Teacher keeps 100 pencils in a jar. there are 16 more sharp pencils than dull pencil. how many pencils are dull and how many pencils are sharp

42 dull pencils

58 sharp pencils

Step-by-step explanation:

Dull pencils = x

Sharp pencils = x + 16

Therefore, the total is:

x + (x + 16) = 100

Combine like terms:

2x + 16 = 100

Subtract 16 from both sides:

2x = 84

Divide both sides by 2:

x = 42

Recall that x represents dull pencils, so there are 42 dull pencils. Also recall that x + 16 represents sharp pencils, so there are 42 + 16 = 58 sharp pencils.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

answer

step-by-step explanation: