The product of sin 30° and sin 60° is same as?

Answer:

a) [tex]P(x > 2) = \frac{1}{6}[/tex]

b) [tex]P(x < 5) = \frac{1}{3}[/tex]

c) 50 times

Step-by-step explanation:

Given

[tex]S = \{1,2,3,4,5,6,7,8,9,10,11,12\}[/tex]

Solving (a): P(x > 10)

First, list all outcomes of x

[tex]x = \{11,12\}[/tex] --- 2 outcomes

So, the probability is:

[tex]P(x > 2) = \frac{2}{12}[/tex]

Simplify

[tex]P(x > 2) = \frac{1}{6}[/tex]

Solving (b): P(x < 5)

First, list all outcomes of x

[tex]x = \{1,2,3,4\}[/tex] --- 4 outcomes

So, the probability is:

[tex]P(x < 5) = \frac{4}{12}[/tex]

Simplify

[tex]P(x < 5) = \frac{1}{3}[/tex]

Solving (c): Expected outcome of 4, 6 or 9 in a roll of 200

We have:

[tex]n = 200[/tex]

First, list all outcomes of x

[tex]x = \{4,6,9\}[/tex] --- 3 outcomes

So, the probability is:

[tex]P(x ) = \frac{3}{12}[/tex]

Simplify

[tex]P(x ) = \frac{1}{4}[/tex]

The expected number of rolls (E(x)) is calculated as:

[tex]E(x) = P(x) * n[/tex]

[tex]E(x) = \frac{1}{4} * 200[/tex]

[tex]E(x) = 50[/tex]

Answer

x+5

Step-by-step explanation:

2x+10 = 2(x+5)

Answer:

18 ÷ (-2) = -9

Step-by-step explanation:

18 ÷ (-2) = -9 is the least possible quotient.

To meet the requirement, we should divide the biggest positive number by smallest negative number

Answer:

Step-by-step explanation:

Area of circle:

Answer: 25 in.

Step-by-step explanation:

Given

Arc length is 34 inches

The angle subtended by the arc is [tex]78^{\circ}[/tex]

arc length l subtending an angle [tex]\theta[/tex] is given by

[tex]\Rightarrow l=\dfrac{\theta }{360^{\circ}}\times 2\pi R[/tex]

Put the values

[tex]\Rightarrow 34=\dfrac{78^{\circ}}{360^{\circ}}\times 2\pi R\\\\\Rightarrow R=24.97\approx 25\ in.[/tex]

Answer:

D. X=6.08, x=-0.58

Step-by-step explanation:

Given the rational expression

[tex]\frac{2x}{x-4}-\frac{2x-5}{x^2-10x+24} = \frac{-3}{x-6}\\\frac{2x}{x-4}-\frac{2x-5}{x^2-4x-6x+24} = \frac{-3}{x-6}\\\frac{2x}{x-4}-\frac{2x-5}{x(x-4)-6(x-4)} = \frac{-3}{x-6}\\ \\\frac{2x}{x-4}-\frac{2x-5}{(x-4)(x-6)} = \frac{-3}{x-6}\\Rerrange;\\\frac{2x-5}{(x-4)(x-6)} = \frac{2x}{x-4}+ \frac{3}{x-6}\\\frac{2x-5}{(x-4)(x-6)} = \frac{2x(x-6)+3(x-4))}{(x-4)(x-6)}\\[/tex]

Cancel out the denominator on both sides

[tex]2x-5 = 2x(x-6)+3(x-4)\\Expand\\2x-5 =2x^2-12x+3x-12\\2x-5 = 2x^2-9x-12\\Equate \ to \ zero\\2x^2-9x-12-2x+5 = 0\\2x^2-11x - 7 = 0\\[/tex]

Factorize

[tex]x = -(-11)\pm\frac{\sqrt{(-11)^2-4(2)(-7)} }{2(2)}\\x = 11\pm\frac{\sqrt{121+56} }{4}\\x = 11\pm\frac{\sqrt{177} }{4}\\x = 11\pm\frac{13.3 }{4}\\x = \frac{11+13.3}{4} \ and \ x = \frac{11-13.3}{4} \\x = 6.08 \ and \ - 0.58[/tex]

Hence the required solution is X=6.08 and -0.58

Answer:

5 and 3

Step-by-step explanation:

please mark me brainlist

Answer:

∠ 1 = 99°, ∠ 2 = 81°, ∠ 4 = 81°

Step-by-step explanation:

∠ 1 and ∠ 3 are vertical angles and are congruent, then

∠ 1 = 99°

∠ 1 and ∠ 2 are adjacent angles and sum to 180° , so

∠ 2 = 180° - 99° = 81°

∠ 2 and ∠ 4 are vertical angles and are congruent, so

∠ 4 = 81°

x^2 - 3x = x ( x - 3 )

ʜᴏᴘᴇ ʏᴏᴜ ɢᴇᴛ ᴡᴇʟʟ

Answer:

791.68

Step-by-step explanation:

have a nice day! :)

Answer:

Hope it helps you!!!

