Answer:
The probability that a car driver can complete the transaction in less than 5 minutes is 0.4647.
Step-by-step explanation:
Let <em>X</em> = times required by drivers to fill their car's tank and pay.
The average time required by drivers is, <em>β</em> = 8 minutes.
The random variable <em>X</em> is Exponentially distributed with parameter,
.
The probability distribution function of exponential distribution is:

Compute the probability that a car driver can complete the transaction in less than 5 minutes as follows:

Thus, the probability that a car driver can complete the transaction in less than 5 minutes is 0.4647.
Answer:

Step-by-step explanation:
Please refer to the attachment.
By AA Similarity, the two triangles are similar.
Therefore, corresponding parts of them are proportional.
Therefore, we can write the following proportion:

We will solve for x. Cross-multiply:

Distribute:

Subtract 21 from both sides:

Divide both sides by 7. So, the value of x is:

However, that is only the value of x.
The shadow of the tree is (x+3).
Hence, we will need tot add 3 to our value. Therefore, the actual length of the shadow of the tree is approximately:
