\(\boxed{\sf Trigonometry}\)

Solve for x

\(\\ \rm\rightarrowtail tan^{-1}x+2cot^{-1}x=\dfrac{2\pi}{3}\)


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Answer:

The first one is y = 8 and the second one is y = 4.

Step-by-step explanation:

You plug the numbers in for x and then solve the equations.

Answer:

560

Step-by-step explanation:

Answer:

6.12

Step-by-step explanation:

tan 27≈0.51

Know that tan=\(\frac{opposite}{adjacent}\)

0.51=\(\frac{x}{12}\)

Multiply 12 on both sides

6.12=x

Answer:

You can use symbolab for problems such as these, they'll provide step-by-step guides on how to do it. Symbolab is a math calculator that shows you how to solve each problem.

Vanessa's daily commute to school involves traveling a distance of 19.33 kilometers on horseback and 2.27 kilometers by train. The total duration of the journey is 26.48 minutes.

Vanessa's daily commute to school consists of two modes of transportation: horseback riding and taking a train. The distance traveled on horseback is 19.33 kilometers, while the train covers a distance of 2.27 kilometers. In total, the duration of the entire journey is 26.48 minutes.

Combining these distances and times, Vanessa spends a significant portion of her commute on horseback, covering a distance of 19.33 kilometers. The remaining portion of her journey, covering a distance of 2.27 kilometers, is completed by train. The total duration of the commute is 26.48 minutes, which includes the time spent on both modes of transportation.

This daily routine allows Vanessa to reach her school efficiently by utilizing the combination of horseback riding and taking a train, enabling her to cover the necessary distance within a reasonable timeframe.

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Answer:

x + 5/4

Step-by-step explanation:

Answer:

350 ml

Step-by-step explanation:

there are 3 sugar parts so each one is worth 70

70x5 = 350

Answer:

Step-by-step explanation:

We are given that T varies as the square root of the ratio of s and t, and we are trying to find the value of T when s=33 and t=18.

The relationship between T, s and t can be represented by the following equation:

T = k * √(s/t)

Where k is a constant.

We are given that when S=36, t=16, T=18. We can use this information to find the value of k.

We know that T = k * √(s/t)

and, T = 18 when s=36, t=16.

So we can substitute these values in the equation

18 = k * √(36/16)

Solving for k, we get:

k = 18/2 = 9

Now that we know the value of k, we can use it to find the value of T when s=33 and t=18.

T = k * √(s/t) = 9 * √(33/18) = 9 * √(11/6) = 9 * √(11/6)

The value of T when s=33, t=18 is 9 * √(11/6),

It is not possible to give the exact value of T because the value of the square root of (11/6) is not a whole number.

The volume of the first cylinder is 395.64 cubic inches and the second cylinder is 98.91 cubic inches.

The volume of a cylinder is the capacity of the cylinder which calculates the amount of material quantity it can hold. In geometry, there is a specific volume of a cylinder formula that is used to measure how much amount of any quantity whether liquid or solid can be immersed in it uniformly. A cylinder is a three-dimensional shape with two congruent and parallel identical bases.

Assuming the second cylinder has the same height as the first cylinder, we can compare their volumes with one another.

v = πr²h

In the first cylinder;

diameter = 6 inches

radius = diameter / 2

radius = 6 / 2 = 3 in

v = πr²h

v = 3.14 * 3² * 14 = 395.64in³

The volume of the second cylinder will be

diameter = radius * 2

radius = diameter / 2

radius = 3/2 = 1.5in

v = πr²h

v = 3.14 * 1.5² * 14

v = 98.91in³

The volume of the first cylinder is 395.64in³ while the second cylinder is 98.91in³.

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Answer:

I would assume the answer would be 10 mm³ since you are asking for volume.

10 mm is wrong because it represents a length, but 10 mm³ is correct because it represents a volume of an object.

The work required to pump all the water out over the top of the pool is 468,000 foot-pounds (ft-lb).

To find the work required to pump all the water out of the rectangular swimming pool, we can calculate the weight of the water and then use the work formula.

