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Question

asked 2021-04-18

A 2.0-kg projectile is fired with initial velocity components \(\displaystyle{v}_{{{0}{x}}}={30}\) m/s and \(\displaystyle{v}_{{{0}{y}}}={40}\) m/s from a point on the earth's surface. Neglect any effects due to air resistance. What is the kinetic energy of the projectile when it reaches the highest point in its trajectory? How much work was done in firing the projectile?

asked 2021-08-09

Use the information provided to write the general conic form equation of each ellipse.

\(\displaystyle{\frac{{{x}^{{2}}}}{{{36}}}}+{\frac{{{y}^{{2}}}}{{{81}}}}={1}\)

\(\displaystyle{\frac{{{x}^{{2}}}}{{{36}}}}+{\frac{{{y}^{{2}}}}{{{81}}}}={1}\)

asked 2020-10-23

1. Find each of the requested values for a population with a mean of \(? = 40\), and a
standard deviation of \(? = 8\)
A. What is the z-score corresponding to \(X = 52?\)
B. What is the X value corresponding to \(z = - 0.50?\)
C. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of z-scores?
D. What is the z-score corresponding to a sample mean of \(M=42\) for a sample of \(n = 4\) scores?
E. What is the z-scores corresponding to a sample mean of \(M= 42\) for a sample of \(n = 6\) scores?
2. True or false:
a. All normal distributions are symmetrical
b. All normal distributions have a mean of 1.0
c. All normal distributions have a standard deviation of 1.0
d. The total area under the curve of all normal distributions is equal to 1
3. Interpret the location, direction, and distance (near or far) of the following zscores: \(a. -2.00 b. 1.25 c. 3.50 d. -0.34\)
4. You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with \(\mu = 78\) and \(\sigma = 12\). Recently, a new person joined the team, and you think the scores have gotten better. Use hypothesis testing to see if the average score has improved based on the following 8 weeks’ worth of score data: \(82, 74, 62, 68, 79, 94, 90, 81, 80\).
5. You get hired as a server at a local restaurant, and the manager tells you that servers’ tips are $42 on average but vary about \($12 (\mu = 42, \sigma = 12)\). You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don’t know if you will make more or less in tips. After working 16 shifts, you find that your average nightly amount is $44.50 from tips. Test for a difference between this value and the population mean at the \(\alpha = 0.05\) level of significance.

asked 2021-08-10

Find the equation of the graph for each conic in general form. Identify the conic, the center, the vertex, the co-vertex, the focus (foci), major axis, minor axis, \(\displaystyle{a}^{{2}}\), \(\displaystyle{b}^{{2}}\), and \(\displaystyle{c}^{{2}}\). For hyperbola,find the asymtotes.Sketch the graph

\(\displaystyle{2}{\left({y}+{2}\right)}^{{2}}+{4}{\left({x}-{4}\right)}^{{2}}={8}\)

\(\displaystyle{2}{\left({y}+{2}\right)}^{{2}}+{4}{\left({x}-{4}\right)}^{{2}}={8}\)