Andrés, in his shop, stores the buttons in bags. In box A, he has bags of 24 buttons each with no buttons left. In box B, he has
1 answer:
You might be interested in
Answer:
<u>It</u><u> </u><u>moved</u><u> </u><u>for</u><u> </u><u>1</u><u>5</u><u>2</u><u>.</u><u>7</u><u> </u><u>seconds</u>
Step-by-step explanation:
Time taken/ period, T :
substitute the variables:
In seconds:
Answer:
The 99% two-sided confidence interval for the average sugar packet weight is between 0.882 kg and 1.224 kg.
Step-by-step explanation:
We are in posession of the sample's standard deviation, so we use the student's t-distribution to find the confidence interval.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 16 - 1 = 15
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 35 degrees of freedom(y-axis) and a confidence level of ). So we have T = 2.9467
The margin of error is:
M = T*s = 2.9467*0.058 = 0.171
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 1.053 - 0.171 = 0.882kg
The upper end of the interval is the sample mean added to M. So it is 1.053 + 0.171 = 1.224 kg.
The 99% two-sided confidence interval for the average sugar packet weight is between 0.882 kg and 1.224 kg.
Compound Interest
A total of $20,000 is invested in different assets.
45% is invested in a Treasury bond for 3 years at 4.35 APR compounded annually.
For this investment, the principal is P = 0.45*$20,000 = $9,000.
The compounding period is yearly, thus the interest rate is:
i = 4.35 / 100 = 0.0435
The duration (in periods) is n = 3
Calculate the final value with the formula:
Substituting:
The second investment is a CD at 3.75% APR for 3 years compounded annually. The parameters for the calculations are as follows:
P = 15% of $20,000 = $3,000
i = 3.75 / 100 = 0.0375
n = 3
Calculating:
The third investment is in a stock plan. The initial value of the investment is
P = 20% of $20,000 = $4,000
By the end of the first year, the stock plan increased by 8%, thus its value is:
M1 = $4000 * 1.2 = $4,800
By the end of the second year, the stock plan decreased by 4$, thus the value is:
M2 = $4,800 * 0.96 = $4,608
Finally, the stock plan increases by 6%, resulting in a final balance of:
M3 = $4,608 * 1.06 = $4,884.48
Finally, the last investment is in a savings account at 2.90% APR compounded annually for 3 years (not mentioned, but assumed).
P = $20,000 - $9,000- $3,000 - $4,000 = $4,000
i = 2.90 / 100 = 0.029
n = 3
Calculating:
To summarize, the final balances for each type of investment at the end of the third year are:
Investment 1; $10,226.33
Investment 2: $3,350.31
Investment 3: $4,884.48
Investment 4: $4,358.19
Total balance: $22,819.32