Find the nth term:
2 answers:
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Answer:
The probability of getting 6's on both cubes is .
The probability that the total score is at least 11 is .
Step-by-step explanation:
Consider the provided information.
A red cube has faces labeled 1 through 6, and a blue cube has faces labeled in the same way.
Part (A) Both cubes show 6’s.
Probability of getting 6 on red cube is
Probability of getting 6 on blue cube is
Thus, the probability of getting 6's on both cubes is:
Hence, the probability of getting 6's on both cubes is .
Part (B) The total score is at least 11.
The possible number of outcomes in which total score is at least 11 is:
Red shows 6 and Blue shows 5.
Blue shows 6 and Red shows 5.
Blue shows 6 and Red shows 6.
Thus, the probability of total score is at least 11.
Hence, the probability that the total score is at least 11 is .
It is given that two vertices of square are (0,0) and (4,2).
Now the problem is that you haven't given that whether these two vertices are adjacent vertices or opposite vertices of the square.
1. By Supposing that these two are adjacent vertices of Square
The third vertex will be at (-4,2) which lies in third quadrant.
Suppose the coordinate of fourth vertex be (x,y).
Mid point of line joining (4,2) and (-4,2) is{ [4+(-4)]/2,(2+2)/2} is (0,2).
Mid point of line joining (x,y) and (0,0) is (x/2,y/2).
Since diagonals of square bisect each other,
∵ x/2=0
⇒x=0
and
y/2=2
⇒y=4
So, The Coordinate of fourth vertex is (0,4).
Now coming back to second condition if these are two opposite vertex of Square.
Let the third coordinate be (a,b).
Length of diagonal=
Now,let side of Square be A.
Then length of Diagonal of square =√2 A
⇒√2 A=2√5
⇒A =√10
As third vertex is (a,b).
Using distance formula
a² + b²=10 -------------(1)
(a-4)²+ (b-2)²=10 --------------(2)
Solving expression (1) and (2), we get
⇒a²+ b²=(a-4)² +(b-2)²
⇒2a + b =5
⇒b=5-2a
Putting the value of b in (1),we get
⇒a² +(5-2a)²=10
⇒a²+25+4a²-20a =10
⇒5a²-20a+15=0
⇒a² - 4a + 3=0
Splitting the middle term,we get
⇒(a-3)(a-1)=0
⇒a=3 ∧ a=1
we get b=5-2×1=3 and b=5-2×3=5-6=-1
So,the other vertex are (1,3) and(3,-1).
Given:
On a map to cities are about 50 mm apart.
Scale is 1 cm equals 15.5 miles.
To find:
The distance between two cities.
Step-by-step explanation:
We have,
1 cm = 15.5 miles
It means
10 mm = 15.5 miles [1 cm = 10 mm]
Now,
10 mm on a map = 15.5 miles
1 mm on a map = miles
= 1.55 miles
50 mm on a map = 50 × 1.55 miles
= 77.5
Therefore, the two cities are 77.5 miles apart.