Money raised by Jin = x = 37.26
Money raised by Bashir = x + 29 = 37.26 + 29 = 66.26
Money raised by Deb = x - 5 = 37.26 - 5 = 32.26
<h3>What is an equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount raised by Jin, hence:
Money raised by Bashir = x + 29
Money raised by Deb = x + 29 - 34 = x - 5
Hence:
x + x + 29 + x - 5 = 135.78
Money raised by Jin = x = 37.26
Money raised by Bashir = x + 29 = 37.26 + 29 = 66.26
Money raised by Deb = x - 5 = 37.26 - 5 = 32.26
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Answer:
(a) E (X) = 61 and SD (X) = 9
(b) E (Z) = 0 and SD (Z) = 1
Step-by-step explanation:
The time of the finishers in the New York City 10 km run are normally distributed with a mean,<em>μ</em> = 61 minutes and a standard deviation, <em>σ</em> = 9 minutes.
(a)
The random variable <em>X</em> is defined as the finishing time for the finishers.
Then the expected value of <em>X</em> is:
<em>E </em>(<em>X</em>) = 61 minutes
The variance of the random variable <em>X</em> is:
<em>V</em> (<em>X</em>) = (9 minutes)²
Then the standard deviation of the random variable <em>X</em> is:
<em>SD</em> (<em>X</em>) = 9 minutes
(b)
The random variable <em>Z</em> is the standardized form of the random variable <em>X</em>.
It is defined as:
Compute the expected value of <em>Z</em> as follows:
![E(Z)=E[\frac{X-\mu}{\sigma}]\\=\frac{E(X)-\mu}{\sigma}\\=\frac{61-61}{9}\\=0](https://tex.z-dn.net/?f=E%28Z%29%3DE%5B%5Cfrac%7BX-%5Cmu%7D%7B%5Csigma%7D%5D%5C%5C%3D%5Cfrac%7BE%28X%29-%5Cmu%7D%7B%5Csigma%7D%5C%5C%3D%5Cfrac%7B61-61%7D%7B9%7D%5C%5C%3D0)
The mean of <em>Z</em> is 0.
Compute the variance of <em>Z</em> as follows:
![V(Z)=V[\frac{X-\mu}{\sigma}]\\=\frac{V(X)+V(\mu)}{\sigma^{2}}\\=\frac{V(X)}{\sigma^{2}}\\=\frac{9^{2}}{9^{2}}\\=1](https://tex.z-dn.net/?f=V%28Z%29%3DV%5B%5Cfrac%7BX-%5Cmu%7D%7B%5Csigma%7D%5D%5C%5C%3D%5Cfrac%7BV%28X%29%2BV%28%5Cmu%29%7D%7B%5Csigma%5E%7B2%7D%7D%5C%5C%3D%5Cfrac%7BV%28X%29%7D%7B%5Csigma%5E%7B2%7D%7D%5C%5C%3D%5Cfrac%7B9%5E%7B2%7D%7D%7B9%5E%7B2%7D%7D%5C%5C%3D1)
The variance of <em>Z</em> is 1.
So the standard deviation is 1.
<span>a.{x | x is a real number such that x^2 = 1}
x^2 = 1 => x = +/- 1
=> {-1, 1} <------ answer
b.{x | x is a positive integer less than 12}
1 ≤ x < 12 => {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} <------ answer
c.{x | x is the square of an integer and x < 100}
x = n^2 < 100 => n^2 - 100 < 0
=> (n - 10) (n + 10) < 0
=> a) n - 10 > 0 and n + 10 < 0 => n > 10 and n < - 10 which is not possible
b) n - 10 < 0 and n + 10 > 0 => n < 10 and n > - 10 => - 10 < n < 10
=> n = { - 9, - 8, - 7, - 6, - 5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
=> x = {0, 1, 4, 9, 16, 25, 36, 49, 64, 81} <---- answer
d.{x | x is an integer such that x^2 = 2}
</span>
x = {∅ } because x is √2 which is not an interger but an irrational number
=> Answer: { ∅ }
8 ÷ 10 = 0.8
So the unit rate would be 0.8
Hope it helps!
Answer: 0.09 , 0.1 , 0.19
Step-by-step explanation:
