It looks like you've provided a series of statements and answers related to American history, specifically during the Age of Jackson and Westward expansion. Here are some clarifications and corrections based on your text:
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Henry Clay proposed a compromise tariff that eventually eased tensions - Correct, this refers to the Tariff of 1833 which helped ease tensions during the Nullification Crisis.
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Adam supported efforts to promote the growth of business while Jackson supported efforts to help the ordinary man - This likely refers to the differences in economic policy between John Quincy Adams and Andrew Jackson.
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Some settlers loaded their animals and wagons on flatboats to float down rivers - This is an accurate description of how some settlers traveled by river during westward expansion.
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Some felt he had used his powers inappropriately in vetting legislation to recharter the bank - This refers to Andrew Jackson's opposition to the Second Bank of the United States.
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Andrew Jackson opposed the renewal of the bank - Correct, Jackson famously vetoed the recharter of the Second Bank in 1832.
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It ignored the fact that Native American lands were sovereign and not technically part of the United States - This reflects Andrew Jackson’s policies toward Native Americans, particularly the Indian Removal Act.
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John C. Calhoun - Correct, he was a proponent of states' rights and argued for nullification.
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He claimed that states had the right to cancel any federal law deemed unconstitutional - Correct, referring to Calhoun's doctrine of nullification.
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It shows the long distances they were forced to walk to reach their designated lands - This could refer to the Trail of Tears, which forcibly removed Native Americans from their lands.
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Pioneers carried all their possessions on long and dangerous trails - This describes the hardship faced by settlers on trails like the Oregon Trail.
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The slave population roughly doubled as several new slave states were admitted to the union - This refers to the expansion of slavery as the U.S. territory expanded.
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There were more economic opportunities in the west due to the success of the canal system - This reflects the improved transportation facilitating westward migration.
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Abundant natural resources - This highlights one of the attractions of the West for settlers.
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The mass migration of 49ers transformed San Francisco into an economic hub practically overnight - Correct, this refers to the California Gold Rush of 1849.
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The Oregon Trail grew from small beginnings to a major migration route - This describes the development of one of the most significant migration routes during westward expansion.
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Henry Shreve's modified steamboat could carry more without getting stuck on the riverbed - Correct, Shreve made important improvements to steamboat design.
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The United States annexed Texas - Correct, this occurred in 1845.
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It encouraged Texans to plead with the United States for support - Correct, following the Texas Revolution and independence from Mexico.
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It gave the United States territory known as the Mexican cession - Correct, this occurred after the Mexican-American War (1846-1848).
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If the United States had annexed Texas, slave states would almost certainly outnumber free states - This refers to the contentious debate over the balance of slave and free states leading up to the Civil War.
If you're looking for specific insights or if you have any particular questions related to these statements, feel free to ask!