What is the domain of the following function?

Therefore , the solution of the given problem of trigonometry comes out to be  B = arcsin(9/14) - 180° = 140.0°.

Correlations between triangles' angles and sides are studied in the branch of mathematics known as trigonometry. Since every straight-sided form may be reduced to a collection of triangles, trigonometry can be found throughout geometry. The relationships between trigonometry and other branches of mathematics, in particular calculus, real or complex, infinite series, logarithms, and infinite series, are astonishingly complicated.

Here,

There are two potential solutions because the supplied angle is opposite the given side that is the shortest.

Using the sine law,

B = b/asin(A)arcsin(9/7sin(30°))arcsin(9/14)

Angle B may take on the following values:

B is equal to arcsin(9/14) = 40.0°.

B = arcsin(9/14) - 180° = 140.0°

Therefore , the solution of the given problem of trigonometry comes out to be  B = arcsin(9/14) - 180° = 140.0°.

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The perimeter of the right triangle is 228 inches

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter.

Since it is a right triangle,

c² = 57² +76²

c² = 3249 + 5776

c² =  9025

c=  √ 9025 = 95

Perimeter is the sum of all sides

Perimeter = 57+76+95 = 228 inches

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Therefore , the solution of the given problem of probability comes out to be  P =0.286(approx).

Probability is the likelihood or potential for something to event.  For instance, there is only one way to get a head and a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) must equal 12. Classical: (equally likely results) (equally probable outcomes) S, the sample location (the collection of all distinct outcomes that could occur), Definition of Relative Frequency and Subjective Probability.

Here,

Given : S = {9,10,11,12,13,14,15}

If A is a subset of S, A could be {14,15}.

If a subset A represents the complement of spinning a number greater than 13, its sample space is A = {14,15}.

Thus,

To find the probability that it will land on number greater than 13

P = likelihood of event / total no of events

=> P = 2/7

=> P = 0.2857

=> P =0.286(approx)

Therefore , the solution of the given problem of probability comes out to be  P =0.286(approx).

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Approximately 66(2s f) percentage of the logo does the circle cover.

What is percentage?

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.

To find the percentage we must first find the area of the circle:

We can find the radius of the circle using the distance formula;

⇒ [tex]d=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]

⇒  [tex]r = \sqrt{(6.3-0)^2+(1.6-0)^2}[/tex]

⇒   r = 6.5

Now we calculate the area;

⇒ [tex]A = \pi r^2[/tex]

⇒  [tex]A = \pi (6.5)^2[/tex]

⇒  [tex]A = \frac{169}{4} \pi[/tex]

To get the percentage we divide the area of the circle by the square’s are and multiply by 100;

⇒ Percentage = [tex]\frac{42.25*\pi }{200}*100[/tex]

⇒ Percentage = 66(2s f)

Hence, approximately 66(2s f) percentage of the logo does the circle cover.

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Answer:

Y-intercept: (0, -7)

X-intercept: (-14,0)

Step-by-step explanation:

To find the y-intercept, we need to put 0 in for x

0 + 2y = -14

2y = -14

y = -7

So, the y-intercept is located at (0, -7)

To find the x-intercept, we need to put 0 in for y

x + 2(0) = -14

x = -14

So, the x-intercept is located at (-14,0)

Step-by-step explanation:

To find the y-intercep, we need to put 0 in for x

0 + 2y= -14

2y = -14

y = - 7

So, the y - intercept is located at ( 0, - 7)

Answer:

Step-by-step explanation:

Given the value function v(t) = 20000·0.86^t, you want the value after 4 years and 10 years.

Put the value of t in the formula where t is, and do the arithmetic.

The attached calculator output tells us ...

  value after 4 years: $10,940

  value after 10 years: $4,426

__

Additional comment

When you are asked to do the same evaluation with different numbers, it is convenient to process them as a list, or using a spreadsheet.

Using trigonometric functions, we can  find a side length of a right triangle with an angle and a side.

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.

You can determine the hypotenuse by dividing the length of the side by sin(θ) if you have an angle and the side opposite to it. Alternatively, to find the length of the side next to the angle, divide the length by tan(θ).

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The total surface area of the hemisphere is 108 pi cm^2.

Surface area is the amount of space covering the outside of a three-dimensional shape. We calculate the surface area for three dimensional objects. The surface area of a 3-D object is not same as its volume.

The surface area of a sphere with the radius r is 4 pi r^2

The surface area of a hemisphere with the radius r = 2 pi r^2 +   pi r^2

where pi r^2 represents the area of the circular base of the hemisphere of radius r.