First, let's calculate the volume of the pool that is filled with water:

Volume = length × width × depth

Volume = 50 ft × 10 ft × 5 ft

Volume = 2500 ft³

Next, let's calculate the weight of the water using the density of water:

Weight = Volume × density

Weight = 2500 ft³ × 62.4 lb/ft³

Weight = 156,000 lb

Now, let's calculate the work required to pump all the water out. Work is equal to the force applied multiplied by the distance over which the force is applied. In this case, the force required is the weight of the water, and the distance is the height from which the water is pumped.

Work = Force × Distance

Work = Weight × Height

The height from which the water is pumped is the depth of the pool minus the depth to which the pool is filled:

Height = 8 ft - 5 ft

Height = 3 ft

Substituting the values:

Work = 156,000 lb × 3 ft

Work = 468,000 ft-lb

Therefore, the work required to pump all the water out over the top of the pool is 468,000 foot-pounds (ft-lb).

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Answer:

A

Step-by-step explanation:

TX=XZ=ZU=3

XU=XZ+ZU=3+3=6

Answer:

D. 3

Step-by-step explanation:

The absolute value function can be written as:

f(x) = 5*(10x - 25) if x ≥ 2.5

f(x) = -5*(10x - 25) if x < 2.5

We have the absolute value function:

y = 5 |10x - 25|

Remember that the general absolute value function y = |x| can be defined as the piecewise function:

|x| = x  if x ≥ 0

|x| = -x  if x < 0.

Here we can rewrite the equation:

y = 5*|10x - 25|

Here the vertex is at:

10x - 25 = 0

10x = 25

x = 25/10 = 2.5

Then:

f(x) = 5*(10x - 25) if x ≥ 2.5

f(x) = -5*(10x - 25) if x < 2.5

That is the piecewise function.

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Answer:

x=31

Step-by-step explanation:

Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

An Agile methodology aims for customer satisfaction through early and continuous delivery of useful software components developed by an iterative process using the bare minimum requirements.

Agile methodology is a software development approach that emphasizes flexibility, collaboration, and iterative development. It focuses on delivering value to customers by prioritizing their satisfaction and adapting to changing requirements throughout the development process. Agile methodologies, such as Scrum or Kanban, promote regular and incremental delivery of working software components.

This allows customers to provide feedback early on, ensuring that the final product meets their needs. By using an iterative approach, Agile methodologies enable teams to continuously refine and improve the software based on customer feedback and changing priorities. The emphasis on delivering useful software components and involving customers throughout the development process sets Agile apart from traditional waterfall methodologies.

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a. Using the cash basis of accounting, Al's gross income for 2021 is $479,400.

b. Using the accrual basis of accounting, Al's gross income for 2021 is $614,600.

c. Al should use the accrual basis of accounting for reporting his gross income.

a. Under the cash basis of accounting, income is recognized when it is received in cash. In this case, Al received cash of $516,600 for medical services in 2021. However, $37,200 of this amount was for services provided in 2020. Therefore, Al's gross income for 2021 using the cash basis is $516,600 - $37,200 = $479,400.

b. Under the accrual basis of accounting, income is recognized when it is earned, regardless of when the cash is received. In this case, Al earned $516,600 for medical services in 2021, including the $37,200 from 2020. Additionally, Al had accounts receivable of $88,000 at the end of 2021 for services rendered in 2021. Therefore, Al's gross income for 2021 using the accrual basis is $516,600 + $88,000 = $604,600.

c. It is advisable for Al to use the accrual basis of accounting because it provides a more accurate representation of his income by recognizing revenue when it is earned, even if the cash is received later. This method matches revenues with the expenses incurred to generate those revenues, providing a better overall financial picture. Using the accrual basis will also allow Al to track and report his accounts receivable accurately, providing a clearer understanding of his practice's financial health.

