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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.
The credit score of a 35 year old applying for a mortgage at Ulysses Mortgage Associates is normally distributed with a mean of 600 and a standard deviation of 100.
Use a two proportion z-test to perform the required hypothesis test. State the conclusion.
Q2 is dummy variable equal to 1 in second quarter and 0 otherwise; and Q3 is final dummy variable equal to 1 in third quarter and 0 otherwise. Determine the Base Quarter?
Suppose that verbal scores on SAT exam have a normal distribution with a population mean 500 points and population standard deviation of 100.
A student team examined parked cars in four different suburban shopping malls. One hundred vehicles were examined in each location. Research question: At α = . 05, does vehicle type vary by mall location?
A random sample of 7 students selected from a large class revealed the following scores: midterm 70, 62, 57, 68, 89, 63, 82 and on the final 80, 79, 87, 88, 85, 79, 91. Is there evidence of an improvement on the final?
Draw the distribution of the random variable X, representing her time of arrival. (Be sure to include labels and values on the axes.)
Following sample data shows the weekly closing price of ABC stock. Compute the sample mean and variance from this data set.
Over the past 30 years in the United States, there has been a strong negative correlation between the number of infant deaths at birth and the number of people over age 65. What lurking variables might be causing the changes in each of the variabl..
The lifetimes of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. What percentage of bulbs has lifetimes that lie within 1 standard deviation of the mean on either side?
Show that Pearson's Chi-square statistic for testing Ho : 1 = 2 when there are k-categories reduces to Z^2 when k = 2, where Z = 2 sqrt(n)(p1-1/2) is the standard Z-test for testing Ho : 1 = 1=2
Explain clearly, in your own words, what is a Type I error in this context.
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