An equation was created for the line of best fit from the actual enrollment data. It was used to predict the dance studio enroll

The ratio is 2: 7: 14.

The function in vertex form is evaluated to be.

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

Answer:

Step-by-step explanation:

The probability distribution for the random variable X is provided.

X 4 5 6 7 Total

P 0.2 0.4 0.3 0.1 1

x*p 0.8 2 1.8 0.7 5.3

x^2*p 3.2 10 10.8 4.9 28.9

a) The expected value E(X), representing the mean of X, equates to 5.3.

Standard deviation is the square root of the variance, which amounts to 0.9.

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b) For the mean of the sample, we find:

Mean = 5.3

Variance = var(x)/n =

c)

A minimum sample size of 75 is necessary. Step-by-step explanation: We need to determine our level, which is calculated by subtracting 1 from the confidence interval divided by 2. Now, we need to find the z value in the Z table that corresponds to a p-value of [Z value]. Therefore, it is the z value with a p-value of [specific value]. Next, we calculate the margin of error M, where [insert equation], with [standard deviation] representing the population standard deviation and n as the sample size. The standard deviation equals the square root of the variance. With a 0.95 probability level, if the margin of error desired is 5 or below, a sample size of at least 75 is required.