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Using the formula they gave us:

Cost of shipping = 2.79 + 0.38(8)

Cost of shipping = 2.79 + 3.04

Cost of shipping = 5.83(currency unit)

The score that 75% of the students' exam scores fall below is 0.the 75th percentile is equal to the mean minus 1 standard deviation, or 73 - 5 = 0.

The 75th percentile of a normally distributed set is the point at which 75% of the data falls below that point and 25% of the data falls above that point. In this case, the 75th percentile is equal to the mean minus 1 standard deviation, or 73 - 5 = 0.

Question (b):

The minimum score for an A is -1

The 2.5th percentile of a normally distributed set is the point at which 2.5% of the data falls below that point and 97.5% of the data falls above that point. In this case, the 2.5th percentile is equal to the mean minus 2 standard deviations, or 73 - 2 * 5 = -1.

Here is a more detailed explanation of how to calculate the percentiles in these two questions:

Question (a):

The 75th percentile can be calculated using the following formula:

percentile = mean + (z * standard deviation)

where:

The z-score for the 75th percentile is 0.6745. This can be found using a z-table or by using a calculator.

Plugging in the mean and standard deviation, we get the following:

percentile = 73 + (0.6745 * 5)

percentile = 0

Question (b):

The 2.5th percentile can be calculated using the following formula:

percentile = mean - (z * standard deviation)

where:

The z-score for the 2.5th percentile is -1.96. This can be found using a z-table or by using a calculator.

Plugging in the mean and standard deviation, we get the following:

percentile = 73 - (-1.96 * 5)

percentile = -1

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The total amount of that Harry will need for the project is nineteen and seven twentieth feet. option A

Addition of Fraction

Wood 1:

Length of each = 2 5/8 feet

Number of pieces = 6

Total = Length of each × Number of pieces

= 2 5/8 × 6

= 21/8 × 6

= 126 / 8

= 15 3/4 meters

Wood 2:

Length of each = 1 1/5 feet

Number of pieces = 3

Total = Length of each × Number of pieces

= 1 1/5 × 3

= 6/5 × 3

= 18/5

= 3 3/5 meters

Total amount of wood needed for the project = 15 3/4 meters + 3 3/5 meters

= 126/8 + 18/5

= (630+144) / 40

= 774/40

= 19 14/40

= 19 7/20 meters

Therefore, the total amount of wood that Harry will need for the project is nineteen and seven twentieths feet. option A

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The values of Relations, domain, range, and functions are calculated below.

What are the Relations, domain, range, and functions?

The domain of a function or relation is the set of all possible independent values the relation can take. It is the collection of all possible inputs. The range of a function or relation is the set of all possible dependent values the relation can produce from the domain values.

Domain - Set of x-values

Range - Set of y-values

3). Since, x values vary from x = -6 to x = 5,

   The domain of the graph = [-6, 5]

   Since, y-values vary from y = -2 to y = 3

   Range of the graph = [-2, 3]

4).

   The domain of the graph = [-3, 3]

   Range of the graph = [-6, 5]

5).

   Domain of the graph = (-∞, ∞)

   Range of the graph = (-∞, ∞)

6).

   Domain of the graph = (-∞, 4]

   Range of the graph = (-∞, ∞)

7).

   Domain of the graph = (-∞, ∞)

   Range of the graph = [-1, 5]

8)

   The domain of the graph = [-1, 5)

   Range of the graph = [-3, 3)

Hence, the values of Relations, domain, range, and functions are calculated above.

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Show that each field is a subset of the other and that f(a, b) = f(b)(a) is a subset of f(a, b). Therefore, f(a, b) = f(a, b) = f(b)(a) holds for a and b belonging to the extension e of f.

To prove that f(a, b) = f(a, b) = f(b)(a) holds for a and b belonging to the extension e of f, we need to first understand what the expression means. Here, f(a, b) represents the field generated by a and b over the field f, i.e., the smallest field containing a and b and all elements of f.

Now, to show that f(a, b) = f(a, b) = f(b)(a), we need to demonstrate that each field is a subset of the other.