The surface area of a hemisphere sphere with the radius r is 3 pi r^2

For radius r=6cm

TSA of  the hemisphere is 3 pi (6x6) cm^2

TSA = 108 pi cm^2

108 pi cm^2 is the total surface area of a hemisphere with the radius 6 cm.

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The value of x will be; x = 3

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

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that  the equation 5x+7=6x+4

Here, we need to solve for x;

5x+7=6x+4

combine the like terms;

5x - 6x = -7 +4

-x= - 3

x = 3

Therefore, the solution will be as;

x = 3

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Step-by-step explanation:

20 workers finish work in 21 days.

the necessary work effort is 20×21 = 420 workdays.

the same effort is needed even if the overall time is shorter.

x workers in 15 days.

x × 15 = 420

x = 420/15 = 28 workers.

so, 28-20 = 8 additional workers are needed to finish the work in 15 days.

The perimeter of ΔAEB is 18.5 feet.

A triangle's other two sides are divided in the same proportion if a line drawn parallel to either one of its sides intersects the other two sides at two different spots.

As,  side AB║DF hence we will use Triangle Proportionality theorem to calculate the length of side AE.

Since, AE/AD = EB/ BF

AE/2 = 7.2/8.4

AE = 6.5 feet

So, the perimeter of ΔAEB is

= AE + EB + BE

=6.5+4.2+7.8

=18.5 ft.  

Hence, the perimeter  is 18.5 feet.

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In the given diagram beside a coffee, the value of x is 38.

A diagram is a visual, symbolic representation of data. Diagrams have been used on cave walls since prehistoric times, but they became more common during the Enlightenment. The method occasionally employs the projection of a three-dimensional visualisation onto a two-dimensional surface. Sometimes the word "graph" is used in place of the word "diagram."

We know that all angles here add up to 360°

And with the vertical angles theorem we get the equation

2(36°) + 2(78 - x)° + 2(3x - 10) = 360°

2(36 + 78 - x + 3x - 10) = 360°

2(104 + 2x) = 360°

208 + 4x = 360°

4x = 360 - 208

4x = 152

x = 152/4

x = 38

Thus, In the given diagram beside a coffee, the value of x is 38.

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Each person will pay $49.056. The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.

A percentage, often known as percent, is a division by 100. Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Amount of bill = $124.72

and tip they left = 18% of $124.72

total amount is =$124.72 + $124.72*18%=$147.1696

so, each person pay= $147.1696/3=$49.056

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In the expression 52 + 6 + ya,

The terms are the individual parts of the expression that are being added together. The coefficient is the numerical factor that is multiplied by a variable in a term, and the constant is a term that has no variable.

Any expression with variables will either add or delete one or more variables. Any one of a variety of numbers to represent a generic idea. An absolute number is a constant. A constant is a number, whereas a coefficient is a number that is "in front of" a variable.

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The remaining miles are 660 miles.

This month, Diaz drives 28 miles each day using the car allotted to him by his company.

But the company allows him to drive up to 1500 miles each month by his car.

To calculate the remaining miles that Diaz has not traveled this month, we have to use the formula m = 1500 - 28d, where d is the number of days in that particular month.

A month general consists of 30 days.

So, this month Diaz has traveled 28×30 miles = 840 miles ( using multiplication)

Therefore, the remaining miles(m) that Diaz has not traveled this month comes to 1500 - 840 = 660 miles.

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The complete question is:

Diaz has a company car that allows him to drive up to 1,500 miles each month. He averages 28 miles each day. The remaining miles for this month can be calculated using the formula m = 1500 - 28d where m is the remaining miles and d is the number of days driven this month. What are the remaining miles?

Answer:

(2, -1)

Step-by-step explanation:

2(2)+ (-1) = 4-1 = 3.

If the value of y = 0, then it make the straight line on the graph.

The term graph in math is defined as the way that is used to represent a set of data to make it easier to understand and interpret statistical information.

Here we have the expression y = 0.

And here we know that the y coordinate is constant which is 0 for given equation and only x coordinate is variable.

Therefore it represent the x-axis.

Therefore, basically y=0 is the linear equation to denote the x - axis, here as all the points on the x- axis, then we have their y co-ordinate = 0.

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Answer:

x - intercept = (15, 0)

y - intercept = (0, 6)

Step-by-step explanation:

x-int. is when y = 0

y-int. is when x=0

Plug in y = 0 and x = 0 to get intercepts.

