randy presses on his calculator twice to obtain two random numbers between and . let be the probability that these two numbers and form the sides of an obtuse triangle. find .

Answers

Answer 1

We are to calculate the value of 4p. The value of 4p will be π / 4.

Let's give the numbers we get from the calculator the names x and y. Independent random variables with a uniform[0,1] distribution are x and y.

Let's take notice that since x and y are both between 0 and 1, 1 is the triangle's longest side.

Let's start by interpreting geometry. If the triangle were a rectangle, the side with length 1 would be the hypotenuse, and x and y would then need to meet the following criteria:

x²+y² = 1

Keep in mind that we are supposing the triangle to be a rectangle in this instance. However, the task requires us to create an acute triangle.

To do that, we must widen the angle formed by the sides of length x and y. We can do that by 'growing' the triangle, but if we do so while maintaining the x and y values, the length of side 1 should rise, which is not what we want.

Therefore, if we enlarge the triangle, we should likewise decrease the value of x and/or y so that the length of the first side may be maintained. This insight allowed us to conclude that

x²+y² < 1

Let's now employ a more mathematical strategy. The Cosine Theorem states that a triangle with three sides of length a, b, and c is satisfying.

A2 is equal to b2+c2 - 2bc* cos(), where is the angle formed by the lengths of b and c's sides.

The result of applying this formula to our triangle is that

[tex]1+x^{2} +y^{2} - 2bc * cos\alpha[/tex] , where aplha is the angle between x and y.

Let's call the figures we obtain from the calculator x and y. X and Y are independent random variables with uniform[0,1] distribution.

Consequently, we must ascertain P(x2+y2 1). This likelihood may be calculated using integration. You need polar coordinates.

(X, Y) = (r*cos, r*sen), where r is an integer between 0 and 1, and (that way, the numbers are positive).

Because the Jacobian matrix has determinant r, X2 + Y2 = 1.

On integrating, we get out answer as π / 4

To learn more about probability from given link

https://brainly.com/question/13914115

#SPJ4


Related Questions

= f(x)= 4 -x, for what input is the output 7

Answers

Answer:

-3

Step-by-step explanation:

Rewrite as follows and solve for x:

7 = 4 - x

Add x to both sides to get positive x

x + 7 = 4  

Subtract 7 from both sides to get x by itself

x = -3

What is the greatest commen factor of 338

Answers

Answer:

2

Step-by-step explanation:

find the measure of each lettered angle. a=, b=, c=, d=, e=

Answers

Answer:

a= 20

b= 70

c= 20

d=70

e=110

Step-by-step explanation:

a + the 70 degree angle have to equal 90 degrees (the right angle marking) and the same with b + a. So to ind a, you do 90-70 and to find b, because you now have the value of a, you do 90-20.

a+b+c+70 is equal to a 180 degree angle, so since you know the value of a and b, now you can figure out c by doing 180-(70+20+70).

d and the 70 degree angle are vertical angles so they are equal to each other.

lastly for e, d+e is equal to 180 degrees so since you know the value of d, you just do 180-70 to find e.

Answer:

a = 20°

b = 70°

c = 20°

d = 70°

e = 110°

Step-by-step explanation:

Angle A is complementary with 70°, so they add together to = 90° (as indicated by the 90° mark).

90° - 70° = 20°

Angle A = 20°

Angle B is complementary with angle A, 20°, so they also add together to = 90°.

90° - 20 = 70°

Angle B = 70°

Although not indicated by a 90° mark, Angle C and Angle B are complementary since they share a straight line with the complementary angles A and 70°. This means Angles C + B = 90°

90° - 70° = 20°

Angle C = 20°

Angle D is vertical to 70°, so Angle D = 70°

Angle E is supplementary to 70°, so they should combine to = 180°

180° - 70° = 110°

Angle E = 110°

Charlotte is driving at 61.4 mi/h and receives a text message. she looks down at her phone and takes her eyes off the road for 3.93 s. how far has charlotte traveled in feet during this time?

Answers

The distance travelled by Charlotte in feet is 354 feet. This is obtained by using the concept of speed and distance on the given problem.

