Since you are given a list of choices, you can go through each choice to plug them into the equations. It turns out that choice B is the answer
(3,1) means that a = 3 and b = 1
Plug in a = 3 and b = 1 into the first equation
2a - 5b = 1
2*3 - 5*1 = 1.... replace 'a' with 3, replace b with 1
6 - 5 = 1
1 = 1
we get a true equation, so we have confirmed the first equation
Do the same for the second equation
3a+5b = 14
3*3+5*1 = 14 .... replace 'a' with 3, replace b with 1
9+5 = 14
14 = 14
we get a true equation, so the second equation has been confirmed
Both equations are true when (a,b) = (3,1). So the answer (3,1) has been confirmed fully
Answer:
- 4x³ - 33x² + 31x - 3
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
x²(- 4x + 3) + 9x(- 4x + 3) - 1 (- 4x + 3) ← distribute all 3 parenthesis
= - 4x³ + 3x² - 36x² + 27x + 4x - 3 ← collect like terms
= - 4x³ - 33x² + 31x - 3
Complete Question
A certain university estimated that the proportion of students who prefer 2 day a week classes to 1 day a week classes was somewhere in the interval (0.451, 0.872) . If a 95% confidence interval was used, find the point estimate of the proportion and the margin of error
Answer:
The point estimate is ![\^ p =0.6615](https://tex.z-dn.net/?f=%5C%5E%20p%20%3D0.6615)
The margin of error is ![E = 0.2105](https://tex.z-dn.net/?f=E%20%3D%200.2105)
Step-by-step explanation:
From the question we are that
The estimate of the proportion of students who prefer 2 day a week classes to 1 day a week classes is (0.451, 0.872)
Generally the point estimate is mathematically represented as
![\^ p = \frac{ 0.872 + 0.451 }{2}](https://tex.z-dn.net/?f=%5C%5E%20p%20%3D%20%5Cfrac%7B%200.872%20%2B%200.451%20%7D%7B2%7D)
=> ![\^ p =0.6615](https://tex.z-dn.net/?f=%5C%5E%20p%20%3D0.6615)
Generally the margin of error is mathematically represented as
![E = \frac{0.872 - 0.451}{2}](https://tex.z-dn.net/?f=E%20%3D%20%20%5Cfrac%7B0.872%20-%200.451%7D%7B2%7D)
=> ![E = 0.2105](https://tex.z-dn.net/?f=E%20%3D%200.2105)
Answer:
x²-10x+29
Step-by-step explanation:
(x-5)²+4
x²-10x+25+4
x²-10x+29