A wholesale distributor of packaged nuts sells two different mixes of peanuts and cashews, mix A and mix B. Each package of mix A nuts contains 8 ounces (oz.) of peanuts and 4 oz. of cashews. Each package of mix B nuts contains 6 oz. of peanuts and 6 oz. of cashews. Let x represent the number of packages of mix A nuts and let y represent the number of packages of mix B nuts. No more than 120 oz. of peanuts and no more than 96 oz. of cashews can be used each day. Which graph represents the numbers of packages of mix A and mix B that can be produced?

step by step explanation: when u removing the parentheses and combined them that would be : x+3y-x-y=2y

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.

vince wrote the sequence below.

1/3, 1, 5/3, 7/

which of the following explains whether the sequence is geometric?

the sequence is geometric because 2/3 was added to each term to get the next term.

the sequence is geometric because 3 was multiplied to each term to get the next term.

the sequence is not geometric because 2/3 was added to each term to get the next term.

the sequence is not geometric because 3 was multiplied to each term to get the next term.

step-by-step explanation: