we know that in direct variation as x increase y also increases.
in indirect variation x decreases y increase and vice versa.
in part a we have x at top (numerator ) and y at denominator it mean indirect variation (as x increases y decreases).
to find k we know that for indirect variation xy=k
if we rewrite the equation x=9/y we get xy=9
which mean k=9 .
in part b we have 4xy=20 if we simplify this equation we get
![xy=20/4=5](https://tex.z-dn.net/?f=%20xy%3D20%2F4%3D5%20)
so here if we rewrite in terms of x.
we get x=5/y which represents indirect variation.
and we know xy=k
we have xy=5 .so k=5
Answer:
Interval [16.34 , 21.43]
Step-by-step explanation:
First step. <u>Calculate the mean</u>
![\bar X=\frac{(23+18+23+12+13+23)}{6}=18.666](https://tex.z-dn.net/?f=%5Cbar%20X%3D%5Cfrac%7B%2823%2B18%2B23%2B12%2B13%2B23%29%7D%7B6%7D%3D18.666)
Second step. <u>Calculate the standard deviation</u>
![\sigma =\sqrt{\frac{(23-18.666)^2+(18-18.666)^2+(23-18.666)^2+(12-18.666)^2+(13-18.666)^2+(23-18.666)^2}{6}}](https://tex.z-dn.net/?f=%5Csigma%20%3D%5Csqrt%7B%5Cfrac%7B%2823-18.666%29%5E2%2B%2818-18.666%29%5E2%2B%2823-18.666%29%5E2%2B%2812-18.666%29%5E2%2B%2813-18.666%29%5E2%2B%2823-18.666%29%5E2%7D%7B6%7D%7D)
![\sigma=\sqrt\frac{18.783+0.443+18.783+44.435+5.666+18.783}{6}](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%5Cfrac%7B18.783%2B0.443%2B18.783%2B44.435%2B5.666%2B18.783%7D%7B6%7D)
![\sigma=\sqrt{17.815}=4.22](https://tex.z-dn.net/?f=%5Csigma%3D%5Csqrt%7B17.815%7D%3D4.22)
As the number of data is less than 30, we must use the t-table to find the interval of confidence.
We have 6 observations, our level of confidence DF is then 6-1=5 and we want our area A to be 80% (0.08).
We must then choose t = 1.476 (see attachment)
Now, we use the formula that gives us the end points of the required interval
![\bar X \pm t\frac{\sigma}{\sqrt n}](https://tex.z-dn.net/?f=%5Cbar%20X%20%5Cpm%20t%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%20n%7D)
where n is the number of observations.
The extremes of the interval are then, rounded to the nearest hundreth, 16.34 and 21.43
Answer:
A single-digit odd number you'll get from dividing a two-digit number with 2 is 7.
Step-by-step explanation:
If you were to divide 14 by 2, you would get 7, which is a single-digit odd number.
For 1. The answer is “x = 4”
Explanation: 5 X 4 = 20 and 4 - 3 = 1
By adding all equal sides together the sum is 42 so x is 4
Answer:
a
Step-by-step explanation: