Joanie runs the concession stand for the school's baseball games. At each game, the best selling items are pretzels and hot dogs

Answer:

Confidence Interval

Lower Limit = $4,233.3

Upper Limit = $4,766.7

With 95% certainty, SoftBus can anticipate that the average profit per customer will fall within the range of $4,233.30 to $4,766.7, based on the provided sample data.

Step-by-step explanation:

The z-score corresponding to 95% is 1.96

             Profit         Mean      Square Root

                           Difference    of MD

P1        $5,000       $500        $250,000

P2         4,500          0              0

P3         4,000       -500         $250,000

Total $13,500                        $500,000

Mean $4,500 ($13,500/3)    $166,667 ($500,000/3)

Standard Deviation = Square root of $166,667 = 408.2

Margin of error = (z-score * standard deviation)/n

= (1.96 * 408.2)/3

= 266.7

= $266.7

Confidence Interval = Sample mean +/- Margin of error

= $4,500 +/- 266.7

Lower Limit = $4,233.3 ($4,500 - $266.7)

Upper Limit = $4,766.7 ($4,500 + $266.7)

34.56%. This is a binomial probability that can efficiently be calculated using the following formula: Here, n signifies the total number of trials (in this case, 4), x denotes the number of "successes" (which is 3), p is the success probability (60% or 0.6), and q indicates the failure rate (1 - p, thus 0.4). Plugging these values into the formula yields the solution: in percentage form, the probability is found to be 34.56%.

Response:

D=4 hours

Detailed explanation:

Answer:

Step-by-step explanation:

Refer to the attached digram.

The track's perimeter consists of the rectangle's perimeter plus the perimeters of the two semicircles.

The perimeter of a rectangle can be expressed as 2(x+r) where:

x is the length

2r represents the rectangle's width, equivalent to the semicircle's diameter.

The perimeter of one semicircle is calculated as 2πr/2, simplifying to πr.

Thus, the total perimeter contributed by the two semicircles is 2πr.

Therefore, the full track perimeter is expressed as 2(x+2r) + 2πr

where r indicates the semicircle's radius.

Expanding this gives us

Perimeter of the track = 2x + 4r + 2πr

which can also be represented as Perimeter of the track = 2(x + 2r + πr)

b) Given P = 2(x + 2r + πr), we need to rearrange the equation to isolate x.

P = 2x + 4r + 2πr

By subtracting 4r and 2πr from both sides, we get P - 4r - 2πr = 2x

Next, we divide each side by 2.

(P - 4r - 2πr) / 2 = 2x

Thus, x = (P - 4r - 2πr) / 2

c) Given

P = 600ft

r = 50ft

x = (600 - 4(50) - 2π(50)) / 2

x = (600 - 200 - 100(3.14)) / 2

x = 400 - 314 / 2

x = 86 / 2

x = 43ft

Therefore, rounding to the nearest foot, the value of x is 43ft