Could you please help me with the following question:
Square root of x^3=8
would I square both of the sides to undo it or would I cube each side?
the answer is 2root2
2/2
Ms.Thomson's class consists of 12 girls and 13 boys. They all put their names in a hat and the teahcer was going to randomly choose two different students to be assistant teachers for the week. What is the probability that it will be a boy and a girl?
To solve the equation: square root of x^3 = 8, you would need to cube both sides.
Here is the step-by-step explanation:
1. Start with the equation: square root of x^3 = 8.
2. To undo the cube root operation on x^3, we need to raise both sides to the power of (1/3), which is equivalent to cubing.
3. Cube both sides of the equation: (square root of x^3) ^ 3 = 8^3.
4. The cube root and cube operation cancel out on the left side, and we are left with x^3 = 8^3.
5. Simplify the equation: x^3 = 512.
6. Take the cube root of both sides to find x: x = cube root of 512.
7. The cube root of 512 is 8.
Thus, the solution to the equation is x = 8.
Now, moving on to the second question:
To find the probability that it will be a boy and a girl when randomly choosing two students, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
Since there are 12 girls and 13 boys, the total number of students is 12 + 13 = 25.
We need to choose two students, so the total number of possible outcomes is given by the combination formula: C(25, 2) = 25! / (2!(25-2)!) = 25! / (2!23!) = (25 * 24) / (2 * 1) = 300.
Number of favorable outcomes:
We need to choose one boy and one girl. The number of ways to choose a boy is 13, and the number of ways to choose a girl is 12.
Therefore, the number of favorable outcomes is given by: 13 * 12 = 156.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes = 156 / 300 = 13 / 25.
So, the probability that it will be a boy and a girl is 13/25 or 0.52 (rounded to two decimal places).