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The information has "the necessary degree of confidence about it"

I don't believe that anyone can answer your questions with any degree of confidence.

But computers can give you a greater degree of confidence.

"The President has the highest degree of confidence in him."

You will recognize it and build a degree of confidence in the process.

And I would have done - eventually - he told himself, with a fair degree of confidence.

But people must have that security in order to move from one job to another with a degree of confidence.

"I have a high degree of confidence that we're going to hit it the first time," he says.

Nothing specific about the author's life is known with any degree of confidence.

I've got a solution in which we have a high degree of confidence.