There are 1800 students in a school, if the ratio of teachers to students is 2: 7. How many teachers are at the school?

The unit circle is best suited for dealing with angles and trigonometric functions of multiple angles, right triangles are best for finding the lengths of the sides of triangles with a right angle, and trigonometric identities are best for simplifying or manipulating trigonometric expressions.

Each tool has its own strengths and weaknesses and is better suited for certain types of problems.

Unit Circle is a powerful tool used to relate angles to trigonometric functions. It is particularly useful when dealing with angles in radians, as it allows for easy conversion between radians and degrees. The unit circle is also useful when dealing with trigonometric functions of multiple angles, such as sine and cosine of the sum or difference of two angles.

A good example will be if we want to find the exact value of sin(π/6), we can use the unit circle to visualize the angle π/6, which corresponds to 30 degrees. The unit circle tells us that at this angle, sin(π/6) = 1/2.

Right triangles are useful when we have a right angle in the triangle, as they allow us to use the Pythagorean theorem and trigonometric ratios to find the lengths of the sides of the triangle. Right triangles are particularly useful when we know one angle and one side length, as we can use trigonometric ratios such as sine, cosine, and tangent to find the lengths of the other sides.

If we have a right triangle with an angle of 30 degrees and a hypotenuse of 2, we can use the sine ratio to find the length of the opposite side. sin(30) = opposite/hypotenuse, so opposite = sin(30) * 2 = 1.

Trigonometric identities are useful when we want to simplify or manipulate trigonometric expressions. These identities are derived from the definitions of the trigonometric functions and can be used to simplify complex expressions or prove trigonometric identities.

For example, we can use the identity:

sin²(x) + cos²(x) = 1

to simplify the expression

sin²(x) - cos²(x).

We can rewrite this expression as:

sin²(x) - cos²(x) = sin²(x) + (-1)*cos²(x)

Learn more about trigonometry here:

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Answer:

good point I don't know that either

Answer:

LCM = 1440

Step-by-step explanation:

           2 | 72 , 96 , 120

           2 | 36, 48, 60

           2 | 18 , 24 , 30

           2 | 9 , 12 , 15

           2 | 9 , 6 , 15

           3 | 9 , 3 , 15

           3 | 3 , 1 , 5

           5 | 1 , 1 , 5

             | 1 , 1 , 1

LCM = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 = 1440

Step-by-step explanation:

We have,

[tex]g(x)=x^3+x^2-x-2[/tex]

To find g(-1), put -1 in place of x i.e.

[tex]g(-1)=(-1)^3+(-1)^2-(-1)-2\\\\=-1[/tex]

To find g(1), put 1 in place of x i.e.

[tex]g(1)=1^3+1^2-1-2\\\\=-1[/tex]

To find g(2), put 2 in place of x i.e.

[tex]g(2)=2^3+2^2-2-2\\\\=8[/tex]

g(2) + g(1) = 8+(-1)

= 7

Hence, this is the required solution.

Answer:7

Step-by-step explanation: mark brainliest pls lol

Answer:

Kindly check explanation

Step-by-step explanation:

Given :

Pool dimension :

rectangular floor that measures 22 feet by 13 feet and a flat ceiling that is 7 feet above the floor

Floor area = length * width

Floor area = 22 * 13 = 286 ft²

Volume of the pod :

Floor area * height = 286ft² * 7ft = 2002 ft³

2.)

Surface area = length * width

Surface area = 28 * 20 = 560 ft²

Volume of the pool :

Surface area * deptb = 560ft² * 7ft = 2002 ft³

3.)

Area of flower bed = length * width

Floor area = 30 * 5 = 150 ft²

Volume of the soil flowerbed holds :

Depth = 1.1 m

Area of flowerbed * depth =150ft² * 1.2ft = 180 ft³

Answer:

we arrive at the conclusion that the new employee installs the vertical blinds faster on average.

