answer:The proposition is a universal proposition. According to the rule that the negation of a universal proposition is a particular proposition, the negation of the proposition is: There exists xinmathbb{R}, sin x > 1. Therefore, the answer is boxed{A}. By applying the rule that the negation of a universal proposition is a particular proposition, we can reach the conclusion. This problem primarily tests the negation of propositions involving quantifiers. The key to solving this problem is understanding that the negation of a universal proposition is a particular proposition, and vice versa.

answer:1. **Define the centers of edges ( AB ) and ( CD ):** Let ( K ) be the midpoint of edge ( AB ) and ( L ) be the midpoint of edge ( CD ). 2. **Consider a plane ( p ) through ( AB ) and parallel to ( CD ):** Any plane ( p' ) parallel to ( p ) that intersects the segment ( KL ) will intersect the tetrahedron in a parallelogram. This is because the intersection of a plane parallel to ( CD ) with the tetrahedron will always form a parallelogram. 3. **Intersection of plane ( p' ) with the tetrahedron:** The plane ( p' ) intersects the tetrahedron in a parallelogram ( PQRS ) with center on the line ( KL ). This is because ( K ) and ( L ) are midpoints, and any plane parallel to ( CD ) will intersect ( AB ) and ( CD ) in such a way that the resulting figure is a parallelogram. 4. **Plane ( q ) through ( KL ):** Any plane ( q ) through ( KL ) will pass through the center of the parallelogram ( PQRS ) and hence divide it into two equal parts. This is because the center of a parallelogram divides it into two equal areas. 5. **Division of the tetrahedron into two parts ( T ) and ( T' ):** Suppose plane ( q ) divides the tetrahedron into two parts ( T ) and ( T' ). We have established that the area of the intersection of ( p' ) and ( T ) is equal to the area of the intersection of ( p' ) and ( T' ). 6. **Application of Cavalieri's principle:** By Cavalieri's principle, if two solids have equal cross-sectional areas at every height, then they have equal volumes. Since the areas of the intersections of ( p' ) with ( T ) and ( T' ) are equal for every plane ( p' ) parallel to ( p ), it follows that the volumes of ( T ) and ( T' ) are equal. [ boxed{text{Therefore, every plane that contains the line } KL text{ divides the tetrahedron into two parts of equal volume.}} ]

answer:To find out how many red markers Connie has, we can subtract the number of blue markers she has from the total number of markers. Total markers = Red markers + Blue markers 105 = Red markers + 64 Now, we subtract the number of blue markers from the total number of markers to find the number of red markers. Red markers = 105 - 64 Red markers = 41 Connie has boxed{41} red markers.

answer:To find the percentage of the stock, we need to calculate the dividend yield, which is the income received from the investment as a percentage of the total investment. First, let's calculate the actual investment amount after accounting for the brokerage fee. The brokerage fee is 1/4%, which is 0.25% of the investment amount. Brokerage fee = 0.25% of Rs. 8000 Brokerage fee = (0.25/100) * 8000 Brokerage fee = 0.0025 * 8000 Brokerage fee = Rs. 20 Now, let's subtract the brokerage fee from the total investment to get the net investment amount. Net investment amount = Rs. 8000 - Rs. 20 Net investment amount = Rs. 7980 Next, we'll calculate the dividend yield using the income received (Rs. 756) and the net investment amount (Rs. 7980). Dividend yield = (Income / Net investment amount) * 100 Dividend yield = (Rs. 756 / Rs. 7980) * 100 Dividend yield = (756 / 7980) * 100 Dividend yield = 0.09473684210526316 * 100 Dividend yield = 9.473684210526316 Therefore, the percentage of the stock is approximately boxed{9.47%} .