Find the principal value of Arctan (1.5) to the nearest minute.

Answer:

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Step-by-step explanation:

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Hence, the cylinder's content determines the apparent volume of the glassware, and also the difference between the cylinder as well as spherical volumes determines the glass's true capacity.

Capacity can be defined as the amount which can be held by any kind of vessel. This can depend upon their depth as well as their size.

Actual capacity is the volume of liquid that a glass vessel can contain while it is only partially filled, as opposed to capacity, which refers to the volume of liquid when the glass vessel is fully filled to the brim.

The distinction between both apparent capacity versus Actual capacity in parameters of surface area, as well as volume, is that the former refers to the entire surface area proportional volume of the vessel, whilst the latter refers to the surface area but instead the volume of the liquid that could also fit.

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The number of gallons of paint nearest to tenth will be 0.0358 gallon.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The area of the wall is given as,

A = 6 inches x 172 inches

A = (6 / 12) feet x (172 / 12) feet

A = 0.50 x 14.33

A = 7.167

A ≈ 7.2 gallons

Then the number of gallons of paint is given as,

⇒ 7.167 / 200

⇒ 0.0358 gallon

The number of gallons of paint nearest to tenth will be 0.0358 gallon.

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Answer:

10

Step-by-step explanation:

Using the midpoint formula we will see that the coordinates of B are (-9, 1)

We know that for two points (x, y) and (a, b) the midpoint is at:

( (x  + a)/2,  (y + b)/2)

In this case if the coordinates of B are (x, y), we can write the equation:

(-2, 4) = ( (x + 5)/2, (7 + y)/2)

We can solve these two equations to find the coordinates of point B, we will get:

(x + 5)/2 = -2

x + 5 = -4

x = -4 - 5 = -9

And:

(7 + y)/2 = 4

7 + y = 4*2 = 8

y = 8 - 7 = 1

The coordinates of B are (-9, 1)

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Answer: The equation that represents the relationship between the price of oranges last week, x, and the price of oranges this week, y is:

y = x + 1/5x

The equation states that the price of oranges this week is equal to the price of oranges last week plus 1/5 of the price of oranges last week.

Step-by-step explanation:

Answer: The annual percentage yield (APY) takes into account both the interest rate and the frequency of compounding. It is a measure of the effective rate of return over a year, taking into account the effect of compounding.

In Oxana's account, with a 7.1% interest rate

Step-by-step explanation:

The initial investment was $4,176.69

Investment is the dedication of money to purchase of an asset to attain an increase in value over a period of time.

To find initially invested we can use the formula for continuously compounded interest to find the initial investment:

A = Pe^(rt)

Where:

So, solving for P:

P = A / e^(rt)

P = $10,775.05 / e^(0.07 * 17)

P = $10,775.05 / 2.56724943786794

P = $4,176.69

Therefore, the initial investment was $4,176.69.

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The value of the given expression is -6

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

f(-2) value is the value of f(x) when x= -2

From the graph ,

f(-2)= 0

g(7)=2

Given:

 -5 * f(-2) - 3*g(7)

= -5*0 - 3*2

First multiplication ,then subtraction from left to right

= 0- 3*2

=0-6

= -6

So, the value of the given expression is -6

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The table shows the amounts of each day is attached below.

An equation is an expression that shows the relationship between two or more numbers and variables.

The total amount of snow that falls in three days equals the sum of the amount of snow that falls each day, then

s1 + s2 + s3 = Ts

Here s1 is the snow that fell on day 1, s2 on day 2, s3 on day 3 and Ts is the total amount of snow that fell over the three days.

We need to calculate the amount of snow that fell on the first two days by multiplying the total snow by the given fractions, like this:

s1 = 1/6 * 2 = 1/3

s2 = 7/12*2 = 7/6

Now ,

1/3+ 7/6+ s3 = 2

1.5 + s3 = 2

1.5 - 1.5 + s3 = 2 - 1.5

s3 = 2 - 1.5

s3 = 1/2

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Of the given four estimators, the one that shows the most bias is Mean = 20, SE = 1. Hence, Mean = 20, SE = 1 is the accurate choice.

