Bob won a $200,000 lottery. he invests part of the money in real estate with an annual return of 3% and the rest in a money market account at 4.5% interest. if the annual interest on the money was $8250, how much was invested at each rate?

Bob invested $50,000 in real state and $150,000 in a money market.

Step-by-step explanation:

Assuming that x is the investment in real state:

(200,000-x)*0.045 + x * 0.03 = 8,250

Apply distributive property:

(200,000*0,045) - 0.045x +0.03x = 8,250

9,000 - 0.045x +0.03x = 8,250

We must clear x:

- 0.045x +0.03x = 8,250 - 9,000

-0.015x = -750

x = -750/-0.015

x = 50,000

So, the invest in real state is $50,000.

$200,000 - $50,000 = $150,000 is the invest in a money market.

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

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.