Is it ever possible that cos(a−b)=cos ⁡a − cos ⁡b?

yes

Step-by-step explanation:

I'm going to give you a slightly different answer, but it's going to make sense :-)

First, let's review what "sin" and "cos" really mean. They are functions that take as an input an angle, which we call theta. They output the base (cos) and height (sin) of a triangle which as a hypotenuse of length 1.    

Now, let's pick some examples. If we happen to set theta to 45 degress, you will get a triangle that looks like this:

In this case, both sin(theta) and cos(theta) are the same number, the square root of 1/2. So cos(theta) + cos (theta) is 2 times the square tool of 1/2.

Now imagine that we now want to find cos (theta + theta). Remember that theta was 45 degrees, so this will be cos (45 + 45), or cos (90).

But remember that cos is the base of a triangle where theta is the angle with the base. Well, that's not a triangle at all, is it? It's just a vertical line. In fact, cos(90) will be zero.

the correct answer is

c. 4

step-by-step explanation:

the given polynomial is

the degree of the polynomial is the highest exponent which is 4.

the -4 is called the leading coefficient.

this polynomial has only one term so it is a monomial.

the correct answer is option c.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560