Noah finds an expression for V(x) that gives the volume of an open-top box in cubic inches in terms of the length x in inches of

Answer:

a) The average of the time interval is 45 minutes.

b) There is a 27.78% chance that the time gap between two successive defective light bulbs will lie between 10 and 35 minutes.

c) The standard deviation for the time duration is 25.98 minutes.

d) There is an 11.11% likelihood that the time interval between two successive defective light bulbs will be under 10 minutes.

Step-by-step explanation:

A uniform probability situation occurs when all outcomes have an equal chance of happening.

In this context, we identify a lower and upper limit for the distribution known as 'a' and 'b', respectively.

The likelihood of finding a value X that is less than x is determined by this formula.

The likelihood of obtaining a value X that lies between c and d is expressed as:

The average of the uniform distribution is:

The standard deviation of the uniform distribution can be calculated as:

The uniform distribution covers an interval from 0 to 90 minutes.

This indicates that

a) What is the mean of the time interval?

The mean of the time interval is 45 minutes.

b) What is the probability that the time gap between two consecutive defective light bulbs will be between 10 and 35 minutes?

There is a 27.78% chance that the time interval between two successive defective light bulbs falls between 10 and 35 minutes.

c) What is the standard deviation of the time interval?

The standard deviation of the time interval is 25.98 minutes.

d) What is the probability that the time interval between two consecutive defective light bulbs will be less than 10 minutes?

There is an 11.11% likelihood that the time duration between two consecutive defective light bulbs will be shorter than 10 minutes.

Answer:

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Step-by-step explanation:

Answer:

Part A) = D) 13.33 m/sec

Part B) = A) Deer triumphs by 2.08 seconds

Step-by-step explanation:

For Part A, we know that the White-tailed deer can sprint at 48 kilometers per hour for short durations. The question asks us, How many meters per second does the deer run?

The question hints at this (Keep in mind there are 1,000 meters in a kilometer, 60 seconds in a minute, and 60 minutes in an hour.)

1 km = 1000 meters

48 km = x meters

Cross Multiply

= 1km × x meters = 48km × 1000 meters

x meters = 48km × 1000 meters/1 km

= 48000 meters/ hour

Now we must convert this to meters/ second

60seconds = 1 minute

60 minutes = 1 hour

Therefore, the number of seconds in one hour = 60 × 60

= 3600 seconds

Thus 48000meters/hour converted to meter per seconds

= 48000meters/3600 seconds

= 13.333333333 meters/seconds

Affectively 13.33m/s

Part B

In Part B we are informed that Usain Bolt established a world record of 9.58 seconds for the 100-meter sprint.

The White-tailed deer can sprint at a speed of 48 kilometers per hour for brief spans.

If Mr. Bolt and a white-tailed deer compete in a 100-meter dash at these speeds, who would emerge victorious, and by what margin?

Using our earlier answer,

We find that the deer covers

48,000 meters in 3600 seconds.

Next, we determine how many seconds it requires to complete a 100-meter race

Thus,

48,000 meters = 3600 seconds

100 meters = y seconds

Cross Multiplying gives us

48,000 meters × y seconds = 3600 seconds × 100 meters

y seconds = 3600 seconds × 100 meters/ 48,000 meters

y second = 7.5 seconds

This indicates that the deer can complete a 100-meter dash in 7.5 seconds.

According to the question, we learned that Usain Bolt's record stands at 9.58 seconds for a 100-meter dash.

The time difference between Usain Bolt and the deer = 9.58seconds - 7.5 seconds

= 2.08 seconds

Consequently, the deer wins the race, finishing in 7.5 seconds and winning by 2.08 seconds. Hence, Option A) Deer wins by 2.08 seconds is the accurate choice

The diagram below illustrates the normal distribution curve. The likelihood that his commuting time surpasses 61 minutes is represented by the area under the standard normal curve located to the right of X=61. To determine the z-score, we standardize X=61.

Wang Yong has a debt of $8500 to the bank. Each month, he repaid a certain amount. After a year, his owed amount was reduced to $6460. The monthly payment from Wang Yong is $170.