Step-by-step explanation:

null hypothesis; m₁-m₂ =0

alternative hypothesis; m₁-m₂<0

Given the information in this question, we first have to solve for the t statistic

[tex]t=\frac{22-24.8}{\sqrt{\frac{0.90^{2} }{10}+\frac{0.75^{2} }{10} } }[/tex]

[tex]t=\frac{-2.6}{\sqrt{o.081+0.05625} }[/tex]

[tex]t=\frac{-2.6}{0.37047}[/tex]

t = -7.018

the degree of freedom = n₁+n₂-2

= 10+10-2

= 18

Alpha α = 0.05

from these results the t critical value = -1.734

because the test statistic -7.018 < -1.734,

at 0.05 level of testing, we arrive at the conclusion that the new employee installs the vertical blinds faster on average than the veteran.

the answer is b no trend

Answer:

Answer:

g(x) = f(x) - 2

g(x) = f(x + 2)

Step-by-step explanation:

y-intercept of a function:

The y-intercept of a function is the value of y when x = 0.

Function f:

Graph given in this question

When [tex]x = 0, y = 6[/tex], so the y-intercept is 6.

Additionally, when [tex]x = -2, y = 4[/tex]

If g has a y-intercept at 4, which of the following functions could represent g?

Either we subtract 2 from f, that is:

[tex]g(x) = f(x) - 2[/tex]

Or we can also add 2 on the domain, that is, moving 2 units to the right, so:

[tex]g(x) = f(x+2)[/tex]

So the first two options are correct.

Answer:

the answer would be g(x)=f(x)-2

Step-by-step explanation:

i got it right

Answer:

3

Step-by-step explanation:

(10, 5) and (15,20)

m = rise/run

m = ∆y/∆x

m = (y₂ - y₁) / (x₂ - x₁)

m = (20 - 5) /(15 - 10)

m = 15/5

m = 3

Answer:

(a) Amplitude = 4

(b) [tex]T = \frac{2\pi}{3}[/tex] --- Period

(c)

[tex]C = \frac{\pi}{3}[/tex] --- phase shift

[tex]D =1[/tex] --- vertical shift

Step-by-step explanation:

Given

[tex]f(x) = -4\cos(3x - \pi) + 1[/tex]

Rewrite the function as:

[tex]f(x) = -4\cos(3(x - \frac{\pi}{3}) + 1[/tex]

Solving (a): The amplitude

A cosine function is represented as:

[tex]f(x) = A\cos[B(x - C)] + D[/tex]

Where:

[tex]|A| \to Amplitude[/tex]

So, in this equation (by comparison):

[tex]|A| = |-4|[/tex]

[tex]|A| = 4[/tex]

The amplitude is 4

Solving (b): The period (T)

This is calculated as:

[tex]T = \frac{2\pi}{B}[/tex]

By comparison:

[tex]B =3[/tex]

So:

[tex]T = \frac{2\pi}{3}[/tex]

Solving (c): The shift

The phase shift is C

The vertical shift is D

By comparison:

[tex]C = \frac{\pi}{3}[/tex] --- phase shift

[tex]D =1[/tex] --- vertical shift

Answer:

8 inches

Step-by-step explanation:

Let w represent the width.

If the length is 14 inches longer than the width, it can be represented by w + 14.

Use the perimeter formula, p = 2l + 2w. Plug in 60 as the perimeter and w + 14 as l, then solve for w:

p = 2l + 2w

60 = 2(w + 14) + 2w

60 = 2w + 28 + 2w

60 = 4w + 28

32 = 4w

8 = w

So, the width is 8 inches

Answer:

Event 4 (0%), Event 2 (45%), Event 3 (80%), Event 1 (100%)

Step-by-step explanation:

Answer:

Step-by-step explanation:

In order to determine the perpendicular slope to the given line, we first need to determine the slope of the given line, which is not apparent in its current form. We need to solve the equation for y to determine the slope:

2y = 3x + 1 in slope-intercept form is

[tex]y=\frac{3}{2}x+\frac{1}{2}[/tex] .  Therefore, the perpendicular slope, the opposite reciprocal of the given slope of 3/2 is -2/3. Passing through the point (3, 2):

[tex]y-2=-\frac{2}{3}(x-3)[/tex] and

[tex]y-2=-\frac{2}{3}x+2[/tex]  so

[tex]y=-\frac{2}{3}x+4[/tex], the second choice down.

