98 points! question + answers in photo! use squared identities to simplify the following

2sin^2xcos^2x

Using trig functions we know:

sin^2(x) = 1- cos(2x)/2

cos^2(x) = 1 + cos(2x) /2

Now we have:

2sin^2xcos^2x  =  2 * 1- cos(2x)/2 * 1 + cos(2x) /2

Simplify to: (1- cos(2x) * 1+cos(2x))/2

Difference of squares is (a-b) (a+b) = a^2 -b^2

(1- cos(2x) * 1+cos(2x))/2 = 1^2 -cos^2(x)/2 *1^2 +cos^2(x) /2

Multiply to get 1-cos(4x) /4

The answer is D.

The probability that EXACTLY 10 will show that the above three food items were ordered is 0.1859 or 18.59%.

Given information:

Sixty percent of the customers of a fast-food chain order whopper, french fries, and a drink.

A random sample of 15 cash register receipts is selected.

It is required to calculate the probability that EXACTLY 10 will show that the above three food items were ordered.

The events of choosing an item are independent. So, binomial distribution can be used to calculate the required probability.

So, the value of n is 15 and the value of x will be 10.

The probability of success will be 60% or 0.6 and that of failure will be 1-0.6=0.4. So, and .

So, the required probability can be calculated as,

Therefore, the probability that EXACTLY 10 will show that the above three food items were ordered is 0.1859 or 18.59%.

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