Hard Maths Questions Quiz!

The given question is asking for the product of all the numbers from 1 to 10. This is represented by the factorial notation, which is denoted by an exclamation mark (!). Therefore, 10! means multiplying all the numbers from 1 to 10 together. In this case, 10! equals 3628800.

Let's use variables to represent the unknowns:

Let 'h' be the number of humans

Let 'x' be the number of horses

We can set up two equations based on the given information:

Equation 1 (heads): h + x = 74

Equation 2 (legs): 2h + 4x = 196

Now we can solve for 'h' and 'x'.

Solve Equation 1 for 'h': h = 74 - x

Substitute this value of 'h' into Equation 2: 2(74 - x) + 4x = 196

Simplify and solve for 'x': 148 - 2x + 4x = 196 2x = 48 x = 24

Substitute the value of 'x' back into the equation h = 74 - x: h = 74 - 24 h = 50

Therefore, there were 50 humans and 24 horses.

Antarctica at -40 degrees is the only place in the world where Fahrenheit and Celsius degrees can be equal. This is because -40 degrees Fahrenheit is equal to -40 degrees Celsius. In all other options, the Fahrenheit and Celsius degrees are not equal.

The equation y = log x represents a logarithmic function where the base is implicitly 10. To find the value of x when y = 10, we need to express the equation in exponential form.

Since y = log₁₀x, then 10ʸ = x.

Substituting y = 10, we get 10¹⁰ = x.

The given expression can be simplified as follows: square root of 3 to the square root of 2 power is equal to 3^(sqrt(2)). Similarly, square root of 3 to the negative square root of 2 power is equal to 3^(-sqrt(2)). Therefore, the given expression becomes 3^(sqrt(2)) * 3^(-sqrt(2)), which is equal to 3^(sqrt(2) - sqrt(2)). Since the exponent is zero, any number raised to the power of zero is equal to 1. Hence, the answer is 1.

Two angles are called supplementary if the sum of their measures is equal to 180 degrees. In this question, we are given two angles: one is x-15 degrees and the other is 2x degrees. To find the value of x, we need to set up an equation. The sum of the measures of the two angles is (x-15) + (2x) = 180. Simplifying this equation, we get 3x - 15 = 180. Adding 15 to both sides, we have 3x = 195. Dividing both sides by 3, we find x = 65 degrees. Therefore, the value of x is 65 degrees.

The square root of 2 to the square root of 2 power can be simplified as 2^(√2). Then, raising 2 to the power of √2 is equivalent to taking the square root of 2. Therefore, the square root of 2 to the square root of 2 power is equal to 2.

To simplify the expression, we need to evaluate the square root of 2 to the negative 9 plus 3 power. First, we simplify the exponent by adding -9 and 3, which gives us -6. Then, we take the square root of 2 to the power of -6. The square root of 2 is approximately 1.414, and raising it to the power of -6 gives us a very small number. Therefore, the answer is 1/8, as it is the only option that represents a small fraction.

The given equation represents an infinite geometric series with a common ratio of 1/2. To find the value of y, we can use the formula for the sum of an infinite geometric series: S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio. In this case, a = 1/2x and r = 1/2. Plugging these values into the formula, we get y = (1/2x) / (1 - 1/2) = (1/2x) / (1/2) = (1/2x) * (2/1) = 1/x. Therefore, y = 1/x. Since the answer is given as 1, we can conclude that x must equal 1.