Please answer this for me really struggling thanks
1 answer:
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Given:
μ = 500 days, the population mean
σ = 60 days, the population standard deviation
Therefore
μ + σ = 560
μ - σ = 440
μ + 2σ = 620
μ - 2σ = 380
μ + 3σ = 680
μ - 3σ = 320
The figure shown below illustrates the normal distribution
About 68% of the total area lies in x = (μ-σ, μ+σ)
About 95% of the total area lies in x = (μ-2σ, μ+2σ)
About 99.7% of the total area lies in x = (μ-3σ, μ+3σ).
μ = 500 days, the population mean
σ = 60 days, the population standard deviation
Therefore
μ + σ = 560
μ - σ = 440
μ + 2σ = 620
μ - 2σ = 380
μ + 3σ = 680
μ - 3σ = 320
The figure shown below illustrates the normal distribution
About 68% of the total area lies in x = (μ-σ, μ+σ)
About 95% of the total area lies in x = (μ-2σ, μ+2σ)
About 99.7% of the total area lies in x = (μ-3σ, μ+3σ).
Okay, let's see...
The problem is asking for a linear equation most likely in the form of y=mx+b
y is another way to say f(x)
<em>m = slope </em>
<em>b = y intercept </em>
Let's start with the y intercept first.
Y intercept means ' When does the line touch (intercept) the y axis.
In this case, if you look at the graph, the line <em>touches </em>the y axis at -1.
-1 will replaces b
To find the slope we are going to take 2 precise points from the graph.
Lets use <em>(0,-1)</em> and <em>(-6,4) </em>
To find the slope, we're going to use
4 - (-1) / -6 - 0
Solve, our slope is 5/-6
That is our m
Our final equation is
Using the normal distribution, it is found that 25.14% of the batteries will last more than 420 hours.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, we have that the mean and the standard deviation are given, respectively, by:
.
The proportion of the batteries will last more than 420 hours is <u>one subtracted by the p-value of Z when X = 420</u>, hence:
Z = 0.67
Z = 0.67 has a p-value of 0.7486.
1 - 0.7486 = 0.2514.
0.2514 = 25.14% of the batteries will last more than 420 hours.
More can be learned about the normal distribution at brainly.com/question/24663213
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If all three side lengths are INTEGERS and form PYTHAGOREAN TRIPLE then we know decimals are not allowed
if 24 and 51 are both legs then
x = 3177
and squre root of that gives us 56.364.... NOT an integer
So that means one of them is not a leg and since hypotenuse is longer than both legs, 51 must be the hypotenuse so to get the third side
![51^{2} - 24^{2} = x^{2}[tex] [tex] x^{2}](https://tex.z-dn.net/?f=%2051%5E%7B2%7D%20-%20%2024%5E%7B2%7D%20%20%3D%20%20x%5E%7B2%7D%5Btex%5D%20%5Btex%5D%20x%5E%7B2%7D%20)
=2025
x=45, leg B
if 24 and 51 are both legs then
x = 3177
and squre root of that gives us 56.364.... NOT an integer
So that means one of them is not a leg and since hypotenuse is longer than both legs, 51 must be the hypotenuse so to get the third side
x=45, leg B