What is speed?

Speed is defined as the distance per unit of time. It is the numerical quantity that specifies how fast an object is moving. The basic unit of speed is given by m / s.

Calculation of the distance travelled by Charlotte in feet

Given:

Speed = 61.4 mi / h

Time = 3.93 s

The basic step to solve this problem is to convert miles per hour to feet per second

(61.4 mi / hr) * (5280 feet / mi) * (1 hr / 3600 sec) = 90.0533 feet / sec

Now, multiply the speed by the number of seconds to find the value of distance in feet

(90.0533 feet / sec) * (3.93 sec) = 353.909 feet.    

Hence, the distance travelled by Charlotte in feet is 354 feet.

To learn more about speed, visit the link below:

https://brainly.com/question/13943409

#SPJ4

Given that f(x)=6x+5 and g(x)=2x−7, what would be the composite function (f∘g)(x)?

Answers

Answer:

f ◦ g is the composition function that has f composed with g. ... Find (f ◦ g)(x) for f and g below. f(x)=3x + 4. (6) g(x) = x2 +. 1 x. (7).

Step-by-step explanation:

If c^2+s^2=1 what does c+s=

Answers

I don't have a lot of info to go off of to properly solve the question, however I think I may be able to help. If you are trying to solve using the Quadratic Formula:

_______________________________________________________

Solve the rational equation by combining expressions and isolating the variable c.

[tex]c=\sqrt{(1+s)(1-s)[/tex]

[tex]c=-\sqrt{(1+s)(1-s)}[/tex]

If this is not what you are looking for, please comment below on what you really need and I'll see what else I can do to help. Thanks!

PLEASE HELP ME ASAP THIS NEEDS TO BE DONE TODAY.

Answers

Answer:

#1

[tex]{ \tt{119 \degree + 34 \degree + b = 180 \degree}} \\ { \tt{b = (180 - 34 - 119) \degree}} \\ { \tt{b = 27 \degree}}[/tex]

#2

[tex]{ \tt{ \red{❗ \: image \: not \: clear}}}[/tex]

What is the slope-intercept form of the equation of the line that passes through the point (-6, 1) and is perpendicul
to the graph of 2x + 3y = -5?
y=-x-8
y=-3x+1
y=x+1
y = x + 10

Answers

The equation of the line as it passes through the point (-6, 1) is

y = 3x/2 + 10

How to Calculate a Slope ?

Slope is the same as gradient which is the ratio of change in y to change in x. That is,

gradient m = Δy / Δx

Given that the equation of the line passes through the point (-6, 1) and is perpendicular to the graph of 2x + 3y = -5

Let us first find the slope, 3y = -2x - 5

y = -2x/3 - 5/3

Slope m = -2/3

Let us use the formula Mm = -1

M = -1/m

M = -1 × -3 /2

M = 3/2

The equation of the line as it passes through the point (-6, 1) will be

M = (Y - Y1) / (X - X1)

3/2 = (y - 1) / (x + 6)

Cross multiply

2(y - 1) = 3(x + 6)

2y - 2 = 3x + 18

Collect the like time

2y = 3x + 18 + 2

2y = 3x + 20

y = 3x/2 + 10

Therefore, the equation of the line as it passes through the point (-6, 1) is y = 3x/2 + 10

Learn more about Gradient here: https://brainly.com/question/21727173

#SPJ1

is this statement true or false? the imaginary line which passes through the north and south poles, upon which the earth rotates once every 24 hours is called the prime meridian.

Answers

It is False that the imaginary line which passes through the north and south poles, upon which the earth rotates once every 24 hours is called the prime meridian. .

Where is prime meridian located?

In a geographic coordinate system, a prime meridian is any line of longitude when longitude is defined to be 0°. A great circle is formed by a prime meridian and its anti-meridian (the 180th meridian in a 360° system).

A spheroid, like the Earth, is divided into two hemispheres by this vast circle: the Eastern Hemisphere and the Western Hemisphere (for an east-west notational system).

