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question:f we count by 3text{'s} starting with 1, the following sequence is obtained: 1, 4, 7, 10, dots. What is the 100^text{th} number in the sequence?
answer:Since the successive terms of the sequence increase by 3, we relate the sequence to nearby multiples of 3 and display the table below. Compare each of the terms of the sequence with the multiple of 3 directly below it. Notice that each term of the sequence is 2 less than the corresponding multiple of 3 directly below it. Since the 100^text{th} multiple of 3 is 300, the corresponding term of the sequence is 300-2=boxed{298}. begin{array}{|c|c|c|c|c|c|c|} hline text{order of terms} & 1 & 2 & 3 & 4 & dots & 100 hline text{terms of sequence} & 1 & 4 & 7 & 10 & dots & ? hline text{multiples of 3} & 3 & 6 & 9 & 12 & dots & (300) hline end{array}
question:w many degrees are in the sum of the measures of the six numbered angles pictured? [asy] draw((3,8)--(10,4)--(1,0)--cycle,linewidth(1)); draw((7,8)--(9,0)--(0,4)--cycle,linewidth(1)); label("1",(3,8),SSE); label("2",(7,8),SSW); label("3",(10,4),2W); label("4",(9,0),NW+NNW); label("5",(1,0),NE+NNE); label("6",(0,4),2E); [/asy]
answer:The angles numbered 1, 3, and 5 are the three interior angles of a triangle, so they sum to 180^circ. Similarly, the angles numbered 2, 4, and 6 are the three interior angles of a triangle, so they also sum to 180^circ. Combining these, the sum of all six angle measures is 180^circ + 180^circ = boxed{360^circ}.
question:Two more than three times B is equal to 20. What is the value of B?
answer:From the problem, we can write the following equation: [3B + 2 = 20.]Simplifying, begin{align*} 3B &= 18 B &= boxed{6}. end{align*}
question:The NASA Space Shuttle transports material to the International Space Station at a cost of 22,!000 per kilogram. What is the number of dollars in the cost of transporting a 250 g control module?
answer:Two hundred fifty grams is frac{1}{4} of a kilogram. Therefore, the cost of transporting a 250 g control module is 22,!000/4=boxed{5500} dollars.