Answer:
Step-by-step explanation:
Answer:
The principal must be = $8991.88
Step-by-step explanation:
Formula for compound interest is:
Where A is the amount after 't' years.
P is the principal amount
n is the number of times interest is compounded each year.
r is the rate of interest.
Here, we are given that:
Amount, A = $15000
Rate of interest = 13 % compounded quarterly i.e. 4 times every year
Number of times, interest is compounded each year, n = 4
Time, t = 4 years.
To find, Principal P = ?
Putting all the given values in the formula to find P.
So, <em>the principal must be = $8991.88</em>
A plausible guess might be that the sequence is formed by a degree-4* polynomial,
From the given known values of the sequence, we have
Solving the system yields coefficients
so that the n-th term in the sequence might be
Then the next few terms in the sequence could very well be
It would be much easier to confirm this had the given sequence provided just one more term...
* Why degree-4? This rests on the assumption that the higher-order forward differences of eventually form a constant sequence. But we only have enough information to find one term in the sequence of 4th-order differences. Denote the k-th-order forward differences of by . Then
• 1st-order differences:
• 2nd-order differences:
• 3rd-order differences:
• 4th-order differences:
From here I made the assumption that is the constant sequence {15, 15, 15, …}. This implies forms an arithmetic/linear sequence, which implies forms a quadratic sequence, and so on up forming a quartic sequence. Then we can use the method of undetermined coefficients to find it.
Answer:
The area between z = 1.74 and z = 1.25 is of 0.065.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation , the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The area between two values of Z is given by the subtraction of the pvalue of the larger value by the smaller.
The area between z = 1.74 and z = 1.25.
This is the pvalue of z = 1.74 subtracted by the pvalue of z = 1.25.
z = 1.74 has a pvalue of 0.959
z = 1.25 has a pvalue of 0.894
0.959 - 0.894 = 0.065
The area between z = 1.74 and z = 1.25 is of 0.065.