Find the solution sets for 4
1 answer:
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Answer:
See the explanation.
Step-by-step explanation:
We are given the function f(x) = x² + 2x - 5
Zeros :
If f(x) = 0 i.e. x² + 2x - 5 = 0
The left hand side can not be factorized. Hence, use Sridhar Acharya formula and
and
⇒ x = -3.45 and 1.45
Y- intercept :
Putting x = 0, we get, f(x) = - 5, Hence, y-intercept is -5.
Maximum point :
Not defined
Minimum point:
The equation can be expressed as (x + 1)² = (y + 5)
This is an equation of parabola having the vertex at (-1,-5) and axis parallel to + y-axis
Therefore, the minimum point is (-1,-5)
Domain :
x can be any real number
Range:
f(x) ≥ - 6
Interval of increase:
Since this is a parabola having the vertex at (-1,-5) and axis parallel to + y-axis.
Therefore, interval of increase is +∞ > x > -1
Interval of decrease:
-∞ < x < -1
End behavior :
So, as x tends to +∞ , then f(x) tends to +∞
And as x tends to -∞, then f(x) tends to +∞. (Answer)
Using the normal distribution, it is found that the probability is 0.16.
<h3>Normal Probability Distribution</h3>In a normal distribution with mean and standard deviation
, the z-score of a measure X is given by:
- It 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, which is the percentile of X.
In this problem, the mean and the standard deviation are given by, respectively, .
The proportion of students between 45 and 67 inches is the p-value of Z when <u>X = 67 subtracted by the p-value of Z when X = 45</u>, hence:
X = 67:
Z = -1
Z = -1 has a p-value of 0.16.
X = 45:
Z = -8.3
Z = -8.3 has a p-value of 0.
0.16 - 0 = 0.16
The probability is 0.16.
More can be learned about the normal distribution at brainly.com/question/24663213