The solution set of the given inequality has a domain of (-∞, ∞) and the vertex(h,k) = (1, -9)
<h3>What is the solution set for inequality?</h3>
The solution set for inequality is the set of all solutions for which the inequality is defined. It can also be represented in an interval notation.
Given that:
By rewriting the equation in the parabola standard form 4p(y-k) = (x - h)², we have:
![\mathbf{4\times \dfrac{1}{4}(y-(-9)) = (x-1)^2}](https://tex.z-dn.net/?f=%5Cmathbf%7B4%5Ctimes%20%5Cdfrac%7B1%7D%7B4%7D%28y-%28-9%29%29%20%3D%20%28x-1%29%5E2%7D)
Therefore, the parabola properties are:
- The solution set of the domain is (-∞, ∞)
- Vertex(h,k) = (1, -9)
- Focal length |p| = 1/4
Learn more about the solution set of inequality here:
brainly.com/question/1496731
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Step-by-step explanation:
h(t) = -5t² + 20t + 18
this is a parabola (the curve an object follows when thrown up into the air and then falling back down).
and as such it will most likely have 2 solutions (one for when going up, and one for when falling back down again).
33 = -5t² + 20t + 18
15 = -5t² + 20t
-3 = t² - 4t
t² - 4t + 3 = 0
the solution of such a quadratic equation is
t = (-b ±sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = -4
c = 3
t = (4 ±sqrt(16 - 4×1×3))/(2×1) = (4 ±sqrt(16-12))/2 =
= (4 ±sqrt(4))/2 = (4 ± 2)/2
t1 = (4+2)/2 = 6/2 = 3
t2 = (4-2)/2 = 2/2 = 1
the object reaches the height of 33 m first after 1 second (while going up), and then again after 3 seconds (while falling down again).
Answer:
Non-Linear
Includes a cluster
Positive Association
Includes an outlier
Step-by-step explanation:
Answer:
84.13% of homes will have a monthly utility bill of more than $135
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
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 pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
![\mu = 143, \sigma = 8](https://tex.z-dn.net/?f=%5Cmu%20%3D%20143%2C%20%5Csigma%20%3D%208)
What percentage of homes will have a monthly utility bill of more than $135?
We have to find 1 subtracted by the pvalue of Z when X = 135.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{135 - 143}{8}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B135%20-%20143%7D%7B8%7D)
![Z = -1](https://tex.z-dn.net/?f=Z%20%3D%20-1)
has a pvalue of 0.1587
1 - 0.1587 = 0.8413
84.13% of homes will have a monthly utility bill of more than $135