After crossing the delaware on christmas night, 1776, washington and his troops were victorious in which two battles?

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explanation:

the american entry into world war i came in april 1917, after more than two and a half years of efforts by president woodrow wilson to keep the united states out of the war.

apart from an anglophile element urging early support for the british, american public opinion reflected that of the president: the sentiment for neutrality was particularly strong among irish americans, german americans, and scandinavian americans, as well as among church leaders and among women in general. on the other hand, even before world war i had broken out, american opinion had been more negative toward germany than toward any other country in europe. over time, especially after reports of atrocities in belgium in 1914 and following the sinking of the passenger liner rms lusitania in 1915, american citizens increasingly came to see germany as the aggressor in europe.

wilson, as president, made virtually all the key decisions over foreign policy. while the country was at peace american banks made huge loans to britain and france, which were used mainly to buy munitions, raw materials, and food from across the atlantic. until 1917, wilson made minimal preparations for a land war and kept the united states army on a small peacetime footing, despite increasing demands for enhanced preparedness. he did, however, expand the united states navy.

in 1917, with russia experiencing political upheaval, and with britain and france low on credit, germany appeared to have the upper hand in europe, while the ottoman empire, germany's ally, held on to its territory in modern-day iraq, syria and israel. at this point germany decided to resume unrestricted submarine warfare. its goal was to starve britain into surrender, although it realized that this would almost certainly bring the united states into the war. germany also made a secret offer to mexico regain territories lost in the mexican–american war in an encoded telegram known as the zimmerman telegram, which was intercepted by british intelligence. publication of that communique outraged americans just as german u-boats started sinking american merchant ships in the north atlantic. wilson then asked congress for "a war to end all wars" that would "make the world safe for democracy", and congress voted to declare war on germany on april 6, 1917.

on december 7, 1917, the u.s. declared war on austria-hungary.

u.s. troops began arriving on the western front in large numbers in 1918.

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a hypothesis is an expected answer to a question, usually based on some theory or prior research. hypothesis testing is a method of determining the viability of a hypothesis. let’s use the us presidential election as an example. there are many hypotheses (questions) about how people feel or whom they will vote for. the only way to know the 100% “truth” about the answers to these questions is to ask every single possible voter – something that is impossible, expensive, time consuming etc. instead, we take samples and use statistics to make “best guesses” about the answer to a particular hypothesis. we never know for sure if our conclusion is right at the time we accept/reject it, but these techniques, when used appropriately can get us close to the truth most of the time (which is a lot better than guessing, flipping coins or throwing darts to get answers).

the tricky part about hypothesis testing is that we have to think somewhat backwards about it – we have to test what is known as the “null hypothesis”. as an example, the hypothesis might be “obama is more popular than romney” while the null hypothesis is “there is no difference in popularity between obama and romney”. we focus on the null hypothesis because it tells us exactly what the expected value of our tests should be (obama popularity = romney popularity) and we can collect data and see if it comes out that way (see next section on “significance”). if it does, then we “accept the null hypothesis” and reject our original hypothesis. if the null hypothesis is disproven, we look at the data to see if our original hypothesis holds (obama> romney).