Last year, a soft drink manufacturer had 21% of the market. in order to increase their portion of the market, the manufacturer has introduced a new flavor in their soft drinks. a sample of 400 individuals participated in the taste test and 100 indicated that they like the taste. we are interested in determining if more than 21% of the population will like the new soft drink. determine the p-value. select one: a. p-value = 0.096 b. p-value = 0.025 c. p-value = 0.048 d. p-value = 0.073

I will do the hypothesis test.

The null hypothesis is: p <= 0.21

The alternative hypothesis is: p > 0.21

Since the confidence interval for this problem is 95%

The critical value for this is 1.960

So the alpha is .05, the p value is equal to 0.05/2 = 0.025 since it is a 2 tailed test. (letter b)

So p value = 0.025 < 0.5, therefore, reject null hypothesis. More than 21% like the new soft drink.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions