Acoin-operated coffee machine made by big corporation was designed to discharge a mean of ounces ounces of coffee per cup. if it dispenses more that that on average, the corporation may lose money, and if it dispenses less, the customers may complain.
believing that the mean amount of coffee dispensed by the machine, , is less than ounces, big plans to do a statistical test of the claim that the machine is working as designed. technicians gather a random sample of fill amounts and find that the mean of the sample is ounces and that the standard deviation is ounces.

what are the null hypothesis and the alternative hypothesis that should be used for the test?

in the context of this test, what is a type i error?

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

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d

step-by-step explanation:

the 2000 florida legislature amended section 322.05, florida statutes, changing the requirements to obtain a class e license for a driver under the age of 18 holding a learner's license. the following requirements must be met in order to obtain a regular class e license if a learner's license is issued on or after october 1, 2000:

must hold a learner's license for at least 12 months or until the 18th birthday.

must have no convictions 12 months from the issue date of the learner's license.

may have one traffic conviction within 12 months from the issue date of the learner's license if adjudication is withheld.

a parent, legal guardian, or responsible adult over 21 years old must certify that the driver has 50 hours driving experience, including 10 hours of night time driving.