1.
What is pi (3.14159265) to the power of pi?
Correct Answer
A. 36.4621596072
Explanation
When you calculate pi (π), approximately 3.14159265, raised to the power of pi, the result is about 36.4621596072. This operation involves exponential mathematics, where pi is both the base and the exponent. The outcome is an irrational number, which means it cannot be neatly expressed as a fraction and features an endless sequence of non-repeating decimal places, demonstrating the complexity and unique properties of irrational numbers.
2.
What is the square root of pi?
Correct Answer
C. 1.77245385
Explanation
The square root of pi, approximately 3.14159265, is about 1.77245385. This value is obtained by performing the mathematical operation of taking the square root of pi. The square root function finds the number that, when multiplied by itself, gives the original number, pi in this case. Thus, the square root of 3.14159265 results in a value of approximately 1.77245385.
3.
4(1+1)= ________
Correct Answer
D. 8
Explanation
The equation provided is 4(1+1). To solve this, you start by addressing the expression inside the parentheses, which is 1+1, equating to 2. Following this, you multiply 4 by the result, 2, leading to the final solution of 8. This simple arithmetic demonstrates the process of order of operations, where you first resolve operations inside parentheses before proceeding with multiplication.
4.
1.1111111111 x 2.2222222222= _________
Correct Answer
D. 2.4691358
Explanation
When multiplying two decimal numbers, you multiply the numbers as if they were whole numbers and then count the total number of decimal places in the original numbers. In this case, the original numbers have 10 decimal places combined (10 in the first number and 10 in the second number). So, when multiplying 1.1111111111 by 2.2222222222, the product will have 10 decimal places. The correct answer, 2.4691358, has 10 decimal places, which matches the explanation.
5.
If you have a cube with a volume of 73.560059, what is the length of the cube?
Correct Answer
B. 4.19
Explanation
To determine the length of a cube from its volume, you calculate the cube root of the volume. For a cube with a volume of 73.560059, you find the cube root to establish the side length. Taking the cube root of 73.560059 yields approximately 4.19. This figure represents the length of each side of the cube, demonstrating how the dimensions of a cube are interconnected with its volume through the mathematical operation of extracting the cube root.
6.
1x0+1= __________.
Correct Answer
A. 1
Explanation
The process you've described seems to involve some misunderstanding of the operations. In the equation where 1 is multiplied by 0, the result is indeed 0. Multiplication by zero always results in zero, regardless of the other number. If you then add 1 to this result, as stated, the final result would correctly be 1 (0 + 1 = 1). This is a straightforward calculation following basic arithmetic rules.
7.
3/33= __________
Correct Answer
C. 0.0909090909
Explanation
Yes, when dividing 3 by 33, the result is a repeating decimal, specifically 0.0909090909. This decimal repeats the sequence "09" indefinitely, which can be denoted more succinctly in mathematical notation as 0.09. This recurring pattern arises because 3 divided by 33 simplifies to 1/11, and when you perform the division, 1 divided by 11 results in the repeating decimal 0.090909..., illustrating a common outcome in divisions involving numbers where the divisor is a multiple of 11.
8.
2.82842712 i ________ by 2.82842712 i = -8
Correct Answer
A. X
Explanation
The equation 2.82842712i multiplied by 2.82842712i equals -8 can be represented as 2.82842712i^2 = -8. To solve for i, we need to find the square root of -8. The square root of -8 is not a real number, but it can be expressed as 2.82842712i. Therefore, the correct answer is "x," indicating that i is equal to 2.82842712.
9.
100+200+300+100+150x0+50+200+50 =?
Correct Answer
C. 1000
Explanation
In your explanation of solving the equation, you correctly summed the numbers sequentially: 100, 200, 300, 100, 0, 50, 200, and 50. Adding these numbers together indeed results in a total of 1000. Thus, the correct answer to the equation, based on the sum of these values, is 1000. This straightforward addition confirms the final total as you calculated.
10.
(-10)x(-10)=?
Correct Answer
C. 100
Explanation
When you multiply two negative numbers together, the result is always positive. In your example, multiplying −10−10 by −10−10 indeed equals 100100. This rule stems from the mathematical principle that the product of two negatives becomes a positive, which applies regardless of the magnitude of the numbers involved.