The Point-Slope Equation: Pt 3

Mathematics

1 answer:

NARA [144]3 years ago

3 0

Answer:

y = -1/20x + 22

Step-by-step explanation:

The family trip is a linear model and its equation can be written as a linear equation y = mx + b where m is the slope and b is the y-intercept. The slope is the constant rate of change. The rate of change here is 1 gallon per 20 miles or -1/20 since each gallon used decreases from the overall gas tank. Substitute m = -1/20.

The y-intercept is the starting point or the number of gallons the tank in the van holds. Since the van had 16 gallons after 120 miles, this means there was 22 gallons. Since 120 miles has been spent at 20 miles a gallon, it took 120 / 20 = 6 gallons to drive that far. So 16 + 6 = 22 gallons. Substitute b = 22.

y = mx + b

y = -1/20x + 22

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After an extensive advertising campaign, the manager of a company expects the proportion of potential customers that recognize a

lina2011 [118]

Answer:

Step-by-step explanation:

Hello!

The study variable is:

X: number of customers that recognize a new product out of 120.

There are two possible recordable outcomes for this variable, the customer can either "recognize the new product" or " don't recognize the new product". The number of trials is fixed, assuming that each customer is independent of the others and the probability of success is the same for all customers, p= 0.6, then we can say this variable has a binomial distribution.

The sample proportion obtained is:

p'= 54/120= 0.45

Considering that the sample size is large enough (n≥30) you can apply the Central Limit Theorem and approximate the distribution of the sample proportion to normal: p' ≈ N(p; $\sqrt{\frac{p(1-p)}{n} }$ )