Triangle ABC below has a right angle C and a height CD. (A height in a triangle connects its vertex and the opposite side, and is perpendicular to that side.) d If AC is 3 units long and BC is 4 units long, what is the length of CD?

2.4 units

Step-by-step explanation:

This question can be solved using the principle of area of triangle

Area of triangle = 1/3(base* height)

given

AC = 3 unit

BC = 4 unit

length of hypotenuse is found by using formula =

where a and b are sides of right angled triangle other than hypotenuse

therefore hypotenuse(AB) is =

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Area of triangle when height is 4 unit(BC) and base is 3 unit(AC)

= 1/3( 4 * 3) = 4 square unit

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Now given that there is another height CD  

CD is perpendicular drawn from point CD to side AB

If CD is height for the triangle then its corresponding base will be the side on which this perpendicular is dropped.

in this problem it is Side AB which hypotenuse with side length 5 unit as calculated above

now again finding area for same triangle with height CD and base AB

we can also say Area of triangle ABC = 1/3(CD * AB) = 1/3(CD * 5) ------------equation A

since triangle ABC has area 4 square unit

1/3(CD * 5)   = 4 square unit

CD = (4 * 3)/5 = 12/5 = 2.4 units

length of CD = 2.4 units

.24

step-by-step explanation:

the probability is   .24

the first player had the highest probability of getting a silver marble

the game could be made fair by adding back the marble that was drawn after each draw

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497