What is a trigonometric ratio

Using the normal distribution, it is found that:

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

Question 1:

1.1 standard deviations above the mean, hence, a z-score of Z = 1.1.

Question 2:

The proportion is the p-value of Z when X = 57000 subtracted by the p-value of Z when X = 54000, then:

X = 57000:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{57000 - 54800}{2600}\)

\(Z = 0.846\)

\(Z = 0.846\) has a p-value of 0.801.

X = 54000:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{54000 - 54800}{2600}\)

\(Z = -0.307\)

\(Z = -0.307\) has a p-value of 0.379.

0.801 - 0.379 = 0.422

0.422 x 100% = 42.2%

42.2% of people in this profession earn annual salaries between $54,000 and $57,000.

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The area of the given rectangle in simplest fraction form is: 81³/₅ m²

The formula for the area of a rectangle is expressed as:

A = L * W

Where:

A is Area

L is length

W is width

We are given the parameters:

Length = 12³/₄ meters = 51/4 meters

Width = 6.4 meters = 6²/₅ meters = 32/5 meters

Thus:

Area = 51/4 * 32/5

= 408/5 m²

= 81³/₅ m²

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Answer:

The Area is 25

Step-by-step explanation:

You will need distance formula for this questions

for AD, (0,4) and (4,7)

The formula is here

\(\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)

which gives you

\(\sqrt{\left(4-0\right)^2+\left(7-4\right)^2} = 5\)

for AB

(0,4),(3,0)

\(\sqrt{\left(3-0\right)^2+\left(0-4\right)^2}=5\)

The answer will be 5*5, which is 25

Answer:

n=-2.16

Step-by-step explanation:

1. put zero after equal sign (25n+54=0)

2. subtract 54 from zero (54-0=-54)

3. then youre left with (25n=-54) so you then cancel out the 25n by doing (25/25=0) so then you have to do the same to the other side (-54/25=-2.16)

4. so the answer would be (n=-2.16)

The area inside the polar curve R = 2cos(3θ) for three full rotations is 6π.

The polar curve R = 2cos(3θ) is symmetric about the x-axis, with three petals that extend from θ = 0 to θ = π/3, π to 4π/3, and 5π/3 to 2π. To find the area inside the curve, we need to integrate the expression for the area element in polar coordinates over the desired region:

dA = (1/2) \(R^{2}\) dθ

The limits of integration for θ are from α = -6π to β = 6π, since we want to find the total area inside the curve for three full rotations. Thus, the integral for the area is:

A = ∫(β=6π, α=-6π) (1/2) \(R^{2}\)dθ

= ∫(β=6π, α=-6π) (1/2) (2cos(3θ))^2 dθ

= 2∫(β=6π/3, α=-6π/3) cos^2(3θ) d(3θ) (using the identity cos^2(3θ) = (1 +    cos(6θ))/2)

= ∫(β=6π/3, α=-6π/3) (1/2 + (1/2)cos(6θ)) d(3θ)

= (1/2)θ + (1/12)sin(6θ) ∣(β=6π/3, α=-6π/3)

= (1/2)(6π - (-6π)) + (1/12)(sin(36π) - sin(-36π))

= 6π

Correct Question :

Find The Area Inside R=2cos(3θ) (Tip: Use Α=−6π And Β=6π )

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Answer:

85

Step-by-step explanation:

-4x-8=-16

+8 +8

-4x = -8

-4/-8 = 2

Answer:

1180

Step-by-step explanation:

(42×28)+4 =x

x= 1180

Answer:3,190 centimeters

Step-by-step explanation:

math is easy

Answer:

Step-by-step explanation:

Anything raised to zero  = 1

\(a^{0} = 1\\\\a^{m}*a^{n} =a^{m+n}\\\\\dfrac{a^{m}}{a^{n}}=a^{m- n}\\\)

In exponent multiplication, if base are same, just add the powers.

In exponent division, if bases are same, subtract the powers.

\((a^{m})^{n} =a^{m*n}\)

\((3^{-2}* 4^{-5}*5^{0})^{-3} * \left(\dfrac{4^{-4}}{3^{3}} \right)^{3}*3^{3} \\\\\\= (3^{-2}* 4^{-5}*1)^{-3} * \left(\dfrac{4^{-4}}{3^{3}} \right)^{3}*3^{3}\\\\\\= 3^{-2*(-3)} *4^{-5*(-3)} * \dfrac{4^{-4*3}}{3^{3*3}}*3^{3}\\\\\\=3^{6}*4^{15}*\dfrac{4^{-12}}{3^{9}}*3^{3}\\\\\\= 3^{6+3-9}* 4^{15+(-12)}\\\\=3^{0}*4^{3}\\\\=1*4^{3}\\\\=4^{3}\)

Answer:

A(3,3), B(3,7), C(8,7), D(8,3)

Step-by-step explanation:

it was the correct answer hope this helps!!

The Pythagorean theorem is the idea that the sum of the two legs which are both squared is equal to the hypotenuse's length squared.

     *look at the image I attached for a better explanation

By looking at the picture, we are missing the leg's length, and by using the Pythagorean theorem, we get the equation

    \(?^2+5^2 = 13^2\\?^2 + 25 = 169\\?^2 = 144\\? = 12\)

Thus the missing side length is 12 cm

Hope that helps!

