answer:To find the smallest positive value that is both a multiple of 4 and a multiple of 14, we need to find the least common multiple (LCM) of 4 and 14. The prime factorization of 4 is 2^2 and the prime factorization of 14 is 2 cdot 7. The LCM is the product of the highest power of each prime factor. So, the LCM of 4 and 14 is 2^2 cdot 7 = boxed{28}. The answer is: 28

answer:First, we need to convert all measurements to the same unit. Since the brick measurements are given in centimeters, we'll convert the wall measurements to centimeters as well. The wall dimensions in centimeters are: - Length: 8 m = 800 cm - Height: 6 m = 600 cm - Thickness: 2 cm Now, let's calculate the volume of the wall and the volume of a single brick. Volume of the wall = Length x Height x Thickness Volume of the wall = 800 cm x 600 cm x 2 cm Volume of the wall = 960,000 cubic centimeters Volume of a single brick = Length x Width x Height Volume of a single brick = 5 cm x 11 cm x 6 cm Volume of a single brick = 330 cubic centimeters Now, we'll find out how many bricks are needed by dividing the volume of the wall by the volume of a single brick. Number of bricks needed = Volume of the wall / Volume of a single brick Number of bricks needed = 960,000 cm³ / 330 cm³ Number of bricks needed ≈ 2909.09 Since we can't have a fraction of a brick, we'll round up to the nearest whole number. Number of bricks needed = 2910 So, you would need boxed{2910} bricks to build the wall.

answer:1. **Analyze Isosceles Triangles**: Since AB = BC = CD, triangles triangle ABC and triangle BCD are isosceles. - angle BCA = angle BAC = frac{180^circ - 50^circ}{2} = 65^circ. - angle DBC = angle CBD = frac{180^circ - 150^circ}{2} = 15^circ. 2. **Calculate Angles at Diagonal Intersection**: Assuming BD and AC meet at I, use the properties of isosceles triangles and angles around point I: - angle BIA = angle CID = 180^circ - (65^circ + 15^circ) = 100^circ. 3. **Determine angle BAD**: - angle BAD = angle BAI + angle IAD. - Since angle BAI = angle IAD = frac{100^circ}{2} = 50^circ. - Thus, angle BAD = 50^circ + 50^circ = 100^circ. Conclusion: The degree measure of angle BAD is 100^circ. The final answer is boxed{B}.

answer:- Cara has 6 friends including three males (M1, M2, M3) and three females (F1, F2, F3). - At the circular table, the condition stipulates that she must sit between pairs that include at least one female. - Total ways to choose any two friends from six: {6 choose 2} = 15. - Out of these, the male-only combinations we need to exclude are pairs (M1, M2), (M1, M3), and (M2, M3), which totals 3 pairs. - Therefore, Cara can sit between 15 total pairs minus 3 male-only pairs, which gives us 15 - 3 = 12 pairs that satisfy the condition. boxed{12} possible pairs conform to the new condition.