Answer: a) x = 2 and -4 b) p = 4.12 and -2.4
Step-by-step explanation:
a) Using the completing the square me those to solve x²+2x = 8
firstly, we divide the equation by the coefficient of x² to give
x²+2x=8
Secondly, we need to get the constant of the equation x²+2x by adding the value gotten from dividing coefficient of x by 2 and squaring it i.e(2/2)² to give 1 as the constant
The equation becomes
x²+2x+1-1= 8
Note that 1 was subtracted just to ensure the question isn't altered
(x²+2x+1)-1 = 8
(x+1)(x+1)-1= 8
(x+1)(x+1)= 8+1
(x+1)² = 9
Squaring both sides of the equation
√(x+1)² = +/-√9
x+1 = +/-3
x = +3-1 = 2
x = -3-1 = -4
therefore x = 2 and -4
b) Using the same funny concept to solve the equation
7p² − 12p + 4 = 0
7p²-12p = -4
Dividing by coefficient of p²
p²-12/7p= -4/7
Completing the equation at the right hand side i.e p²-12/7p
We will add the square of half of the coefficient of p to both sides of the given equation (-12/7×1/2)² = (-12/14)²
= 144/196
p²-12/7p+144/196 = -4+144/196
(p-12/14)² = 640/196
Squaring both sides
√(p-12/14)² = +/-√640/196
p-12/14 = +/-3.26
p = +3.26+12/14 = 4.12
and p = -3.26+12/14 = -2.4
Answer:
Step-by-step explanation:
From the information given, the population is divided into sub groups. Each group would consist of citizens picking a particular choice as the most important problem facing the country. The choices are the different categories. In this case, the null hypothesis would state that the distribution of proportions for all categories is the same in each population. The alternative hypothesis would state that the distributions is different. Therefore, the correct test to use to determine if the distribution of "problem facing this country today" is different between the two different years is
A) Use a chi-square test of homogeneity.
19 - 34 which is 15/2= 7.50 dollars each on snacks