What is the following profuct? ( sqrt 14 - sqrt 3) ( sqrt 12 + sqrt 7)
1 answer:
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Answer:
.
Step-by-step explanation:
In any triangle, the sum of the lengths of any two sides should be strictly greater than the length of the third side. For example, if the length of the three sides are ,
, and
:
,
, and
.
In this question, the length of the sides are ,
, and
. The length of these sides should satisfty the following inequalities:
,
, and
.
Since , the inequality
is guarenteed to be satisfied.
Simplify to obtain the inequality
.
Similarly, simplify to obtain the inequality
.
Since needs to be a whole number, the greatest
that satisfies
would be
. Similarly, the least
that satisfies
would be
. Thus,
could be any whole number between
and
(inclusive.)
There are a total of distinct whole numbers between
and
(inclusive.) Thus, the number of possible whole number values for
would be
.
Incomplete Question (See Complete Question Below)
A bag contains 10 red marbles and 15 green marbles.If Yuki selects a marble from the bag without looking, what is the probability that she will pull a red marble?
A-1/5
B-2/5
C-1/2
Answer:
The probability of pulling a red marble is
Step-by-step explanation:
Given
Red Marble = 10
Green Marble = 15
Required
The probability of picking a red marble
First, the total number of marble has to be calculated
Total = Red Marble + Green Marble
Total = 10 marbles + 15 marbles
Total = 25 marbles
The probability of an event is often calculated by dividing the number of required outcomes by the number of possible outcomes.
In this case, the probability of pulling a red marble is calculated as follows:
Where P(R) represents probability of pulling a red marble
n(R) represents number of red marbles
n(R) = 10
T represents total number of marbles
T = 25
By substitution,
becomes
Reduce fraction to lowest term by dividing the numerator and denominator by 5
Hence, the probability of pulling a red marble is