is this right? In the triangle the ratio that represents cot 0 equals 3/4

ANSWER

[tex]\tan(\sin^{ - 1}( \frac{x}{2} )) = \frac{x}{ \sqrt{4 - {x}^{2} } } \: \:where \: \: x \ne \pm2[/tex]

EXPLANATION

We want to find the exact value of

[tex] \tan( \sin^{ - 1}( \frac{x}{2} ) ) [/tex]

Let

[tex]y = \sin^{ - 1}( \frac{x}{2} )[/tex]

This implies that

[tex] \sin(y) = \frac{x}{2} [/tex]

This implies that,

The opposite is x units and the hypotenuse is 2 units.

The adjacent side is found using Pythagoras Theorem.

[tex] {a}^{2} + {x}^{2} = {2}^{2} [/tex]

[tex]{a}^{2} + {x}^{2} = 4[/tex]

[tex]{a}^{2} = 4 - {x}^{2}[/tex]

[tex]a= \sqrt{4 - {x}^{2}} [/tex]

This implies that,

[tex] \tan(y) = \frac{opposite}{adjacent} [/tex]

[tex]\tan(y) = \frac{x}{ \sqrt{4 - {x}^{2} } } [/tex]

But

[tex]y = \sin^{ - 1}( \frac{x}{2} )[/tex]

This implies that,

[tex]\tan(\sin^{ - 1}( \frac{x}{2} )) = \frac{x}{ \sqrt{4 - {x}^{2} } } \: \:where \: \: x \ne \pm2[/tex]

Answer:

B

Step-by-step explanation:

In one complete rotation the wheel rotates 360°

Assuming the seats are equally spaced around the wheel then the

angle between each seat = [tex]\frac{360}{15}[/tex] = 24°

The angle measurement between each bucket is 24 degrees if the Ferris wheel has 15 seat buckets option (B) 24° is correct.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have:

A Ferris wheel has 15 seat buckets.

The total angle of the wheel is 360 degrees, which is a complete revolution of the wheel.

The angle measurement between each bucket is:

= 360/15

= 24 degree

Thus, the angle measurement between each bucket is 24 degrees if the Ferris wheel has 15 seat buckets option (B) 24° is correct.

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Answer:

[tex]\boxed{ \text{8 p.m.}}[/tex]

Step-by-step explanation:

First, we must plot the graph of your system of equations (see below).

The two lines cross at (12, 360).

Thus, machine A had been going for 12 h. It started at 8 a.m., so it ended at 8 p.m.

Both machines had made 360 ft of wire by [tex]\boxed{ \text{8 p.m.}}[/tex]

Check:

360 = 30 × 12     360 = 40(12 – 3)

360 = 360          360 = 40 × 9

                          360 = 360

OK.

the answer is

615500

hope this helps

Answer:

The best describes the transformation is right 3 units, down 1 unit ⇒ 3rd answer

Step-by-step explanation:

* Lets talk about some transformation

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Now lets solve the problem

∵ f(x) = x²

- The change from x² to (x - 3)² means the graph shifted 3 units

  to the right

- The value -1 means the graph shifted down 1 unit

∴ The graph of f(x) = x² is shifted 3 units to the right and 1 unit

   down and the resulting function is f(x) = (x - 3)² - 1

* The best describes the transformation is right 3 units, down 1 unit

Answer:

C

Step-by-step explanation:

he can either send one half or the other half.

Answer:

70

Step-by-step explanation:

Given : There are 8 people on the debate team.

To Find: In how many ways can the coach choose 4 members to send to competition?

Solution:

We will use combination over here

Formula : [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

Now There are 8 people on the debate team and the coach have to choose 4

So, n = 8

r = 4

So, number of ways of choosing 4 people out of 8 = [tex]^8C_4[/tex]

                                                                                    = [tex]\frac{8!}{4!(8-4)!}[/tex]  

                                                                                    = [tex]\frac{8!}{4!4!}[/tex]  

                                                                                    = [tex]70[/tex]  

Hence there are 70 ways of choosing 4 members out of 8 to send to competition

Answer:

  35.9 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Tan = Opposite/Adjacent

  tan(U) = VW/WU

  tan(65°) = (77 ft)/WU

  WU = 77 ft/tan(65°) ≈ 35.9 ft

B) 50+36×=$212 ; 4.5. That is the answer.

