A discount store normally sells DVDs for $14.44. If the DVDs go on sale for $13.72, which of the following is closest to the per

Answer:

b = 5√3

b = -5√3

Step-by-step explanation:

We have

Keep in mind, the root of a function corresponds to the value of x at which the function's output is zero.

In this case

The roots of the equation are the b values for which f(b) equals zero.

Thus

For f(b)=0

Take the square root of both sides

Now simplify

 and

So we find that

b = 5√3

b = -5√3

The correct choice is option D. The given equations are:...[1]...[2] Multiply equation [1] by 5 on both sides; we have...[3]. By using the elimination method, we can add equations [2] and [3] to eliminate y and determine x, resulting in... Dividing both sides by 13 yields x = 3. Substituting x back into equation [1] results in 2(3) - y = -4, which simplifies to 6 - y = -4. After subtracting 6 from both sides, we find -y = -10. Dividing through by -1 gives y = 10. Hence, the solution is (3, 10). Consequently, a valid equation that can replace 3x + 5y = 59 in the original set while still yielding the same result is 13x = 39.

Answer:

The chance of remaining dry throughout the whole festival is 0.19

Step-by-step explanation:

According to the Complement Rule, the aggregate of the probabilities of an event and its opposite is always equal to 1.

Here, we consider the likelihood of rain each day, so we need to find the chances of it NOT raining.

On the first day, there's a 45% possibility of rain; thus, the complement is 55%

On the second day, the chance of rain is 55%, making its complement 45%

For the third day, the likelihood is 10%, giving a complement of 90%

On the fourth day, the rain chance remains 10%, so the complement stays at 90%

The fifth day presents a 5% chance of rain, resulting in a complement of 95%

To determine the probability of not encountering rain for the entire festival, we multiply all the complements.

P(not raining) = 0.55 x 0.45 x 0.90 x 0.90 x 0.95= 0.19

Answer:

Step-by-step explanation:

The trigonometric expression given is:

11 cos² x +3 sin² x + 6sin x cos x + 5

Alternatively, we can present it as:

(9 cos² x + 2 cos² x) + (2 sin² x + sin² x) + 6sin x cos x + 5

After rearranging, the expression can be rewritten as:

(9 cos² x + sin² x + 6sin x cos x) + (2 cos² x + 2 sin² x) + 5

If we factor the highlighted part similarly to a polynomial:

(9 cos² x + sin² x + 6sin x cos x) + (2 cos² x + 2 sin² x) + 5

This results in:

(3 cos x + sin x)² + 2 (cos² x + sin² x) + 5

Notably, the term in the second set of brackets (cos² x + sin² x) is a well-known trigonometric identity and equals one.

Consequently, the expression simplifies to:

(3 cos x + sin x)² + 7

The maximum and minimum values of the entire expression rely on the max and min values of (3 cos x + sin x), which follows the format (a cos x + b sin x).

The max and min values can be easily determined.

I've included a screenshot from related material below:

Here, a=3 and b=1, thus, R= √10

As the cosine value for any angle ranges between -1 and 1, the value of cos(x − α) will also fall within this range.

This means the max and min for (a cos x + b sin x) will be -R to R, and all resultant values will be between those limits.

In this case, we observe that it falls between (-√10) and √10.

Returning to our original expression:

(3 cos x + sin x)² + 7

The bracketed term ranges between (-√10) and √10.

Nevertheless, since squaring a negative value yields a positive result, we cannot use a negative value for determining the minimum. The minimum occurs at the lowest non-negative value, which is zero.

Thus, the minimum value is:

(0)² + 7 = 7

And the maximum is:

(√10)² + 7 = 17