Answer:

Step-by-step explanation:

Answer:

x < 3

Step-by-step explanation:

Given

4x - 7 < 5 ( add 7 to both sides )

4x < 12 ( divide both sides by 4 )

x < 3

Answer:

hope it's helpful for you

-125

BEDMAS, like its counterpart BODMAS, is used as an acronym which gives the order of precedence of certain mathematical operations. It stands for:

B - Brackets

E - Exponentials

D - Division

M - Multiplication

A - Addition

S - Subtraction

This specifies the order in which arithmetic operations take place. That is brackets expressions should be solved first, followed by exponentials, then division and so on.

Using BEDMAS, let's solve 9+10-8(9)x2

Follow these steps;

i. Solve the bracket first.

9+10-72x2

ii. Next solve the multiplication

9+10-144

iii. Then solve the addition

19-144

iv. Now, the subtraction

-125

Therefore;

9+10-8(9)x2 = -125 using bedmas

It's in p/q form where p = 16 and q = 33.

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Work Shown:

x = 0.484848.....

100x = 48.4848.....

I multiplied both sides by 100 to move the decimal over 2 spots. Both decimal values for x and 100x have an infinite string of "48"s repeated after the decimal point. When we subtract, those infinite strings will cancel out

100x - x = 99x

48.4848..... - 0.484848..... = 48

So after subtracting straight down, we have the new equation 99x = 48 which solves to x = 48/99

Divide both parts by the GCF 3 to fully reduce

48/3 = 16

99/3 = 33

Therefore, x = 48/99 = 16/33 = 0.484848...

I recommend using a calculator to confirm that 16/33 = 0.484848...

Side note: your calculator may round the last digit, but this is of course rounding error

Answer:

The awnser should be 3.

Step-by-step explanation:

if f(x) means the same thing as x + 1. Than that means f = 1. So if re write the question. 1 plus 2 equals 3.

Answer:

x = 1.7

Step-by-step explanation:

Answer:

its a three in seven chance, since there are seven total outcomes and there is only one favorable outcome. Hope that helps.

Step-by-step explanation:

Answer:

294 in

Step-by-step explanation:

set a ratio w/l

11/14

set it equal to 231/x

x = length

[tex]\frac{11}{14}[/tex] = [tex]\frac{231}{x}[/tex]

cross multiply

11x = 3234

divide by 11

x = 294

Hi, I'm so sorry I can't answer that. but I have something you can answer that. Search in browser or anything searcher that you have "Quickmath" or "Cymath" all your equations,problems can solved

Step-by-step explanation:

i hope it helps

Answer:

x=6

Step-by-step explanation:

Answer:

£70.00

Step-by-step explanation:

You basically want to find what she spent in total, then subtract the amount she spent on ingredients.

50 glasses of lemonade at £2.10 each would be £105. (50*2.1)

Subtract the cost of ingredients, which is £35, with the total she made, £105, to get £70 (105-35)

Answer:

y = 6/5x -7

Step-by-step explanation:

Answer:

Step-by-step explanation:

A). "If you do not study and fail the next test"

  Two statements are combined in the given statement.

  "If you don't study" and "fail the next test"

  Second statement is the consequence of the first statement.

  Therefore, events are dependent.

B). If you select a card from a deck and without replacing it, you select another card.

  Here, selection of a card from a deck without replacing it doesn't affects the selection of another card.

  Therefore, both the events are independent.

Answer:

[tex]4 ^{-3}[/tex]

or

[tex]\frac{1}{4^3}[/tex]

or

[tex]\frac{1}{64}[/tex]

Step-by-step explanation:

four to the negative power of 3 is =  4⁻³

Step-by-step explanation:

The answer is A (the first one). 4 to the negative 3rd power is 4^-3