FOR X-INT.:

12x + 30(0) = 180

12x = 180

x = 15

x-int. is (15, 0)

FOR Y-INT. :

12(0) + 30y = 180

30y = 180

y = 6

y-int. is (0, 6)

On solving the provided question we can say that  so the value of the data from histogram graphs will be x [tex]\alpha[/tex] 0.123 * 125 / 100  = 0.15375

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

the best way to describe the data that was used to create this histogram (keep in mind that there is no scale on the horizontal axis, so you must choose based simply on the appearance of the histogram graphs

so the value of the data from histogram graphs will be

z = 0.123

u = 100

x = 125

x [tex]\alpha[/tex] 0.123 * 125 / 100  = 0.15375

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The domain of the function f(x) = log x is (0, ∞). The value of x belongs to (0, ∞).

What is a logarithm?

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

The given function is f(x) = log x.

When the value of x is less than or equal to 0, then the value of log x is undefined.

The possible value of x where f(x) exists is the domain of a function.

In the given function the value of x must be greater than zero.

The domain of the function is (0,∞).

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The price of a stock share has decreased by 15% and suddenly increased by 5%.

The percentage is a fraction of a number represented as a number out of a hundred. The % symbol is used to denote percentages. The percentage signifies the frequency.

The selling price for a share of the same stock at a later date was represented by the expression 1.05(0.85d).

When a % decrease occurs, the number is deducted from 100, and when a percentage increase occurs, the number is added to 100.

100 - 15% = 85% = 0.85

100 + 5% = 105% = 1.05

original selling price = d

selling price at a later date = 1.05(0.85d)

0.85d means that the original price was discounted by 15%

1.05 means that the price increased by 5%

Thus, the price of a stock share has decreased by 15% and suddenly increased by 5%.

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The domain of the given function would be x > 0.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The function f(x) = log is the natural logarithm function, also known as ln(x). The domain of this function is the set of all positive real numbers x such that x > 0, because the natural logarithm of a non-positive number is undefined.

Hence, the domain of the given function would be x > 0.

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The domain of the given function would be x > 0.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The function f(x) = log is the natural logarithm function, also known as ln(x). The domain of this function is the set of all positive real numbers x such that x > 0, because the natural logarithm of a non-positive number is undefined.

Hence, the domain of the given function would be x > 0.

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Plotting method is the graphical representation of mathematical expression.

A plot is a graphical representation of a list of data. Besides, a plot is the graphical analysis of mathematical expressions and equations because plot can show the relationship between two or more variables. There are many plotting methods such as hand plotting method, computer aided plotting method and so on.

At first, we need to choose the coordinate system by which we plot the point.

suppose we choose a XY coordinate plane. At first identify the horizontal or X axis and vertical or Y axis.

besides, we need to determine the required value that will be plotted on the plan.

if we have a list of X and Y value then find the value of X on the x axis and next find the value of Y on the Y axis.

we will notice some points for every pair of x and y value. Finally, we will join the points to achieve a required shaped graph.

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ES is 8√2 units from the given graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given two points from the graph are S(4, 4) and E(-4, -4)

We need to find ES which means the distance between two points in units.

The length along a line or line segment between two points on the line or line segment.

Distance=√(x₂-x₁)²+(y₂-y₁)²

√(-4-4)²+(-4-4)²

√(-8)²+(-8)²

√64+64

√64×2

8√2 units.

Hence, ES is 8√2 units from the given graph.

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Answer:

[tex]\displaystyle x < \frac{12}{7}[/tex]

Step-by-step explanation:

This is an inequality, not an equation. Notice the sign is a "less than" sign and not an "equal" sign. You still solve it like a normal equation, however:

[tex]\displaystyle 7x-2 < 10\\\\\rightarrow 7x < 12\\\\\rightarrow x < \frac{12}{7}[/tex]

Jane should land 1.5 mi down the shoreline and walk the remaining 4.5 mi to the village to minimize her travel time.

Let x = distance travelled along the shore over water.

Then, 6 − x = distance travelled along the shore over land.

Let T = the total time taken to reach the destination.

T = distance/velocity = √(4 + x²)/3 + (6-x)/5 on [0, 6].

Note that T must be non negative and that x = 6 means the destination

is reached solely by rowing and without the benefit of faster land

travel. In actual fact, T is valid over [0, ∞) but [0, 6] is reasonable here.

T' = x/3√(4 + x²) - 1/5 = 5x - 3√(4 + x²) = 0

⇒5x = 3√(4 + x²)

⇒25x² = 9(4 + x²)

⇒16x² = 36

⇒x = ±6/4 = ±1.5

The negative x value is discarded since it does not belong to [0,6].

