Maggie and her friends are each able to recruit a certain number of people each year to sample a product. The number of people per year is represented by the function f(t) = 3(2)t. What does the t represent? How many people were recruited in 6 years?.

Step-by-step explanation:

The given information tells us that f(x) is a continuous function, and it passes through the points (-2, 10) and (-7, -5). Additionally, it has exactly one value of x for which f(x) = 0. We need to find which of the given options (-3, -8, 0, 2) could be that x value.

Let's analyze each option:

a) -3: If f(-3) = 0, it's a possibility, but we need to check the others.

b) -8: If f(-8) = 0, it's a possibility, but we need to check the others.

c) 0: If f(0) = 0, it's a possibility, but we need to check the others.

d) 2: If f(2) = 0, it's a possibility, but we need to check the others.

Since we are told that there is only one value of x for which f(x) = 0, and there are multiple possibilities in this case (a, b, c, and d), the information provided does not allow us to determine a unique answer from the given options. Any of these values could be the x for which f(x) = 0, given that the function is continuous.

Final answer:

The question uses the concept of Intermediate Value Theorem in mathematics. The answer is option a) -3 as it falls between the range by the theorem, which states that for any continuous function within a certain range, the function must cross all values within that range.

Explanation:

This question is about the Intermediate Value Theorem, which states that if a function is continuous on a closed interval from a to b, and k is any number between f(a) and f(b), then there is at least one number c in the interval (a, b) such that f(c) = k.

Since the function is continuous for all real numbers and f(-2) = 10 and f(-7) = -5, the function must pass through 0 between -2 and -7 as it moves from 10 to -5. Therefore, the x value for which f(x) = 0 could be between -2 and -7. In the provided options, the only value falling within the interval (-2, -7) is -3.

So, based on the Intermediate Value Theorem, the answer is option a) -3.

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After solving the equation, the value obtained for w will be equal to 2.

What are arithmetic Operations?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the data in the question,

The equation given in the question,

w + 1/2 = 1/4w + 2

Add similar terms,

w - 1/4w = 2 - 1/2

(4w - w)/4 = (4 - 1)/2

3w/4 = 3/2

w = 12/6

w = 2

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Answer:

w = 2

Step-by-step explanation:

Answer:

C. Corresponding angles

Step-by-step explanation:

Corresponding angles are angles formed by a transversal on the same side of the transversal and on the same side of each parallel lines.