Solve 12g=12(2/3g-1)+11

Answer:  [tex]\tan \theta=\dfrac{1}{\sqrt3}.[/tex]

Step-by-step explanation:  Given that

[tex]\sin\theta=-\dfrac{1}{2}[/tex] and [tex]\theta[/tex] lies in Quadrant III.

We are to find the value of [tex]\tan \theta.[/tex]

We will be using the following trigonometric identities:

[tex](i)~sin^2\theta+\cos^2\theta=1,\\\\(ii)~\dfrac{\sin\theta}{\cos{\theta}}=\tan \theta.[/tex]

We have

[tex]\tan\theta\\\\\\=\dfrac{\sin\theta}{\cos\theta}\\\\\\=\dfrac{\sin\theta}{\pm\sqrt{1-\sin^2\theta}}\\\\\\=\pm\dfrac{-\frac{1}{2}}{\sqrt{1-\left(\frac{1}{2}\right)^2}}\\\\\\=\pm\dfrac{\frac{1}{2}}{\sqrt{1-\frac{1}{4}}}\\\\\\=\pm\dfrac{\frac{1}{2}}{\frac{\sqrt3}{2}}\\\\\\=\pm\dfrac{1}{\sqrt3}.[/tex]

Since [tex]\theta[/tex] lies in Quadrant III, so tangent will be positive.

Thus,

[tex]\tan \theta=\dfrac{1}{\sqrt3}.[/tex]

Adding two right angles, each being 90 degrees, always results in a straight angle, which is 180 degrees, so this is always true.

The sum of two right angles always results in a straight angle. This can be justified with a basic understanding of angles in a flat plane. A right angle is 90 degrees and a straight angle is 180 degrees. So, if you add two right angles together (90 + 90), you get 180, which is the measure of a straight angle. Hence, this is always true, regardless of the vectors or other elements you are working with. It's also important to note that in broader geometric terms, this statement is also always true: two angles that add up to form a straight line (180 degrees) are referred to as supplementary angles.

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56×10= 560 so the answer is 560

To find the balance after 3 years in a savings account with $12,000 and a 3.5% interest rate compounded monthly, we can use the formula for compound interest.

To find the balance after 3 years, we can use the formula for compound interest:

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

where:

Plugging in the given values:

The formula gives us:

A = $12,000(1 + 0.035/12)^(12*3)

Calculating this expression will give us the balance after 3 years.

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The required Integers  are 13, 15, 17

What are the Integers?

Integers are the collection of whole numbers and negative numbers.

Given that twice the three consecutive odd Integers is nine more than the largest.

Let the numbers be x , x+2 , x+4

According to question

2x = 9+x+4

x = 13

Hence the Integers are 13, 15, 17

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Answer: 500

Step-by-step explanation:

Since,  The monthly salary is modeled by the function,

f(c) = 250 c + 500.

According to the question,

Adam earns a base pay plus a commission for each car he sells at Crazy Carl's Cool Cars.

In the given function c is a variable.

Thus, c must show the number of cars.

Thus, the base pay must be free from any variable.

In the above expression 500 is free from the variable c therefore, 500 is the base pay of Adam.

⇒ f(c) is the total earning by Adam after selling a car.

If he Does not sell any car then c=0,

f(0) = 250×0+500 = 500

Therefore, if he does not sell any car then his earning is 500.

The inequality describes the solution to 5(3 - x) < -2x + 6 will be x > 3. The correct option is B.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The given expression 5(3 - x) < -2x + 6 will be solved as below:-

5(3 - x) < -2x + 6

15 - 5x < -2x + 6

-5x + 2x < -15 + 6

-3x < -9

x > 3

Therefore, the inequality describes the solution to 5(3 - x) < -2x + 6 will be x > 3. The correct option is B.

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The standard deviation decreases and the sampling distribution becomes more normal as the sample size increases in x bar distribution.

The variability of the x bar distribution changes as the sample size increases. As the sample size increases, the standard deviation of the sampling distribution of the means will decrease, approaching the standard deviation of X. The sampling distribution of the mean becomes more normal as the sample size grows, showing less variability.

The length of the apothem of a regular polygon that has a radius of 10 inches would be 9 inches .

The apothem of a regular polygon is defined as a line segment from the center to the midpoint of one of its sides.

It is Given that the hexagon has a radius of 10 inches and the length of the radius is equal to the length of each side of the hexagon.

The apothem AB divides the side of the hexagon into two equal parts of 5 Inches.

Using Pythagoras Theorem

[tex]10^2 = 5^2 + AB^2\\AB^2 = 10^2 -5^2\\AB^2 = 100 - 25\\AB^2 = 75\\AB = \sqrt{75}[/tex]

AB = 8.66

So, rounded up, we get the apothem closest to D that is 9 in.

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For an hour of assistance if a student charged $10.25 than total number hours a student need to work to earn $8,425 is 821.95 hours and this can be determine by the help of unitary method.

Given :

Charge for 1 hour assistance = $10.25

Total earning through assistance = $8425

In this problem unitary method can be use to determine the total number of hours need to work to earn $8425. In unitary method, single unit value is determine first to evaluate the necessary value by multiplying the single unit value.

For an hour of assistance if a student charged $10.25 than total number hours a student need to work to earn $8,425 can be:

[tex]= \dfrac{8425}{10.25} \times 1[/tex]

= 821.95 hours

So a student need to work a total of 821.95 hours to earn $8425.

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Final answer:

A variable is a name assigned to a quantity that can take on various values, and is used by mathematicians, economists, and statisticians in different contexts to represent data or elements of an equation.

Explanation:

A variable is the name given to a quantity that may assume a range of values. Mathematicians and economists often use variables in equations to represent different aspects of a problem or scenario. For example, in the equation of a line, commonly expressed as y = mx + b, the variables are 'x' and 'y'. Here, 'x' typically represents values on the horizontal axis, and 'y' represents values on the vertical axis, while 'b' is the y-intercept, and 'm' is the slope of the line. To understand how an equation with variables functions, we can look at a numerical example.

In statistics, variables can also refer to characteristics or measurements that can be determined for each member of a population. These variables can be numerical or categorical. A numerical variable, such as 'X' representing the number of points earned by a math student, allows for mathematical calculations like averaging. A categorical variable, like 'Y' indicating a person's political party affiliation, places individuals into categories and doesn't lend itself to mathematical operations like averaging.

Answer:

The total cost of the car be $35162.5 .

Step-by-step explanation:

As given

John Gray bought a basic car for $32,750.00, with options that cost $375.00.

Cost of the car = Car cost + Option cost

                          =  $32750 + $375

                          = $33125

As given

There's a 6% sales tax in his state .

6% is written in the decimal form.

[tex]= \frac{6}{100}[/tex]

= 0.06

Sales tax price = 0.06 × 33125

                        = $ 1987.5

As given

A combined $50.00 license and registration fee.

Than

Total cost of the car  =   Cost of the car  + Sales tax price +  license and registration fee.

                                  =  $33125 + $ 1987.5 + $ 50

                                 = $35162.5

Therefore the total cost of the car be $35162.5 .