Are you able to find tri-sector (equally divided by 3) rays for an arbitrary angle with straightedge-and-compass construction?

Answer:

the formular is

p(B/A)=P(AnB)/P(A)

so the missing probability is:-

P(AnB)=P(B/A)×23

And the other missing probablility is:-

p(B/A)=P(AnB)/23

Step-by-step explanation:

Which is the first sincetist of world

Answer:

45° or 135°

Step-by-step explanation:

Cos 2x = 0

2x = cos^-1 0

2x = 90° or 270°

x= 45° or 135°

Answer:

Step-by-step explanation:

● cos 2x = 0

We khow that Pi/2 equals 0.

So

● 2x = Pi/2 or 2x= -Pi/2

Then:

● x = Pi/4 or x = -Pi/2

So the solutions are:

● x = Pi/4 + 2×k×Pi

● or x = -Pi/4 + 2×k×Pi

Where k is an integer

The picture below has a graphical solution

● Pi/4 is approximatively 0.785 and -Pi/4 is approximatively -0.785

● the output of both Pi/4 and -Pi/4 is 0

So our answer was righr

Answer:

Hello,

P=(30,6)

Step-by-step explanation:

[tex]x=6t^2+6\\y=t^3-2\\\\\dfrac{dx}{dt}= 12t\\\dfrac{dy}{dt}= 3t^2\\\\\dfrac{dy}{dx} =\dfrac{\dfrac{dy}{dt} }{\dfrac{dx}{dt} } =\dfrac{3t^2}{12t} =\dfrac{t}{4} \\\\\dfrac{t}{4} =\dfrac{1}{2} \Longrightarrow t=2\\\\\\x=6t^2+6=6*2^2+6=30\\\\y=t^3-2=2^2-2=8-2=6\\\\\\Tangence\ point=(30,6)\\[/tex]

The point on the curve x = 6t² + 6, y = t³ - 2 where the tangent line have slope 1/2 is (30, 6).

From the information given, x = 6t² + 6, y = t³ - 2. We'll find the first order derivative of x and y which will be:

dx/dt = 12t

dy/dt = 3t²

Therefore, 3t²/12t = t/4, t = 2.

We'll put the value of t back into the equations.

x = 6t² + 6,

x = 6(2)² + 6

x = 24 + 6 = 30

y = t³ - 2.

y = (2)³ - 2

y = 8 - 2 = 6

In conclusion, the correct options is (30, 6).

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Answer:

Yes

Step-by-step explanation:

Yes, and it’s a right triangle.

3²+4²=5²

9+16=25

25=25

Answer:

Yes

Step-by-step explanation:

In order to determine if a triple of values will form a triangle, we must apply the Triangle Inequality Theorem, which states that for a triangle with lengths a, b, and c:

a + b > c

a + c > b

b + c > a

Here, let's suppose that since the ratio of the sides is 3 : 4 : 5, then let the actual side lengths be 3x, 4x, and 5x, where x is simply a real value.

With loss of generality, set a = 3x, b = 4x, and c = 5x. Plug these into the Triangle Inequality to check:

a + b > c  ⇒  3x + 4x  >?  5x  ⇒  7x > 5x  ⇒  This is true

a + c > b  ⇒  3x + 5x  >?  4x  ⇒  8x > 4x  ⇒  This is also true

b + c > a  ⇒  4x + 5x  >?  3x  ⇒  9x > 3x  ⇒  This is true

Since all three conditions are satisfied, we know that a true triangle can be formed given that the ratio of their sides is 3 : 4 : 5.

~ an aesthetics lover

first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.

here,

7. (-154) ➗ (-14) =11

11. (-40) ➗10=-4

15. 90 ➗ (-15)=-6

16. 108 ➗ (-9)=-12

17. (-48) ➗ (-6)=8

18. (-105) ➗ 7=-15

hope it helps you......

Answer:

18.90

Hope i got it right

Answer:

first... You think and Conceptualize

A diameter divides a circle into equal halves

We're given the end points of the Diameter.

With this we can fine the Center of the circle.

The End Points are

(-6, -1) and ( 2, 3)

Half-way through the diameter gives the center of the circle

So We'd apply the Mid-Point formula to get the co-ordinate of the center.

X= x₁ + x₂/2 , Y = y₁ + y₂/2

X = -6 + 2/2, Y = -1 + 3/2

X= -2. Y = 1

The Midpoint is (-2, 1)

The Radius would be the distance between the center and a point on the circumference.

We already have 2 points of the circumference (Which are the endpoints of the diameter).

So we can pick any of them arbitrarily.

