A company rents out 10 food booths and 25 game booths at the county fair. The fee for a food booth is $100 plus $2 per day. The fee for a game booth is $50 plus $3 per day. The fair lasts for n days, and all the booths are rented for the entire time. Enter and simplify an expression for the amount in dollars that the company is paid.

2,250 + 95n

Step-by-step explanation:

Cost of a food booth = 100 + 2n

Cost of 10 food booth = 10(100 + 2n)

= 1,000 + 20n

Cost of a game booth = 50 + 3n

Cost of 25 game booth = 25(50 + 3n)

= 1,250 + 75n

Total amount earned by the company = Cost of 10 food booth + Cost of 25 game booth

= (1,000 + 20n) + (1,250 + 75n)

= 1,000 + 20n + 1,250 + 75n

= 1,000 + 1,250 + 20n + 75n

= 2,250 + 95n

Total amount earned by the company = 2,250 + 95n

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 ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x