Answer:
Step-by-step explanation:
Data provided in the question:
Number of cups of tea offered = 3
Number of cups marked = 9
Number of cups tasted by each = 4
Now,
The probability that a contestant does not taste all of the samples
= contestant tastes only 2 samples of tea
= 
C₆⁴ = number of ways to choose 4 cups out of 6 cups of two samples
C₃² = number of ways to choose which 2 samples will be tasted
[ as 2 samples × 3 cups each = 6 cups ]
C₉⁴ = Number of ways to choose 4 cups out of 9
=
Hence,
the correct answer is option (B) 5/14
Y= -2X
Y= -2•3
Y= -6
X=3
Y= -2X
Y= -2•(-3)
Y=6
X= -3
Answer is y= -2X
Answer:
B
Step-by-step explanation:
I would use the Pythagorean theorem to solve distances between 2 points, and this case is no exception.
We need to find the positive difference in their x coordinates and y coordinates.
The difference in x coordinates: 7
The difference in y coordinates: 8
Now we can use the Pythagorean theorem:
7^2+8^2 = x^2
49+64 = x^2
113 = x^2
x = sqrt(113)
Therefore, the answer is B.
A) I would make the positive integer x and then form an equation.
x + 30 = x^2 - 12
x + 42 = x^2
0 = x^2 - x - 42 this can be factorised
(x - 7) ( x + 6) Therefore x = 7 or x = -6
Since the question asks for a positive integer the answer is 7.
B) two positive numbers x and y.
X - y = 3
x^2 + y^2 = 117
Use these simultaneous equations to figure out each number.
Rearrange the first equation
x = y + 3
Then substitute it into the second equation.
(y+3)^2 + y^2 = 117
y^2 + 6y + 9 + y^2 = 117
2y^2 + 6y - 108 = 0
then factorise this.
(2y - 12) (y + 9)
This means that y = 6 or y = -9 but it’s 6 because that’s the only positive number.
Use y to find x
x = y + 3
x = 6 + 3
x = 9
So the answers are x = 9 and y = 6.
It's 4. The factors of 12 are: 1,2,3,4,6,12. The factors of 20 are: 1,2,4,5,10,20.
