I am Pat, Good Legs Lance, and Colorado Bronze are horses in a horse race. Their probabilities of winning the race are as follow

The equation can be expressed as: 12x + by = 185.

Answer: The least amount spent amounts to £12.92 Step-by-step explanation: Given Number of Cartons = 38 A carton costs 45 pence 4 cartons cost £1.56 In order to minimize expenses, one must opt for the cheaper choice. Since there are 100 pence in £1, this means that £1.36 is equivalent to x pence, where x * 1 = 1.36 * 100, leading to x = 136 pence for four cartons. To find the cost of a single carton, divide x by 4; thus, x/4 = 136p/4, resulting in x/4 = 34 pence. This indicates that a carton of juice can be purchased at 34 pence and 45 pence, with 34 pence being the better deal. Therefore, the total expenditure equals 34 * 38, which converts to 1292p and subsequently to £12.92.

Response:

0.5; 0.34458

Detailed explanation:

Given the following:

Mean (m) = 28

Standard deviation, s = 5

To calculate the Z-score:

Z = (x - m) / s

1.) P(x > 28)

Z = (28 - 28) / 5

Z = 0

P(Z > 0) = 0.5 (Z probability calculator)

2.) P(x < 26)

Z = (26 - 28) / 5

Z = -0.4

P(Z > -0.4) = 0.34458 (Z probability calculator)

For this scenario, we start with the function:
 <span>w (x) = - 5 (x-8) (x + 4)
 </span><span>Reorganizing yields:
 </span><span>w (x) = - 5 (x² + 4x - 8x - 32)
 </span><span>w (x) = - 5x² - 20x + 40x + 160
 </span><span>w (x) = - 5x² + 20x + 160
 </span><span>Next, we take the derivative:
 </span><span>w '(x) = - 10x + 20
 </span><span>Setting this to zero and solving for x:
 </span><span>0 = -10x + 20
 </span><span>10x = 20
 </span><span>x = 20/10
 </span><span>x = 2 seconds
 </span><span>Substituting back:
 </span><span>w (2) = - 5 (2-8) (2 + 4)
 </span><span>w (2) = - 5 (-6) (6)
 </span><span>w (2) = 180 meters
 </span>Conclusion:
 The peak height attained by the stone is:
 w (2) = 180 meters