4. Ben has $100 in his savings account. He
is looking at two investment plans, Under
Plan A, he will increase his account
balance by $20 a year, Under Plan B, he
will increase his account balance by 15%
each year. Approximately how much will
Ben save after 3 years with each plan?
A Plan A: $160; Plan B: $145
B Plan A: $160; Plan B: $152
C Plan A: $173; Plan B: $152

Plan A: $160, Plan B: $152

Step-by-step explanation:

PLAN A

add 20 dollars a year you would get

year one = $120

year two = $140

year three = $160

PLAN B

multiple your value by 1.15 (adding 15%) each year

year one = 100 x 1.15 = 115

year two = 115 x 1.15 = 132.25

year three = 115 x 1.15 = 152.08

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

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: