To solve the expression \((-4) \times (75) \times (-34) \div (715)\), we will first handle the multiplication and then the division.
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Multiply \(-4\) by \(75\): \[ (-4) \times (75) = -300 \]
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Now multiply \(-300\) by \(-34\): \[ (-300) \times (-34) = 10200 \] (Since multiplying two negative numbers results in a positive number.)
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Now we will divide \(10200\) by \(715\): \[ 10200 \div 715 \approx 14.25 \]
Since we are looking for a whole number or a simplified fraction in the provided responses, we can express \(10200\) divided by \(715\) in fraction form:
The fraction is: \[ \frac{10200}{715} \]
Now to simplify \(\frac{10200}{715}\):
- Find the greatest common divisor (GCD) of \(10200\) and \(715\).
- It can be simplified to \(\frac{14775}{75} = 14775\).
However, based on standard calculations: \[ 10200 \div 715 = 14.25 \text{ which is not in the options presented.} \]
None of the suggested answers match this result. The integers presented do not simplify correctly. Still, the value is positive since it comes from the multiplication of two negative and one positive numbers.
However, the closest response related to actual simplification (albeit incorrectly stated) may indicate there is confusion in the choice of presented results.
The answer is 14.25, which when checked, none of the provided answer align. The correct answer from the work should be that \(10200\) reduced does not yield a whole number.
As such, correspondence to answer:
- None would map exactly, since all options are incorrect when verifying actual divisions as proposed.
If we consider \(text{14775}\) possible under division and half-measures, my formal response would lead to statement showing inconsistency in answer format which might have entries leading to confuse. The final checked based measure would be thus plain:
Answer: (from plausible reflect on choice) → 14775