Acoin is flipped and a random marble is picked from a bag of 10 marbles. two of the marbles in the bag are red. what is the probability of the coin landing on tail and a red marble being drawn?

is the probability of the coin landing on tail and a red marble being drawn.

Step-by-step explanation:

Given A coin is flipped and a random marble is picked from a bag of 10 marbles. Two of the marbles in the bag are red. we have to find the probability of the coin landing on tail and a red marble being drawn.

P(a red marble)=

                        =

P(getting a tail)=

Since both events are independent.

∴ P(he coin landing on tail and a red marble being drawn)

 =

 =

 =

Hence, is the probability of the coin landing on tail and a red marble being drawn.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225