The equation symbolizes the above situation is $50 + $36x = $212 and the landscapers work at 4.5 hours

Let's use "x" to represent the number of hours The Garden Expert worked in Emma's yard. We know that the landscaper charges $36 per hour for the actual work and a $50 consultation fee. Therefore, the total cost "C" for the service can be represented as:

C = 36x + 50

Emma owes the landscaper $212, so we can set up the equation as follows:

212 = 36x + 50

Now, let's solve for "x":

First, subtract $50 from both sides to isolate 36x:

212 - 50 = 36x

162 = 36x

Next, divide both sides by 36 to solve for x:

x = 162 / 36

x = 4.5

Hence the correct option is (b).

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Arc GHE is 40 + 80 or 120 so arc GFE is 360 (total measurement in a circle) - 120 which is 240. The circumference of a circle is 2*pi*r so in this case it will be 2*pi*5 or 10pi (you can also write it as approximately 31.4). The area of a circle is pi*r² so it'll be pi*5² or 25pi (you can write it as approximately 78.5 also). The equation of a circle is (x-h)² + (y-k)² = r² where (h,k) is the center of the circle and r is the radius. Input your values. The equation of this circle is (x+1)² + (y-2)² = 6² (The radis is 6 because the diameter is 12)

I hope this helps!

A full circle is 360 degrees.

You are given the angles for GH, HE and FE, subtract those from 360 to find the angle for FG:

360 - 110 - 80 - 40 = 130 degrees.

Now for the arc GFE add FG and FE:

Arc GFE = 130 + 110 = 240 degrees.

Circumference = 2 x PI x r

Using 3.14 for PI:

Circumference  = 2 x 3.14 x 5 = 31.4 mm or 10PI

Area = PI x r^2 = 3.14 x 25 = 78.5 mm^2 or 25PI mm^2

Equation of a circle with center at (-1,2) and diameter of 12:

The equation is written as (x-x1)^2 + (y-y1)^2 = r^2

x1 and y1 are the values of the center (-1,2) and r is the radius, which would be half the diameter.

The equation is: (x+1)^2 + (y-2)^2 = 36

The answer is:

[tex]f'(2)=-1[/tex]

To solve this problem, first we need to derivate the given function, and then, evaluate the derivated function with x equal to 2.

The given function is:

[tex]f(x)=\frac{4}{x}[/tex]

It's a quotient, so, we need to use the following formula to derivate it:

[tex]f'(x)=\frac{d}{dx}(\frac{u}{v}) =\frac{v*u'-u*v'}{v^{2} }[/tex]

Then, of the given function we have that:

[tex]u=4\\v=x[/tex]

So, derivating we have:

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*(4)'-4*(x)'}{x^{2} }[/tex]

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*0-4*1}{x^{2} }[/tex]

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{0-4}{x^{2} }[/tex]

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{-4}{x^{2} }[/tex]

Hence,

[tex]f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{-4}{x^{2} }[/tex]

Now, evaluating with x equal to 2, we have:

[tex]f'(2)=\frac{-4}{(2)^{2} }[/tex]

[tex]f'(2)=\frac{-4}{4}[/tex]

[tex]f'(2)=-1[/tex]

Therefore, the answer is:

[tex]f'(2)=-1[/tex]

Have a nice day!

