We'll start with side AC first. We can see that A is (-8, -4) and C is (-6, -2). That means to get from A to C, we need to go 2 units to the right, and 2 units up. Which means we have our two sides to work out the length from Pythagoras' theorem. 2² + 2² = c², c = √8.

Now we'll move onto side AB. We already know A is (-8, -4) from above, and B is (-7, -8). That means to get from A to B, we have to go 4 units down, and 1 unit to the right. So once again: 4² + 1² = c², c = √17.

Lastly, we'll work out side BC. We know that B is (-7, -8) and C is (-6, -2). That means to get to C from B, we have to go 1 unit to the right and 6 units up. So, again: 1² + 6² = c², c = √37.

Now that we have all of our lengths, we simply just add them up!

√8 + √17 + √37 ≈ 13.03 units.

(I've also attached something to help you visualise how I worked it out.)

6 0

3 years ago

The annual rainfall (in inches) in a certain region is normally distributed with = 40 and = 4. What is the probability that star

sdas [7]

Answer:

0.93970

Step-by-step explanation:

Solution:-

- Denote a random variable "X" The annual rainfall (in inches) in a certain region . The random variable follows a normal distribution with parameters mean ( μ ) and standard deviation ( σ ) as follows:

X ~ Norm ( μ , σ^2 )

X ~ Norm ( 40 , 4^2 ).

- The probability that it rains more than 50 inches in that certain region is defined by:

P ( X > 50 )

- We will standardize our test value and compute the Z-score:

P ( Z > ( x - μ ) / σ )

Where, x : The test value

P ( Z > ( 50 - 40 ) / 4 )

P ( Z > 2.5 )

- Then use the Z-standardize tables for the following probability:

P ( Z < 2.5 ) = 0.0062

Therefore, P ( X > 50 ) = 0.0062

- The probability that it rains in a certain region above 50 inches annually. is defined by:

q = 0.0062 ,

- The probability that it rains in a certain region rains below 50 inches annually. is defined by:

1 - q = 0.9938

n = 10 years ..... Sample of n years taken

- The random variable "Y" follows binomial distribution for the number of years t it takes to rain over 50 inches.

Y ~ Bin ( 0.9938 , 0.0062 )

- The probability that it takes t = 10 years for it to rain:

= 10C10* ( 0.9938 )^10 * ( 0.0062 )^0

= ( 0.9938 )^10

= 0.93970

3 0

3 years ago

consider the point (x,y) lying on the graph of y=(x+3)^1/2. let L be the distance between the points (x,y) and (4,0). write l as

olga_2 [115]

$L=\sqrt{ (x-4)^2 + y^2 }$
and
$y=\sqrt{x+3} \Rightarrow x = y^2-3$

$L=\sqrt{ (x-4)^2 + y^2 }=\sqrt{ (y^2 - 3-4)^2 + y^2 }=\sqrt{ (y^2-7)^2 + y^2 }$

6 0

3 years ago

Which property does the following<br> equation represent?<br> 62? + 43 = 43+ 6x2

timurjin [86]

Answer:

commutative

Step-by-step explanation:

you are typing the same numbers but in different order

8 0

3 years ago