Different conventions have been used or supported for Earth's prime meridian throughout history in various places. The IERS Reference Meridian is the current international prime meridian for the Earth. It is developed from the former Greenwich Meridian, however it is somewhat different.

To learn more about prime meridian from given link

https://brainly.com/question/4039625

#SPJ4

A rectangular book measures 12 x 15. What is the length of
its diagonal?
Round the answer to the nearest tenth.

Answers

Use Pythagoras

a² + b² = c²
12² + 15² = c²
144 + 225 = 369

Square root of 369 = 19.2

Mio bought a tablet and pays monthly for internet service for it. She graphed the relationship between the number of months she has had the tablet and the total amount she has spent on it. What does the y-intercept represent in this context?

A) The number of months after which the cost is 0 dollars.


B) The cost per month of internet service.


C) The cost of buying the tablet.

Answers

Answer:

B) The cost per month of internet service.

Kiara and Donovon attend different middle schools. They both went to their schools’ winter carnivals. Kiara paid a $5 entrance fee and bought several tickets costing $0.75 each for games and rides. Donovon paid a $7 entrance fee and bought several tickets costing $0.50 each for games and rides. How many tickets, x , must Kiara and Donovan each buy in order for the cost of attending their school carnivals to be the same?
A. 8 tickets
B. 10 tickets
C. 28 tickets
D. 48 tickets

Answers

Answer:B

Step-by-step explanation:

how many groups of 9/2 are in 1​

Answers

Answer:

Step-by-step explanation:

9/2 = 4 1/2

9/2=4.5

So, we divide 1 by 9/2 to find the answer

1/4.5 = 0.2222222222

Hope this helps! ^^

There are 0.22 groups or 2/9 groups of 9/2 in unity.

What are fractions?

A common fraction is a numeral which represents a rational number. That same number can also be represented as a decimal, a percent, or with a negative exponent. Example -

2/5, 5/6, 7/9

We have a fraction and a whole number.

Assume that there are [x] groups of 9/2 each. Then, we can write -

9x/2 = 1

x = 2/9

x = 0.22 (rounded of)

Therefore, there are 0.22 groups or 2/9 groups of 9/2 in unity.

To solve more questions on fractions, visit the link below-

https://brainly.com/question/1627825

#SPJ5

During her visit to zoo, Ivy stops by the café and orders a chicken fajita taco and a juice. If she
pays for her order with a $10.00 bill, how much change will she receive? Show your work

Answers

Answer:

$4.7

Step-by-step explanation:

what is inverse function of f(x) = sqrt-3x-27

Answers

Answer: [tex]f^{-1} (x) = -\frac{x^{2} }{3} -18x -243[/tex]

Step-by-step explanation: that would be the inverse function

Assignment
Find the midpoint of the line segment with the given endpoints
1) (7,2), (-7, -9)

Answers

I believe the answer is 0,5.5
Midpoint formula is x1-x2/2 , y—y2/2
7- (-7) /2 = 0 , 2-(-9)/2 = 5.5

2/3 of a number is 12. What is 1/2 the number?​

Answers

Answer:

Step-by-step explanation:

the number is 18, so half of that would be

which of these equations are shown on the graph?

Answers

The equation shown on the graph is y = 2x + 3. The correct answer is C. y = 2x +3

Equation of a line

From the question, we are to determine the equation that represent the given line

To determine the equation, we will pick two points on the line and determine the equation of the line

Picking the points (0, 3) and (3, 9)

Using the formula for the finding the equation of a line with two given points

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

x₁ = 0

y₁ = 3

x₂ = 3

y₂ = 9

Then,

(y - 3)/(x - 0) = (9 - 3)/(3 - 0)

(y - 3)/x= 6/3

(y - 3)/x= 2

y - 3 = 2x

y = 2x + 3

Hence, the equation shown on the graph is y = 2x + 3. The correct answer is C. y = 2x +3

Learn more on Equation of a line here: https://brainly.com/question/4074386

#SPJ1

Please Help!! Find the sum. In your final answer, include your calculations.

