((0.00042*10^(-8))*15000)/((5000*10^7)*(0.0021*10^14))
AAAaannndd the bot gets it wrong yet again!
((0.00042*10^(-8))*15000)/((5000*10^7)*(0.0021*10^14))
= (6.3*10^-8) / (1.05*10^22)
= 6*10^-30
I apologize for the mistake in my previous response. You are correct, the answer is 6 * 10^-30 after simplifying the expression. Thank you for bringing it to my attention.
In an examination, every student took Accounting or costing or both out of 600 students,55% took Accounting while 72% took costing.
How many candidates took both?
Let's denote the number of students who took accounting as x and the number of students who took costing as y.
From the given information:
- Total number of students who took accounting or costing or both = 600
- 55% took accounting, so x = 0.55(600) = 330
- 72% took costing, so y = 0.72(600) = 432
To find the number of students who took both:
- We know that x + y includes students who took both accounting and costing, so we need to subtract the students who took both to find out y.
- Let's denote the number of students who took both as z. Then we have:
x + y - z = 600
Substituting the values we found earlier:
330 + 432 - z = 600
z = 162
Therefore, 162 students took both accounting and costing.
To solve this expression step-by-step, first let's simplify the numerator:
0.00042 * 10^(-8) = 4.2 * 10^(-11)
Next, let's simplify the denominator:
5000 * 10^7 = 5 * 10^10
0.0021 * 10^14 = 2.1 * 10^11
Now, we can substitute these values back into the expression:
(4.2 * 10^(-11) * 15000) / ((5 * 10^10) * (2.1 * 10^11))
Let's calculate the numerator:
4.2 * 10^(-11) * 15000 = 6.3 * 10^(-6)
Now, let's simplify the denominator:
(5 * 10^10) * (2.1 * 10^11) = 10.5 * 10^21 = 1.05 * 10^22
Finally, we can substitute these values back into the expression:
(6.3 * 10^(-6)) / (1.05 * 10^22)
Dividing both the numerator and the denominator by 10^6:
(6.3 / 10^6) / (1.05 * 10^22)
Simplifying further:
6.3 / 10^6 = 6.3 * 10^(-6)
So, the final answer is:
(6.3 * 10^(-6)) / (1.05 * 10^22)
To solve the given expression ((0.00042*10^(-8))*15000)/((5000*10^7)*(0.0021*10^14)), we can follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication/Division, and Addition/Subtraction.
Step 1: Simplify the exponents first.
In this expression, we have powers of 10. To simplify them, we need to remember the rule that a number raised to a negative power is equal to 1 divided by the number raised to the positive power.
So, let's simplify the exponents:
0.00042 * (10^-8) = 0.00042 * (1/10^8) = 0.00042 / (10^8)
0.0021 * (10^14) = 0.0021 * (10^14/1) = 0.0021 * (1/10^-14) = 0.0021 / (10^-14)
This gives us:
(0.00042 / (10^8)) * 15000 / ((5000 * 10^7) * (0.0021 / (10^-14)))
Step 2: Perform the multiplications and divisions from left to right.
First, let's simplify the numerator:
0.00042 / (10^8) = 0.0000000042
Now, let's simplify the denominator:
0.0021 / (10^-14) = 0.0021 * (10^14) = 21000
This gives us:
(0.0000000042 * 15000) / ((5000 * 10^7) * 21000)
Step 3: Continue evaluating the remaining multiplication and division operations.
0.0000000042 * 15000 = 0.000063
5000 * 10^7 = 50000000000
Let's substitute these values back into the expression:
0.000063 / (50000000000 * 21000)
Step 4: Simplify further by evaluating the next division operation:
(0.000063) / (50000000000 * 21000) ≈ 3.00 * 10^(-22)
So, the final answer, rounded to two decimal places, is approximately 3.00 * 10^(-22).