T(0) = 28/15 = 1.8667

T(1.5) = 1.733

T(6) = 2.1082

Therefore, Jane should land 1.5 mi down the shoreline and walk the

remaining 4.5 mi to the village to minimize her travel time.

Her minimum travel time will be T(1.5) = 1.733 hrs. or 1hr 44 min.

--The given question is incomplete, the correct question is

"Jane is 2 mi, offshore in a boat and wishes to reach a coastal village 6 mi, down a straight shoreline from the point nearest the boat. She can row at 3mph and can walk at 5 mph. Where should she land her boat to reach the village in the least amount of time?"--

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Solving for x in the angle bisector which resulted to the proportion  x over 18 = 45 over 20 results to x = 40.5

In geometry, a line that divides an angle into two equal angles is referred to as an angle bisector.

By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.

The division from angle bisectors gave rise to the proportion which is given by

x / 18 = 45 / 20

cross multiplying

x = 18 * 45 / 20

x = 40.5

hence x is solved to get 40.5

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The probability that the distance is at most 100m is 0.749926 and at most 200 m is 0.9375 between 100 and 200 m is 0.1876 and the probability that distance exceeds the mean distance by more than 2 standard deviations is 0.04979

What is Probability ?

probability can be defined as the ratio of the number of favourable outcomes and the total number of outcomes.

We are given with an exponential distribution with

λ=0.01386.

The probability distribution function is:

F(x)=λ * e power (−λx)

Cumulative distribution function is

F(x) = 1- e power (−λx)

The mean of the exponential distribution function

E(X) = 1 / λ

= 1/0.01386

= 72.15

Hence, E(X) = 72.15

The variance of the exponential distribution function

V(X) = 1 / λ ^{2}

= 1/0.01386*0.01386

= 5205.63

V(X) = 5205.63

Probability that the distance is at most 100m

P(X <= 100 ) = F (100)

= 1- e power (−λx)

= 1 - e power (-0.01386*100)

= 1- e power (-1.386)

= 1-0.25007

= 0.749926

Therefore, P(X<=100) = 0.749926

probability that the distance is at most 200m

P ( X<= 200) = F(200)

=1-e power (−λx)

=1-e power (-0.01386*200)

= 1 - e power (-2.772)

= 1-0.06253

= 0.9375

P(X<= 200) = 0.9375

Probability that the distance is between 100 and 200m

P(100<= X <= 200) = F(200) - F(100)

= 0.9375-0.7499

=01876

P(100 <= X <= 200) = 0.1876

Probability that the distance exceeds the mean distance by more than 2 standard deviation.

P( X + P>μ+2σ) = P(X>72.15+2√5205.63)

= P(X > 72.15 +144.3)

P(X>216.45)

= 1-P(X<= 216.45)

1 - (1- e power (-0.01386*216.45)

=  e power (-2.9999)

= 0.04979

P( X + P>μ+2σ) = 0.04979

Hence , The probability that the distance is at most 100m is 0.749926 and at most 200 m is 0.9375 between 100 and 200 m is 0.1876 and the probability that distance exceeds the mean distance by more than 2 standard deviations is 0.04979

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For the given Augmented Matrix ,the correct option is :

A) The solution set has exactly one element.

The exact solution is x = -25 , y = 2 and z = 2.

Augmented Matrix:

An augmented matrix is ​​a means of solving simple linear equations. Coefficients and constant values ​​of linear equations are represented as matrices called augmented matrices. Simply put, an augmented matrix is ​​a combination of two simple matrices along columns. If the first matrix has m columns and the second matrix has n columns, then the augmented matrix has m + n columns.

Now, as given the Augmented matrix:

[1 7 3 -5]

[0 0 0 3]

[0 0 1 2]

[0 1 -1 4]

From this system we get:

y - z = 4       --------------------------- (1)

    z = 2

and, z = 3

and, x + 7y + 3z =-5   ---------------- (2)

Now, Solving the equation with z = 2,

    y - 2 = 4

⇒ y = 6

and, putting y = 6 and z = 2

   x + 7× 6 + 3×2 = -5

⇒ x + 42 + 6 = -5

⇒ x +48 = -5

⇒ x = -53

Therefore, x = -53, y=6 and z =2

Now, for z = 3 in equation (1)

   y - 3= 4

⇒ y = 7

Putting y =7  and z =3, we get:

   x + 7 × 7 + 3×3 = -5

⇒ x + 49 + 9 =-5

⇒ x + 58 = -5

⇒ x = -63

Therefore, x = -63, y =7 and z =3

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