GK: Math Practice Quiz!

Explanation
A hexagon is a shape with six sides and six angles. In a hexagon, the sum of all interior angles is always equal to 720 degrees. This is because each angle in a regular hexagon measures 120 degrees, and there are six angles in total. Therefore, a hexagon is the shape where its angles add up to 720 degrees.

Explanation
Complementary angles are two angles that add up to 90 degrees. In this case, the two angles measuring 58 degrees and 32 degrees add up to 90 degrees, making them complementary angles.

Explanation
A trapezoid is a shape that has 2 parallel sides and 2 perpendicular sides, with angles adding up to 360 degrees. A cylinder is a three-dimensional shape, not a polygon, so it does not fit the description. A rectangle has 4 right angles, but all four sides are parallel, not just two. A polygon is a general term for any closed shape with straight sides, so it does not necessarily have 2 parallel and 2 perpendicular sides. Therefore, the correct answer is trapezoid.

Explanation
The average weight loss for four men can be calculated by adding up the weight losses of all four men (55 + 36 + 15 + 74 = 180) and then dividing it by the number of men (4). Therefore, the average weight loss is 180 divided by 4, which equals 45.

Explanation
The question asks for the value of g(1/4) when g(x) = x/4. To find this, we substitute x with 1/4 in the equation g(x) = x/4. Therefore, g(1/4) = (1/4)/4 = 1/16. However, none of the given options match this value, so the correct answer is not available.

Explanation
The probability of rolling less than a 4 when tossing a single die is 2 out of 6, or 1/3. This is because there are 3 possible outcomes (1, 2, or 3) out of the 6 total possible outcomes (1, 2, 3, 4, 5, or 6).

Explanation
The question is asking for the number of ways a group of 7 people can choose a committee of 4. This can be calculated using the combination formula, which is nCr = n! / (r! * (n-r)!). In this case, n = 7 and r = 4. Plugging these values into the formula, we get 7! / (4! * (7-4)!) = 35. Therefore, there are 35 ways to choose a committee of 4 from a group of 7.

Explanation
When m is divided by 6, it leaves a remainder of 5. This means that m can be expressed as 6n + 5, where n is an integer. Now, if we multiply 4m by 4, we get 24n + 20. When this expression is divided by 6, the remainder is 2. Therefore, the remainder when 4m is divided by 6 is 2.

Explanation
The equation given is 3x - x = 2x + x + 20. By simplifying both sides of the equation, we get 2x = 20. Dividing both sides by 2, we find that x = 10. However, this contradicts the given answer of -20. Therefore, the given answer is incorrect and the correct answer cannot be determined from the given equation.

Explanation
Since we know that a + b = 40 and a < 15, we can deduce that b must be greater than 25. This is because if a is less than 15, then the sum of a + b cannot be equal to 40 unless b is greater than 25. Therefore, the statement b > 25 must be true.

Explanation
To find the value of x, we subtract 50,505 from both sides of the equation 50,505 + x = 55,555. This gives us x = 5,050.5. Now, to find the value of 50,505 - 10x, we substitute the value of x into the equation. Plugging in x = 5,050.5, we get 50,505 - 10(5,050.5) = 50,505 - 50,505 = 0. Therefore, the answer is 0.

Explanation
To find the sum of the fractions 2/3, 4/5, and 1/2, we need to find a common denominator. The least common multiple of 3, 5, and 2 is 30. So, we can rewrite the fractions with the denominator of 30. 2/3 becomes 20/30, 4/5 becomes 24/30, and 1/2 becomes 15/30. Adding these fractions together gives us 20/30 + 24/30 + 15/30 = 59/30. Therefore, the correct answer is 59/30.

Explanation
Since the question states that the uncle got a ticket for driving 103 km/h, it implies that he was driving over the speed limit. However, the answer choices provided are in miles per hour (MPH). Therefore, to determine the speed in MPH, we convert 103 km/h to MPH. By using the conversion factor of 1 km = 0.621371 MPH, we can calculate that 103 km/h is approximately equal to 64 MPH.

Explanation
To find out how many bags are needed to seed 1 acre, we need to determine the number of square feet in 1 acre. Since 1 acre is equal to 43,560 square feet, we divide this number by the coverage of one bag (720 square feet). The result is approximately 60.5, which means that approximately 60.5 bags are needed to seed 1 acre of land.

Explanation
If two lines have the same slope and do not share any points, they are called parallel lines. Parallel lines never intersect and can be represented by the equation y = mx + b, where m is the slope. In this case, since both lines have a slope of 1/3 and do not intersect, they are parallel.