Robbie was given $80 to spend at the Fair. His admission to the park costs $15.50 and each ride cost $5. He anticipates the cost of food at the fair will be $25. What is the maximum number of rides he can take at the Fair?

the maximum number of rides he can take at the Fair is 7.

Step-by-step explanation:

Let x represent the number of rides that he wants to take at the Fair.

His admission to the park costs $15.50 and each ride cost $5. This means that the cost of x rides would be expressed as

15.5 + 5x

He anticipates the cost of food at the Fair will be $25. This means that the expression for the total amount that he would spend is

15.5 + 5x + 25

If Robbie was given $80 to spend at the Fair, it means that

15.5 + 5x + 25 = 80

5x + 40.5 = 80

5x = 80 - 40.5 =

5x = 39.5

x = 39.5/5

x = 7.9

Since the number of rides cannot be a fraction, then the maximum number of rides he can take at the Fair is 7

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