Find the unit place of 2^{1!+2!+3!+ .....+10!} + 3^{1!+2!+3!+ .....+10!}+ 4^{1!+2!+3!+ .....+10!}+ 5^{1!+2!+3!+ .....+10!} +........+9^{1!+2!+3!+ .....+10!} ?

The annual rainfall in a city over the past 50 years is its historical average rainfall (HAR). The graph above shows the annual rainfall in City X over a seven-year period. All figures are rounded to the nearest integer.

Is it true that the rounded historical average rainfall (HAR) for City X over the past 50 years is 47 mm or greater?

（1） In the seven-year period in City X, the annual rainfall was greater than the HAR in exactly two of the consecutive years.

（2）In the seven-year period in City X, the annual rainfall was less than the HAR in exactly four of the years.

The chart above displays Forbes data for the distribution of billionaires by country in 2007, when there were 946 billionaires worldwide.

Fill each blank using the drop-down menu to create the most accurate statement on the basis of the information provided.

1. In 2007, the United States had approximately more billionaires than Russia, the United Kingdom, and Germany combined.

2. If the portion labeled “Other” on the chart above represented 21 countries with equal numbers of billionaires, then each of these countries would have approximately billionaires.

Although Victor Turner’s writings have proved fruitful for fields beyond anthropology, his definition of ritual is overly restrictive. Ritual, he says, is “prescribed formal behavior for occasions not given over to technological routine, having reference to beliefs in mystical beings or powers.” “Technological routine” refers to the means by which a social group provides for its material needs. Turner’s differentiating ritual from technology helps us recognize that festivals and celebrations may have little purpose other than play, but it obscures the practical aims, such as making crops grow or healing patients, of other rituals. Further, Turner’s definition implies a necessary relationship between ritual and mystical beliefs. However, not all rituals are religious; some religions have no reference to mystical beings; and individuals may be required only to participate in, not necessarily believe in, a ritual. Turner’s assumption that ritual behavior follows belief thus limits the usefulness of his definition in studying ritual across cultures.

The dimensions of rectangular cake are 11 inches x 7 inches x 6 inches.. The cake is to be wrapped in a sheet of aluminum foil so that the entire surface of the cake is covered. If the aluminum foil must remain in one untorn sheet, which of the following could be the dimensions of the sheet of aluminum foil?

A one foot long rod was marked off in sevenths and also in fourths. If the rod is then cut into separate pieces along the markings, which one of the following gives all the different lengths (in feet) of the pieces thus formed?

A business needs a $240,000 loan for one year and has two options to decide between. Option 1 is a fixed rate loan for the entire amount, with a simple annual interest rate of 5%. Option 2 involves two loans: a fixed rate loan for $190,000, with a simple annual interest rate of 4%, and a second fixed rate loan for $50,000, with a simple annual interest rate of r%. Both options have otherwise identical terms and require payment in full of interest and principal at the end of the year.

In the first column, identify the interest rate r% at which the two options require the same total interest payment. In the second column, identify the interest rate r% at which the annual interest on the $190,000 loan in Option 2 would be exactly twice the annual interest on the $50,000 loan. Make only two selections, one in each column.

Jim and Beth are in a ticket line along with 43 other people, and Jim is ahead of Beth in the line. If there are 20 people behind Jim and 30 people ahead of Beth, how many people in the line are between Beth and Jim?

A set of 7 different integers has a median of 11, range of 10, and average of 12. What is the highest possible value of the greatest integer in the set?

A certain city with population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?