Walnuts, peanuts, and chocolate chips are mixed in a ratio of 7:2:5. What is the weight of the mixture if 2.5 lbs. of chocolate chips were used for making it?

The weight of the misture if of 7 lbs.

Step-by-step explanation:

The total misture is T.

The ratio means that:

Walnuts are responsible for 7/(7+2+5) = 7/14 = 1/2 of the weight.

Peanuts are responsible for 2/(7+2+5) = 2/14 = 1/7 of the weight.

Chocolate chips are responsible for 5/(7+2+5) = 5/14 of the weight.

2.5 lbs. of chocolate chips were used for making it:

This means that:

Simplifying by 5

The weight of the misture if of 7 lbs.

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

well your weight will go up if you are not going to burn the calories/ carbs

step-by-step explanation: