Answer:
5 years
Step-by-step explanation:
In the question we are given;
- Amount invested or principal amount as $5048
- Rate of interest as 4% compounded 12 times per year
- Amount accrued as $6,163.59
We are required to determine the time taken for the money invested to accrue to the given amount;
Using compound interest formula;

where n is the interest period and r is the rate of interest, in this case, 4/12%(0.33%)
Therefore;



introducing logarithms on both sides;

But, 1 year = 12 interest periods
Therefore;
Number of years = 60.61 ÷ 12
= 5.0508
= 5 years
Therefore, it will take 5 years for the invested amount to accrue to $6163.59
Using the normal distribution, the probabilities are given as follows:
a. 0.4602 = 46.02%.
b. 0.281 = 28.1%.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean
and standard deviation
is given by:

- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
The parameters are given as follows:

Item a:
The probability is <u>one subtracted by the p-value of Z when X = 984</u>, hence:


Z = 0.1
Z = 0.1 has a p-value of 0.5398.
1 - 0.5398 = 0.4602.
Item b:

By the Central Limit Theorem:


Z = 0.58
Z = 0.58 has a p-value of 0.7190.
1 - 0.719 = 0.281.
More can be learned about the normal distribution at brainly.com/question/4079902
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Answer:
The order doesn’t matter, as the two events are probabilistically independent of one another. There are 13 spades in a standard 52 card deck, so the probability of drawing the number 5 is 13/52 or 1/4. The probability of heads is 1/2. The probability of both occurring is the product of the two probabilities, or 1/4*1/2 = 1/8 or 12.5%.
2x-2y
parallel means that the x part is the same
and it is -2y because the y-coordinate is -2