Sentence 1: and he was able to count the number of toothpicks just by a mental image unbelievable

Sentence 2: He was able to count objects.
Is this second sentence entailed by the first?

Answer: yes

Sentence 1: Explanations could range from (for example) failures of managing returns actually filed, which are quite susceptible to improvement, to economic cycles that affect business circumstances and that may be less susceptible to change.

Sentence 2: Failures were often a failure to manage returns that were filed.
Is this second sentence entailed by the first?

Answer: yes

Sentence 1: and uh we found it cheaper even during the summer for me to uh take off for half a day since we work a four and a half day work week and come home on these Thursdays that she goes to work at uh eleven and get's off at seven thirty at night

Sentence 2: It was cheaper for me to take time off.
Is this second sentence entailed by the first?

Answer:
yes