A bag containing 15 ounces of mixed nuts contains 40% cashews. Liam adds 45 ounces of mixed nuts containing 60% cashews in the bag. What percent of the mixed nuts in the bag is cashews? A.27
B.33
C.45
D.55

The answer is D. 55%

40% cashews in 15 ounces = 40/100 × 15 = 600/100 = 6 ounces of cashew

60% cashew in 45 ounces = 60/100 × 45 = 2700/100 = 27 ounce of cashew

total weight of the mixed nuts = 15 + 45 = 60 ounces

total weight of cashew = 27 + 6 = 33 ounces

% of cashew in the 60 ounce bag = 33/60 × 100 = 3300/60 = 55%

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

step-by-step explanation: