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Determine whether the following equations real or complex solutions; justify your answer. Note: It is not necessary to find the solutions; just determine if they are real or complex and explain why.
a) 5x2 + 8x + 7 = 0
b) (7)1/2y2 - 6y - 13(7)1/2 = 0
c) 2x2 + x - 1 = 0
d) 4/3x2 - 2x + 3/4 = 0
e) 2x2 + 5x + 5 = 0
f) p2 - 4p + 4 = 0
g) m2 + m + 1 = 0
h) 3z2 + z - 1 = 0
2. Form a quadratic equation that passes through the x-axis at x = 3 and x = -5. (must be an equation, not an expression.)
3. What type of solution do you get for quadratic equations where D < 0? Give reasons for your answer. Also provide an example of such a quadratic equation and find the solution of the equation.
4. Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.
A machine that manufactures automobile parts is estimated to produce defective parts 5% of the time. If this estimate is correct, and 9 parts produced by this machine are randomly selected
Calculate a 95% confidence interval on the average weight of packaged mustard seed. Explain very carefully to the packaging workers what the 95% confidence interval numbers mean. Include your Excel output. Is there anything you would want to note ..
A fair coin is flipped 3 times. Compute the odds of flipping 3 tails.
For two samples from what are assumed to be normally distributed populations, the sample size and standard deviations are n1 = 10, s1 = 23.5, n2 =9 and s2=10.4.
What does a squared correlation coefficient represent? Also, does the strength of the correlation depend on the direction? Finally, does correlation imply causation.
Clearly identify the independent and dependent variables you would study, including the number of levels of the independent variable.
Sample data recently collected indicate that Dough Boy's crusts average 30 centimeter in diameter, with a standard deviation of 1.1 centimeters.
Construct a 95 percent confidence interval for the true mean.
Given the binomial distribution with n = 23 and p = 0.79, would the normal distribution provide the reasonable approximation? Why or why not?
The president of Doerman Distributors, Inc., believes that 34% of the firm's orders come from first-time customers. A simple random sample of 120 orders will be used to estimate the proportion of first-time customers
Of the estimated natural gas reserves in North America, 4.59 *10^9 m ^3 are in United States. 2.66*10^9 m^3 are in Canada, and 1.99*10^9 m^3 are in Mexico.
Suppose that the scores of architects on a particular creativity test are normally distributed.
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