Answer:
Part a. t = 7.29 years.
Part b. t = 27.73 years.
Part c. p = $3894.00
Step-by-step explanation:
The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.
Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!
Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!
Part c. It is given that A = $5000, r = 2.5%, and t = 10 years. In this part, p is unknown. Therefore 5000 = p*e^(0.025*10). This implies 5000 = p*e^(0.25). Making p the subject gives p = 5000/e^0.25. This means that p = $3894.00(rounded to the nearest 2 decimal places)!!!
Answer:
38%
Step-by-step explanation:
The additional wage compared 12 years of education to 16 years of education is:
Answer:
Probablity of getting six in at most three roll= 0.199.
Step-by-step explanation:
Given: Dice rolled at most 3 times untill a 6 occurs.
First, finding the probablity of getting 6 in a dice if rolled once.
Probablity= 
We know, dice have six side, therefore, total number of event will be 6.
∴ Probablity of getting six in one roll= 
As given, Dice is rolled at most 3 times.
Now, finding the probablity of getting 6 in a dice if rolled 3 times.
∴ Probablity of getting six in three roll= 
⇒ Probablity of getting six in three roll= 
Taking LCD 216
⇒Probablity of getting six in three roll= 
⇒Probablity of getting six in three roll= 
∴Probablity of getting six in three roll=0.199
In this problem there are several vital information's that have been given. Based on them it is possible to find the required answer.It is already mentioned that the amount of bill for the family is $113. Percentage of tips to be given is 19%
Then
The amount of tips given by the family = 113 * (19/100)
= 113 * 0.19
= 21.47
So the family should leave a tips of $21.47. Sometimes it could additionally be required to find the total amount that the family has to pay. In that case it is required to add the amount of tips with the billed amount.
