1. Each letter in VALENTINE is written on a separate piece of paper and put into a bag. You randomly choose a piece of paper from the bag. Find the probability of choosing an
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The triangles are similar. what is the value of x? show your work.

Ernest is purchasing a $175,000 home with a 30-year mortgage. he will make a $15,000 down payment. use the table below to find his monthly pmi payment.

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e. g. 98.76543).