportion) / sample size)

Standard error of the sample proportion = sqrt(0.15 * (1 - 0.15) / 800) = 0.0128

Confidence interval = (0.15 - 1.96 * 0.0128, 0.15 + 1.96 * 0.0128)

Confidence interval = (0.148, 0.192)

Step-by-step explanation:

The graphs of l₁ and l₂ for x from -4 to 6 is attached

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

y = 1/2x + 3

y = x + 6

The domain is given as

x = -4 to 6

So, we plot the graph of the functions in this domain

See attachment for the graphs

A linear function is represented as

y = mx + c

Where

Gradient = m

So, we have

y = 1/2x + 3 => Gradient = 1/2

y = x + 6  => Gradient = 1

The coordinates of the point when l₁ cuts l₂​ is the point were the lines of both equations intersect

Using the graph plot in (a), the coordinates of the point when l₁ cuts l₂​ does not exist

This is because the lines do not intersect in the given domain

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A function is a relation between a set of inputs (called the domain) and a set of outputs (called the range) where each input is associated with exactly one output.

Out of the given options, the function is:

y = 2x + 1

In this equation, for every value of x, there is a unique corresponding value of y. Therefore, it satisfies the definition of a function.

The other options:

Answer:

option 2

Step-by-step explanation:

They both travel x miles per week

option 1: SUV (15 + 1)mpg + hybrid (65)mpg = 81combined mpg

option 2: SUV (15)mpg + hybrid (80) mpg = 95 combined mpg

getting 95mpg is better than 81mpg.

so they should choose option 2

The correct answer is Pelicans. they have a larger mean value of about 22.5 inches.To determine which team has the largest overall size hat for their players, we can compare the measures of center for the two teams. The measures of center commonly used are the median and the mean.

To find the median, we arrange the hat sizes in ascending order and find the middle value. For the Pelicans, when we arrange their hat sizes in ascending order, we get:

21 21.5 22 22 22.5 23 23.5 24 24.5

The median is the middle value, which is 22.5 inches

.For the Falcons, when we arrange their hat sizes in ascending order, we get:

20 20.5 21 21.5 22 22.5 23 23.5 24 24.5

The median is also 22.5 inches.

Since both teams have the same median value, we need to compare the mean. To find the mean, we sum up all the hat sizes and divide by the total number of measurements.

For the Pelicans, the sum of their hat sizes is 22 + 21 + 22 + 22 + 23.5 + 22 + 23 + 24 + 21.5 + 24.5 = 225 inches.

Dividing by 10 (the number of measurements) gives a mean value of 22.5 inches.

For the Falcons, the sum of their hat sizes is 20 + 20.5 + 21 + 21.5 + 22 + 22.5 + 23 + 23.5 + 24 + 24.5 = 222 inches.Dividing by 10 (the number of measurements) gives a mean value of 22.2 inches.

Comparing the means, the Pelicans have a larger mean value of about 22.5 inches compared to the Falcons' mean value of about 22.2 inches.

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The given integral is: ∫∫R 5/√(2) xy dA, where R is the region in the xy-plane bounded by the curves y = 0, x = √(25 - y^2) and x = 0. The volume of the solid is (5^5/8) cubic units.

Converting to polar coordinates, we have:

x = r cos(θ), y = r sin(θ), and the limits of integration become:

0 ≤ θ ≤ π/2, 0 ≤ r ≤ 5.

Also, the differential of area becomes dA = r dr dθ.

Substituting for x and y, and dA, we have:

∫∫R 5/√(2) xy dA = ∫θ=0π/2 ∫r=0^5 5/√(2) (r cos(θ)) (r sin(θ)) r dr dθ

= 5/√(2) ∫θ=0π/2 ∫r=0^5 r^3 cos(θ) sin(θ) dr dθ

= 5/√(2) ∫θ=0π/2 [sin(θ)/4] ∫r=0^5 r^4 cos(θ) dr dθ

= 5/√(2) ∫θ=0π/2 [sin(θ)/4] [(5^5 cos(θ))/5] dθ

= (5^5/4√(2)) ∫θ=0π/2 sin(θ) cos(θ) dθ

= (5^5/8)

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The Rule for the dilation is (x, y) → (2x, 2y).

The rule that best represents the dilation applied to Triangle E to create Triangle F is:

(x, y) → (2x, 2y)

This rule shows that the dilation is centered at the origin and has a scale factor of 2, which means that all the coordinates of Triangle E are multiplied by 2 to obtain the corresponding coordinates of Triangle F.

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The perimeter of the rhombus is 4√117 feet.

What is rhombus?

A rhombus is a special type of quadrilateral (a polygon with four sides) where all four sides are equal in length. It is also known as a diamond shape because of its symmetrical appearance.

In a rhombus, the diagonals are perpendicular bisectors of each other. This means that they divide the rhombus into four congruent right triangles.

Let's denote the length of one diagonal as d1 and the length of the other diagonal as d2. In this case, d1 = 18 feet and d2 = 12 feet.

Each right triangle formed by the diagonals has legs equal to half the lengths of the diagonals. Therefore, the lengths of the legs are d1/2 = 18/2 = 9 feet and d2/2 = 12/2 = 6 feet.

Using the Pythagorean theorem, we can find the length of the hypotenuse of each right triangle, which is also a side of the rhombus.

[tex]h^2 = (leg1)^2 + (leg2)^2\\\\h^2 = 9^2 + 6^2\\\\h^2 = 81 + 36\\\\h^2 = 117[/tex]

Taking the square root of both sides:

h = √117

Since the rhombus has four congruent sides, the perimeter is given by:

Perimeter = 4 * h = 4 * √117

Thus, the perimeter of the rhombus is 4√117 feet.

