What is the probability that a two-digit number selected at random has a tens digit less than its units digit
1 answer:
The probability that a two-digit number selected at random has a tens digit less than its units digit is 0.2667 (4/15).
There are 90 two-digit numbers (99-9). Of these, six numbers are divisible by 15 (15, 30, 45, 60, 75, 90). This is also divisible by 5. Therefore, the preferred case is 30-6 = 24. Therefore, the required probability is 24/90 = 4/15.
The probability of an event can be calculated by simply dividing the number of favorable results by the total number of possible results using a probabilistic expression. Whenever you are uncertain about the outcome of an event, you can talk about the probability of a particular outcome, that is, its potential.
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Answer:
a)
b)
If we want to minimize the cost then we should rent the Acme Truck company.
Step-by-step explanation:
Assuming the following questions.
(a) Find the daily cost of leasing from each company as a function of the number of miles driven and sketch the graph of these functions.
For the Ace truck we know that leases its 10-ft box truck at $20/day and $0.50/mi. So then f(x) representing the daily cost is given by:
Where x represent the number of miles driven
For the Acme Truck we know that leases a similar truck at $15/day and $0.55/mi, so then the g*x( representing daily cost would be given by:
Where x represent the miles driven.
We can see the plot on the figure attached.
(b) Which company should you rent a truck from for 1 day if you plan to drive 70 miles and wish to minimize cost?
If we replace the value x=70 for both functions we got:
If we want to minimize the cost then we should rent the Acme Truck company.
For purely rational functions, the general strategy is to compare the degrees of the numerator and denominator.
A)
because both numerator and denominator have the same degree (2), so their end behaviors are similar enough that the ratio of their coefficients determine the limit at infinity.
More precisely, we can divide through the expression uniformly by <em>x</em> ²,
Then each remaining rational term converges to 0 as <em>x</em> gets arbitrarily large, leaving 2 in the numerator and 7 in the denominator.
B) By the same reasoning,
C) This time, the degree of the denominator exceeds the degree of the numerator, so it grows faster than <em>x</em> - 1. Dividing a number by a larger number makes for a smaller number. This means the limit will be 0:
More precisely,
D) Looks like this limit should read
which is just another case of (A) and (B); the limit would be
That is,
However, in case you meant something else, such as
then the limit would be different:
since the degree of the denominator is larger.
One important detail glossed over here is that
for all real <em>t</em>. But since <em>t</em> is approaching *positive* infinity, we have <em>t</em> > 0, for which |<em>t</em> | = <em>t</em>.
E) Similar to (D) - bear in mind this has the same ambiguity I mentioned above, but in this case the limit's value is unaffected -
Again,
but <em>x</em> ⁴ is non-negative for real <em>x</em>.
F) Also somewhat ambiguous:
or
G) For a regular polynomial (unless you left out a denominator), the leading term determines the end behavior. In other words, for large <em>x</em>, <em>x</em> ⁴ is much larger than <em>x</em> ², so effectively