If we assume the description means y = 7.2x, the rate 7.2 means each increase in x of 1 mile results in an increase in y of 7.2 minutes. That is the rate is 7.2 minutes per mile.

4 0

2 years ago

Suppose the names of the months of the year are placed in a hat and a name is drawn at random. (a) list the sample space for thi

ollegr [7]

(a)

The sample space is a set whose elements are all the possible outcomes for the experiment. Since we will extract one of the months of the years, the sample space is the set composed by all the 12 months:

$\Omega = \{ \text{January},\ \text{February},\ldots,\text{December}\}$

(b)

An event is a subset of the sample space. Events are often defined by their properties. In this example, the event E is the subset of the sample space defined as

$E = \{ x \in \Omega: x \text{ starts with the letter J}\}$

So, we have

$E = \{\text{January},\ \text{June},\ \text{July}\}$

(c)

If all outcomes have equal probability, then the probability of an event is the ratio bewteen its cardinality, and the cardinality of the whole sample space:

$P(E) = \dfrac{n(E)}{n(\Omega)} = \dfrac{3}{12} = \dfrac{1}{4}$

In words, since there are three months beginning with J out of 12 months, we have a probability of 3 over 12 to pick a month starting with J, which simplifies to 1 over 4.

3 0

3 years ago

if you add the digits in a two-digit number and multiply the sum by 7, you get the original number. If you reverse the digits in

ANTONII [103]

Let m the tens digit and n the ones
the Original number is 10m+n
7(m+n) =10m+n
7m+7n=10m+n
6n=3m

Reversing the number 10n+m
10n+m=18+n+m
9n=18
n=2

6n=3m
6(2)=3m
3m=12
m=4
the number is 10m+n=10(4)+2=42

4 0

3 years ago