Help with question 3
1 answer:
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Answer:
We can only be certain that <em>a</em> weighs 12.
There are infinitely many possiblities for <em>b</em> and <em>c</em>.
Step-by-step explanation:
We have the equation:
Each variable indicates a weight.
We would like to determine the weights of each variable (if possible).
First, we can rearrange the equation to acquire:
We can combine like terms:
Notice that both sides have 2<em>b</em> and 3<em>c</em>. Therefore, it is possible for us to cancel them since each nullify the other side. So, we will subtract 2<em>b</em> and 3<em>c</em> from both sides. This yields:
Therefore, we can solve for <em>a</em>. Subtract 2<em>a</em> from both sides:
Hence, the weight of <em>a</em> is 12.
Using the newly acquired information, we can go back to our simplified equation:
Since <em>a</em> is 12:
Evaluate:
Simplify:
We can subtract 36 from both sides:
As you can see, this is a true statement.
Since this is a true statement, there are infinitely many possible values for <em>b</em> and <em>c</em>.
Therefore, the only weight we are <em>certain</em> of knowing is weight <em>a</em> weighing 12.
Answer:
Step-by-step explanation:
If you want a solution:
<em>subtract 5 from both sides</em>
<em>multiply both sides by 3</em>
There are
total ways to draw any 6 numbers from the range 1 to 51, regardless of order.
Given 6 selected numbers that match those drawn by the lottery, there are
ways of rearranging them. So the probability of winning 1st prize is
Next, given 6 selected numbers of which 5 match those drawn by the lottery, there are
ways of rearranging those 5 matching numbers. There are 46 remaining numbers that didn't get drawn, so the probability of winning 2nd prize is