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2 years ago

In a race, there are 14 runners. Trophies for the race are awarded to the runners finishing in first through fourth place.

1 answer:

7 0

There are 14 possible runners for the 1st place, then 13 for the 2nd place ( we already have one runner on the first place ) etc.
14 * 13 * 12 * 11 = 24,024
Answer:
The 1st through the 4th place can be determined in 24,024 ways.

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The graph represents the function where electricity usage in kilowatts per hour of a clock radio varies directly with the number

geniusboy [140]

Answer:

Reasonable estimation for constant of variation is 0.25 kWh per day.

Step-by-step explanation:

We are given the following information in the question:

The graph represents the function where electricity usage.

Electricity usage in kilowatts per hour of a clock radio varies directly with the number of days.
The x-axis shows the number of days and usage in kilo-watt per hour is showed on the y-axis.
Some coordinates of the graph are: (0,0), (2,0.5) and (6,1.5)

Formula for constant of variation:

$\displaystyle\frac{y_2-y_1}{x_2-x_1}$

Putting the values from the coordinates (2,0.5) and (6,1.5), we get:

$\displaystyle\frac{1.5-0.5}{6-2} = \frac{1}{4} = 0.25\text{ kilowatt-hours per day}$

Hence, reasonable estimation for constant of variation is 0.25 kWh per day.

7 0

2 years ago

Read 2 more answers

In choice situations of this type, subjects often exhibit the "center stage effect," which is a tendency to choose the item in t

victus00 [196]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The probability that he or she would choose the pair of socks in the center position is $p =\frac{1}{5}$

The correct answer choice is

X has a binomial distribution with parameters n=100 and p=1/5

The mean is $\mu = 20$

The standard deviation is $\sigma=4$

The probability, $P =0.0002$

The correct answer is

The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.

Using the R the probability $Pe = 0.0003$

The probabilities $P \approx Pe$

Step-by-step explanation:

Since the person selects his or her desired pair of socks at random , then the probability that the person would choose the pair of socks in the center position from all the five identical pair is mathematically evaluated as

$p =\frac{1}{5}$

$=0.2$

The mean of this distribution is mathematical represented as

$\mu = np$

substituting the value

$\mu = 100 * 0.2$

$\mu = 20$

The standard deviation is mathematically represented as

$\sigma = \sqrt{np (1-p)}$

substituting the value

$= \sqrt{100 * 0,2 (1-0.2)}$

$\sigma=4$

Applying normal approximation the probability that 34 or more subjects would choose the item in the center if each subject were selecting his or her preferred pair of socks at random would be mathematically represented as

$P=P(X \ge 34 )$

By standardizing the normal approximation we have that

$P(X \ge 34) \approx P(Z \ge z)$

Now z is mathematically evaluated as

$z = \frac{x-\mu}{\sigma }$

Substituting values

$z = \frac{34-20}{4}$

$=3.5$

So using the z table the $P(Z \ge 3.5)$ is 0.0002

The probability P and Pe that 34 or more subject would choose the center pair is very small So

The correct answer is

The experiment supports the center stage effect. If participants were truly picking the socks at random, it would be highly unlikely for 34 or more to choose the center pair.