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Based on the information, we can infer that the dimensions of rectangle A are length = 2√6 cm and width = 3√2 cm, and the dimensions of rectangle B are length = 4√6 cm and width = √6 cm.

To find the dimensions of the rectangle we must take into account the dimensions of the square model as a reference to know the dimensions of the rectangle. Let's represent the dimensions of rectangle A as x and y, and the dimensions of rectangle B as z and w.

We know that the area of rectangle A plus the area of rectangle B equals 36 cm²:

We also know that the ratio of the area of rectangle A to rectangle B is 2:1:

We can use this ratio to write one of the dimensions of rectangle B in terms of one of the dimensions of rectangle A:

Substituting this expression into the first equation, we get:

Simplifying:

Now we can use the ratio again to find the values of z and w:

Substituting this into the area equation for rectangle B:

Solving for w:

Finally, we can find the values of x and y using the fact that xy = 24:

Substituting into the ratio expression for rectangle B:

Solving for x:

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Step-by-step explanation:

Decimal interset per period (day) = .05/365

# periods = 365 *6 = 2190

FV = 15800 ( 1 + .05/365)^2190  = 21327.33 Euros

Answer:

pear

Step-by-step explanation:

60/5 = 12

72/8 = 9

so one pear is cheaper than one apple

Two years from now, there will be a total of 36 lakh (3.6 million) students using Khan Academy in India.

If 16 lakh students in India are currently using Khan Academy, and the number of users is expected to grow by 50% every year, then the number of users two years from now can be calculated as follows:
- After one year: 16 lakh x 1.5 = 24 lakh
- After two years: 24 lakh x 1.5 = 36 lakh
Therefore, two years from now, it is expected that 36 lakh students in India will be using Khan Academy.
To calculate the number of students using Khan Academy in India two years from now, we'll use the given growth rate of 50% per year.
Currently, there are 16 lakh (1.6 million) students using Khan Academy. After the first year, the number of users will grow by 50%, which is an increase of 8 lakh (0.8 million) students. This will bring the total to 24 lakh (2.4 million) students.
After the second year, the number of users will again grow by 50%. This time, the increase will be 12 lakh (1.2 million) students. So, two years from now, there will be a total of 36 lakh (3.6 million) students using Khan Academy in India.

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Answer:

Step-by-step explanation:

Given that vector (g, h) moves a shape g squares right and h squares up, you want the description for the vector (7, 9).

As with a numerical expression, you can substitute the values for the letters in the English description. When (g, h) = (7, 9), it means "g" can be replaced by "7" and "h" can be replaced by "9". The sentence with these replacements is ...

  vector (7, 9) moves a shape 7 squares right and 9 squares up

__

Additional comment

It's not math. It's reading comprehension.

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The trigonometric equation is (sinθ+cosθ)²−(sinθ−cosθ)² is equal to 2sin2θ

We can use the identity (a+b)² = a² + 2ab + b² to simplify the left-hand side of the equation:

The trigonometric expression is (sinθ+cosθ)²−(sinθ−cosθ)²

Expand the trigonometric expression by using the identity  (a+b)² = a² + 2ab + b²

(sinθ+cosθ)² will be sin²θ + 2sinθcosθ + cos²θ

(sinθ−cosθ)² is sin²θ - 2sinθcosθ + cos²θ

Now plug in these in the above trigonometric equation

= sin²θ + 2sinθcosθ + cos²θ - (sin²θ - 2sinθcosθ + cos²θ)

= sin²θ + 2sinθcosθ + cos²θ - sin²θ + 2sinθcosθ - cos²θ

= 4sinθcosθ

= 2 × 2sinθcosθ

= 2sin2θ

Hence, the trigonometric equation is (sinθ+cosθ)²−(sinθ−cosθ)² is equal to 2sin2θ

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Here is a paragraph about the transformations I used to create my logo.

I started with a basic shape, a square. I then reflected the square across the horizontal axis, creating a mirror image. I then translated the reflected square up and to the right, creating a new shape. I then rotated the new shape 45 degrees, creating a third shape. The third shape is symmetric, meaning that it can be divided into two identical halves.

I then used these three shapes to create my logo. I used the first shape as the background, the second shape as the foreground, and the third shape as the logotype. I chose these shapes because they represent the three stages of transformation: the beginning, the middle, and the end.

The reflection represents the beginning of the transformation, when something is changed from its original state. The translation represents the middle of the transformation, when something is in the process of being changed. The rotation represents the end of the transformation, when something has been completely changed.

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To answer this question, we need to look at the data from part (a) and only consider the people who named a rainbow color. Out of those people, we can see that 35% preferred red.

To calculate the percentage, we can divide the number of people who preferred red (14) by the total number of people who named a rainbow color (40), and then multiply by 100.
So, (14/40) x 100 = 35%.
Therefore, 35% of the people who named a rainbow color preferred red. It's important to note that this percentage only applies to the subset of people who named a rainbow color, not the entire group of people surveyed.
Overall, it's always important to clarify the specific subset of data you're analyzing when discussing percentages or statistics.

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The measure of I'J' is 18 units.

We have,

Scale factor= 2

length of IJ = 9

Now, If the segment IJ is dilated by a scale factor of 2, the length of I'J' will be:

I'J' = 2 x IJ

I'J' = 2 x 9

I'J' = 18

Therefore, the measure of I'J' is 18 units.

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The sum of the 4th and 6th square numbers is 52.

The formula for the nth square number is as below

n²

Using this formula we can find the 4th and 6th square numbers

4th square number = 4² = 16

6th square number = 6² = 36

The sum of the 4th and 6th square numbers is solved by addition

16 + 36 = 52

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