The estimator with the highest value (Mean = 20) compared to the population parameter (15) is the most biased. The lower the standard error (SE = 1), the more confident the estimate, but if the estimate is far from the population parameter, it is considered biased.

In this case, the Mean = 20 estimator is the most biased because it has the greatest difference from the population parameter and the lowest standard error, indicating a high level of confidence in the estimate despite it being significantly different from the actual population parameter.

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the best answer i got for a is 5 days (1.5 hours a day)

b was 3 days (an hour a day) but I am not that sure but thats the best answer I could come up with

Answer: A

Step-by-step explanation:

If there is a $5000 Unearned Revenue credit on the accounting worksheet, it means that the company has received payment for products or services that have not yet been delivered. Therefore, when the delivery is made, an adjusting entry is needed to reflect the change in the company's financial statements.

The adjusting entry would be a debit to the Unearned Revenue account for $5000 and a credit to the Revenue account for $5000, reflecting the delivery of the products and the recognition of revenue. The entry would be recorded in the Adjustment column of the worksheet.

Therefore, the correct answer is option A, a $5000 Adjustment debit.

Answer:

A. a $5000 Adjustment debit

Step-by-step explanation:

The delivery of products listed as a $5000 Unearned Revenue credit would be recorded on an accounting worksheet with a $5000 Adjustment debit.

Unearned revenue is a liability account that represents payments received from customers for goods or services that have not yet been provided. When the delivery is made and the products are provided, the unearned revenue is "earned" and the revenue is recognized in the accounting records.

To record the delivery and recognize the revenue earned, the company would make an adjusting entry to decrease the unearned revenue account and increase the revenue account. Since the unearned revenue account has a credit balance, the adjusting entry would require a debit to reduce the balance. This would result in a $5000 Adjustment debit to Unearned Revenue and a $5000 Adjustment credit to Revenue.

The required function f ∶ R² → R given by f(x, y) = eˣ does not have any local or global extrema.

A global extreme point, also known as a global maximum or minimum, is the highest or lowest value that a function attains over its entire domain. In other words, it is the maximum or minimum value of the function over the whole range of inputs, rather than just a specific interval or region.

Here,

The function f(x, y) = eˣ only depends on x and is not a function of y. This means that it does not have any extrema since its value can be arbitrarily close to zero or arbitrarily close to infinity for different x-values, and therefore it does not attain a maximum or minimum value. This holds both locally and globally.

Thus, the required function f ∶ R² → R given by f(x, y) = eˣ does not have any local or global extrema.

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Answer: Alicia had 3 feet of wood and she used 3 feet, so she has 3 - 3 = 0 feet of wood left.

Since we are asked to estimate the amount of wood, we could round 3 to the nearest whole number and say that Alicia has approximately 0 feet of wood left.

Step-by-step explanation:

The area of the rectangle is given by the equation A = 500 inches²

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the area of the rectangle be represented as A

Now , the equation will be

The perimeter of the rectangle P = 120 inches

The length of the rectangle L = 5 ( width of rectangle )

Now , Perimeter P of rectangle = 2 ( Length + Width )

Substituting the values in the equation , we get

2 ( 5W + W ) = 120

Divide by 2 on both sides of the equation , we get

6W = 60

Divide by 6 on both sides of the equation , we get

W = 10 inches

So , the width of the rectangle = 10 inches

Now , L = 5W

So , the length of the rectangle = 50 inches

And , the area of the rectangle = L x W

Substituting the values in the equation , we get

The area of the rectangle A = 50 x 10

The area of the rectangle A = 500 inches²

Hence , the area of the rectangle is 500 inches²

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Option A and B : This statements is generally false in probability theory.

A. P(A ∪ B) = P(A) + P(B) - This statement is generally false in probability theory. This is known as the inclusion-exclusion principle, which states that the probability of the union of two events is equal to the sum of their individual probabilities minus the probability of their intersection.

B. P(A | B) = P(A) - This statement is generally false in probability theory. In general, P(A | B) is not equal to P(A) because the occurrence of event B affects the probability of event A.

C. P(A ∩ B) = P(A)P(B) - This statement is generally true in probability theory. This is known as the independent events rule, which states that the probability of the intersection of two independent events is equal to the product of their individual probabilities.

