4) Hiroaki uses the expression \( a + 0.05 a \) to represent an amount increasing by \( 5 \% \) . Allen uses the expression \( 1.05 a \) . Explain why both Hiroaki's and Allen's expression are correct.
The orbital radius of the newly discovered Sarkiston planet around the Sun is \(447\) billion metres. The planet travels (sweeps) an angle of \(112.5\) degrees in a certain period of time. How many millions of kilometres does the planet travel in its orbit?
\( 676 \)
\( 292 \)
\( 878,000 \)
\( 292,000 \)
\( 149,000 \)
\( 51,337 \)
None of the given options are correct
A machine has a three-stage gear drive system. The speed ratio between the driver shaft and the first jackshaft is \( 3 : 1 \) , the speed ratio between the first jackshaft and the second jackshaft is \( 3.5 : 1 \) and the speed ratio between the second jackshaft and the final driven shaft is \( 4 : 1 \) . What is the compound speed ratio?
A. \( 10.51 \)
B. \( 3.51 \)
C. \( 1.10 .5 \)
D. \( 42.1\)
The length of a new rectangular playing field is 2 yards longer than quadruple the width. If the perimeter of the rectangular playing field is 584 yards, what are its dimensions
Heaven and Tara are 96 miles apart, traveling towards each other. If Tara travels 10 mph and Heaven travels 6 mph how long until they meet?