I am currently a high school educator and have experience doing all kinds of math!
Express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)
There are 24 people who work in Dane’s department. Next week, one person will be selected at random to bring in doughnuts. Find the probability that Dane will be selected. Round your answer to the nearest thousandth.
Under certain water conditions, the free chlorine (hypochlorous acid, HOCl) in a swimming pool decomposes according to the law of uninhibited decay. After shocking his pool, Ben tested the water and found the amount of free chlorine to be 2.5 parts per million (ppm). Twenty-four hours later, Ben tested the water again and found the amount of free chlorine to be 2.2 ppm. What will be the reading after 3 days (that is, 72 hours)? When the chlorine level reaches 1.0 ppm, Ben must shock the pool again. How long can Ben go before he must shock the pool again?
Use Gaussian elimination or Gauss-Jordan elimination in Exercises $41-44$Greenfield Manufacturing borrowed $\$ 30,000$ to buy a new piece of equipment. Part of the money was borrowed at $8 \%,$ part at $10 \%,$ and part at $12 \% .$ The annual interest was $\$ 3040,$ and the total amount borrowed at $8 \%$ and at $10 \%$ was twice the amount borrowed at $12 \% .$ How much was borrowed at each rate?
The law ofcosines states that in $\triangle X Y Z$$x^{2}=y^{2}+z^{2}-2 y z \cos X$a. Explain how the law of cosines allows you to make a quick test to see if angle $X$ is acute, right, or obtuse, as shown:Property: Test for the Size of an Angle in a TriangleIn $\triangle X Y Z:$If $x^{2}<y^{2}+z^{2},$ then $x$ is an acute angle.If $x^{2}=y^{2}+z^{2},$ then $x$ is a right angle.If $x^{2}>y^{2}+z^{2},$ then $x$ is an obtuse angle.b. Without using your calculator, find whether angle $x$ is acute, right, or obtuse if $x=7 \mathrm{cm}$ $y=5 \mathrm{cm},$ and $z=4 \mathrm{cm}$.
Sketch the graph of the function by (a) applying the Leading Coefficient Test, (b) finding the zeros of the polynomial, (c) plotting sufficient solution points, and (d) drawing a continuous curve through the points.$f(x)=3 x^{3}-24 x^{2}$
A Statistics class is estimating the mean height of all female students at their college. They collect a random sample of "23, 24, 25, 26, 27" female students and measure their heights. The mean of the sample is "65.1, 65.2, 65.3, 65.4, 65.5" inches. The sample has a standard deviation of "5.5, 5.4, 5.3, 5.2, 5.1" inches. What is the 90% confidence interval for the mean height of all female students in their school? Assume that the distribution of individual female heights at this school is approximately normal.
Let A ={1,2,3,4,5,6}, and consider the following relation R on AR={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(2,3),(3,2),(4,5),(5,4),(4,6),(6,4),(5,6),(6,5)}List the equivalence classes of R.
1. Which of the three carts appears to move with constant speed? Explain how you can tell.
2. Represent the motion of this cart on theposition vs. time graph provided.
3. Determine both the speed and initial position of the cartthat you identified as having constant speed.
4. Using the symbols x and t, write an equation that describes a model of the position for the cart thatyou identified. Include appropriate units with any numerical values in write in your equation.
Find the area of the triangle with vertices (0, 0, 0), (2, 4, -5), and (2, 3, -3). A =?
as shown in the picture