Firstly, we show that f(a, b) is a subset of f(a, b) = f(b)(a). This can be done by observing that a and b are both elements of f(a, b) and hence, they are also elements of f(b)(a), which is the field generated by the set {a, b}. Therefore, any element that can be obtained by combining a and b using the field operations of addition, subtraction, multiplication, and division is also an element of f(b)(a), and hence, of f(a, b) = f(b)(a).

Secondly, we show that f(a, b) = f(b)(a) is a subset of f(a, b). This can be done by observing that f(b)(a) is the smallest field containing both a and b, and hence, it is a subset of f(a, b), which is the smallest field containing a, b, and all elements of f. Therefore, any element that can be obtained by combining a, b, and the elements of f using the field operations of addition, subtraction, multiplication, and division is also an element of f(a, b), and hence, of f(a, b) = f(b)(a).

Hence, we have shown that f(a, b) = f(a, b) = f(b)(a) holds for a and b belonging to the extension e of f.

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The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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Answer:

-1 < m ≤ - 5

Step-by-step explanation:

Your expression includes: m, -1, -5, >, ≤

m is the value being compared so it will be in the middle.

# sign m sign #

m is no less than -1: no less than means it is greater than -1, but does not include -1. Therefore, our sign is >

m > -1

m is less than or equal to -5. This means we use ≤ because it can equal -5.

m ≤ -5

Now combine the two expressions

m > -1 – This can also be written as -1 < m.

m ≤ -5

-1 < m ≤ - 5

The area of the triangle is 3/4 units.

What is area of the triangle?

The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h. Therefore, we need to know the triangular polygon's base (b) and height (h) in order to calculate its area.

Suppose

x is the shorter leg of the triangle.

As the longer leg of a right triangle is three times as long as the shorter leg.

⇒ 3x is the longer leg of the triangle.

The hypotenuse of the triangle is, √5.

By using Pythagorean theorem,

\(x^2 + (3x)^2 = (\sqrt{5} )^2\\x^2 + 9x^2 = 5\\10x^2 = 5\\x^2 = \frac{5}{10}\\ x^2 = \frac{1}{2} \\x = \frac{1}{\sqrt{2} }\)

⇒ Shorter leg of the triangle is 1/√2.

⇒ Longer leg of the triangle is 3/√2.

Now to find the area of the triangle.

Area of triangle = \(\frac{1}{2}(\frac{1}{\sqrt{2} })(\frac{3}{\sqrt{2} } )\)

\(A = \frac{3}{4}\)

Hence, the area of the triangle is 3/4 units.

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Given data:

The length of the wire is l= 50 foot.

The given base length is b= 35 feet.

The expression for the height of the antena is,

Substitute the given values in the above expression.

Thus, the height of the antena is 36 ft.

Given:

A geometric figure.

To find:

The values of x and y.

Solution:

The given figure is a kite because it has two disjoint pairs of consecutive congruent sides.

Kite has one pair of congruent opposite angles. The angled included between non-congruent sides are congruent.

\((4x+13)^\circ=(5x-15)^\circ\)

\(4x+13=5x-15\)

\(13+15=5x-4x\)

\(28=x\)

The diagonal bisects the other pair of opposite angles.

The missing angle of the above triangle is \(y^\circ\).

Using angle sum property, we  get

\((y-9)^\circ+y^\circ+(4x+13)^\circ=180^\circ\)

\((2y-9)^\circ+(4(28)+13)^\circ=180^\circ\)

\((2y-9)^\circ+(125)^\circ=180^\circ\)

\((2y-9)^\circ=180^\circ-125^\circ\)

On further simplification, we get

\((2y-9)^\circ=55^\circ\)

\(2y-9=55\)

\(2y=55+9\)

\(2y=64\)

Divide both sides by 2.

\(y=32\)

Therefore, the value of x is 28 and the value of y is 32.

Answer:

16 mph

Step-by-step explanation:

Givens:

4 hours total time

48 miles total distance

So our equation should look like this.

48 = 2x(2) + x(2)

Where x = speed second half of trip.

x = 8

x*2 = 16 mph