A vending machine is designed to dispense a mean of 7.6 oz of coffee into an 8-oz cup. If the standard deviation of the amount of coffee dispensed is 0.3 oz and the amount is normally distributed, find the percent of times the machine will dispense less than 7.57 oz.

46.02%

Step-by-step explanation:

We have been given that a vending machine is designed to dispense a mean of 7.6 oz of coffee into an 8-oz cup. The standard deviation of the amount of coffee dispensed is 0.3 oz and the amount is normally distributed.

We are asked to find the percent of times the machine will dispense less than 7.57 oz.

First of all, we will find the z-score corresponding to 7.57 using z-score formula.

, where,    

z = z-score,

x = Random sample score,

=  Mean,

 = Standard deviation.    

Now we will use normal distribution table to find the probability of z-score less than -0.1 that is

Using normal distribution table we will get:

Let us convert into percentage as:

Therefore, 46.02% of times the machine will dispense less than 7.57 oz.

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step-by-step explanation:

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answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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