To determine this, we will apply the simple interest formula:
where
signifies the total amount.
indicates the principal amount.
represents the interest rate in decimal.
denotes the time period in years.
Investment A. The initial investment amount is $10,000, so
. The investment period is 5 years, meaning
. To express the interest rate in decimal, divide it by 100%
Now, we can substitute these values into our formula to find
:
Investment B. 
,
, and
.
In conclusion,
investment A will yield a greater value than investment B at the investment period's conclusion.
Response:
Step-by-step breakdown:
For the null hypothesis,
H0: p = 88
For the alternative hypothesis,
Ha: p < 88
In terms of population proportion, where the probability of success is p = 0.88
q represents the probability of failure = 1 - p
q = 1 - 0.88 = 0.12
Considering the sample,
Sample proportion, P = x/n
Where
x = number of successes = 21
n = total samples = 32
P = 21/32 = 0.66
Next, we determine the test statistic, which represents the z-score
z = (P - p)/√pq/n
z = (0.66 - 0.88)/√(0.88 × 0.12)/32 = - 3.83
The relevant p-value corresponds by referencing the normal distribution table for the area falling beneath the z-score. As a result,
P value = 0.00006
Assuming arcs are measured in degrees, let S represent the following sum:
S = sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360°
By rearranging, S can be reformulated as
S = [sin 1° + sin 359°] + [sin 2° + sin 358°] +... + [sin 179° + sin 181°] + sin 180° +
+ sin 360°
S = [sin 1° + sin(360° – 1°)] + [sin 2° + sin(360° – 2°)] +... + [sin 179° + sin(360° – 179)°]
+ sin 180° + sin 360° (i)
However, for any real k,
sin(360° – k) = – sin k
Thus,
S = [sin 1° – sin 1°] + [sin 2° – sin 2°] +... + [sin 179° – sin 179°] + sin 180° + sin 360°
S results in 0 + 0 +... + 0 + 0 + 0 (... since sine of 180° and 360° are both equal to 0)
Therefore, S equals 0.
Each pair within the brackets negates itself, leading the sum to total zero.
∴ sin 1° + sin 2° + sin 3° +... + sin 359° + sin 360° equals 0. ✔
I hope this clarifies things. =)
Tags: sum summatory trigonometric trig function sine sin trigonometry
