14. When the teachers were talking one day in the workroom one math teacher said she had 2^7 students in all her classes and the pe teacher said he has 6^3 students in all his classes. How many more students does the pe teacher have than the math?
A.6
B.47
C.88
D.135
C.
15. 64 is equal to which expression?
A.1^64
B.2^32
C.16^4
D.8^2
D
16.Which choice gives the correct order of operations needed to find the value of 39-3(6+4) divided by 3
A.+,x,-,/
B.x,x,+,-
C.-,x,/,+
D./,-,+,x
A
All are right. :-)
To find the answer to these questions, you need to evaluate the given expressions using the concepts of exponents, arithmetic operations, and order of operations. Here's how you can solve each question step by step:
14. To find how many more students the PE teacher has than the math teacher, you need to subtract the number of students the math teacher has from the number of students the PE teacher has.
Math teacher: 2^7 students = 2 * 2 * 2 * 2 * 2 * 2 * 2 = 128 students
PE teacher: 6^3 students = 6 * 6 * 6 = 216 students
Subtracting, the PE teacher has 216 - 128 = 88 more students than the math teacher. Therefore, the correct answer is C. 88.
15. You need to determine which expression is equal to 64.
A. 1^64 = 1. Since 1 raised to any power is always 1, this is incorrect.
B. 2^32 is not equal to 64. This is incorrect.
C. 16^4 = (16 * 16 * 16 * 16) = 65,536. This is not equal to 64, so it is incorrect.
D. 8^2 = 8 * 8 = 64. This expression is equal to 64, so the correct answer is D.
16. The problem requires you to follow the correct order of operations (also known as PEMDAS or BODMAS) to find the value of the expression.
The order of operations is as follows:
1. Parentheses (expressions inside parentheses)
2. Exponents (powers and square roots)
3. Multiplication and Division (left-to-right)
4. Addition and Subtraction (left-to-right)
The expression to evaluate is: 39 - 3(6+4) ÷ 3.
1. First, simplify the expression inside the parentheses: 6 + 4 = 10.
2. Next, perform the multiplication: 3 * 10 = 30.
3. Now, carry out the division: 30 ÷ 3 = 10.
4. Finally, subtract from 39: 39 - 10 = 29.
Therefore, following BODMAS, the correct order of operations is: multiplication, addition, subtraction, division. So the correct answer is A. +, x, -, /.
By following these steps, you can find the correct answers to the given questions.