i am not 100% sure but...
(4x+3)=47
<u> - 3 - 3 </u>
4x=44
44/4= 11
so x = 11
![\bf \sqrt{n}< \sqrt{2n+5}\implies \stackrel{\textit{squaring both sides}}{n< 2n+5}\implies 0\leqslant 2n - n + 5 \\\\\\ 0 < n+5\implies \boxed{-5 < n} \\\\\\ \stackrel{-5\leqslant n < 2}{\boxed{-5}\rule[0.35em]{10em}{0.25pt}0\rule[0.35em]{3em}{0.25pt}2}](https://tex.z-dn.net/?f=%5Cbf%20%5Csqrt%7Bn%7D%3C%20%5Csqrt%7B2n%2B5%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bsquaring%20both%20sides%7D%7D%7Bn%3C%202n%2B5%7D%5Cimplies%200%5Cleqslant%202n%20-%20n%20%2B%205%20%5C%5C%5C%5C%5C%5C%200%20%3C%20n%2B5%5Cimplies%20%5Cboxed%7B-5%20%3C%20n%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B-5%5Cleqslant%20n%20%3C%202%7D%7B%5Cboxed%7B-5%7D%5Crule%5B0.35em%5D%7B10em%7D%7B0.25pt%7D0%5Crule%5B0.35em%5D%7B3em%7D%7B0.25pt%7D2%7D)
namely, -5, -4, -3, -2, -1, 0, 1. Excluding "2" because n < 2.
Answer:
The major condition that needs to be satisfied before a t-test is performed that the question satisfies easily is the use of random sampling to obtain sample data.
Step-by-step explanation:
The major conditions necessary to conduct a t-test about a mean include;
- The sample extracted from the population must be extracted using random sampling. That is, the sample must be a random sample of the population.
- The sampling distribution must be normal or approximately normal. This is achievable when the population distribution is normal or approximately normal.
- Each observation in the sample data must have an independent outcome. That is, the outcome/result of each sub-data mustn't depend on one another.
Of the three conditions that need to be satisfied before the conduction of a t-test, the first condition about using a random sampling technique is evidently satisfied.
It is stated in the question that 'A private investigator hired by a competitor takes a random sample of 47 games and tries to determine if there are more than 7 glitches per game'.
Hope this Helps!!!
Answer:
There is no point of the form (-1, y) on the curve where the tangent is horizontal
Step-by-step explanation:
Notice that when x = - 1. then dy/dx becomes:
dy/dx= (y+2) / (2y+1)
therefore, to request that the tangent is horizontal we ask for the y values that make dy/dx equal to ZERO:
0 = ( y + 2) / (2 y + 1)
And we obtain y = -2 as the answer.
But if we try the point (-1, -2) in the original equation, we find that it DOESN'T belong to the curve because it doesn't satisfy the equation as shown below:
(-1)^2 + (-2)^2 - (-1)*(-2) - 5 = 1 + 4 + 2 - 5 = 2 (instead of zero)
Then, we conclude that there is no horizontal tangent to the curve for x = -1.
Perimeter = 2w + 2l = 2(12) + 2(10) = 44
