Grades 7-8 Video Solutions 2013-Grades 7-8 Video Solutions 2013

Video Transcription

Video Summary

The transcript provides solutions to a sequence of mathematical problems, showcasing a variety of problem-solving techniques. Here's a concise summary of key points and solutions:<br /><br />1. The area of the shaded part of an equilateral triangle with total area nine, divided into nine equal parts, is six.<br /><br />2. The expression \( \frac{3333}{101} + \frac{6666}{303} \) simplifies to 55.<br /><br />3. The mass of salt in 1000 kg of seawater with a ratio of 7:193 to freshwater is 35 kg.<br /><br />4. The minimal number of cells remaining after Ann cuts out shapes from a grid is four.<br /><br />5. The smallest product of digits equal to 24 is 38, leading to a sum of 11.<br /><br />6. At least six balls must be taken from a bag to guarantee two of the same color.<br /><br />7. Four candles will still be alight after 55 minutes, given lighting and burn rates.<br /><br />8. Five families' average number of children cannot be 2.5.<br /><br />9. Lisa completes four circuits before Mark catches up with her on a circular track.<br /><br />10. For \( x \times y = 14 \), \( y \times z = 10 \), \( z \times x = 35 \), the sum \( x+y+z \) is 14.<br /><br />11. Karina can fit a 3x1 ship in only eight possible ways on her battleship grid.<br /><br />12. Delta, an angle in a quadrilateral with given angles, is 130 degrees.<br /><br />13. A trapezoid with integer sides and perimeter five has smallest angles of 60 degrees.<br /><br />14. Among several nets, only one cannot form a cube upon folding.<br /><br />15. Among consecutive integers, 45% cannot represent the percentage of odd numbers.<br /><br />16. Point A yields the least value for the coordinate ratio in a specified rectangle.<br /><br />17. For integers 1 to 2013, the relationship in number of squares and cubes is such that \( s = 2013^3 \).<br /><br />18. For a 6x10 grid, 32 cells are not intersected by diagonals.<br /><br />19. Among a group of children, Betty is the youngest based on birth dates provided.<br /><br />20. John, looking at his cube-constructed building, sees 4-3-3-2 in blocks.<br /><br />21. The area of quadrilateral KLMN with given dimensions is 84 cm².<br /><br />Each solution tackles a distinct type of mathematical or logical puzzle, demonstrating thorough analytical skills and step-by-step reasoning to reach conclusions.

Meta Tag

Level 7&8

Year 2013

Keywords

mathematical problems

problem-solving techniques

equilateral triangle

expression simplification

seawater salt mass

grid shapes

product of digits

circular track

battleship grid

quadrilateral angles