Sine rule for a triangle states that
​

Answer:

[tex]k = 1[/tex]

[tex]P(x > 3y) = \frac{2}{3}[/tex]

Step-by-step explanation:

Given

[tex]f \left(x,y \right) = \left{ \begin{array} { l l } { k , } & { 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x } & { \text 0, { elsewhere. } } \end{array} \right.[/tex]

Solving (a):

Find k

To solve for k, we use the definition of joint probability function:

[tex]\int\limits^a_b \int\limits^a_b {f(x,y)} \, = 1[/tex]

Where

[tex]{ 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x }[/tex]

Substitute values for the interval of x and y respectively

So, we have:

[tex]\int\limits^2_{0} \int\limits^{x/2}_{0} {k\ dy\ dx} \, = 1[/tex]

Isolate k

[tex]k \int\limits^2_{0} \int\limits^{x/2}_{0} {dy\ dx} \, = 1[/tex]

Integrate y, leave x:

[tex]k \int\limits^2_{0} y {dx} \, [0,x/2]= 1[/tex]

Substitute 0 and x/2 for y

[tex]k \int\limits^2_{0} (x/2 - 0) {dx} \,= 1[/tex]

[tex]k \int\limits^2_{0} \frac{x}{2} {dx} \,= 1[/tex]

Integrate x

[tex]k * \frac{x^2}{2*2} [0,2]= 1[/tex]

[tex]k * \frac{x^2}{4} [0,2]= 1[/tex]

Substitute 0 and 2 for x

[tex]k *[ \frac{2^2}{4} - \frac{0^2}{4} ]= 1[/tex]

[tex]k *[ \frac{4}{4} - \frac{0}{4} ]= 1[/tex]

[tex]k *[ 1-0 ]= 1[/tex]

[tex]k *[ 1]= 1[/tex]

[tex]k = 1[/tex]

Solving (b): [tex]P(x > 3y)[/tex]

We have:

[tex]f(x,y) = k[/tex]

Where [tex]k = 1[/tex]

[tex]f(x,y) = 1[/tex]

To find [tex]P(x > 3y)[/tex], we use:

[tex]\int\limits^a_b \int\limits^a_b {f(x,y)}[/tex]

So, we have:

[tex]P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {f(x,y)} dxdy[/tex]

[tex]P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {1} dxdy[/tex]

[tex]P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 dxdy[/tex]

Integrate x leave y

[tex]P(x > 3y) = \int\limits^2_0 x [0,y/3]dy[/tex]

Substitute 0 and y/3 for x

[tex]P(x > 3y) = \int\limits^2_0 [y/3 - 0]dy[/tex]

[tex]P(x > 3y) = \int\limits^2_0 y/3\ dy[/tex]

Integrate

[tex]P(x > 3y) = \frac{y^2}{2*3} [0,2][/tex]

[tex]P(x > 3y) = \frac{y^2}{6} [0,2]\\[/tex]

Substitute 0 and 2 for y

[tex]P(x > 3y) = \frac{2^2}{6} -\frac{0^2}{6}[/tex]

[tex]P(x > 3y) = \frac{4}{6} -\frac{0}{6}[/tex]

[tex]P(x > 3y) = \frac{4}{6}[/tex]

[tex]P(x > 3y) = \frac{2}{3}[/tex]

Answer:

A. 66 square cm

Step-by-step explanation:

HOPE IT HELPSS! :D

Answer:

B) 20

The 10-15 x axis bar graph shows 20 cars on the y axis

Answer:

4/11...................

Answer: 4/11

Step-by-step explanation:

The total number of books is 35+20=55, which will be the denominator, because the question is asking what fraction of all the books are hardcover. The number of hardcover books, 20, will be the numerator, so we end up with the fraction 20/55. 20 and 55 are both divisible by 5 (this means that when divided by 5, both numbers have a whole number quotient). 20/5= 4 and 55/5=11

So, the answer is 4/11

484848595969696539577589074969594389

Answer:

2.20832105263

i think it is

Answer:

6.774086

Step-by-step explanation:

Answer:

12) 2.5

the height then is 2.5.

Step-by-step explanation:

42.9/3.3 = 13

32.5/13 = 2.5

Have a nice day!