I'd go with (2,3)

So We'd apply the distance between Points formula to get the magnitude of the radius

(-2,1) (2,3)

D = √(x₁ - x₂)² + (y₁ - y₂)²

D = √(-2-2)² + (1-3)²

D=√(-4)² + (-2)²

D=√20.

Our Radius is √20.

Equation of Circle =

(x-h)² + (y-k)² = r²

Where h and k are the center of the circle(-2,1)

(x-(-2))² + ( y - 1 )²= (√20)²

(x + 2)² + ( y - 1)² = 20

Our Answer

(x + 2)² + (y - 1)² = 20.

This should be it.

Have a great day!

Answer: (3x^2-1)(4x-3)

============================

Work Shown:

Use the factor by grouping method

12x^3-9x^2-4x+3

(12x^3-9x^2)+(-4x+3)

3x^2(4x-3)-1(4x-3)

(3x^2-1)(4x-3)

9514 1404 393

Answer:

  20th

Step-by-step explanation:

The person will receive all gifts if the are all of a multiple of 2, a multiple of 4, and a multiple of 5. Since 4 is already a multiple of 2, the person who will receive all is the one who is a multiple of 4 and 5.

20 is 4×5, so is a multiple of both numbers. There is no smaller number that is a multiple of both 4 and 5.

The 20th person will receive all gifts.

_____

The value we have determined here is called the "least common multiple" (LCM). It is the product of the unique prime factors of the numbers of interest, raised to the highest power that appears in any of the numbers.

  2 = 2¹

  4 = 2²

  5 = 5¹

LCM(2, 4 5) = 2² × 5¹ = 20

Answer:

ans right down there

Step-by-step explanation:

Here,Part 1

if the circle has a radius r so,

15 = r theta

here, theta is in radian.

Part 2

[tex]theta = \frac{15}{6} = 2.5[/tex]

part 3

[tex]theta = \frac{2.5 \times 180}{\pi} [/tex]

or theta =

143.2394487827058021919953870352629258310136811664108038729006

1.

[tex]volume = 64(21 + 4\pi) = 2148.5714 \: cubic \: feets[/tex]

[tex]surface \: area = 752 + 64\pi = 953.143 \: square \: feets[/tex]

2.

[tex]surface \: area = 220 + 9\pi = 248.257 \: square \: feets[/tex]

Answer:

Step-by-step explanation:

i. For navigation purposes, bearing is measured clockwise from north. In (x, y) coordinates, a distance D at a bearing B will have coordinates ...

  (x, y) = (Dsin(B), Dcos(B))

Then 50 steps north (bearing 0°) will put James at coordinates ...

  (x, y) = (50sin(0), 50cos(0)) = (0, 50)

The movement 25 steps west (bearing 270°) will add a displacement of ...

  (x, y) = (25sin(270°), 25cos(270°)) = (-25, 0)

Finally, the movement of 50 steps on bearing 315° will add a displacement of ...

  (x, y) = (50sin(315°), 50cos(315°)) = (-25√2, 25√2)

These movements are shown by the arrows to N, W, and F in the attached diagram.

__

ii. James's final displacement is the sum of the individual displacements:

  (0, 50) +(-25, 0) +(-25√2, 25√2) = (-25(1+√2), 25(2+√2))

James is 25(1+√2) ≈ 60.4 steps west of center.

__

iii. James is 25(2+√2) ≈ 85.4 steps north of center.

__

iv. The distance can be found using the Pythagorean theorem (or distance formula). The distance from the origin to the final position (OF in the diagram) will be the root of the sum of the squares of the north and west displacements:

  distance = √(85.355² +60.355²)

  distance ≈ 104.5 steps

The bearing can be found using the arctangent function. The diagram shows you the reference angle (relative to the +y direction) has an opposite side equal to the west displacement, and an adjacent side equal to the north displacement. Then the bearing angle (β) will be ...

  tan(β) = opposite/adjacent = -60.355/85.355

  β ≈ arctan(-0.707106) ≈ -35.3°

The positive bearing angle is 360° added to this, or

  bearing = 324.7°

Answer:

Known:

• a book have front, back and 200 pages

• front= 0.7 mm

• back= 0.7 mm

• each page= 0,14 mm

ask:

calculate the minimum thickness...?

answer:

a. 200 p × 0,14 = 28 mm

b. front + back = 0.7+0.7= 1.4 mm

Thickness= 28+1,4 = 29,4 mm

I hope this helps

if u have question let me know in comments^_^

Answer:

y = 1/4x+1

Step-by-step explanation:

Using slope intercept form

y = mx+b

where m is the slope and b is the y intercept

y =1/4 x+b

Substituting in the point

3 = 1/4(8)+b

3 = 2+b

Subtract 2 from each side

3-2 = b

1 =b

y = 1/4x+1

Answer:

y=1/4x+1

Step-by-step explanation:

the equation for a line is y=mx+b

where m is the slope and b is the y-intercept. since we have our slope given and and x,y given we can use that to solve for b. we get:

