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[] weeks, where "[ ]" denote the greatest integer function.

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You can buy 47 $0.42-stamps, and you still have $0.26 change...

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From the (circular) arc length formula, , use it to solve for :
radians. In degrees, degrees.

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If you're asking for his EXPECTED EARNINGS, then it is computed as follows:
His chance of winning the grand prize is 1/1000. His earning then would be 500 - 2 = $498.
His chance of winning $100 is 2/1000, and his earning then would be 100 - 2 = $98.
His chance of losing (or not winning any) is 997/1000. He stands to lose -$2 in that case.
His expected earnings is then . Thus he stands to lose $1.30 on the average.

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Are the lines supposed to be parallel or perpendicular?

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, where s is the length of a side of the equilateral triangle.

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Okay...

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If the 2 dice are rolled once, then the probability is . If rolled n times, .

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8 floors, 4 passengers. I will assume that the passengers begin at the first floor all going up, and any passenger gets off BEGINNING at the 2nd floor only (no one gets off at the 1st floor!) We have to find the number of all ordered listings of four numbers out of seven, e.g., 2<3<7<8, 3<6<7<8, 4<5<6<8, etc. That can be done in 7C4 ways. The total numbers of ways 4 passengers can get off at 7 floors (starting at the 2nd!) is . Therefore the probability is .

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. The expression is undefined for y = -5/8 only.

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For ,,, the LCM is .

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20,000*(0.80) + 0.*(0.15) + (-5,000)*(0.05) = 15,750.

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Area would be (To 3 decimal places.)

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Center is (1,0), while radius is 6 (the square-root of 36!).

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. Domain is the interval [ , )

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Determine the theoretical probability of the event that an applicant had a Math SAT in the range 500 - 599 or was admitted. (Round your answer to the nearest .01).
Math SAT
200-399 400-499 500-599 600-699 700-800 Total
Admitted 9 210 1124 2882 5309 9534
Not Admitted 687 3512 8689 12230 5150 30268
Total Applicants 696 3722 9813 15112 10459 39802
P(E) = 1
---------------------------------------------------------------------------------
N(500 - 599 or admitted) = N(500 - 599) + N(admitted) - N(500 - 599 and admitted)
= 9813 + 9534 - 1124 = 18223. Thus P(500 - 599 or admitted) = 18223/39802 = 0.46.

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a. The sample space : {{n,d,q}, {n,d,f}, {n,q,f}, {d,q,f}}, there are four sample points. Note that for each sample point order doesn't matter.
b. 3/4. {{n,d,f}, {n,q,f}, {d,q,f}}
c. 3/4. {{n,d,f}, {n,q,f}, {d,q,f}}

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It means whenever you multiply a non-zero number with its reciprocal, the product is always 1. For example, , , , etc.

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square inches.

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Use the formula . Since is unknown, then , so radians.

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let x = least valued odd integer in the list. Then
x+x+2+x+4+x+6 = 8;
4x + 12 = 8;
4x = -4;
x = -1.
Therefore the four consecutive odd integers are -1, 1, 3, 5.

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If , then E(X + 5) = E(X) + 5 = 80+5 = 85.

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(3x-1)(x+3)=.

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;
;
(x -4)(x - 9) = 0;
x = 4, 9.

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Absolute values are always NON-NEGATIVE, not only positive. The very fact that the absolute value expression is non-negative means that FOR ANY x VALUE you plug in, the inequality is always TRUE, and so the solution set cannot be empty, on the contrary, is the set of all real numbers. Now you know, dear student!

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Use the t-distribution for small samples.
The test statistic is . Then .
Degree of freedom is 22- 2 = 20.
For 20 df and one-tailed test, critical value is -1.725. Since -1.725 > -1.98, r is significant at the 5% level.