Answer:
r = 105
Step-by-step explanation:
Given quadratic equation:
x² − 9x − 6
Quadratic formula is given by:
(-b ± √b² - 4ac) ÷ 2a
For the equation: x² - 9x - 6
a = 1, b = -9 and c = -6
Substitute in the quadratic formula:
(-b ± √b² - 4ac) ÷ 2a
(-(-9) ± √(-9)² - 4(1*-6)) ÷ 2*1
= 9 ± √105 / 2
The solution of x² − 9x − 6 is expressed as 9 plus or minus the square root of r, all over 2
Therefore, the value of r is 105
Step1: Define an odd integer.
Define the first odd integer as (2n + 1), for n = 0,1,2, ...,
Note that n is an integer that takes values 0,1,2, and so no.
Step 2: Create four consecutive odd integers.
Multiplying n by 2 guarantees that 2n will be zero or an even number.
Therefore (2n + 1) is guaranteed to be an odd number.
By adding 2 to the odd integer (2n+1), the next number (2n+3) will also be an odd integer.
Let the four consecutive odd integers be
2n+1, 2n +3, 2n +5, 2n +7
Step 3: require that the four consecutive integers sum to 160.
Because the sum of the four consecutive odd integers is 160, therefore
2n+1 + 2n+3 + 2n+5 + 2n +7 = 160
8n + 16 = 160
8n = 144
n = 18
Because 2n = 36, the four consecutive odd integers are 37, 39, 41, 43.
Answer: 37,39,41,43
If you are using half as much milk every day, you'll never run out because you'll just keep using half as much. You still won't run out with the coffee shop problem or the refrigerator problem.
Answer:
Let x rep the lenght of the shorter one
Then the longer one is 2x+1
Therefore
(2x+1) + x = 16
We now solve for x
2x + 1 + x = 16
Group and evaluate like terms
3x +1 = 16
3x = 16 -1
× = 15/3
x = 5
So the shorter one is 5 ft
The longer one is 2(5)+1= 11
Answer:
Step-by-step explanation:
Using the formula
p +/- z* √(p(1-p) / n)
Where p is sample proportion = 3226/3957 = 0.8153, n = 3957 and z* is 2.576
0.8153 + (2.576 √(0.8153(1-0.8153) / 3957))
0.8153 + (2.576 √ (0.8153(0.1847) /3957)
0.8513 + (2.576 √(0.1572/3957)
0.8513 + (2.576 √0.00003974)
0.8513 + 2.576(0.0063)
0.8513 + 0.016
0.8670 ~ 87%
For the lower interview
0.8513 - 0.016
= 0.8353 ~ 84%
Thus, at 99% confidence interval is 84% and 87%
