LeAnn is purchasing.giftwrap for a box that measures 10 inches long, 6 inches wide, and 6 inches tall. Calculate the total area
1 answer:
You might be interested in
Answer:
= { (4,1) , (3,2) , (2,3) , (1,4) }
Step-by-step explanation:
Let's start writing the sample space for this experiment :
{ (1,1) , (1,2) , (1,3) , (1,4) , (1,5) , (1,6) , (2,1) , (2,2) , (2,3) , (2,4) , (2,5) , (2,6) , (3,1) , (3,2) , (3,3) , (3,4) , (3,5) , (3,6) , (4,1) , (4,2) , (4,3) , (4,4) , (4,5) , (4,6) , (5,1) , (5,2) , (5,3) , (5,4) , (5,5) , (5,6) , (6,1) , (6,2) , (6,3) , (6,4) , (6,5) , (6,6) }
Let's also define the event ⇒
: '' The sum of the two dice is 5 ''
We can describe the event by listing all the favorables cases from ⇒
= { (4,1) , (3,2) , (2,3) , (1,4) }
In order to calculate we are going to divide all the cases favorables to
over the total cases from
. We can do this because all 36 of these possible outcomes from
are equally likely. ⇒
⇒
Finally we are going to define the event ⇒
: '' The number of the first die is exactly 1 more than the number on the second die ''
⇒
= { (2,1) , (3,2) , (4,3) , (5,4) , (6,5) }
Now given two events A and B ⇒
P ( A ∩ B ) =
We define the conditional probability as
with
We need to find therefore we can apply the conditional probability equation :
(I)
We calculate at the beginning of the question. We only need
.
Looking at the sets and
we find that (3,2) is the unique result which is in both sets. Therefore is 1 result over the 36 possible results. ⇒
Replacing both probabilities calculated in (I) :
We find out that
Answer:
Dimensions of the rug = 13 ft × 26 ft
Step-by-step explanation:
Dimensions of the room = 21 ft × 34 ft
Area of the room = 21 × 34 = 714 ft²
Cynthia wants to leave a uniform strip of floor around the rug.
Let the width of the rug = x ft
Then the dimensions of the rug will be = (21- 2x)ft × (34 - 2x)ft
Area of the rug = (21 - 2x)×(34 - 2x) square feet
338 = (21 - 2x)×(34 - 2x)
338 = 714 - 68x - 42x + 4x²
4x² - 110x + 714 - 338 = 0
4x² - 110x + 376 = 0
2x² - 55x + 188 = 0
2x² - 47x - 8x + 188 = 0
x(2x - 47) - 8(x - 47) = 0
(x - 4)(2x - 47) = 0
x = 4,
For x = 23.5 area of the rug will be negative.
Therefore, x = 4 ft will be the width of the rug.
Dimensions of the rug will be 13 ft × 26 ft.