A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

1,184,000 in scientific notation is 1.184 x 10⁶

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 65mph \times 5h \)
325 miles

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{5}{100} \) x 9 = \( \frac{5 \times 9}{100} \) = \( \frac{45}{100} \) = 0.45 errors per hour

So, in an average hour, the machine will produce 9 - 0.45 = 8.55 error free parts.

The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 8.55 = 179.6 error free parts were produced yesterday.

The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 have in common.