A train travels train travels 288 kilometre at a uniform speed. If the speed had been 4 kilometre per hour more it would have ta

Answer:

The chance of completing the entire package installation in under 12 minutes is 0.1271.

Step-by-step explanation:

We define X as a normal distribution representing the time taken in seconds to install the software. According to the Central Limit Theorem, X is approximately normal, where the mean is 15 and variance is 15, giving a standard deviation of √15 = 3.873.

To find the probability of the total installation lasting less than 12 minutes, which equals 720 seconds, each installation should average under 720/68 = 10.5882 seconds. Thus, we seek the probability that X is less than 10.5882. To do this, we will apply W, the standard deviation value of X, calculated via the formula provided.

Utilizing , we reference the cumulative distribution function of the standard normal variable W, with values found in the attached file.

Given the symmetry of the standard normal distribution density function, we ascertain .

Consequently, the probability that the installation process for the entire package is completed within 12 minutes is 0.1271.

Answer: Zeno consumed 51 hot dogs.

The total number of hot dogs consumed was 676.

Step-by-step explanation:

Al started by eating one hot dog. Bob then outperformed him by devouring three hot dogs. Carl, not wanting to fall behind, ate five hot dogs. This pattern continued, with each participant consuming two hot dogs more than the previous one. This indicates that the quantity of hot dogs eaten by each contestant followed an arithmetic sequence.

The formula for finding the nth term in an arithmetic series is given by

Tn = a + (n - 1)d

Where

a denotes the first term in the sequence.

d signifies the common difference.

n stands for the total terms in the sequence.

<pBased on the details provided,

a = 1 hot dog

d = 3 - 1 = 2 hot dogs

We aim to find how many hot dogs the 26th contestant, T26, consumed. Thus,

T26 = 1 + (26 - 1)2 = 1 + 50

T26 = 51 hot dogs

The formula to calculate the sum of n terms in an arithmetic sequence is

Sn = n/2[2a + (n - 1)d]

Hence, to find the total number of hot dogs consumed by 26 contestants, S26 is calculated as

S26 = 26/2[2 × 1 + (26 - 1)2]

S26 = 13[2 + 50]

S26 = 13 × 52 = 676 hot dogs

<span>cy + 3 = 6d - 2y
cy + 2y = 6d - 3
(c + 2)y = 6d - 3
y = (6d - 3)/(c + 2)</span>

Answer:

Please refer below.

Step-by-step explanation:

Given points:

• S(-3,6),T(0,7),U(1,4),and V(-5,2)

Translation rule:

• (x,y) → (x+7,y-9)

New coordinates after applying the rule:

• S'(4, -3), T'(7, -2), U'(8, -5), V'(2, -7)

For the graph, see attached.

The trapezoid highlighted in blue is STUV while the red trapezoid is S'T'U'V'

The maximum value of P is determined to be 33.

Step-by-step explanation: Start by graphing the constraints represented by the lines

5x + y = 16, which has intercepts at (16, 0) and (0, 16), and

2x + 3y = 22, with intercepts at (11, 0) and (0, ). The solutions to both sets of constraints lie beneath the lines. Solve the equations 5x + y = 16 and 2x + 3y = 22 simultaneously to find their intersection point at (2, 6).

The vertices of the feasible region are determined to be (0, 0), (0, 16), (2, 6), and (11, 0). Evaluate the objective function at each vertex.

At (0, 0), P = 0. At (0, 16), P = 32. At (2, 6), P = 18. Finally, at (11, 0), P = 33. Thus, the maximum P value occurs when x = 11 and y = 0.