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3 years ago

Why is f(x)=0 the only odd and even function?

2 answers:

6 0

F is odd if and only f f(-x) = -f(x) so f(x) = 0 works because 0 = 0 always.

f is even if and only if f(-x) = f(x) so f(x) = 0 works because there's no x term so nothing changes. 0 = 0.

inessss [21]3 years ago

3 0

If f is even, then f(-x) = f(x) for all x in the domain
If f is odd, then f(-x) = -f(x) for all x in the domain

Use substitution to find that...
f(-x) = -f(x)
f(x) = -f(x) <<--- replaced f(-x) on the left side with f(x)
f(x)+f(x) = 0 <<--- add f(x) to both sides and isolate f(x)
2*f(x) = 0
f(x) = 0

So if x is both even and odd at the same time, then f(x) = 0 for all values of x in the domain of f. This produces a flat horizontal line through the origin. It is both symmetric with respect to the y axis and it has origin symmetry as well (we can rotate it 180 degrees around the origin to have it line up with itself)

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Choose the graph that represents the following system of inequalities: y ≥ −3x + 1 y ≤ 1 over 2x + 3 In each graph, the area for

svet-max [94.6K]

Answer:

Correct graph is C

Step-by-step explanation:

Given two inequalities are:

1. $y\leq -3x+1$

2. $y\leq x+3$

Step1 : Remove the inequalities

1. $y=-3x+1$

2. $y=x+3$

Step2 : Finding intersection points of equations

By solving linear equation

$y=-3x+1=x+3$

$-3x+x+3$

$x=-0.5$

Replacing value of x in any equations

we get,

$y=x+3\\$

$y=-0.5+3$

$y=2.5$

Therefore, Point of intersection is (-0.5,2.5)

Step3: Test of origin (0,0)

Here, If inequalities holds true for origin then, shades the graph towards the origin.

For equation 1.

$y\leq -3x+1$

$0\leq -3(0)+1$

$0\leq +1$

True, Shade graph towards origin.

For equation 2.

$y\leq x+3$

$0\leq 0+3$

$0\leq 3$

True, Shade graph towards origin.

Thus, Correct graph is C

6 0

3 years ago

The resting heart rate for an adult horse should average about µ = 47 beats per minute with a (95% of data) range from 19 to 75

KatRina [158]

Answer:

a. 0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.

b. 0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.

c. 0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute

Step-by-step explanation:

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean:

$\mu = 47$