3=1/4(8)+b

3=2+b

1=b

therefore the y-intercept is b

so the equation is y=1/4x+1

Complete Question

The  complete question is shown on the first uploaded image

Answer:

The 90% confidence interval is  [tex][108.165 ,112.895][/tex]

The  95%  confidence interval is [tex][107.7123 ,113.3477][/tex]

The  correct option is  D

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  48

     The sample  mean is  [tex]\= x = \$ 110.53[/tex]

    The standard deviation is  [tex]\sigma = \$ 9.96[/tex]

Considering first question

  Given that the confidence level is  90% then the level of significance is mathematically represented as

            [tex]\alpha = (100 - 90)\%[/tex]

           [tex]\alpha = 0.10[/tex]

The  critical value  of  [tex]\frac{\alpha }{2}[/tex] from the  normal distribution table is  

          [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

Generally the margin of error is mathematically represented as

            [tex]E = ZZ_{ \frac{x}{y} } * \frac{\sigma}{ \sqrt{n} }[/tex]

             [tex]E = 1.645 * \frac{9.96}{ \sqrt{ 48} }[/tex]

             [tex]E = 2.365[/tex]

The  90% confidence interval is  

       [tex]\= x - E < \mu < \= x + E[/tex]

=>    [tex]110.53 - 2.365 < \mu < 110.53 + 2.365[/tex]

=>    [tex]108.165 < \mu < 112.895[/tex]

Considering second question

  Given that the confidence level is  95% then the level of significance is mathematically represented as

            [tex]\alpha = (100 - 95)\%[/tex]

           [tex]\alpha = 0.05[/tex]

The  critical value  of  [tex]\frac{\alpha }{2}[/tex] from the  normal distribution table is  

          [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

            [tex]E = Z_{ \frac{x}{y} } * \frac{\sigma}{ \sqrt{n} }[/tex]

             [tex]E = 1.96 * \frac{9.96}{ \sqrt{ 48} }[/tex]

             [tex]E = 2.8177[/tex]

The  95% confidence interval is  

       [tex]\= x - E < \mu < \= x + E[/tex]

=>    [tex]110.53 - 2.8177 < \mu < 110.53 + 2.8177[/tex]

=>    [tex]107.7123 < \mu < 113.3477[/tex]

The solution is 4ln3 - 3ln5, which is correct option(C).

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmatic operation are called arithmatic operators .

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation : Divides left hand operand by right hand operand

For example 4/2 = 2

According to the problem, we will use some of the basic logarithmic properties,

Given expression,

⇒ ln81/125

⇒ ln81 - ln125   [used property : logₐ(x/y) = logₐx - logₐy]

⇒ ln3⁴ - ln5³    [ 81 =3⁴ and 125 = 5³ ]

⇒ 4ln3 - 3ln5   [used property : logₐ(xⁿ) = nlogₐx]

Hence, the solution is 4ln3 - 3ln5

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[tex]3x=x+10[/tex]

We tripple something and get 10 more than something.

Put the x-es on the left and non x-es to the right,

[tex]2x=10[/tex]

Divide both sides by 2,

[tex]x=5[/tex]

Et Viòla.

Hope this helps :)

When a number is tripled, its value increases by 10 then the original number is 5.

Let's call the original number "x". According to the problem, when this number is tripled, its value increases by 10. Mathematically, we can represent this as an equation:

3x = x + 10

Now, we can solve for "x" step by step:

1. Subtract "x" from both sides of the equation:

  3x - x = 10

2. Simplify the left side:

  2x = 10

3. Divide both sides by 2 to solve for "x":

  x = 10 / 2

  x = 5

So, the original number "x" is 5.

In other words, if you take a number, triple it (multiply by 3), and then increase the result by 10, you would end up with the value 5. This can be verified by checking:

3 * 5 = 15

15 + 10 = 25

The equation 3x = x + 10 represents the relationship between the original number and its tripled value with an increase of 10. Solving this equation helps us find the original value that satisfies the given condition.

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Answer:

b

Step-by-step explanation:

b: sin^2 0 + tan^2 0 this is just a gut feelings its been awhile since i done this kind of think i hope i could help

The expression equal to the length of the hypotenuse of a right triangle formed inside the unit circle with a radius of 1 is Option (D) [tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees.

A hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle.

Here,

The length of the hypotenuse of a right triangle, formed inside the unit circle, with a radius of 1 is 1 unit.

