Right triangle XYZ has legs of length XY = 12 and YZ 6. Point D is chosen at random within the triangle XYZ. What is the probability that the area of triangle XYD is at most 20?

Answers

Answer 1

Step-by-step explanation:

a probability is always

desired cases / totally possible cases.

now in our case the totally possible area is the area of the triangle XYZ (when D = Z).

the desired case is the area of 20 (which contains also the possibilities of smaller areas).

so, the probability is 20/area.

now, let's find the area of XYZ :

Pythagoras tells us the length of the Hypotenuse :

XZ² = XY² + YZ² = 12² + 6² = 144 + 36 = 180

XZ = sqrt(180)

the area based on all 3 sides we get via Heron's formula

s = (a+b+c)/2

A = sqrt(s(s-a)(s-b)(s-c))

s = (12+6+sqrt(180))/2 = 9 + sqrt(180/4) = 9 + sqrt(45)

sqrt(180) = 2×sqrt(45)

A = sqrt((9+sqrt(45))(-3+sqrt(45))(3+sqrt(45))(9-sqrt(45)))

(a+b)(a-b) = a² - b²

so,

(9+sqrt(45))(9-sqrt(45)) = 81 - 45 = 36

(-3+sqrt(45))(3+sqrt(45)) = 45 - 9 = 36

A = sqrt(36×36) = 6×6 = 36

the probability that the area of XYD is max. 20 is

20/36 = 5/9


Related Questions

Express $0.3\overline{2}$ as a fraction in simplest form.

Answers

Answer:

3/20

Step-by-step explanation:

[tex]\frac{0.3}{2}=\frac{0.3*10}{2*10}=\frac{3}{20}[/tex]

in a group of 35 students 7 have yellow socks what percentage of the students have yellow socks

Answers

Answer:

20%

Step-by-step explanation:

[tex]\frac{7}{35} =\frac{y}{100}[/tex]

35 · y = 7 · 100

35y = 700

35y ÷ 35 = 700 ÷ 35

y = 20

Kaiya Deangelo each create a number pattern

Answers

There’s no explanation wdy

Can someone PLEASE help I’ll give brainliest

Answers

Answer:

98°

Step-by-step explanation:

3x+89+8x+58=180

11x+147=180

11x=180-147

11x=33

x=3

< MON = 3x+89 = 3(3)+89 = 9+89= 98°

Suppose that you are an elementary school teacher and you are evaluating the reading levels of your students. You find an individual that reads 46.4 word per minute. You do some research and determine that the reading rates for their grade level are normally distributed with a mean of 90 words per minute and a standard deviation of 24 words per minute. At what percentile is the child's reading level (round final answer to one decimal place)?

Answers

Answer:

The child's reading level is at the 3.4th percentile.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

You do some research and determine that the reading rates for their grade level are normally distributed with a mean of 90 words per minute and a standard deviation of 24 words per minute.

This means that [tex]\mu = 90, \sigma = 24[/tex]

You find an individual that reads 46.4 word per minute. At what percentile is the child's reading level?

The percentile is the p-value of Z when X = 46.4, multiplied by 100. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{46.4 - 90}{24}[/tex]

[tex]Z = -1.82[/tex]

[tex]Z = -1.82[/tex] has a p-value of 0.034.

0.034*100 = 3.4

The child's reading level is at the 3.4th percentile.

How do I solve 6,000-5,258

Answers

Answer:

742

Step-by-step explanation:

6000

-5258

   742

What is value of x and y if
Y=-2x+8 and Y=3x-7

Answers

Answer:

X=5 y=-2

Step-by-step explanation:

Set them equal to each other so...

-2x+8=3x-7

Simplify by balancing out the equation so

-5x=-1

So x=5

Now plug it into either y equation

-2(5)+8

-10+8

Y=-2

Hope this helps!

i need to show work it’s algebra 2

Answers

Answer:

a=4 because 4+2=6 on number one

A painting is purchased for $350. If the value of the painting doubles every 5 years, then its value is given by the function
V(t) = 350 - 205, where t is the number of years since it was purchased and Vt) is its value in dollars) at that time. What is
the value of the painting 10 years after its purchase?

