Amachine part consists of a half sphere and a cylinder, as shown in the figure. the total volume of the part is
ti cubic inches.

Aregular pentagon with a perimeter of 21 inches is dilated by a scale factor of 5/3 to create a new pentagon. what is the perimeter of the new pentagon?

Type the correct answer in each box. spell all the words correctly, and use numerals instead of words for numbers. if necessary, use / for the fraction bar(s).

Titus works at a hotel. part of his job is to keep the complimentary pitcher of water at least half full and always with ice. when he starts his shift, the water level shows 4 gallons, or 128 cups of water. as the shift progresses, he records the level of the water every 10 minutes. after 2 hours, he uses a regression calculator to compute an equation for the decrease in water. his equation is w –0.414t + 129.549, where t is the number of minutes and w is the level of water. according to the equation, after about how many minutes would the water level be less than or equal to 64 cups?