A factor of 30 is chosen at random. What is the probability, as a decimal, that it is a 2-digit number?
The positive whole-number factors of 30 are:
1, 2, 3, 5, 6, 10, 15 and 30.
So, there are 8 of them. Of these, 3 have two digits. Writing each factor on a slip of paper, then putting the slips into a hat, and finally choosing one without looking, get that
P(factor of 30 chosen is a 2-digit number) = number of two-digit factors ÷ number of factors
=38=3×.125=.375
In linear models there is a constant additve rate of change. For example, in the equation y = mx + b, m is the constanta additivie rate of change.
In exponential models there is a constant multiplicative rate of change.
The function of the graph seems of the exponential type, so we can expect a constant multiplicative exponential rate.
We can test that using several pair of points.
The multiplicative rate of change is calcualted in this way:
[f(a) / f(b) ] / (a - b)
Use the points given in the graph: (2, 12.5) , (1, 5) , (0, 2) , (-1, 0.8)
[12.5 / 5] / (2 - 1) = 2.5
[5 / 2] / (1 - 0) = 2.5
[2 / 0.8] / (0 - (-1) ) = 2.5
Then, do doubt, the answer is 2.5
0.41567 is:
... rational because it can be expressed as a fraction (e.g., 41567/100000)
... not irrational for the same reason
... not whole (obviously)
... not integer (obviously)
1) 3•5(64-65)
2) 3•5(-1)
3) 3•(-5)
4) -15
Answer:
Since the square root of 25 = 5 and the square root of 36 is 6 it is known that the square root of 33 is between 5 and 6.
Step-by-step explanation:
The key to this is to think about perfect squares, specifically the ones closest to 33. These are 25 and 36, which have square roots of 5 and 6 respectively. Because 33 is between these numbers, you know for certain that its square root is between <em>their</em> square roots too.
Let me know if you need a more in-depth explanation!
