Any locker with a number that is a multiple of 8, 12, and 75 will contain all three animals.
The least common multiple of these three numbers is
and so any multiples of 600 between 1 and 3500 will contain all three animals. These are 600, 1200, 1800, 2400, and 3000.
Why is the LCM 600? You can determine that using the prime factorizations of the three given numbers:
The LCM can be obtained by multiplying as many prime numbers together as are needed to contain the prime factorizations of the three numbers. This is obtained with
(at least three 2s to get the 8; at least one 3 and two of the previous 2s to get 12; and at least two 5s along with the previous 3 to get 75)
The rate in m³/m² is 40m³/m².
1 m³ is literally a cube with sides that are 1 m in length. 1 m = 100 cm, so each side of this cube is 100cm in length. Finding the volume means multiplying length by width by height:
100(100)(100)=1,000,000 cm³ in 1m³.
We know that we have 25,000cm³ of mulch; we divide to find how many cubic meters this is:
1,000,000/25,000 = 40 m³.
This makes the rate 40m³/m².
<h3>
Answer: Choice C) </h3>
This is a more complicated way to write
The range is the set of all possible y outputs of a function. So we use the graph to see what y values are possible. The graph shows that y can be anything smaller than y = 2. We can't actually reach y = 2 itself due to a horizontal asymptote here.
In interval notation, the answer would be with the curved parenthesis to indicate "do not include y = 2 as part of the range".
Answer:B
Step-by-step explanation:
Answer: <em>m = 7</em>
Step-by-step explanation: In this equation, since a -5 is being multiplied by <em>m</em>, in order to get <em>m</em> by itself, we must divide both sides of the equation by -5.
On the left side, our -5's cancel out and we are left with <em>m</em>. On the right side, -35 ÷ -5 gives us 7. So m = 7.
To check our answer, we plug 7 back in for <em>m</em> in the original equation and we get -5 (7) = -35 which is a true statement so we know our answer is correct.
Don't just do this problem in your head. It's extremely important to develop the habit of putting all your steps down on paper or digitally. It will really pay off for you down the line.