The Comfort Coffee Company wants to mix 3030 pounds of their Smooth blend worth $ 5$5 a pound with their Special blend worth $ 7$7 a pound in order to create a new blend of coffee worth $ 5.50$5.50 a pound. How many pounds of the Special blend should be added to the Smooth blend?

10 pounds of Special blend coffee needs to be added to create to new blend of coffee.

Step-by-step explanation:

Given:

Amount of Smooth blend coffee = 30 pounds

Cost of Smooth blend coffee each pound = $5

Cost of Special Blend coffee each pound = $7

Cost of New mix coffee each pound= $5.5

We need to find the Amount Special Blend to be added.

Solution:

Let the Amount Special Blend to be added be 'x'.

Total Cost of Smooth blend coffee will be Amount of Smooth blend coffee multiplied by Cost of Smooth blend coffee each pound.

framing in equation form we get;

Total Cost of Smooth blend coffee =

Now we can say that;

Total Cost of Special Blend coffee is equal to Cost of Special Blend coffee each pound multiplied by the Amount Special Blend to be added.

Total Cost of Special Blend coffee =

Now Total Amount of Coffee to make the mixture is equal to sum of Amount of Smooth blend coffee and Amount Special Blend to be added.

framing in equation form;

Total Amount of Coffee to make the mixture =

Now we can say that;

Cost of New mix coffee each pound will be equal to sum of Total Cost of Special Blend coffee and Total Cost of Smooth blend coffee divided by Total Amount of Coffee to make the mixture.

framing in equation form we get;

By Using Cross multiplication we get;

Applying Distributive property we get;

Combining the like terms we get;

Dividing both side by 1.5 we get;

Hence 10 pounds of Special blend coffee needs to be added to create to new blend of coffee.

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

plants store their excess carbohydrate in the form of starch so that it could be used as energy source later on. the excess carbohydrate is converted into starch in the plastid i.e. chloroplast & this process occurs in the presence of sunlight. it is an insoluble polymer of glucose which gets stored in cell organelles named as amyloplasts. in some plants, starch is also stored in roots and embryos.