Step-by-step explanation:
Simplifying
(7a + 3b)(7a + -3b) = 0
Multiply (7a + 3b) * (7a + -3b)
(7a * (7a + -3b) + 3b * (7a + -3b)) = 0
((7a * 7a + -3b * 7a) + 3b * (7a + -3b)) = 0
Reorder the terms:
((-21ab + 49a2) + 3b * (7a + -3b)) = 0
((-21ab + 49a2) + 3b * (7a + -3b)) = 0
(-21ab + 49a2 + (7a * 3b + -3b * 3b)) = 0
(-21ab + 49a2 + (21ab + -9b2)) = 0
Reorder the terms:
(-21ab + 21ab + 49a2 + -9b2) = 0
Combine like terms: -21ab + 21ab = 0
(0 + 49a2 + -9b2) = 0
(49a2 + -9b2) = 0
Solving
49a2 + -9b2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '9b2' to each side of the equation.
49a2 + -9b2 + 9b2 = 0 + 9b2
Combine like terms: -9b2 + 9b2 = 0
49a2 + 0 = 0 + 9b2
49a2 = 0 + 9b2
Remove the zero:
49a2 = 9b2
Divide each side by '49'.
a2 = 0.1836734694b2
Simplifying
a2 = 0.1836734694b2
take the square root of each side:
a = {-0.428571429b, 0.428571429b}
Answer:
Step-by-step explanation:
(-3 feet)/(4 weeks) = -¾ foot per week
The answer is 20 questions.
The solution would be like this for this specific problem:
H0: p = p0, or <span>
H0: p ≥ p0, or
H0: p ≤ p0 </span>
find the test statistic z
= (pHat - p0) / sqrt(p0 * (1-p0) / n)
where pHat = X / n
The p-value of the test is
the area under the normal curve that is in agreement with the alternate
hypothesis. <span>
H1: p ≠ p0; p-value is the area in the tails greater than |z|
H1: p < p0; p-value is the area to the left of z
H1: p > p0; p-value is the area to the right of z </span>
Hypothesis equation:
H0: p ≥ 0.67 vs. H1: p
< 0.67
The test statistic is: <span>
z = ( 0.5526316 - 0.67 ) / ( √ ( 0.67 * (1 - 0.67 ) / 38 )
z = -1.538681 </span>
The p-value = P( Z < z
) <span>
= P( Z < -1.538681 )
<span>= 0.0619</span></span>