We know that,

[tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ=1

Hence, The expression equal to the length of the hypotenuse of a right triangle formed inside the unit circle with a radius of 1 is Option (D) [tex]sin^{2}[/tex]θ+[tex]cos^{2}[/tex]θ

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Step-by-step explanation:

Hello, there!!

The answer would be 41/9.

The reason for above answer is to change any mixed fraction into improper fraction we should follow a simple step:

look here,

=[tex] \frac{4 \times 9 + 5}{9} [/tex]

we get 41/9.

Hope it helps...

The given fraction into the improper fraction should be [tex]\frac{41}{9}[/tex]

Given that,

[tex]= 4\frac{5}{9}\\\\ = \frac{41}{9}[/tex]

Here we multiply the 9 with the 4 it gives 36 and then add 5 so that 41 arrives.

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Answer:

2152.8

Step-by-step explanation:

First, 2.34 minutes is 140.4 seconds. Next, the bug can flap its wings at a pace of 15.333..... flaps per second. Multiplying this, we get 2152.8

Answer:

  34.43

Step-by-step explanation:

A differential of length in terms of t will be ...

  dL(t) = √(x'(t)^2 +y'(t)^2)

where ...

  x'(t) = 4cos(4t)

  y'(t) = 7cos(7t)

The length of c(t) will be the integral of this differential on the interval [0, 2π].

Dividing that interval into 10 equal pieces means each one has a width of (2π)/10 = π/5. The midpoint of pieces numbered 1 to 10 will be ...

  (π/5)(n -1/2), so the area of the piece will be ...

  sub-interval area ≈ (π/5)·dL((π/5)(n -1/2))

It is convenient to let a spreadsheet or graphing calculator do the function evaluation and summing of areas.

__

The attachment shows the curve c(t) whose length we are estimating (red), and the differential length function (blue) we are integrating. We use the function p(n) to compute the midpoint of the sub-interval. The sum of sub-interval areas is shown as 34.43.

The length of the curve is estimated to be 34.43.

Answer:

since the set of functions expressed are uncountable and they are a subset of real numbers starting from N therefore the set {0,1,2,3,4,5,6,7,8,9} is uncountable as well as its off functions

Step-by-step explanation:

set = {0,1,2,3,4,5,6,7,8,9}

setting up a one-to-one correspondence between the set of real numbers between 0 and 1

The function : F(n)= {0,1} is equivalent to the subset (sf) of (n) , this condition is met if n belongs to the subset (sf) when f(n) = 1

hence The power set of (n) is uncountable and is equivalent to the set of real numbers given

since the set of functions expressed are uncountable and they are a subset of real numbers starting from N therefore the set {0,1,2,3,4,5,6,7,8,9} is uncountable as well as its offfunctions

Answer:

Point b has coordinates (5, -2)

Step-by-step explanation:

If point a has coordinates (5, 2) then its reflection across the x axis would have the same value for the x-coordinate, and exactly opposite value for the y-coordinate (that is y-coordinate = -2.

then point's a reflection is: (5, -2)

since its reflection is point b then point b has this coordinates.

Answer:

0

Step-by-step explanation:

Answer:

the answer is 240 degrees

Recall that a ⇒ b   ⇔   ¬a ∨ b. So we can write

q ⇒ (p ∧ r )   ⇔   ¬q ∨ (p ∧ r )

Then the negation of this would be, for instance,

¬(¬q ∨ (p ∧ r ))   ⇔   ¬(¬q) ∧ ¬(p ∧ r )

…   ⇔   q ∧ (¬p ∨ ¬r )

…   ⇔   (¬p ∧ q) ∨ (q ∧ ¬r )

…   ⇔   ¬(p ∨ ¬q) ∨ (q ∧ ¬r )

…   ⇔   (p ∨ ¬q) ⇒ (q ∧ ¬r )

It's impossible to tell what kind of statement your program is expecting, but since there are 5 slots available, my money would be on q ∧ (¬p ∨ ¬r ), so long as ¬p and ¬r are options.

Answer:

?

Step-by-step explanation:

Brainly challenge

Answer:the one area < with line underneath then -4

St-by-step explanation: I’m pretty sure this is correct

Answer:

Step-by-step explanation:

[tex] \mathrm{16x - 7 \leqslant - 71}[/tex]

Move constant to Right hand side and change its sign

[tex] \mathrm{16x \leqslant - 71 + 7}[/tex]

Calculate

[tex] \mathrm{16x \leqslant - 64}[/tex]

Divide both sides of the equation by 16

[tex] \mathrm{ \frac{16x}{16} \leqslant \frac{ - 64}{16} }[/tex]

Calculate

[tex] \mathrm{x \leqslant - 4}[/tex]

Hope I helped!

Best regards!