Answers

Answer:

$1400

Step-by-step explanation:

350 x 2 = 700 x 2 = $1400

Select the correct answer. Which statement is true about this equation? 3(-y + 7) = 3(y + 5) + 6 A. The equation has one solution, y = 0. B. The equation has one solution, y = -1. C. The equation has no solution. D. The equation has infinitely many solutions.

Answers

the is answer is probably c

the answer makes sense

(Please help) (one question) (NO LINKS)

Answers

Answer:

0.25

Step-by-step explanation:

hope that helps!!!!!!!!!!!!!!!!!!!! :)

How far will the skier travel

Answers

Answer:

2700 meters

Step-by-step explanation:

2 and a half minutes becomes 150 seconds. 150 seconds divided by 4 seconds, the amount of seconds it takes to cover 72 meters, is 37.5. 37.5 multiplied by 72, the meters covered in 4 seconds, is 2700 meters.

I-Ready The map shows an obstacle course at a school fair.

Answers

it’s 25 i used to do it

i will give Brainiest if you are right

Answers

Answer:

G

Step-by-step explanation:

only 3 more brailiest and I will become an expert : )

Answer:

The option 'J' is the correct order from least to greatest

Write an expression to represent: 2 times the difference of x and 3​

Answers

Answer:

2(x-3)

Step-by-step explanation: 2 is being multiplied by the difference (subtraction) of x-3.

The Honda Accord was named the best midsized car for resale value for by the Kelley Blue Book (Kelley Blue Book website). The file AutoResale contains mileage, age, and selling price for a sample of Honda Accords. Click on the datafile logo to reference the data.
a. Develop an estimated regression equation that predicts the selling price of a used Honda Accord given the mileage and age of the car (to decimals). Enter negative value as negative number. 20385.25049
b. Is multicollinearity an issue for this model

Answers

Answer:

a) estimated regression equation = ( 2.039e + 04 - 3.79e - 02 millage , - 6.863e + 02 age )  

b) multicollinearity is an issue for this model

Step-by-step explanation:

a) An estimated regression equation

estimated regression equation = price ~ mileage + age = ( 2.039e + 04 - 3.79e - 02 millage , - 6.863e + 02 age )  

Residuals :

Min 1∅ median 3∅ max

- 1053.73 - 542.06 - 19.61  433.55 1560.81

coefficients :

estimate std errors at t values ( intercept ) 2.039e + 04   2.982e+02  68.366<2e-16

b) multicollinearity is an issue for this  model because the correlation between millage and Fs 0.6681727 is of high degree

attached below is the remaining part of the solution

Use triangles to find the sum of the interior angle measures of the polygon.

SHOW YOUR WORK.

Answers

The sum of the interior angle measures of the polygon is 900 degrees

How to determine the sum of interior angles

From the image shown, we can see that the polygon has 7 sides.

A polygon with seven sides is called a heptagon

It is important to note that the number of triangles in a heptagon is 5.

Also, the sum of angles in a triangle is 180 degrees.

Now, the formula for calculating the sum of interior angles of a polygon is expressed as;

= (n - 2) 180

Where; n is the number of sides of the polygon

Substitute the value

= (7-2)180

Subtract the value

= 5(180)

= 900 degrees

Hence, the sum is 900 degrees

Learn more about polygons here:

https://brainly.com/question/1592456

#SPJ1

A parking lot contains only cars and motor bikes. If there are 18 vehicles and 50 tires in the parking lot, how many cars and bikes are there?

Answers

Answer:

7 cars

11 bikes

Step-by-step explanation:

18 cars would have 72 tires. This is 22 more tires than necessary. If we add a bike, we lose four tires (from the car) and add two (from the bike). This means we lose two tires. 22/2 is 11 so it would be 11 bikes and 7 cars.

11 bikes = 22 tires

7 cars = 28 tires

22+28=50 tires


In 1992, Jason bought a gallon of gas for $1.18. Yesterday, he bought a gallon of gas for $2.10. What is the percentage increase of the price of a gallon of gas
from 1992 to yesterday? If necessary, round to the nearest tenth of a percent.

