Let's go through each expression one by one to find which one is equal to [tex]\( 53462 \div 14 \)[/tex].
First, let's evaluate [tex]\( 53462 \div 14 \)[/tex].
The result of dividing [tex]\( 53462 \)[/tex] by [tex]\( 14 \)[/tex] is approximately [tex]\( 3818.714285714286 \)[/tex].
Now, let's evaluate the given expressions step by step:
1. Expression 1: [tex]\( 3810 \times 14 \times 12 \)[/tex]
[tex]\[
3810 \times 14 \times 12 = 3810 \times 168 = 640080
\][/tex]
This value is much larger than [tex]\( 3818.714285714286 \)[/tex], so it is not equal to [tex]\( 53462 \div 14 \)[/tex].
2. Expression 2: [tex]\( 3818 \times 14 + 10 \)[/tex]
[tex]\[
3818 \times 14 + 10 = 53452 + 10 = 53462
\][/tex]
This value exactly matches the numerator [tex]\( 53462 \)[/tex], which gives the result when divided by 14.
3. Expression 3: [tex]\( 3818 \times 14 \times 10 \)[/tex]
[tex]\[
3818 \times 14 \times 10 = 3818 \times 140 = 534520
\][/tex]
This value is also much larger than [tex]\( 3818.714285714286 \)[/tex], so it is not equal to [tex]\( 53462 \div 14 \)[/tex].
4. Expression 4: [tex]\( 3810 \times 14 + 12 \)[/tex]
[tex]\[
3810 \times 14 + 12 = 53340 + 12 = 53352
\][/tex]
This value is smaller than [tex]\( 3818.714285714286 \)[/tex], so it is not equal to [tex]\( 53462 \div 14 \)[/tex].
After evaluating all the given expressions, we find that the second expression, [tex]\( 3818 \times 14 + 10 \)[/tex], correctly equals [tex]\( 53462 \)[/tex].
Thus, the correct expression equal to [tex]\( 53462 \div 14 \)[/tex] is:
[tex]\[ 3818 \times 14 + 10 \][/tex]
