Advanced Mathematical Concepts and Problem Solving Quiz

The correct answer is obtained by calculating sin(240 degrees) * tan(45 degrees), which results in -√3/2. Incorrect answers are 0 (as tan(45 degrees) is not equal to 0), -1 (as the value is positive) and 1 (as the value is negative).

The cube root of 18 is 2√3 and the cube root of 12 is 2√2. Multiplying them gives us 2√3 * 2√2 = 4√6 which simplifies to 6.

In a convex heptagon, there are 7 sides. From a single vertex, diagonals can be drawn to all other vertices except for the adjacent vertices. This results in 4 diagonals being possible.

Specific gravity is calculated by dividing the density of the object by the density of water, which is 1 g/cm^3. In this case, since the object is 800 grams and has a volume of 800 cm^3 (5 x 40 x 4), the specific gravity is 800/800 = 1.

To find i to the 5687th power, we first need to simplify the power using the fact that i has a periodic cycle of powers. Since the cycle of powers for i is: i, -1, -i, 1; we can see that i to the 5687th power corresponds to -i in this cycle, making the correct answer -i.

To find the maximum area of a rectangle, it must be a square since squares have the maximum area for a given perimeter. The formula for calculating the area of a square is side * side. Given the perimeter of 32 feet, each side of the square would be 8 feet (32 feet / 4 sides). Therefore, the maximum area would be 8 feet * 8 feet = 64 feet squared.

To find the slope and y-intercept of the given equation, we need to rearrange it in the form y=mx+b, where m is the slope and b is the y-intercept. By doing so, we get the correct values of Slope=-5/3 and Y-intercept=19/3.

To evaluate x^-1 + y^-1 with x=7 and y=2, we have 1/7 + 1/2 = 9/14.

When reflecting a point over the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. Therefore, the correct reflected image of (-5,9) over the x-axis is (-5,-9).

The sum of the first n counting numbers is calculated using the formula: n * (n + 1) / 2. So, for the first 18 counting numbers, the sum would be 18 * (18 + 1) / 2 = 171.

In a circle, the diameter is a chord that passes through the center of the circle and is the longest possible chord that can be drawn.

To find the minimum value of the quadratic function f(x), we can use the formula x = -b/2a. Plugging in a = 1, b = 7, we get x = -7/2 which gives the x-value where the function reaches its minimum value.

The radius of the circle is the distance from the center (3,4) to the x-axis, which is 4 units. Since the diameter of a circle is twice the radius, the diameter in this case would be 2 * 4 = 8 units.

To find the number of people who owned both cars and trucks, we can add the number of people who owned cars (18) and the number of people who owned trucks (9), which gives us 27. However, since the total number of people surveyed is 25, we need to subtract the number of people who owned neither cars nor trucks (7) from the total, which gives us 18. Therefore, the correct answer is 9.

To find the numbers not in the domain of the given function, we need to consider the values of x that would result in division by zero. In this case, x = 9 would make the denominator zero, leading to undefined division. Therefore, x = 9 is not in the domain of f(x) = 9x^2/(9-x).

Out of the four conic sections (circle, ellipse, parabola, hyperbola), the hyperbola is the only one that forms a discontinuous curve when graphed over the set of real numbers.

To find out how many papers are in the stack, first convert the height of the stack from yards to inches. 1 yard = 36 inches. Then, divide the total height by the thickness of each paper (1/64 inch) to get the number of papers in the stack.

To find the y-intercepts of the ellipse, we set x = 0 in the equation x squared over 8 plus y squared over 16 equals 1. This simplifies to y squared over 16 equals 1, which further simplifies to y squared equals 16. Taking the square root, we get y = ±4, so the y-intercepts are -4 and 4 or as ordered pairs (0,-4) and (0,4).

When the clock turns the hour, the angle between the hands is 30 degrees. Two hours later, the angle becomes 90 degrees after tripling. This happens at 3 o'clock.

To solve this problem, we first need to find the value of a and b individually using the given equations. From 4 to the power of a equals 1024, we can see that a equals 5. Next, from a to the power of b equals 125, we can deduce that b equals 3. Therefore, the sum of a and b is 8.

To find the value of x where the function reaches its minimum value, use the formula for the x-coordinate of the vertex of a quadratic function, which is -b/2a. For the function f(x) = x^2 + 7x + 13, a = 1 and b = 7. Substituting these values into the formula gives x = -7/2.

The diameter of a circle is twice the length of its radius. Since the circle is tangent to the x-axis, the radius is equal to the y-coordinate of the center, which is 6. Therefore, the diameter is 2 * 6 = 12.

The odds of 9 to 1 for snow means that out of 10 equally likely outcomes, 9 will be snow and 1 will not be snow. Therefore, the probability of it not snowing is 1 out of 10, or 1/10, which is 10%.

Work done is calculated by multiplying the force applied by the distance moved in the direction of the force. In this case, the work done is 30 newtons * 15 meters = 450 newton-meters (or joules) since the force applied is constant.

When expanding (a+b)^5 using the binomial theorem, the coefficients of the terms can be represented by the numbers in the fifth row of Pascal's Triangle. The sum of these coefficients is 32.

In a parabola, the directrix is the horizontal line that is equidistant from the vertex of the parabola and all the points on the parabola.

When dividing numbers in scientific notation, you divide the coefficients and subtract the exponents. In this case, 3.6/6.0 = 0.6 and (10^15) / (10^-3) = 10^(15 - (-3)) = 10^18, resulting in 0.6 times 10^18 which is equivalent to 6.0 times 10^17.

To find the value of y in the equation 3 x squared + 13 x = y when y equals 3, substitute y = 3 into the equation to get 3 x squared + 13 x = 3. Then solve for x which gives x = 3. Substituting x = 3 back into the original equation, we get y = 3(3)^2 + 13(3) = 66.

To calculate the total number of games, we can use the formula n * (n-1), where n represents the number of teams. In this case, we have 11 teams. So, the total number of games = 11 * 10 = 110.

To find the number of people who owned both trucks and cars, we add the number of people who owned trucks (13) and cars (17), then subtract the total number of people surveyed (25) and those who owned neither (3), resulting in 8 people owning both trucks and cars.