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dem82 [27]
3 years ago
12

Explain why the absolute value of a number is never negative

Mathematics
1 answer:
AysviL [449]3 years ago
3 0
Absolute value<span> describes the distance of a </span>number<span> on the </span>number<span> line from 0 without considering which direction from zero the </span>number<span> lies. This pretty much means that absolute value is a distance, and there is no such thing as a negative distance.</span>
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Sample size: A researcher is trying to decide how many people to survey. Which of the following sample sizes will result in a co
oksian1 [2.3K]

Answer:

Step-by-step explanation:

Given that a researcher is trying to decide how many people to survey.

We have confidence intervals are intervals with middle value as the mean and on either side margin of error.

Confidence interval = Mean ± Margin of error

Thus confidence interval width depends on margin of error.

Margin of error = Critical value *\frac{\sigma}{\sqrt{n} }

Thus for the same confidence level and std deviation we find margin of error is inversely proportional to square root of sample size.

Hence for small n we get wide intervals.

So if sample size = 300, the researcher will get wider confidence interval

4 0
3 years ago
Leo made the following container to store his camping gear. This container is the shape of a rectangular prism. It has material
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Step-by-step explanation:

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3 years ago
A triangle has vertices at (1,10), (-5,2), and (7,2). What is its orthocenter. Show your work.
kondor19780726 [428]

Answer:

Question: What is the orthocenter of a triangle with the vertices (-1,2) (5,2) and (2,1)?

The coordinates of point A are (-1,2), point B are (5,2), and point C are (2,1).

The orthocent is the intersection of the three altitudes. An altitude goes from a vertex and is perpendicular to the line containing the opposite side.

In the coordinate plane the equations of the altitudes can be found and then a system of equations can be solved.

Altitude 1. From point C perpendicular to the line containing side AB.

Slope of line AB is 0 (horizontal line), a vertical line is perpendicular to a horizontal line. Thus, the equation of altitude 1 is  x=2 .

Altitude 2. From point B perpendicular to the line containing side AC.

Slope of line AC is  −13 , the slope of a line perpendicular to line AC is 3. The equation of altitude 2 is  y=3x−13  

Altitude 3. From point A perpendicular to the line containing side BC.

Slope of line BC is  13 , the slope of a line perpendicular to line BC is  −3 . The equation of altitude 3 is  y=−3x−1  

The orthocenter is the point where all three altitudes intersect.

x=2  

y=3x−13  

y=−3x−1  

Use substitution to solve the first two equations  y=3(2)−13=−7  

The orthocenter is the point  (2,−7)  

we did not need the third equation, but we can use it as a check, plug the coordinates into the third equation:

−7=−3(2)−1  

−7=−6−1  

−7=−7  it works.

3 0
3 years ago
Fibonacci posed the following problem: Suppose that rabbits live forever and that every month each pair produces a new pair whic
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Answer:

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f_1 = f_2 = 1,f_n = f_n-1 + f_n-2 for any natural n  \geq 3.  

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