Step-by-step explanation:
1.) y = - |x - 4| - 5 is an absolute value graph, where its vertex occurs at point (4, -5). The general form of the absolute value function is y = a |x – h| + k, where where:
- a ≠ 0, and the value of <em>a</em> determines whether the graph opens up or down. If <em>a </em>is <u>between 0 and 1,</u> the graph is wider than the parent function.
- (<em>h</em>, <em>k </em>) represents the vertex.
The given absolute value function, y = - |x - 4| - 5 is a downward-facing graph, where it is <u>translated 4 units to the right</u> (as given by the value of <em>h = </em>4), and <u>5 units downward</u> (as given by the value of <em>k = 5</em>).
2.) The Vertical Line Test allows us to know whether or not a graph is actually a function. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function. To use the vertical-line test, imagine dragging a ruler held vertically across the graph from left to right. If the graph is that of a function, the edge of the ruler would hit the graph only once for every x -value. If you do this for the given graph, every vertical line intersects the graph in at most one point.
Attached is the graph of the given function, where I performed the Vertical Line Test. As evidenced in the graph, every green vertical line intersects the graph at exactly one point (red dots on the graph). Thus, the graph passed the Vertical Line Test, thereby qualifying as a function.
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Suppose that the number u were thinking about is x thus :
Multiply both sides by 4
Divide both sides by 3
Answer:
a) The expected value and the variance for the amount that the bank loses on a typical roll is 0.36
b) The probability that the bank will lose at least 25 cents in 100 rolls is 0.2033
c) The probability that the bank will lose any money in 100 rolls is 0.9995
d) The rolls bank need to collect to have a 99 percent chance of a net loss are 50 rolls.
Step-by-step explanation:
Detailed steps are attached below
We are given the following variables:
μ = the sample mean = 152 pounds
σ = the standard deviation = 26 pounds
x = the sample value we want to test = 180 pounds
n = the sample size = unknown
MOE = margin of error = 4% = 0.04
Confidence level = 96%
The first thing we can do is to find for the value of z
using the formula:
z = (x – μ) / σ
z = (180 – 152) / 26
z = 1.0769 = 1.08
Since we are looking for the people who weigh more than
180 pounds, therefore this is a right tailed z test. The p value is:
p = 0.1401
Then we can use the formula below to solve for n:
n = z^2 * p * (1 – p) / (MOE)^2
n = 1.08^2 * 0.1401 * (1 – 0.1401) / (0.04)^2
n = 87.82 = 88
Therefore around 88 people must be surveyed.