D. P(A | B) + P(A' | B) = 1 - This statement is generally true in probability theory.

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Let A and B be any two events. Which of the following statements, in general, are false? P(A∣B)+P(A∣B)=1                                                                                                                                    

A. P(A ∪ B) = P(A) + P(B)

B. P(A | B) = P(A)

C. P(A ∩ B) = P(A)P(B)

D. P(A | B) + P(A' | B) = 1

The second largest of the four angles is angle ∠1

Triangle is a closed polygon that is formed by connecting 3 line segments which are called sides of the triangle. In a triangle, the shortest side will always be placed opposite the smallest interior angle. Similarly, the longest side will always be opposite the largest interior angle.

Here we have

The side included by <1 and <2 is 11 cm

The side included by ∠2 and ∠3 is 16 cm  

The side included by ∠3 and <1 is 14 cm  

As we can observe angle ∠4 is an obtuse angle

Hence, ∠4 is the largest angle among the 4 angles

As we know the shortest side is placed opposite the smallest interior angle and the longest side is opposite the largest interior angle.

From the given data,

The side included by ∠2 and ∠3 is the longest side

Hence, the largest angles among ∠1, ∠2, and ∠3 are the angles ∠1

Therefore,

The second largest of the four angles is angle ∠1

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Answer:

The $19,000 in expenses should be entered by the accountant as a debit in the following journal entry:

Date Account Account Number Debit Credit

1 - Oct Expenses 19000 5050

The most precise classification of BCDE is a square.

Quadrilaterals are four sided polygons which also have four vertices and four angles.

Sum of all the interior angles of a quadrilateral is 360 degrees.

We have to find the length of adjacent sides of the quadrilateral BCDE.

If they are equal, then the quadrilateral is either square or rhombus.

If they are not equal, then they are either rectangle or parallelogram.

B(-1, -1), C(6, -2), D(5, -9), and E(-2, -8)

BC = [tex]\sqrt{(6--1)^2+(-2--1)^2}[/tex] = √50

CD = [tex]\sqrt{(5-6)^2+(-9--2)^2}[/tex] = √50

Adjacent sides are equal. So it is either square or rhombus.

If it is rhombus, length of diagonals BD and CE are not equal.

If it is square, length of diagonals BD and CE are equal.

BD = [tex]\sqrt{(5--1)^2+(-9--1)^2}[/tex] = √100 = 10

CE = [tex]\sqrt{(-2-6)^2+(-8--2)^2}[/tex] = √100 = 10

Length of diagonals are same. So it is a square.

Hence the given quadrilateral is a square.

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The solution for the equation is [tex]x=\frac{\pi }{2} +2\pi n[/tex] ,for any integer n.

An equation is the statement that asserts th equality of the two expressions with 'equal to' (=) sign.

cot [tex]\frac{x}{2} =1[/tex],

Taking inverse on both sides we get,

[tex]\frac{x}{2}[/tex] = [tex]cot^{-1} (1)[/tex]⇒[tex]\frac{x}{2}=\frac{\pi}{4}[/tex]

                ⇒[tex]x=\frac{\pi }{2}[/tex].

cot is positive in first and third quadrant. To find the second solution add π to it.

[tex]\frac{x}{2} =\pi +\frac{\pi }{2}[/tex]

[tex]x=\frac{5\pi }{2}[/tex]

to find period for cot([tex]\frac{x}{2}[/tex])  

The periodic function can be calculated by [tex]\frac{\pi }{|b|}[/tex], replace b with [tex]\frac{1}{2}[/tex]  

we get [tex]2\pi[/tex]. we get period for  cot([tex]\frac{x}{2}[/tex])  is [tex]2\pi[/tex] so values will repeat every

radians in both directions.

[tex]x=\frac{\pi }{2} +2\pi n, \frac{5\pi }{2} +2\pi n,[/tex] for any integer n.

consolidating we get,

[tex]x=\frac{\pi }{2} +2\pi n[/tex], for any integer.

Hence, the solution for the equation cot [tex]\frac{x}{2}[/tex]= 1 is [tex]x=\frac{\pi }{2} +2\pi n[/tex]

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The intersection of the set of integers and multiples of 5 will be (5,15).

What exactly are integers?

In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.

