If p and q vary inversely and p is 29 when q is 16, determine q when p is equal to 116.

q = 4

Step-by-step explanation:

given p and q vary inversely then the equation relating them is

p = ← k is the constant of variation

to find k use the condition p = 29 when q = 16 , then

29 = ( multiply both sides by 16 )

464 = k

p = ← equation of variation

when p = 116 , then

116 = ( multiply both sides by q )

116q = 464 ( divide both sides by 116 )

q = 4

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

The answer is in the image 

The total nom of  code that can be used is equal to 5+3 = 8

The solution is in the following image

The solution is given in the image below

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

30% of 420 are first year students

first year students = (30/100 )*420

=126 students

Student who are not in first year = 420-126

=294 students