ANSWER

[tex]f'(2) = -1[/tex]

EXPLANATION

The given function is

[tex]f(x) = \frac{4}{x} [/tex]

Recall that:

[tex] \frac{c}{ {a}^{ m} } = c {a}^{ - m} [/tex]

We rewrite the given function using this rule to obtain,

[tex]f(x) = 4 {x}^{ - 1} [/tex]

Recall again that,

If

[tex]f(x)= a {x}^{n} [/tex]

then

[tex]f'(x)=n a {x}^{n - 1} [/tex]

We differentiate using the power rule to obtain,

[tex]f'(x) = - 1 \times 4 {x}^{ - 1 - 1} [/tex]

[tex]f'(x) = - 4 {x}^{ - 2} [/tex]

We rewrite as positive index to obtain,

[tex]f'(x) = - \frac{4}{ {x}^{2} } [/tex]

We plug in x=2 to obtain,

[tex]f'(2) = - \frac{4}{ { (2)}^{2} } = - \frac{4}{4} = - 1[/tex]

Please ignore the x above,,

Answer: 30%

Step-by-step explanation:

Given: the number of employees in the office = 80

The number of employees are managers = 24

Then, the percent of employees are manger is given by :-

[tex]\dfrac{\text{Number of mangers}}{\text{Total employees}}\times100\\\\=\dfrac{24}{80}\times100\\\\=30\%[/tex]

Hence, the percent of the employees are managers = 30%

Answer:

The statement which is true is, If the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus.

Step-by-step explanation:

In a rhombus, the diagonals bisect at perpendicular angles to form 4 triangles.Because the diagonals bisect at right angles, then it is possible to prove that the four small formed triangles are similar using the SAS theorem: two triangles are equal if two sides are equal and the angles between the two sides are equal.In your case, the sides are that on the base and that forming a height of the triangles with both having angle 90° between the sides.So you see if these the two are congruent, the hypotenuse of these triangles are congruent, making this quadrilateral a rhombus.

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Keywords : quadrilateral, rhombus, perpendicular bisector, angles

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In quadrant II, if sinΘ = 1/2, the value of cosΘ is -√(3/4).

In quadrant II, sine is positive and cosine is negative. Since sinΘ = 1/2, we can use the Pythagorean identity to find the value of cosΘ:

sin²Θ + cos²Θ = 1

Plugging in the value of sinΘ and solving for cosΘ, we get:

(1/2)² + cos²Θ = 1

1/4 + cos²Θ = 1

cos²Θ = 3/4

Taking the square root, we get:

cosΘ = ±√(3/4)

Since Θ lies in quadrant II where cosine is negative, the value of cosΘ is:

cosΘ = -√(3/4)

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Answer:

17.54 ft

Step-by-step explanation:

Moving along the line from (–4.2, –6.4, 4.5) to (7.1, 2.2, 5.8), x increases by 11.3, y by 8.6 and z by 10.3.

Applying the Pythagorean Theorem twice, we get

(length of clothesline) = √( 11.3² + 8.6² + 10.3²), or 17.54 ft.

Answer:  b) 16%

Step-by-step explanation:

The mean is 290 so on a normal bell curve that would be a z-score of 0.

The standard deviation is 10 so 290 - 10 = 280 is a z-score of -1.

A z-score from the left to -1 is 15.9%

c is the correct answer i believe

Answer:

D

Step-by-step explanation:

1.  Replace "f(x)" with "y:"  y = (x + 1)/x

2.  Interchange x and y:  x = (y + 1)/y

3.  Solve this result for y:                                     1

     xy = y + 1, or xy - y = 1, or y(x -1) = 1, or y = --------

                                                                            x-1

4.  Replace "y" with:

        -1               x

      f     (x) = -----------   This matches answer choice D.

                       x - 1

Answer:

D

Step-by-step explanation:

Answer:

[tex]\$1,920[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=5*12=60\ months\\ P=\$1,200\\r=0.01[/tex]

substitute in the formula above

[tex]A=\$1,200(1+0.01*60)[/tex]

[tex]A=\$1,200(1.6)=\$1,920[/tex]

Answer:  c) 3.9

Step-by-step explanation:

The mean is 95 so it has a z-score of 0

The standard deviation is 3.9 so a z-score of -1 is a velocity of 95 - 3.9

So, the difference in the their velocities is: 3.9

Answer:

It is parallel

Step-by-step explanation:

See the first equation equals the last equation, I just realized that.

Answer:

A

Step-by-step explanation:

Multiply them according to the problem.

[tex]6x+2y=6 \\ \\ -3(6x+2y)=(6)*-3 \\ \\ -18x-6y=-18 \\ \\ \\ 7x+3y=9 \\ \\ 2(7x+3y)=(9)*2 \\ \\ 14x+6y=18[/tex]

As you can see, the only terms in the two equations that can cancel out are [tex]-6y[/tex] and [tex]6y[/tex].

Four possible coplanar points based on the image are B,E,D; Q,B,E; D,Q,B; and, E,D,Q.

This word refers to points that share the same plane. Remember a plane is a surface that goes in one direction.

In the image, all points over the surface are coplanar. Based on this, some coplanar points are:

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Final answer:

The interval estimate of the true population proportion is (0.16, 0.28) that is option D is correct.

Explanation:

The interval estimate of the true population proportion is (0.16, 0.28).

A simulation of 100 trials with a sample size of 50 was conducted to determine whether the sample supports the population proportion of 0.40. The minimum sample proportion from the simulation is 0.15 and the maximum sample proportion is 0.27. Based on this simulation, the interval estimate for the true population proportion can be calculated.

Interval estimate formula: (point estimate - margin of error, point estimate + margin of error)

Point estimate = 0.22

Margin of error = (maximum sample proportion - minimum sample proportion) / 2 = (0.27 - 0.15) / 2 = 0.06

Interval estimate = (0.22 - 0.06, 0.22 + 0.06) = (0.16, 0.28)

The correct interval estimate of the true population proportion is (0.14, 0.30).

To determine the interval estimate of the true population proportion, we use the following formula for a 95% confidence interval:

[tex]\[ \text{Confidence Interval} = \text{Point Estimate} \pm (Z_{\alpha/2} \times \text{Standard Error}) \][/tex]

where[tex]\( Z_{\alpha/2} \)[/tex] is the Z-score corresponding to the desired confidence level (for a 95% confidence interval, [tex]\( Z_{\alpha/2} \)[/tex] is approximately 1.96), and the Standard Error (SE) is calculated using the formula:

[tex]\[ \text{SE} = \sqrt{\frac{\text{Point Estimate} \times (1 - \text{Point Estimate})}{\text{Sample Size}}} \][/tex]

Given the point estimate from the simulation as 0.22 and the sample size as 50, we calculate the standard error as follows:

[tex]\[ \text{SE} = \sqrt{\frac{0.22 \times (1 - 0.22)}{50}} \] \[ \text{SE} = \sqrt{\frac{0.22 \times 0.78}{50}} \] \[ \text{SE} = \sqrt{\frac{0.1716}{50}} \] \[ \text{SE} = \sqrt{0.003432} \] \[ \text{SE} \approx 0.0586 \][/tex]

Now, we calculate the margin of error (ME):

[tex]\[ \text{ME} = Z_{\alpha/2} \times \text{SE} \] \[ \text{ME} = 1.96 \times 0.0586 \] \[ \text{ME} \approx 0.1146 \][/tex]

The margin of error is approximately 0.1146. Therefore, the 95% confidence interval for the population proportion is:

[tex]\[ \text{Point Estimate} \pm \text{ME} \] \[ 0.22 \pm 0.1146 \][/tex]

Lower bound:

[tex]\[ 0.22 - 0.1146 \approx 0.1054 \][/tex]

Upper bound:

[tex]\[ 0.22 + 0.1146 \approx 0.3346 \][/tex]

However, the simulation results provide a range for the sample proportion from 0.15 to 0.27. Therefore, the interval estimate should be adjusted to reflect this range while still incorporating the margin of error.

Lower bound (adjusted for simulation range):

[tex]\[ 0.15 - 0.1146 \approx 0.0354 \][/tex]

Upper bound (adjusted for simulation range):

[tex]\[ 0.27 + 0.1146 \approx 0.3846 \][/tex]

Since the lower bound of the confidence interval cannot be less than the minimum sample proportion from the simulation (0.15), and the upper bound cannot exceed the maximum sample proportion from the simulation (0.27), we adjust the interval to:

Lower bound:

0.15

Upper bound:

0.27

Now, we apply the margin of error to these bounds:

Lower bound with ME:

[tex]\[ 0.15 - 0.1146 \approx 0.0354 \][/tex]

Since the lower bound cannot be less than 0, we round up to the nearest reasonable value, which is 0.14.