−3.45 + 5.1

Answers

8.55

Here's a video that could explain

https://youtu.be/WwKLA-6S-e0

Also when doing the math ignore the - sign, the larger number will determine if the answer will be a whole or a minus , let me explain, so as you see in the question the 5.1 is the largest so that means the answer will be a whole.


Name the geometric term modeled by the given object.
a knot in a rope

Answers

The geometric term modeled by the given object (knot in a rope) is a point

How to determine the geometric term?

The given object is a knot in a rope

The knot of a knot in a rope is often represented by a dot

This means that the knot in a rope can be modelled by a line point

Hence, the geometric term modeled by the given object (knot in a rope) is a point

Read more about geometric terms at

brainly.com/question/17432486

#SPJ1

18 12 over 7 minus 2

Answers

Answer: whats the answer choices

Step-by-step explanation: i dont get it

Answer:

1,798/7

Step-by-step explanation:

1812/7-2 (or it can be written as 14/1 because you getting rid of two sevenths)

what is the inverse of g (x)= 2x-4/3

Answers

Answer:

this is the answer of this question

if the chance of getting a disease is 20 out of 100, this would be the same as having how much of a percent chance of getting the disease?

Answers

If the chance of getting a disease is 20 out of 100, This would be the same as having a 20% chance of getting the disease

Define diseases?

A disease is a specific abnormal state that adversely affects an organism's structure or function on the whole or in part, and which is not immediately brought on by any external trauma.  It's common knowledge that diseases are medical illnesses with recognizable indications and symptoms. A disease can be brought on by either internal dysfunctions or external sources like infections.

In humans, the term illness is frequently used to refer to any condition that results in suffering, dysfunction, anguish, social issues, or death for the person who is afflicted, as well as problems similar to these for those who come into touch with the person.

To learn more about diseases, visit:

https://brainly.com/question/943439

#SPJ4

Both lines on the graph represent proportional relationships. What is the constant
of proportionality for each relationship? Explain how you know.

Answers

Each relationship's proportionality constants are k=3 and k=1, respectively.

What is the proportionality constant?

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.

Given that the relationship is proportional,

the equation linking the quantities is y = k x k, where k is the proportional constant.

Divide both sides by x to determine k

k = y/x

For graph a use the point (2, 6 ), then

k = 6/2

= 3

For graph b use the point (4, 4 ), then

k = 4/4

= 1

To know more about proportionality constant visit;

https://brainly.com/question/14864328

#SPJ9

Please help please I’m in desperate need

Answers

Answer:

ok I will help u don't worry

please help me find this answer
PLEASE IM BEGGING​

Answers

Answer: The length of the side is 14 inches

Step-by-step explanation: Using the formula V=(b^2xh):3

Input the numbers we are given: 196=(b^2x3):3 now calculate 196=(14^2x3):3 side b=14 inches

What is this type of polynomial?
13x² + 17x +3

Answers

Answer:

This is a quadratic (second-degree) polynomial.

How many three-digit numbers may be formed using elements from the set {1,2,3,4,5,6,7,8}. if no element may be used more than once in a number and the number must be even?

Answers

126 three-digit numbers may be formed using elements from the set {1,2,3,4,5,6,7,8}. if no element may be used more than once in a number and the number must be even

For given question,

We need to find number of three-digit numbers formed using elements from the set {1,2,3,4,5,6,7,8}  if no element may be used more than once in a number and the number must be even.

3-digit even  numbers are to be formed using the given six digits,1 ,2,3,4,6,7, and 8 without repeating the digits.

Then, units digits can be filled in 4 ways by any of the digits, 2,4, 6 or 8.

Since the digits cannot be repeated in the 3-digit numbers and units place is already occupied with a digit (which is even), the hundreds and tens place is to be filled by the remaining 7 digits.

So, the number of ways in which hundreds and tens place can be filled with the remaining 7 digits is the permutation of 7 different digits taken 2 at a time.

