Miguel's batting average is roughly 0.330
Explanation
Miguel Cabrera achieved 205 hits in 622 at-bats.
To calculate batting average, we need to divide the hits by the total at-bats and round the result to three decimal places since batting average is conventionally rounded in this manner.
Hence, Miguel's batting average 
≈ 0.330 (Rounded to three decimal points)
Dolls = d
trains = t
8d + 10t = 150
I believe we can express it like that.
Response:
a) 8
b) 15
c) 34
Detailed explanation:
Section a) Options for neck-wear
Regular ties count = 3
Bow ties count = 5
Overall ties count = 3 + 5 = 8
Any tie can be selected from these 8 available options. Thus, the options for neck-wear total 8.
Section b)
We now calculate choices for using both regular and bow ties.
Selecting a regular tie is independent of the bow tie selection. According to counting principles, if two events are independent, the total ways to realize both equal the product of their individual possibilities. Thus,[
Number of ways to select both ties = Count of ways to choose each tie
So,
Ways for wearing both types of ties = 3 x 5 = 15 ways
Section c)
Count of shirts = 5
Count of skirts = 4
Count of pants = 3
Count of dresses = 7
Choice options for outfits include:
- Shirt paired with Skirt or Pants
- Or simply a dress
Pants can be chosen in 3 ways. Pairing a skirt or pant provides 9 options.
Reapplying counting rules:
Ways to wear a shirt with a skirt or pant = 3 x 9 = 27
Choices for dresses = 7
Consequently, the total is 27 + 7 = 34 outfit combinations.
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