Answers

Answer:

1.77 percent increase

What is the slope of the line that is parallel to the line y = -2x + 5?
slope =

Answers

Answer:

-2

Step-by-step explanation:

Slope intercept form is

y = mx + b

Where m is the slope

Parallel lines have the same slope

----------------------------

y = -2x + 5

is in slope intercept form

the slope, m = -2

The slope of the parallel ine will be the same

m = -2

Hello there!

Parallel lines have the same slope.

So if one line has a slope of -2, then the slope of the line parallel to it is -2 as well.

Hope it helps! :)

If you have any query, please feel free to ask me! :)

~An excited gal

[tex]MagicalNature[/tex] here to help

Find three consecutive integers such that 4 times the first decreased by the second is 12 more than twice the third

Answers

The three consecutive number are 17 , 18 and 19 respectively

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be = x

Let the second number be = ( x + 1 )

Let the third number be = ( x + 2 )

Now ,

A = 4 times the first decreased by the second is 12 more than twice the third

Substituting the values in the equation , we get

4x - ( x + 1 ) = 12 + 2 ( x + 2 )

On simplifying the equation , we get

4x - x - 1 = 12 + 2x + 4

3x - 1 = 16 + 2x

Subtracting 2x on both sides of the equation , we get

x - 1 = 16

Adding 1 on both sides of the equation , we get

x = 17

Therefore , the value of x is 17

Hence , the consecutive numbers are 17 , 18 and 19

To learn more about equations click :

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Aurielle bought 13 packs of
cookies for $51.48 from the
supermarket. How many packs
of cookies can she buy for
$43.56?

Pls help

Answers

Answer:

She could buy 11 packs of cookies for $43.56.

Step-by-step explanation:

to find the answer you have to find how much 1 pack of cookies costs.

First, you divide 51.48 by 13

51.48/13 = 3.96

now that you know 1 pack of cookies cost $3.96 you can use that to find how many packs you could buy for 43.56

43.56/3.96 = 11

find the area if each shaded sector.

plz help im confusedddddddd

Answers

Find a ratio of the angle given to an angle that is easily known. So if you were given 90 degrees, you could say that it is 1/4 of the circle since 90x4 is a full circle.

if the nth term of a sequence is 2n+2n squared, find the first 3 terms and the 10th term please help​

Answers

Answer:

3rd term: 24

10th term: 220

Step-by-step explanation:

For the 3rd term

2*3 + 2*(3^2) = 6 + 2*9 = 6 + 18 = 24

For the 10th term

2*10 + 2*(10^2) = 20 + 2*100 = 20 + 200 = 220

no links please
Evaluate 10v for v = -8.

A.
2

B.
-90

C.
80

D.
-80

Answers

Answer: D. -80

Step-by-step explanation:

10(-8) substitute (-8) for V

10 • -8 = -80 Then solve by multiplying

An

Can anyone help me with this plz

Answers

Answer:

B.

Step-by-step explanation:

So we know right off the bat the angles ABE and CBD are congruent because of vertical angles.

Now we can look at the sides.

The ratio for 27:18 = 3:2

The ratio for 36:24 = 3:2

They check out.

That means that the answer is B. SAS

Max kicks a football up at a velocity of 25 meters per second. If the ball makes contact with his foot 0.5 meter off the ground, how long will the ball stay in the air?

Answers

Answer:

25*0.5 = 12.5

2. Marquan sells pretzels at Auntie Anne and earns $15 per hour,
(a) Write an expression to show the relationship between the number of hours
worked (h) and the total earnings.
(b) Use the expression to determine the amount of money he earns if he
worked for 2 hours (b) 3 hours (c) 5 hours
Yes

Answers

dollars per hour = salary

a

dollars per hours multiplied with hours worked (h) = total earnings

b

15 x 2 = 30

15 x 3 = 45

15 x 5 = 75

(h)

Which expression represents the product of x3 + 2x - 1 and x4 - x3 +3?

Answers

Answer:

x^4 + 2x + 2

Step-by-step explanation:

Show your work please!!!

Answers

Answer:

Error is in line 3

Error description: Root of 4 is 2 not 4

Correct answer should be 9*√5 (12*√5 - 3*√5)

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