|1/4 x +2| -3 =5 solve for x and graph on number line

Mathematics

1 answer:

kaheart [24]2 years ago

7 0

The value of x on the number line is 24 and - 40

A number line in elementary mathematics is a representation of a graduated straight line that acts as an abstraction for real numbers, represented by the letter R. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

When seen as a geometric space, namely the one-dimensional Euclidean space, the number line, also known as a real line in advanced mathematics, is technically defined as the set R of all real numbers. It can be conceptualized as a linear continuum, metric space, topological space, vector space (or affine space), measure space, or topological space.

The given equation is

$|\frac{1}{4}x+2 | -3=5$

Solving the equation:

$or,|\frac{1}{4}x+2 | =5+3\\or,|\frac{1}{4}x+2 |=8\\or,\frac{1}{4}x+2=\pm8\\or,x+8=\pm32\\or,x=-8\pm32$

Now we take the two separate values of x:

either x=-8+32 or x=-8-32

or,x=24 or x=-40

The value of x is 24 and - 40.

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An article suggests the uniform distribution on the interval from 7.5 to 20 as a model for x = depth (in centimeters) of the bio

Ede4ka [16]

Answer:

a) Figure attached

b) For this case we want this probability:

$P(X>16)$

And we can use the complement rule:

$P(X>16) = 1-P(X$

And we can use the cumulative distribution function given by:

$F(x)= \frac{x-a}{b-a}, a\leq X \leq b$

And replacing we got:

$P(X>16) =1- \frac{16-7.5}{20-7.5} = 1-0.68 = 0.32$

Step-by-step explanation:

For this case we define the random variable X= depth (in centimeters) of the bioturbation layer in sediment for a certain region, and we know the distribution for X, given by:

$X \sim Unif (a=7.5, b=20)$