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Answer:

Step-by-step explanation:

y = 20x

Answer:

since the adjacent is given which is 6.3 and we are to solve for the hypotenuse, it's best to use Cos

since Cos(27°)=adjacent/hypotenuse

we can substitute in the values

therefore we have Cos(27°)=6.3/x

x=6.3/Cos(27°)

x=7.06...

rounding this to the nearest tenth will be 7.1

therefore x=7.1

Answer:

cos x° = adjacent ÷ hypotenuse

Step-by-step explanation:

Option (A) cos x° = adjacent ÷ hypotenuse is correct because cos is the ratio of the side adjacent to the angle to the hypotenuse option (A) is correct.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have given trigonometric ratios in the options.

As we know the trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

In the 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)

cos is the ratio of the side adjacent to the angle to the hypotenuse

cos x° = adjacent ÷ hypotenuse

tan is the ratio of the side opposite to the angle to the side adjacent to the angle.

tan x° = opposite ÷ adjacent

Thus, option (A) cos x° = adjacent ÷ hypotenuse is correct because cos is the ratio of the side adjacent to the angle to the hypotenuse option (A) is correct.

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Answer:

(-1/2, 1)

Step-by-step explanation:

I just used the midpoint formula, and plugged in the points. I hope this helps!

=(x^2+x^1 /2 , y^2+y^1 /2)

=(-2+1 /2 , -5+3 /2)

=(-1/2, 1)

Answer: (-0.5, -1 ) or (-1/2,-1)

Step-by-step explanation:

(-2,-5) (1,3)

To find the midpoint between these two numbers find the average of the x and y coordinates.

-2 + 1 = -1 /2 = -0.5

-5 + 3 = -2/2 = -1  

Your instructions got messed up, but I'll try my best to figure out what you said.
Lets set the equations to equal each other

x² + 4 + 2x = 3x+2

x² - x + 2 = 0

x² - x + (-0.5)² = 2

(x-0.5)² = 2

x-0.5 = √2

x=0.5 \(+\\-\)1.414

x= 1.914
or/and

x= -0.914

Having the following equation given in the problem:

You can solve for "B" by applying the Addition property of Equality. This property states the following:

Then, based on that Addition property of Equality, you can add "f" to both sides of the equation.

Therefore, you get that the equation solved for "B" is the following:

Answer:

Odd

Explanation:

The function is odd if

Meaning that for every x value that gives y, - x gives -y.

Now, let us test our function using x = 1

and

Therefore we see that

therefore, the function is odd.

Answer:

Step-by-step explanation:

At least 75% of the data might very well fall between $3.25 and $3.81. According to Chebyshev's theorem, at least 75% of the value systems in a distribution are well within 2 the mean standard deviation.

A delivery has at least 89% of its values inside of three of the mean's standard deviation.

We have the following in this problem:

Mean = $3.53

$0.14 is the standard deviation.

Using Chebyshev's Theorem, determine the range that contains least 75% of the information will live.

2 standard deviations from the mean.

So 3.53 - 2*0.14 = $3.25 becomes 3.53 + 2*0.14 = $3.81.

At least 75% of the data might very well fall between $3.25 and $3.81.

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Answer:

The distance between the points is √164

Step-by-step explanation:

the formula for the distance between two points is:

√[(x₂ - x₁)² + (y₂ - y₁)²]

We substitute the values and get:

Our final answer is √164.

Hope this helps!!

Answer:

x=11

Step-by-step explanation:

And you didnt give the equation for FDE but substitute 11 in for X

Answer:

237

Step-by-step explanation:

This is a system of equations.

The theater sold 364 adult and child tickets, so a + c = 364

They made a total of $1930. Each adult ticket was $6 & child tickets were $4. The second equation is 6a + 4c = 1930.

Let's line them up

a  +  c = 364

6a + 4c = 1930

Since we need to solve for the number of adult tickets, we want to get rid of the c variable. I'm going to multiply the entire first equation by -4 to do this. The second equation stays the same. Now, I have:

-4a - 4c = -1456

6a + 4c = 1930            Add them together

----------------------

2a = 474                      Divide by 2 to solve for a

a = 237

There were 237 adult tickets sold

Answer:

96.25%

Step-by-step explanation:

The empirical rule regarding mean and standard deviation is that

Therefore between mean and +2 standard deviation or between mean and -2 standard deviation you will find  approximately 95/2 = 47.5% of the values

Between mean and ± 3 standard deviations you will find approximately 97.5/2 = 48.75% of the values

Therefore between 2 standard deviations above and 3 standard deviations below you will find approximately 47.5 + 48.75 = 96.25% of values

Answer: The two numerical expressions that correctly represent the phrase "twice the sum of nine and four" are:

2 * (9 + 4) = 2 * 13 = 26

2(9 + 4) = 2(13) = 26

Both expressions use the correct mathematical operations to represent the phrase "twice the sum of nine and four" and both will yield the same result of 26.

Step-by-step explanation:

The value of z in the circle is 2.3 units

In the question, the following statements represents the given parameters

As a general rule, the diameter of a circle is the radius doubled

So, we have

2 * (z + 3.6) = 11 4/5

Express as decimal

2 * (z + 3.6) = 11.8

So, we have

z + 3.6 = 5.9

Evaluate the like terms

z = 2.3

Hence, the value of z is 2.3

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Answer:

S = {(3,p), (3,0), (4,q), (1,4)} is a set of ordered pairs, where the first element of each ordered pair is an integer and the second element is a variable. The set consists of four ordered pairs:

(3,p): The first element is 3 and the second element is p.

(3,0): The first element is 3 and the second element is 0.

(4,q): The first element is 4 and the second element is q.

(1,4): The first element is 1 and the second element is 4.