At the warm-up event for Oscar’s All Star Hot Dog Eating Contest, Al ate one hot dog. Bob then showed him up by eating three hot

Response:

When combining two fractions that each exceeds 1/2, their sum will invariably exceed 1.

Detailed breakdown: 1/2 + 1/2 = 1    

Since both fractions exceed this amount, it is evident that the sum must as well.

Examples: 2/3+3/4= 1 5/12        4/6+6/9= 1 1/3

Hope this adds clarity

Solution Procedure

Considering the spool as a cylindrical shape, and calculating the circumference based on the area cited, we establish the connection between circumference and area as follows:

... C = 2√(πA)

To find ten times this circumference, we calculate:

... 10C = 20√(π·20 cm²) = 40√(5π) cm ≈ 159 cm

Derivation of Formulas

The standard formulas for circumference and area are:

... C = 2πr

... A = πr²

Multiplying the area formula by π and extracting the square root yields:

... πA = (πr)²

... √(πA) = πr

Doubling this value results in the circumference formula:

... C = 2√(πA) = 2πr

Assume that the number of overdue days for the library book is X, and the total fine is Y.

Liability charges a fee of $0.30 per day for lateness,

Thus, for one day late, the fee equals: 1 * $0.30

For X days late, the fee becomes: X * $0.30.

The total fee Y corresponds to being X days late, so: Y = 0.30 * X.

Next, we'll verify which possible answers satisfy the equation Y = 0.30 * X.

Options one (-3, -0.9) and two (-2.5, -0.75) are invalid since the number of late days cannot be negative, and these give negative values for X.

Option three (4.5, 1.35) is also incorrect because the library charges per whole day; 4.5 days is not an integer, so they would charge 4 or 5 days, not 4.5.

Option four (8, 2.40) matches the equation perfectly:

Y = 0.30 * X

2.40 = 0.30 * 8

2.40 = 2.40.

Therefore, the only correct answer is option four (8, 2.40).

Answer:

a. 0.82%

b. 71.11%

c. 0.564 micrometer

Step-by-step explanation:

To find the z value for each measurement, we must calculate and determine the percentage they correspond to, and the difference will give us the percentage between those two statistics.

The equation for z is:

z = (x - m) / (sd)

Here, x is the value being evaluated, m denotes the mean, and sd represents the standard deviation.

a.

For 0.62 copies, we calculate:

z = (0.62 - 0.5) / (0.05)

z = 2.4

This translates to 0.9918.

Therefore, p (x > 0.62) = 1 - 0.9918

p (x > 0.62) =  0.0082 = 0.82%

b.

For 0.47 copies, we have:

z = (0.47 - 0.5) / (0.05)

z = -0.6, which equates to 0.2742.

For 0.63 copies:

z = (0.63 - 0.5) / (0.05)

z = -2.6, which yields 0.9953.

Hence, p (0.47 > x > 0.63) = 0.9953 - 0.2742

p (0.47 > x > 0.63) = 0.7211 = 72.11 %

c.

For x copies, we find:

p = 0.9 corresponds to z = 1.28.

Thus, 1.28 = (x - 0.5) / (0.05)

From which we derive:

x = 1.28*0.05 + 0.5

x = 0.564 micrometer

Answer:

  2.5 hours

Step-by-step explanation:

Distance equals speed multiplied by time. For constant distance, time varies inversely with speed. When traveling at 60/50 = 6/5 times the original speed, the return journey takes 5/6 of the initial duration:

  (5/6)(3 hours) = 2.5 hours... return trip duration