Now,

Odd Integers between 0 and 20=1,3,5,7,9,11,13,15,17,19

Multiples of 5 between 0 and 35=5,10,15,20,25,30,35

Then the common integers are=5,15

Hence,

          The intersection of the set of integers multiples of 5 will be (5,15).

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Answer:

40 ft²

Step-by-step explanation:

First way:

A = 1/2bh = 1/2(16)(5) = 40

2nd way:

Length of dotted line at top = x

16² - 8² = x²

x² = 192

x = √192 = 13.86

Area rectangle = 8 x 13.86 = 110.85

Find the shaded area:

110.85 - 1/2(8)(13.86) - 1/2(8)(13.86 - 10) = 40

Answer:

  40 ft²

Step-by-step explanation:

You want the area of a triangle two different ways. The height from the 10 ft base is given as 8 ft; the height from the 16 ft base is given as 5 ft.

The area formula for a triangle is ...

  A = 1/2bh . . . . . . where b is the base, and h is the height from that base

The base (side) dimensioned in red is 10 ft. The perpendicular distance to the opposite vertex is shown in red as 8 ft. Then the area is ...

  A = 1/2(10 ft)(8 ft) = 40 ft²

The base dimensioned in green is 16 ft. The perpendicular distance to the opposite vertex is shown in green as 5 ft. Then the area is ...

  A = 1/2(16 ft)(5 ft) = 40 ft²

The area of the triangle is 40 ft².

The coordinate of the y-intercept of the line y = 4x + 1 is (7.5, 10). And the value of 'k' is 7.5.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

a) The equation is given as,

y - 4x = 1

y = 4x + 1

Then coordinate of the y-intercept is (0, 1).

b) The equation is given as,

y = 2x + c

From the graph, the y-interept is -3. Then the equation is given as,

y = 2x - 3

At y = 10, the value of 'k' is given as,

10 = 2k - 3

2k = 13

k = 7.5

The coordinate of the y-intercept of the line y = 4x + 1 is (7.5, 10). And the value of 'k' is 7.5.

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The amount of the down payment that is required to be paid is = $17025

The down payment is the initial amount that the buyer has to offer for the merchandise before they would later have to make the full payment. The down payment is a sign of seriousness on the part of a buyer

The amount that the house is selling for is $113,500.

The percentage that is to be considered for the down payment is 15 percent of the total amount.

This is given as 15 percent of $113,500.

down payment is 0.15 * $113,500

= $17025

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None of the equations in Problems 1 through 8 is exact, so they cannot be solved using the method of integration factors.

If an ODE is exact, it can be solved using the method of integration factors.

Here is the determination of whether each of the equations in Problems 1 through 8 is exact, and if it is, finding the solution:

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

This equation is not exact.

2. (2x + 4y) + ( 2x - 2y)y' = 0

This equation is not exact.

3. (3x^2 - 2xy + 2) + ( 6y^2 - x^2 + 3) y' = 0

This equation is not exact.

4. dx/dt = bx + cy, dy/dt = ax - by

This system of ODEs is not exact.

5. dx/dt = bx - cy, dy/dt = ax + by

This system of ODEs is not exact.

6. (ye^(2x) -2e^(2x)x sin(2x)+2x)+(xe^(2x)y cos(2x) -3) y'=0

This equation is not exact.

7. (y/x+6x) +(In x - 2)y' = 0, x > 0

This equation is not exact.

8. (y^2)dy/dx + 0 = (x^2 + y^2)^(3/2)

This equation is not exact.

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Answer: Let x be the number of days it takes for y workers to weed the field. Then, we know that x and y are inversely proportional, meaning that x * y = k, where k is a constant.

Since it takes 6 days for 10 workers to weed the field, we have:

6 * 10 = k

So, k = 60.

Now, to find the number of days it would take if there were 12 workers, we can plug in y = 12 and solve for x:

x * 12 = 60

x = 60/12

x = 5

Therefore, it would take 5 days for 12 workers to weed the field.

Step-by-step explanation:

In the image you can see some rectangles with different dimensions, to scale.

A rectangle is a geometric figure that is characterized by:

To find the perimeter of a rectangle we must add all its sides. In this case we must illustrate a 20 m rectangle so we can draw the following variants:

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