[tex]\Rightarrow ~^7P_2=\frac{7!}{(7-2)!} \\\\\Rightarrow ~^7P_2=42[/tex]

Thus, by multiplication principle, the required number of 3-digit numbers is 3 × 42 = 126

Therefore, 126 three-digit numbers may be formed using elements from the set {1,2,3,4,5,6,7,8}. if no element may be used more than once in a number and the number must be even

Learn more about the permutation here:

https://brainly.com/question/16837159

#SPJ4

Rewrite in simplest terms: -10(-5f +7f+2) - f

Answers

Answer:

-21f - 20

Step-by-step explanation:

Rewriting in the simplest terms,

→ -10(-5f + 7f + 2) - f

→ 50f - 70f - 20 - f

→ -20f - 20 - f

→ -21f - 20

Hence, simplest term is -21f - 20.


Find missing length.
The area of a rhombus is 168 square centimeters. If one diagonal is three times as long as the other, what are the lengths of the diagonals?

Answers

Given the area, the lengths of the diagonals p and q of the rhombus are 4√7 cm and 12√7 cm respectively.

What are the lengths of the diagonals of the rhombus?

A rhombus which is called an equilateral quadrilateral is simply a quadrilateral whose all four sides have the same length.

The area of a rhombus is expressed as;

A = ( p × q )/2

Where p and q are the diagonals

Given the data in the question;

Let one of the diagonal be x.

Area of the rhombus = 168cm²Diagonal p = xDiagonal q = 3x

Plug in the given values into the equation above and solve for x.

A = ( p × q )/2

168 = ( x × 3x )/2

168 = ( 3x² )/2

3x² = 168 × 2

3x² = 336

Divide both sides by 3

x² = 112

Take the square root of both sides

x = ±√112

x = ±4√7

Since the dimension of the rhombus cannot be negative,

x = 4√7

Hence, the length of the diagonals are;

Diagonal p = x = 4√7 cm

Diagonal q = 3x = 3( 4√7 ) = 12√7 cm

Given the area, the lengths of the diagonals p and q of the rhombus are 4√7 cm and 12√7 cm respectively.

Learn more about rhombus here: https://brainly.com/question/22825947

#SPJ1

Other Questions
Members of a softball team raised $1885.50 to go to a tournament. They rented a bus for $949.50 and budgeted $52 per player for meals. Determine the number of players the team can bring to the tournament. find parametric equations for the line through (3, 3, 8) that is perpendicular to the plane x y 4z The __________ serves as a border between the northeastern united states and canada. a. mackenzie river b. mississippi river c. st. lawrence river d. rio grande please select the best answer from the choices provided. a b c d If you worked for honda, how would you determine fair wages for workers in the foshan factory? What two factors determine the speed of a transverse wave? Explain how these two factors affect the speed of the wave. for each of the following situations, decide whether it is an example of weather or climate. put "w" for weather or "c" for climate on the line next to each scenario. Evaluate the degree to which trans-atlantic exchanges influenced the development of different regions of the british colonies in north america in the period from 1607 to 1754. I need help asap thank you What is the difference between a protein kinase and a second messenger? Can both operate in the same signal transduction pathway? Is a = 8 a solution to 6 = a/4 + 2 What does it mean for an atom to be stable? Write and expression equivalent to 62.7 - 82.4 Who made up the Grange, and what effect did they have on the writing of the Texas Constitution of 1876?O a. They were early wildcatters who wanted land grants from the state so they could explore for oil.O b. They were a consortium of railroad entrepreneurs who wanted a constitution that would aid business interests.O c. They were an agricultural group who wanted a government that would improve the plight of farmers.O d. They were a group of pro-Union Republicans who controlled the state after the Civil War. The value of any asset is the present value of the cash flows the asset is expected to provide. The cash flows a business is able to provide to its investors is its free cash flow. This is the reason that fcf is so important in finance. Which of the following is an example of universal app?a) taskbar b) weatherc) snap What is a product that is produced by both fermentation reactions (lactic acid fermentation or ethanol fermentation) and the electron transport chain? why is magellans expedition to the philippines significant? If the intquantity and decprice variables contain the numbers 3 and 15.75, respectively, the condition if intquantity > 0 andalso intquantity < 10 orelse decprice > 20 will evaluate to ____. m Z 2.In the figure below, m1= 59. Find m Making clients aware of their choices is inherent in which social work ethical obligation?