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question:w many values of x, with 0 degrees less than or equal to x and x less than 360 degrees, satisfy the equation sin x = -0.73?
answer:Since the sine function has a period of 360 degrees, we only need to consider solutions in the interval [0, 360). To find the values of x that satisfy sin x = -0.73, we can use the inverse sine function. Using a calculator, we find that sin^(-1)(-0.73) is approximately -45.32 degrees. Since the sine function is negative in the third and fourth quadrants, we can add 180 degrees to get the solution in the third quadrant: -45.32 + 180 = 134.68 degrees. Similarly, we can subtract -45.32 degrees from 360 to get the solution in the fourth quadrant: 360 - 45.32 = 314.68 degrees. Therefore, there are 2 values of x that satisfy the equation sin x = -0.73 in the given interval, which is the answer. The answer is: 2
question:f point M(2,5) is the midpoint of line segment AB and point A(3,1) is one endpoint, what is the product of the coordinates of point B?
answer:Since M is the midpoint of AB, the coordinates of M are the average of the coordinates of A and B. This gives us the equations: frac{x_1+x_2}{2}=2 and frac{y_1+y_2}{2}=5. Plugging in the coordinates of M and A, we get: frac{3+x_2}{2}=2 and frac{1+y_2}{2}=5. Solving for x_2 and y_2, we find that x_2=1 and y_2=9. Therefore, the product of the coordinates of point B is x_2 cdot y_2=1 cdot 9=boxed{9}. The answer is: 9
question:Luke started working on a 1000-piece jigsaw puzzle. The first day he worked on it, he put together 10% of the pieces. On the second day, he put together another 20% of the remaining pieces from the first day. On the third day, he put together 30% of the remaining pieces from the previous day. How many pieces does he have left to complete after the third day?
answer:On the first day, Luke put together 10% of the 1000-piece puzzle, which is 1000 * 0.10 = 100 pieces. So after the first day, he has 1000 - 100 = 900 pieces left. On the second day, he put together 20% of the remaining 900 pieces, which is 900 * 0.20 = 180 pieces. So after the second day, he has 900 - 180 = 720 pieces left. On the third day, he put together 30% of the remaining 720 pieces, which is 720 * 0.30 = 216 pieces. So after the third day, he has 720 - 216 = 504 pieces left. 504 The answer is: 504
question:a classroom of 81 students, two-thirds are wearing striped shirts while the others are wearing checkered shirts. If there are 19 more students wearing shorts than checkered shirts, how many more students are wearing striped shirts than shorts?
answer:Two-thirds of the students are wearing striped shirts, so there are (2/3) * 81 = 54 students wearing striped shirts. The rest of the students, (1 - 2/3) * 81 = 27 students, are wearing checkered shirts. There are 19 more students wearing shorts than checkered shirts, so there are 27 + 19 = 46 students wearing shorts. Therefore, there are 54 - 46 = 8 more students wearing striped shirts than shorts. 8 The answer is: 8