Answer:

[tex]6 \frac{1}{5} [/tex]

Step-by-step explanation:

31/5

6/1/5

Answer:

2,1,0 is the sequence of its terms

Answer:

Perimeter of rectangle EFGH = 24 unit

Step-by-step explanation:

Given:

E: (4,2)

F: (10,2)

G: (10,8)

H: (4,8)

Find:

Perimeter of rectangle EFGH

Computation:

Distance = √(x1 - x2)² + (y1 - y2)²

Distance between EF = √(4 - 10)² + (2 - 2)²

Distance between EF = √36

Distance between EF = 6units

Distance between FG = √(10 - 10)² + (2 - 8)²

Distance between FG = √36

Distance between FG = 6 units

Distance between GH = √(10 - 4)² + (8 - 8)²

Distance between GH = √36

Distance between GH = 6 units

Distance between HE = √(4 - 4)² + (8 - 2)²

Distance between HE = √36

Distance between HE = 6 units

Perimeter of rectangle EFGH = 6 + 6 + 6 + 6

Perimeter of rectangle EFGH = 24 unit

Answer:

13. rational, integer, white number, natural

14. irrational

Step-by-step explanation:

the third root of 125 is 5.

so, it is everything of the list except for irrational.

pi is a prime example of an irrational number. any calculation not eliminating the irrational number is also irrational.

Answer:

C

Step-by-step explanation:

All four sides of the triangle are 4 cm. An equilateral triangle has equal sides

Answer:

[tex]1) 3x+45=90[/tex]

[tex]3x=90-45[/tex]

[tex]3x=45[/tex]

[tex]\frac{3x}{3} =\frac{45}{3}[/tex]

[tex]x=15[/tex]

1) The angles are complementary

[tex]--------[/tex]

[tex]2)x-20+x=90\\[/tex]

[tex]2x=90+20[/tex]

[tex]2x=110[/tex]

[tex]x=55[/tex]

2) The angles are complementary

[tex]--------[/tex]

[tex]3)2x+(3x+25)=180[/tex]

[tex]2x+3x+25=180[/tex]

[tex]2x+3x=180-25[/tex]

[tex]5x=155[/tex]

[tex]x=\frac{155}{5}[/tex]

[tex]x=31[/tex]

3) The angles are supplementary

[tex]----------[/tex]

hope it helps..

have a great day!!

Answer:

[tex]Period = \pi[/tex]

Step-by-step explanation:

Given

[tex]y = -\frac{1}{3} * \sin(2x)[/tex]

Required

The period

A sine function is represented as:

[tex]y =A \sin(Bx + C) + D[/tex]

Where

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

By comparing:

[tex]y =A \sin(Bx + C) + D[/tex] and [tex]y = -\frac{1}{3} * \sin(2x)[/tex]

[tex]B = 2[/tex]

So, we have:

[tex]Period = \frac{2\pi}{2}[/tex]

[tex]Period = \pi[/tex]

Hence, the period of the function is [tex]\pi[/tex]

Answer:

x= -2 y = ([tex]\frac{1}{49}[/tex])

x= 0 y = 1

x= 2 y = 49

Step-by-step explanation:

x= -2  -> (7)² = 49, negative power makes it inverse to a fraction

y = ([tex]\frac{1}{49}[/tex])

x= 0  -> anything to the power of 0 is always 1

y = 1

x= 2 -> 7² = 7 × 7 = 49

y = 49

Answer:

180...

Step-by-step explanation:

15 x 12 = 180

Answer:

so, where the dotted line is that is called the height, so you would times it and find your answer.

Answer:

56,067

Step-by-step explanation:

there are 52 weeks in a year. and they work 40 hours a week.

[tex]26.96*40=1078\\1078*52=56,067[/tex]

Answer:

The answer is C.

Step-by-step explanation:

Answer:

the difference of m and 5 is graeter than 10

Answer:

Hello Love! Answer: 8000

volume is just length x width x height

so 20 x 20 x 20 = 8000

Answer:

8,000 in³

Step-by-step explanation:

All you have to do is multiply all the sides so it would be

20 · 20 · 20 = 8,000 in³

Hope this helped.

If you are willing to give me a brainliest you can its your choice.

I just need one more to level up.

Well anyways

STAY SAFE!!!!!

Answer:

First, reflect across the x-axis. Then, reflect across the y-axis. Or you could switch, doesn't matter.

Answer:

its 23.5

Step-by-step explanation:

Answer:

d 26

Step-by-step explanation:

AC=24

AB=AC/2=12

AD²=AB²+BD²

AD²=5²+12²=25+144=169

AD=√169=13

AE=2*13=26

Answer:

5in by 7in

Step-by-step explanation:

2*(l+w)= 24 => l+w= 12

Le= 35

It is easy to see that 35=5*7 and 12= 5+7

So 5 and 7 are the dimensions of the card

Answer:

Step-by-step explanation:

Answer:

4/15

Step-by-step explanation:

Answer:

the correct answer is 197 in^2

Answer:

acute

Step-by-step explanation:

Answer:

4x + 12

Step-by-step explanation:

4*x + 4*3 = 4x + 12

That's as far as you can take the problem. You cannot reduce it any further or combine it in any way. The reason is that the x has a 4 in front of it and the 12 has no x.

When those terms are separated by a plus or minus sign, the terms are not the same. Unlike terms cannot be combined.

Answer: 4x+12=4x+12 or 4x+12=4(x+3)

Step-by-step explanation:

Hope this helps!