Answer:
Step-by-step explanation:
2x²+4x -16 = 2(x²+2x-8); factor 2
= 2(x+4)(x-2) ;factor the quadratic equation
4x²-16 = 4(x²-4) ; factor 4
=4(x²- 2²) ; rewrite 4 as 2²
= 4(x-2)(x+2); now use the difference of two squares a²-b²=(a-b)(a+b)
so now we have:
; simplify (x-2) from numerator and denominator
and 2/4 as 1/2
You intend to estimate a population mean μ from the following sample. 26.2 27.7 8.6 3.8 11.6 You believe the population is normally distributed. Find the 80% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to twp decimal places.
Answer:
The Confidence interval = (8.98 , 22.18)
Step-by-step explanation:
From the given information:
mean =
mean = 15.58
the standard deviation =
the standard deviation =
standard deviation = 9.62297
Degrees of freedom df = n-1
Degrees of freedom df = 5 - 1
Degrees of freedom df = 4
For df at 4 and 80% confidence level, the critical value t from t table = 1.533
The Margin of Error M.O.E =
The Margin of Error M.O.E =
The Margin of Error M.O.E =
The Margin of Error M.O.E = 6.60
The Confidence interval = ( )
The Confidence interval = ( ,
)
The Confidence interval = ( 15.58 - 6.60 , 15.58 + 6.60)
The Confidence interval = (8.98 , 22.18)
Answer:
Emma spend 8 hours in homework in a week and Jared spends 16 hours in homework in 2 weeks.
Step-by-step explanation:
Two quantities P and Q are said to be in PROPORTION if and only if for all values of P and q, we get:
Here, k : PROPORTIONALITY CONSTANT
Case: 1
5 hour piano practice in 1 week.
So, the piano practice in 2 weeks( 1 x 2) = 2 x 5 = 10 hours
But here, it is given to be 12 hours in 2 weeks.
Hence, NOT PROPORTIONAL.
Case 2:
70 words in 60 seconds.
So, the words typed in 210 seconds ( 60 x 3.5) = 70 x 3.5 = 240 words
But here, it is given to be 280 words in 210 seconds.
Hence, NOT PROPORTIONAL.
Case: 3
8 hour homework in 1 week.
So, the homework done in 2 weeks( 1 x 2) = 2 x 8 = 16 hours
It is given to be 16 hours in 2 weeks.
Hence, PROPORTIONAL.
Case: 4
15 miles in 78 minutes.
So, the distance covered in 102 minutes (78 x 1.3) = 15 x 1.3 = 19.6 miles
But here, it is given to be 17 miles in 102 minutes.
Hence, NOT PROPORTIONAL.
Case: 5
18 miles in 45 minutes.
So, the distance covered in 55 minutes (45 x 1.2) = 18 x 1.2 = 21.6 miles
But here, it is given to be 22 miles in 55 minutes.
Hence, NOT PROPORTIONAL.
Hence, the only proportional case is Emma spend 8 hours in homework in a week and Jared spends 16 hours in homework in 2 weeks.