Shelley is self-employed in Texas and recently attended a two-day business conference in New Jersey. After Shelley attended the conference, she had dinner with an old friend who lived nearby. Shelley documented her expenditures (described below). What amount can Shelley deduct?

The amount deductible by Shelley is $2,929

Step-by-step explanation:

Using the table below as the missing information:

Airfare to New Jersey $2,180

Meals $238

Lodging in New Jersey $432

Rental car $198

All the above expenses are fully deductible by Shelley except the meal which is half deductible.

Half of the meal expenses is:

= 238 / 2 = $119

So the amount deductible by Shelley is:

2180 + 119 + 432 + 198

= 2929

Therefore, the amount deductible by Shelley is $2,929

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

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