In the coordinate plane, the point X (3, 1) is translated to the point X'(4, -1). Under the same translation, the points Y(-1, -
1 answer:
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1.) We can solve the problem by developing a linear model.
Let x represent the quantity to be used of the grade of coffee that sells for $70 per pound, and y represent the quantity to be used of the grade of coffee that sells for $80 per pound, then
Therefore, 32 pounds of the grade of coffee that sells for $70 per pound, and 48 pounds of the grade of coffee that sells for $80 per pound should be used.
2.) Volume of alcohol in the original mixture
quarts
Let x be the number of quarts of alcohol to be added, then
Volume of alcohol in the new mixture
Therefore, 10 quarts of pure alcohol should be added
3.) Original proportion of white paint in the mixture
Let x be the number of gallons of white paint to be added, then
Therefore, 17 gallons of white paint should be added.
4a.) Let the three consecutive odd integers be x - 2, x and x + 2, then
which is not an integer.
Hence, the sum of three consecutive odd integers cannot be 25.
4b.) Let the three consecutive odd integers be x - 2, x and x + 2, then
Thus, the three consecutive odd intergers whose sum is 45 are 13, 15 and 17.
5.) If all pipes are open and the tank was initially empty, let t be the time it will take to fill the tank, then
Therefore, it will take 7.83 hours to get the tank filled up.
Let x represent the quantity to be used of the grade of coffee that sells for $70 per pound, and y represent the quantity to be used of the grade of coffee that sells for $80 per pound, then
Therefore, 32 pounds of the grade of coffee that sells for $70 per pound, and 48 pounds of the grade of coffee that sells for $80 per pound should be used.
2.) Volume of alcohol in the original mixture
Let x be the number of quarts of alcohol to be added, then
Volume of alcohol in the new mixture
Therefore, 10 quarts of pure alcohol should be added
3.) Original proportion of white paint in the mixture
Let x be the number of gallons of white paint to be added, then
Therefore, 17 gallons of white paint should be added.
4a.) Let the three consecutive odd integers be x - 2, x and x + 2, then
which is not an integer.
Hence, the sum of three consecutive odd integers cannot be 25.
4b.) Let the three consecutive odd integers be x - 2, x and x + 2, then
Thus, the three consecutive odd intergers whose sum is 45 are 13, 15 and 17.
5.) If all pipes are open and the tank was initially empty, let t be the time it will take to fill the tank, then
Therefore, it will take 7.83 hours to get the tank filled up.
Answer:
P-value = 0.4846
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 4.73
Sample mean, = 4.35
Sample size, n = 51
Alpha, α = 0.05
Sample standard deviation, s = 3.88
First, we design the null and the alternate hypothesis
We use Two-tailed z test to perform this hypothesis.
Formula:
Putting all the values, we have
Now,
We can calculate the p-value with the help of standard normal table.
P-value = 0.4846
Since the p-value is higher than the significance level, we fail to reject the null hypothesis and accept it.
We conclude that this college has same drinking habit as the college students in general.