Answer:
The "df" stands for "degrees of freedom", and represents the number of independent observations in a set of data.
Its value in this case is df=32.
Step-by-step explanation:
The sample is of size n=33.
As we do not know the population's standard deviation, we use as estimate the sample's standard deviation. Because of this, we use the t-statistic in place of the z-value.
The "df" stands for "degrees of freedom", and represents the number of independent observations in a set of data (the data in this case is the sample of 33 video games).
In one-sample tests, the degrees of freedom are calculated as:
The would be A 18 for that math problem tell if that works
To solve a system of inequalities we graph both of them.
The inequality representing their combined pay would be
. This is because Jane makes 12.50/hr, Jack makes 10.00/hr, and they want to make at least, so greater than or equal to, $750 combined.
The inequality representing their combined hours working would be
, since they do not want their combined hours to be over 65. In both of these inequalities, <em>x</em> represents the number of hours Jane works and <em>y</em> represent the number of hours Jack works.
To graph these, we solve both of them for <em>y</em>:
The attached screenshot shows what the graph looks like. Going to the point where they intersect, we see that the shaded region that satisfies both inequalities begins when Jane works 40 hours and Jack works 25.
Answer:
one unit vector is ur=(-1/√3 ,1/√3 ,1/√3 )
Step-by-step explanation:
first we need to find a vector that is ortogonal to u and v . This vector r can be generated through the vectorial product of u and v , u X v :![r=u X v =\left[\begin{array}{ccc}i&j&k\\1&0&1\\0&1&1\end{array}\right] = \left[\begin{array}{ccc}0&1\\1&1\end{array}\right]*i + \left[\begin{array}{ccc}1&0\\1&1\end{array}\right]*j + \left[\begin{array}{ccc}1&0\\0&1\end{array}\right]*k = -1 * i + 1*j + 1*k = (-1,1,1)](https://tex.z-dn.net/?f=r%3Du%20X%20v%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Di%26j%26k%5C%5C1%260%261%5C%5C0%261%261%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D%2Ai%20%2B%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D%2Aj%20%2B%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%2Ak%20%3D%20-1%20%2A%20i%20%2B%201%2Aj%20%2B%201%2Ak%20%3D%20%28-1%2C1%2C1%29)
then the unit vector ur can be found through r and its modulus |r| :
ur=r/|r| = 1/[√[(-1)²+(1)²+(1)²]] * (-1,1,1)/√3 =(-1/√3 ,1/√3 ,1/√3 )
ur=(-1/√3 ,1/√3 ,1/√3 )
Answer:
1680 ways
Step-by-step explanation:
In this question, we are tasked with finding the number of ways in which we can select 4 trips out of 8 to make today.
Let us label the the trips we are to select as A B C D, one after the other
For selection A, we have 8 different trips waiting to be selected
For selection B, we have 7 trips to select from
For C, we have 6 to select from
while for D, we have 5 to select from. Thus, the total number of ways in which we can select these trips can be calculated as = 8 × 7× 6× 5 = 1,680 ways
