At the city museum, child admission is $6.30 and adult admission is $9.60. On Sunday, twice as many adult tickets as child tickets were sold, for a total sales of $510.00. How many child tickets were sold that day?

20 child tickets were sold that day.

Step-by-step explanation:

Let x represent the number of child tickets that were sold that day.

Let y represent the number of adult tickets that were sold that day.

On Sunday, twice as many adult tickets as child tickets were sold. It means that

y = 2x

At the city museum, child admission is $6.30 and adult admission is $9.60. The total sales for that day was $510.00. It means that

6.3x + 9.6y = 510- - - - - - - - - - - -1

Substituting y = 2x into equation 1, it becomes

6.3x + 9.6 × 2x = 510

6.3x + 19.2x = 510

25.5x = 510

x = 510/25.5

x = 20

y = 2x = 2 × 20

y = 40

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

answer: the answer is 127 degrees