Please mark as brainliest!!!!

Step-by-step explanation:

The formula for finding the circumference of a circle is pi x diameter. So it would be 3.14 x 2. And when you calculate it you get 6.28.

Answer:

6.28

Step-by-step explanation:

Answer:

B) 144 cm^2

Step-by-step explanation:

Answer:

the length of x must be 10

Step-by-step explanation:

Answer:

The answer is yes to both!

Hope that helps - we're studying the Pythagorean theorem right now! :)

Step-by-step explanation:

Answer:

please give the picture so only I can able to answer

The main question isn't supplied.

Answer:

Kindly check explanation

Step-by-step explanation:

A right - angled triangle is one which has one of its angles being 90°. Once we have a right angled triangle, the rule of Pythagoras can be applied in other to solve problems relating to obtaining sides of the triangle while trigonometric relations including :

Sinθ = opposite / hypotenus

Tanθ = opposite / Adjacent

Cosθ = Adjacent / Hypotenus

To obtain the angle θ; depending on which of the sides are given.

From Pythagoras :

c² = a² + b²

Where, c = hypotenus and the longest side if the triangle.

Answer:

a

Step-by-step explanation:

its a because 12cm×10cm×9cm = 1,080cm

Answer:

Question 2

Step-by-step explanation:

divdtihcdyuvftujvfujvfubf

Answer:

2

Step-by-step explanation:

Answer:

156 cm

Step-by-step explanation:

Answer:

1) .11111

2) 5/9

3) 122/495

4) rational- .167167, 2/9

irrational- π, [tex]\sqrt{225}[/tex]

5) 5.75

Answer:

2n +14 = 30 I can use inverse operations and solve for n.

Step-by-step explanation:

twice means 2 so twice a number,n, means 2 times n thus 2n.

sum means add  so, 2n + 14

is means equal so 2n + 14 = 30

If you solve it you will find n = 8

Answer:

2 square root 14

Step-by-step explanation:

The square root of 56 is 2 square root 14. 56 = 4 * 14, and 4 can be square rooted into an integer.

Answer:

x = -1.434, x = -0.232

Step-by-step explanation:

Answer:

x = 4 and y = −1

(4, -1)

Step-by-step explanation:

I going to solve this system of equations by elimination. (You could also solve by substitution too.)

Multiply the first equation by 1, and multiply the second equation by -2.

1(−2x+9y= -17)

-2(-x - 3y = -1)

Becomes:  

−2x + 9y = −17

2x + 6y = 2

Add these equations to eliminate x:

15y = −15

15y/15 = -15/15

y = -1

Now we solve for x:

-x -3(-1) = -1

-x + 3 = -1

     -3   -3

-x = -4

x = 4

Hope this helped!

Answer:

y = - 3, - 2, - 1

Step-by-step explanation:

Given

- 8 < 2y < 0 ( divide each interval by 2 )

- 4 < y < 0

Then y can equal - 3, - 2, - 1

Answer:

True

Step-by-step explanation:

J(9 , 0) ;   K(-3 , -4)

Midpoint = [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]

               [tex]= (\frac{9+(-3)}{2},\frac{0+(-4)}{2}\\\\\\= (\frac{6}{2},\frac{-4}{2})\\\\=(3 , -2)[/tex]

(3 , -2) lies in quadrant IV

Answer:

[tex]\frac{1}{2}(4x + \frac{2}{5} ) = \frac{4}{5}\\2x + \frac{1}{5} = \frac{4}{5}\\\frac{10x + 1}{5} = \frac{4}{5}\\10x + 1= 4\\10x = 3\\x = \frac{3}{10}[/tex]

Answer:

x = 3/10

Step-by-step explanation:

Given equation,

→ 1/2(4x + 2/5) = 4/5

Let's solve the problem,

→ 1/2(4x + 2/5) = 4/5

→ 2x + (1/5) = 4/5

→ 2x = (4/5) - (1/5)

→ x = (3/5) × (1/2)

→ [ x = 3/10 ]

Thus, the value is 3/10.