answer:Yes, I can help you with that! The half angle formula for cosine is: cos(x/2) = ±sqrt((1 + cos(x))/2) Using this formula, we can find the value of cos(π/3) as follows: cos(π/3) = cos(2π/6) = cos(π/6 + π/6) Let x = π/6, then we have: cos(π/6 + π/6) = cos(2π/12 + 2π/12) = cos(π/6) Now, applying the half angle formula for cosine with x = π/6, we have: cos(π/6) = ±sqrt((1 + cos(π/3))/2) We know that cos(π/3) is positive, so we can take the positive square root: cos(π/3) = 2cos²(π/6) - 1 cos(π/3) = 2(√3/2)² - 1 cos(π/3) = 3/2 - 1 cos(π/3) = 1/2 Therefore, cos(π/3) = 1/2 in radians. To convert to degrees, we know that π radians is equal to 180 degrees, so: cos(π/3) = cos(60°) = 1/2 So the exact value of cos(π/3) using only the half angle formula for cosine is 1/2, expressed in both radians and degrees.

answer:Variance and standard deviation are both measures of how spread out a dataset is, but they differ in their units of measurement. Variance is the average of the squared differences from the mean, while standard deviation is the square root of the variance. For example, let's say we have a dataset of the heights of 10 people: 5'2", 5'5", 5'6", 5'7", 5'8", 5'9", 5'10", 6'0", 6'1", 6'2" To calculate the variance, we first find the mean: (5'2" + 5'5" + 5'6" + 5'7" + 5'8" + 5'9" + 5'10" + 6'0" + 6'1" + 6'2") / 10 = 5'8" Then we find the squared differences from the mean for each height: (5'2" - 5'8")^2 = 36 (5'5" - 5'8")^2 = 9 (5'6" - 5'8")^2 = 4 (5'7" - 5'8")^2 = 1 (5'8" - 5'8")^2 = 0 (5'9" - 5'8")^2 = 1 (5'10" - 5'8")^2 = 4 (6'0" - 5'8")^2 = 16 (6'1" - 5'8")^2 = 9 (6'2" - 5'8")^2 = 16 The variance is the average of these squared differences: (36 + 9 + 4 + 1 + 0 + 1 + 4 + 16 + 9 + 16) / 10 = 10.2 The standard deviation is the square root of the variance: sqrt(10.2) = 3.19 So the variance is 10.2 square feet and the standard deviation is 3.19 feet. These measures can help us understand the distribution of the dataset. In this case, the standard deviation tells us that most of the heights are within about 3 feet of the mean, which is relatively narrow. If the standard deviation were larger, the dataset would be more spread out. The variance can also be useful for comparing the spread of different datasets that have different units of measurement.

answer:The subsequent program assigns the integer 10 to the variable "a", the integer 5 to the variable "b", computes the sum of "a" and "b" and stores the outcome in "c", then prints the value stored in "c". Therefore, the output will be 15. Here is the Python code for this program: ``` a = 10 b = 5 c = a + b print(c) ```

answer:Avocado Toast with Egg Ingredients: - 2 slices of whole grain bread - 1 ripe avocado - 2 eggs - salt and pepper to taste - optional toppings: sliced tomato, chopped cilantro, hot sauce Instructions: 1. Toast the slices of bread until golden brown. 2. While the bread is toasting, slice the avocado in half and remove the pit. Mash the avocado with a fork until it’s chunky or smooth, depending on your preference. 3. Season the avocado with salt and pepper to taste. 4. In a non-stick skillet over medium heat, crack the eggs and cook them sunny-side up or over-easy, depending on your preference. 5. When the bread is toasted, spread the mashed avocado evenly on each slice. 6. Place a cooked egg on top of each avocado toast. 7. Add any desired toppings such as sliced tomato, chopped cilantro, or hot sauce. 8. Serve immediately and enjoy!