Answer:
H0 : μ = 4.50
H1 : μ > 4.50
Test statistic = 1.525
we conclude that there is no sufficient evidence to conclude that the mean wait time for customers is longer than 4.50.
Step-by-step explanation:
H0 : μ = 4.50
H1 : μ > 4.50
Test statistic :
(xbar - μ) ÷ s/sqrt(n)
(4.94 - 4.50) ÷ 2.10/ sqrt(53)
0.44 / 2.10/ sqrt(53)
= 1.525
α = 1 - 98% = 0.02
Decision region :
Reject H0 ; if Pvalue < α
Pvalue = p(Z < 1.525) = 0.936
Pvalue = 0.936
Since Pvalue > α ; We fail to reject H0
Hence, we conclude that there is no sufficient evidence to conclude that the mean wait time for customers is longer than 4.50.
Answer:
A. 7 centimetres and 25 centimetres
Step-by-step explanation:
To see if the lengths make a triangle, use the Pythagorean theorem. Insert the biggest value as c (the hypotenuse, which is always the longest side in a right triangle). If both sides equal each other, it is a right triangle:
![a^2+b^2=c^2](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E2)
A.
![24^2+7^2=25^2\\\\576+49=625\\\\625=625](https://tex.z-dn.net/?f=24%5E2%2B7%5E2%3D25%5E2%5C%5C%5C%5C576%2B49%3D625%5C%5C%5C%5C625%3D625)
This is a right triangle.
B.
![23^2+8^2=24^2\\\\529+64=576\\\\593\neq 576](https://tex.z-dn.net/?f=23%5E2%2B8%5E2%3D24%5E2%5C%5C%5C%5C529%2B64%3D576%5C%5C%5C%5C593%5Cneq%20576)
Not a right triangle.
C.
![9^2+22^2=24^2\\\\81+484=576\\\\565\neq 576](https://tex.z-dn.net/?f=9%5E2%2B22%5E2%3D24%5E2%5C%5C%5C%5C81%2B484%3D576%5C%5C%5C%5C565%5Cneq%20576)
Not a right triangle.
D.
![24^2+10^2=27^2\\\\576+100=729\\\\676\neq 729](https://tex.z-dn.net/?f=24%5E2%2B10%5E2%3D27%5E2%5C%5C%5C%5C576%2B100%3D729%5C%5C%5C%5C676%5Cneq%20729)
Not a right triangle.
Done :D
12in/1foot and 3feet/yard
or 12in = 1foot
3feet= 2Yard
6:57 + 47 = 7: 44
or 6:10
................
Recall your d = rt, distance = rate * time.
keeping in mind that, the distance upstream as well as downstream is the same, 90 miles, let's say the boat has a speed rate of "b", thus when the boat was going upstream, it really wasn't going "b" fast, it was going "b - 8", because the 8mph speed of the current is subtracting from it. Likewise, when the boat was going downstream, it wasn't going "b" fast either, because the current was adding to it, since it was going with the current, then it was really going "b + 8" fast.
now, let's notice the trip took a total of 6 hours, thus, if the trip downstream took say "t" hours, then the trip upstream took the slack from 6 and "t", that is, it took "6 - t" hours.
![\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ Downstream&90&b+8&t\\ Upstream&90&b-8&6-t \end{array} \\\\\\ \begin{cases} 90=t(b+8)\implies \cfrac{90}{b+8}=\boxed{t}\\\\ 90=(6-t)(b-8)\\ ----------\\ 90=\left( 6-\boxed{\cfrac{90}{b+8}} \right)(b-8) \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Blccclll%7D%0A%26%5Cstackrel%7Bmiles%7D%7Bdistance%7D%26%5Cstackrel%7Bmph%7D%7Brate%7D%26%5Cstackrel%7Bhours%7D%7Btime%7D%5C%5C%0A%26------%26------%26------%5C%5C%0ADownstream%2690%26b%2B8%26t%5C%5C%0AUpstream%2690%26b-8%266-t%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cbegin%7Bcases%7D%0A90%3Dt%28b%2B8%29%5Cimplies%20%5Ccfrac%7B90%7D%7Bb%2B8%7D%3D%5Cboxed%7Bt%7D%5C%5C%5C%5C%0A90%3D%286-t%29%28b-8%29%5C%5C%0A----------%5C%5C%0A90%3D%5Cleft%28%206-%5Cboxed%7B%5Ccfrac%7B90%7D%7Bb%2B8%7D%7D%20%5Cright%29%28b-8%29%0A%5Cend%7Bcases%7D)
![\bf 90=\left( \cfrac{6b+48-90}{b+8} \right)(b-8)\implies 90=\left( \cfrac{6b-42}{b+8} \right)(b-8) \\\\\\ 90=\cfrac{(6b-42)(b-8)}{b+8}\implies 90(b+8)=(6b-42)(b-8) \\\\\\ 90b+720=6b^2-48b-42b+336\implies 0=6b^2-180b-384 \\\\\\ 0=b^2-30b-64\implies 0=(b-32)(b+2)\implies b= \begin{cases} \boxed{32}\\ -2 \end{cases}](https://tex.z-dn.net/?f=%5Cbf%2090%3D%5Cleft%28%20%5Ccfrac%7B6b%2B48-90%7D%7Bb%2B8%7D%20%5Cright%29%28b-8%29%5Cimplies%2090%3D%5Cleft%28%20%5Ccfrac%7B6b-42%7D%7Bb%2B8%7D%20%5Cright%29%28b-8%29%0A%5C%5C%5C%5C%5C%5C%0A90%3D%5Ccfrac%7B%286b-42%29%28b-8%29%7D%7Bb%2B8%7D%5Cimplies%2090%28b%2B8%29%3D%286b-42%29%28b-8%29%0A%5C%5C%5C%5C%5C%5C%0A90b%2B720%3D6b%5E2-48b-42b%2B336%5Cimplies%200%3D6b%5E2-180b-384%0A%5C%5C%5C%5C%5C%5C%0A0%3Db%5E2-30b-64%5Cimplies%200%3D%28b-32%29%28b%2B2%29%5Cimplies%20b%3D%0A%5Cbegin%7Bcases%7D%0A%5Cboxed%7B32%7D%5C%5C%0A-2%0A%5Cend%7Bcases%7D)
since the rate of speed wouldn't be a negative unit, then is not -2.