Fine-tuning language models over slow networks using activation compression with guarantees

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‍Natalia sold clips to 48 of her friends in April, and then she sold half as many clips in May. How many clips did Natalia sell altogether in April and May?

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Recall that a palindrome is a number that reads the same forward and backward. Find the greatest integer less than $1000$ that is a palindrome both when written in base ten and when written in base eight, such as $292 = 444_{\\text{eight}}.$

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Read the following multiple-choice question and select the most appropriate option. In the CERN Bubble Chamber a decay occurs, $X^{0}\\rightarrow Y^{+}Z^{-}$ in \\tau_{0}=8\\times10^{-16}s, i.e. the proper lifetime of X^{0}. What minimum resolution is needed to observe at least 30% of the decays? Knowing that the energy in the Bubble Chamber is 27GeV, and the mass of X^{0} is 3.41GeV.

• A. 2.08*1e-1 m
• B. 2.08*1e-9 m
• C. 2.08*1e-6 m
• D. 2.08*1e-3 m

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Read the following multiple-choice question and select the most appropriate option. Trees most likely change the environment in which they are located by

• A. releasing nitrogen in the soil.
• B. crowding out non-native species.
• C. adding carbon dioxide to the atmosphere.
• D. removing water from the soil and returning it to the atmosphere.

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Among the 900 residents of Aimeville, there are 195 who own a diamond ring, 367 who own a set of golf clubs, and 562 who own a garden spade. In addition, each of the 900 residents owns a bag of candy hearts. There are 437 residents who own exactly two of these things, and 234 residents who own exactly three of these things. Find the number of residents of Aimeville who own all four of these things.

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Alexis is applying for a new job and bought a new set of business clothes to wear to the interview. She went to a department store with a budget of $200 and spent $30 on a button-up shirt, $46 on suit pants, $38 on a suit coat, $11 on socks, and $18 on a belt. She also purchased a pair of shoes, but lost the receipt for them. She has $16 left from her budget. How much did Alexis pay for the shoes?