Answer:
This is strong evidence that more than 2% get damaged
Step-by-step explanation:
The company goal is to keep the proportion of damaged machines below 2%


One day an inspector randomly checks 66 washers and finds that 6 of them have scratches or dents
So, x = 6
n = 66


Formula : 



So, the value of test statistic is 4.114
2) What is the P-value of the test statistic?
So, p value using calculator = .00002
p value < α
So, we accept the alternate hypothesis
So, This is strong evidence that more than 2% get damaged
Answer:
Step-by-step explanation:
-2x² + 12x + 32 = 0
discriminant = 12² - 4(-2)(32) = 400
positive discriminant means there are two distinct real roots
x = [-12 ± √(12² – 4(-2)·32)] / [2·(-2)]
= [-12 ± √400] / (-4)
= [-12 ± 20] /(-4)
= 8, -2
The cardinality of the union between two sets is given by

In fact, if an element is in both A and B, it is counted in both N(A) and N(B), so we're counting it twice. By subtracting the cardinality of the interserction, we're taking back one of these "extra-counted" element, and the count is correct. In your case, the numbers are

This means that the two sets cover, without repetitions, 43 of the 66 elements in the sets. So, there are

elements which are in neither A nor B
The average value of a continuous function f(x) over an interval [a, b] is
![\displaystyle f_{\mathrm{ave}[a,b]} = \frac1{b-a}\int_a^b f(x)\,dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_%7B%5Cmathrm%7Bave%7D%5Ba%2Cb%5D%7D%20%3D%20%5Cfrac1%7Bb-a%7D%5Cint_a%5Eb%20f%28x%29%5C%2Cdx)
We're given that
![\displaystyle f_{\rm ave[-1,2]} = \frac13 \int_{-1}^2 f(x) \, dx = -4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_%7B%5Crm%20ave%5B-1%2C2%5D%7D%20%3D%20%5Cfrac13%20%5Cint_%7B-1%7D%5E2%20f%28x%29%20%5C%2C%20dx%20%3D%20-4)
![\displaystyle f_{\rm ave[2,7]} = \frac15 \int_2^7 f(x) \, dx = 8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_%7B%5Crm%20ave%5B2%2C7%5D%7D%20%3D%20%5Cfrac15%20%5Cint_2%5E7%20f%28x%29%20%5C%2C%20dx%20%3D%208)
and we want to determine
![\displaystyle f_{\rm ave[-1,7]} = \frac18 \int_{-1}^7 f(x) \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_%7B%5Crm%20ave%5B-1%2C7%5D%7D%20%3D%20%5Cfrac18%20%5Cint_%7B-1%7D%5E7%20f%28x%29%20%5C%2C%20dx)
By the additive property of definite integration, we have

so it follows that
![\displaystyle f_{\rm ave[-1,7]} = \frac18 \left(\int_{-1}^2 f(x)\,dx + \int_2^7 f(x)\,dx\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_%7B%5Crm%20ave%5B-1%2C7%5D%7D%20%3D%20%5Cfrac18%20%5Cleft%28%5Cint_%7B-1%7D%5E2%20f%28x%29%5C%2Cdx%20%2B%20%5Cint_2%5E7%20f%28x%29%5C%2Cdx%5Cright%29)
![\displaystyle f_{\rm ave[-1,7]} = \frac18 \left(3\times(-4) + 5\times8\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_%7B%5Crm%20ave%5B-1%2C7%5D%7D%20%3D%20%5Cfrac18%20%5Cleft%283%5Ctimes%28-4%29%20%2B%205%5Ctimes8%5Cright%29)
![\displaystyle f_{\rm ave[-1,7]} = \boxed{\frac72}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f_%7B%5Crm%20ave%5B-1%2C7%5D%7D%20%3D%20%5Cboxed%7B%5Cfrac72%7D)
Answer:
$30 is the price of the original pair of sneakers.
Step-by-step explanation:
You wanna cross multiply so you put :
18. 60
_ = _
x. 100
You multiply 18 the cost of the sneakers by 100 and then divide the product (1800) by 60 and you get $30.
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