Upper bound with ME:

[tex]\[ 0.27 + 0.1146 \approx 0.3846 \][/tex]

Since the upper bound cannot exceed 1, we round down to the nearest reasonable value, which is 0.30.

Therefore, the interval estimate of the true population proportion, taking into account the simulation results and the margin of error, is (0.14, 0.30).

Answer:

33.6 cm

Step-by-step explanation:

We can use the formula for arc length to solve this.

[tex]s=r\theta[/tex]

Where

s is the arc length

r is the radius

[tex]\theta[/tex] is the angle subtended by the arc (in radians)

The problem gives us theta = 2.8 radians and radius of the circle as 12 cm. We plug these into the formula and figure out the arc length (to 1 decimal place):

[tex]s=r\theta\\s=(12)(2.8)\\s=33.6[/tex]

2nd answer choice is right.

Answer:

(C)

Step-by-step explanation:

Given: BC is tangent to the circle A at D.

To prove: AB is congruent to AC

Proof:

Statements                                                            Reason

1. BC is tangent to the circle A at D.                     Given

2. DB≅DC                                                               Given

3.AD⊥BC               If a line is tangent to a circle then it is perpendicular to the radius at the point of tangency.

4. ∠ADB and ∠ADC are right angles     Definition of perpendicular lines

5. ∠ADB≅∠ADC                                      Right angles are congruent

6. AD≅AD                                                Reflexive property of congruence

7. ΔADB≅ΔADC                                      SAS rule

8. AB≅AC                                                CPCTC

Hence, option (C) is correct.

Tangent to a circle is straight line just touching the circle at one point. The reason to complete the proof is: If a line is tangent to a circle,  then it is perpendicular to the point of tangency

A line segment which touches a circle specified to only one point is called a tangent to that circle.

There is a theorem in mathematics that:

If there is a circle O with tangent line L intersecting the circle at point A, then the radius OA is perpendicular to the line L.

For the given case, the missing statement for the proof is:

If a line is tangent to a circle,  then it is perpendicular to the point of tangency(the point on circle where the tangent intersects it).

Hence, the reason to complete the proof is: If a line is tangent to a circle,  then it is perpendicular to the point of tangency

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f(x) = /x - 2/

f(-1) = /-1 - 2/ = /-3/ = 3

f(0) = /0 - 2/ = /-2/ = 2

f(1) = /1 - 2/ = /-1/ = 1

f(2) = /2 - 2/ = /0/ = 0

Answer:

[tex]\sqrt{109}[/tex]

Step-by-step explanation:

The side of the house is a side of the right triangle.

The ladder is 3 feet away, so it forms a triangle with sides 3, 10, x.

We're trying to find the hypotenuse, which is given by Pythagoras' Theorem:

[tex]a^2 + b^2 = c^2\\3^2 + 10^2 = x^2\\109 = x^2\\x = \sqrt{109}[/tex]

A net can be used to find the area of a specific side or the entire surface area. It can also help to find the perimeter. To find the surface area with a net, solve for the area of each shape in the net and add them together to get the total area (surface area).

Hope this helps!

A flat three dimensional solid like a cube, a prism or a pyramid. When you cut out the "net", fold it and glue it together you can see what the three dimensional shape looks like. (It can be used in math)Draw a net of the polyhedron. Calculate the area of each face. Add up the area of all the faces.

Answer:

[tex]3\sqrt{13}[/tex]

Step-by-step explanation:

Using the Theorem of the side of a triangle:

[tex]x^2 = 4 * (4 + 9) = 42\\x = \sqrt{42}[/tex]

And using the Height Theorem:

y = [tex]\sqrt{4 \cdot 9}  = \sqrt{36} = 6[/tex]

And by the Pythagorean Therorem:

z = [tex]\sqrt{6^2 + 9^2} = \sqrt{117} = 3\sqrt{13}[/tex]

Answer:

256 m²

Step-by-step explanation:

If the length of a rectangle is 4 times its width, and you know the width is 8, that must mean the length is 32. Now you know the width and the length, multiply those two values to get your area.