Use the drop-down menus to describe the key aspects of the function f(x) = –x2 – 2x

An upscale resort has built its circular swimming pool around a central area that contains a restaurant. The central area is a r

zzz [12365]

The diagram below illustrates the issue at hand.

Question 1:
The maximum area of the pool equals half the area of the circle.

To calculate the area of the circle: Area = πr², with r being half of the diameter.
Thus, Area of circle = π(60)² = 11309.73355 square feet.

Therefore, the area representing half the circle amounts to 11309.73355/2 = 5654.866... ≈ 5654.87 square feet (rounded to 2 decimal places).

Question b:

To find the pool's area, we take the circle's area and subtract the triangle's area.

The area of the circle is 11309.73 square feet.

For the triangle's area calculation: 1/2 × (60×103.92) = 3117.6 square feet.

The area of the pool thus operates as 11309.73 - 3117.6 = 7922.13 square feet.

Calculating the pool's volume: 7922.13 × 4 = 31688.52 cubic feet.

Note: Information related to the fish tank is unavailable, so the above calculation focuses solely on the entire pool's volume.

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2 months ago

The idle time for taxi drivers in a day are normally distributed with an unknown population mean and standard deviation. If a ra

Svet_ta [12734]

Answer:

$172-2.51\frac{16}{\sqrt{23}}=163.626$

$172+2.51\frac{16}{\sqrt{23}}=180.374$

Hence, in this case, the 98% confidence interval would be (163.626;180.374)

Step-by-step breakdown:

Previous concepts

A confidence interval represents a range that is likely to encompass a population value within a specific confidence level, typically expressed as a percentage whereby a population mean falls between an upper and lower limit.

The margin of errorindicates the span of values surrounding the sample statistic in a confidence interval.

A normal distributionillustrates a probability distribution that is symmetrical around the mean, signifying that values near the mean occur more frequently than those farther away from it.

$\bar X=172$ denote the sample mean

$\mu$ population mean (the variable of interest)

s=16 signifies the sample standard deviation

n=23 represents the sample size

The solution to the query

The equation for the confidence interval of the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

To determine the critical value $t_{\alpha/2}$ , we first need to calculate the degrees of freedom, which is expressed as:

$df=n-1=23-1=22$

Since the confidence level is 0.98 or 98%, we find the value of $\alpha=0.02$ and $\alpha/2 =0.01$ using tools like Excel or a calculator, where the Excel command would be: "=-T.INV(0.01,22)". This yields $t_{\alpha/2}=2.51$