Answer:
see below
Step-by-step explanation:
The problem statement tells you the ratio of force to area is the same for all pairs. This means, for example, ...
3750/250 = 5625/x = y/420
Simplifying, this becomes the two equations ...
15 = 5625/x ⇒ x = 5625/15 = 375
15 = y/420 ⇒ y = 420·15 = 6300
The values of x and y are (x, y) = (375, 6300). . . . . matches choice C
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4.
Gradient is the slope
So the slope of the line joining the points A(3,-5) and B(6,k) is 4
Slope of line joining two points =
A(3,-5) and B(6,k) are (x1,y1) and (x2,y2)
slope =
slope =
We know slope =4
Cross multiply and solve for k
k + 5 = 12
k = 7
The value of k = 7
Answer:
<u>Step-by-step explanation:</u>
The probability of Event B given Event A = the intersection of Event A and B divided by the probability of Event A. (see below for the symbols)
P(A) = (1, 6), (1, 5), (1, 4), (1, 3), (1, 2), (1, 1)
(2, 6), (2, 5), (2, 4), (2, 3), (2, 2), (2, 1)
(3, 6), (3, 5), (3, 4), (3, 3), (3, 2), (3, 1)
(4, 5), (4, 4), (4, 3), (4, 2), (4, 1)
(5, 4), (5, 3), (5, 2), (5, 1)
(6, 3), (6, 2), (6, 1)
= 30
P(B) = (1, 2), (2, 1) sum = 3
(1, 5), (2, 4), (3, 3), (4, 2), (5, 1) sum = 6
(3, 6), (4, 5), (5, 4), (5, 4), (6, 3) sum = 9
(6, 6) sum = 12
= 12
P(A ∩ B) = (1, 2), (2, 1)
(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)
(3, 6), (4, 5), (5, 4), (5, 4), (6, 3)
= 11