Answer:
The answer is option (C)=an-1+7
Step-by-step explanation:
A recursive rule is a formula that in which each term is expressed as a function of its preceding term(s), meaning in order to get to the nth term you have to express it in a form of the term that comes before it. In our case the a(n-1) term
So for the sequence -9, -2, 5, 12
The nth term is any number on the sequence and
- -2 is the a(n-1) term for -9
- 5 is the a(n-1) term for -2
- 12 is the a(n-1) term for 5
So we need to find out what we have to do to the preceding term to get the next.
To get -2 from -9 we have to add 7 to -9; -9+7=-2
To get 5 from -2 we have to add 7 to -2; -2+7=5
To get 12 from 5 we add 7 to 5; 7+5=12
So the recursive rule would be= a n-1+7
<em>2400 is increased by 30%.</em>
so,
2400 + (30/100 * 2400)
2400 + (30 * 24)
2400 + 720
3120
<em>this number is decreased by 20%.</em>
so,
3120 - (20/100 * 3120)
3120 - (2 * 312)
3120 - 624
2496
therefore, the final number will be 2496.
Just as you would do it with any other number.
Write out some of it, then move the decimal point 3 places this way <=== .
Some of pi : 3.14159
Divide by 1,000 : 0.00314159
Answer:
The confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory is Lower limit = 2.30, Upper limit = 4.83.
Step-by-step explanation:
The confidence interval for population variance is given as below:
![[(n - 1)\times S^{2} / X^{2} \alpha/2, n-1 ] < \alpha < [(n- 1)\times S^{2} / X^{2} 1- \alpha/2, n- 1 ]](https://tex.z-dn.net/?f=%5B%28n%20-%201%29%5Ctimes%20S%5E%7B2%7D%20%20%2F%20%20X%5E%7B2%7D%20%20%5Calpha%2F2%2C%20n-1%20%5D%20%3C%20%5Calpha%20%3C%20%5B%28n-%201%29%5Ctimes%20S%5E%7B2%7D%20%20%2F%20X%5E%7B2%7D%201-%20%5Calpha%2F2%2C%20n-%201%20%5D)
We are given
Confidence level = 98%
Sample size = n = 81
Degrees of freedom = n – 1 = 80
Sample Variance = S^2 = 3.23
![X^{2}_{[\alpha/2, n - 1]} = 112.3288\\\X^{2} _{1 -\alpha/2,n- 1} = 53.5401](https://tex.z-dn.net/?f=X%5E%7B2%7D_%7B%5B%5Calpha%2F2%2C%20n%20-%201%5D%7D%20%20%20%3D%20112.3288%5C%5C%5CX%5E%7B2%7D%20_%7B1%20-%5Calpha%2F2%2Cn-%201%7D%20%3D%2053.5401)
(By using chi-square table)
[(n – 1)*S^2 / X^2 α/2, n– 1 ] < σ^2 < [(n – 1)*S^2 / X^2 1 -α/2, n– 1 ]
[(81 – 1)* 3.23 / 112.3288] < σ^2 < [(81 – 1)* 3.23/ 53.5401]
2.3004 < σ^2 < 4.8263
Lower limit = 2.30
Upper limit = 4.83.
