proof CAUBIC)= PLA|1B) t plc1B)- p(A nel13)
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- Solve the problem.The following is known about three numbers: If the second number is subtracted from the sum of the first number and 3 times the third number, the result is -7. The third number plus 2 times the first number is -2. The first number plus 5 times the second number plus the third number is 3. Find the three numbers.[Hint: let x represent the first number, y the second number, and z the third number. Use the given conditions to write and solve a system of equations.]A tortoise challenged a hare to a 100-meter race on a track. The tortoise negotiated a 50-meter head start with the hare. When the race started the hare was running at a constant speed of 2.8 meters per second and the tortoise was crawling at a speed of 0.5 meters per second. (They both maintained these speeds for the entire race.) Our goal is to determine who won the race. Read the above problem statement again, then explain in writing on a sheet of paper how you will determine who won the race. Construct a drawing to represent the 100-meter length of the track. Then place the tortoise and hare's starting points on the track. Define the variable t to represent the number of seconds since the start of the race. Write an expression to represent the Tortoise's distance from the starting line in terms of t. Represent the Hare's distance from the starting line in terms of t. Write a formula to represent the distance, d (in meters), that the tortoise is ahead of the hare in…Professor Chauvet wanted to know how quickly her students can type out a text message. So that everyone typed the same thing, she asked the students to type (and send!) the alphabet to someone in a text message. She gave them 15 seconds and asked them to type out as much of the alphabet as possible in that time frame. (Each letter needed to be followed by a space before the next letter was typed.) When time was up, the students pressed send. Then they counted how many characters they typed. Here is a stemplot of the results: Note that the students who only typed 4 and 7 characters claimed to have issues with autocorrect on their phones. Here is a stemplot of the results: 0 47 1389 2 0444555667779 3 0000112234566666888 4 01278999 5 2 512 represents a student who typed the entire alphabet in the 15 allotted seconds. Which of the following correctly displays these data in the form of a histogram? Frequency Frequency Frequency Frequency 101 9- 8- 7- 6- 5- 4- 3- 2- 1 0- 0 10- 9. 8- 7- 4- 3-…
- please answer part d as well. i dont see the solution anywhere here.I bought a new gas lawn mower the other day. This new mower mows faster than the old electric (environmental) one. Why, you ask? It is because the old mower cut a 21 inch path, while the new one cuts a 22 inch path. So how much time did I save? Look at some facts. My lawn is a rectangle measuring 150 feet by 105 feet I mow the lawn in strips and always in the same direction (length or width) My walking speed is 120 feet/minute It takes 5 seconds to turn around after each strip How much time did I save if I mow back and forth along the width or if I mow back and forth along the length? Pick one and figure it out. My neighbor does not like minutes the noise it makes, but I do!A cyclist takes 4 hours to travel from Town A to Town B. The cyelist's average speed for the first hour is nalf the cyclist's average speed for the second hour, and the eyclist's average speed for the first two hours is equal to twice the cyclist's average speed for the last two hours. If the cyclist traveled at an average speed of 9 miles per hour for the 4-hour trip, what was the cyclist's average speed, in miles per hour, during the first hour of the trip?
- Summarize the steps you need to follow in order to determine what type of permutation or combination formula to use for any given problem. Be sure to include explanations of each possible outcome.Does there happen to be more to this solution? I still can't quite followSubtract 1.2a“ – 0.7a from the sum of 0.6 a4 + 1.5a and 0.4 a4 - 1.1a First, we will translate the words of the problem into mathematical symbols. Then we will perform the indicated operations. The words of the problem contain the key phrases subtract from and sum. Since 1.2a4 – 0.7a is to be subtracted from the sum, the order must be reversed when we translate to mathematical symbols. Subtract 1.2a4 0.7a from the sum of 0.6a + 1.5a and 0.4a4 1.1a. [(0.6 a4 + 1.5a) + (0.4 at – 1.1a) ] - (1.2a* – 0.7a) Use brackets [ ] to enclose the sum. Next, we remove the grouping symbols to obtain 0.6 a4 + 1.5a + 0.4 at – 1.1a -1.2a4 + 0.7a Change the sign of each term within (1.2a4 - 0.7a) and drop the parentheses. at+ a Combine like terms. %D Subtract -0.6q? – 0.6q from the sum of 0.1q? - 0.6q and 0.3q² + 0.1q.
- Answer urgently please !!! Show all workingAkira is running around a circular track. Akira runs counterclockwise. From where he starts, it takes him 22 seconds to reach the easternmost point of the track. It takes him 95 seconds to run one complete lap.Bob starts running at the same time as Akira. Bob starts from the northernmost point and runs clockwise. Bob and Akira pass each other for the first time after 26 seconds. How long does Bob take to run one lap of the track? The answer to this question should be the amount of time in seconds rounded to four decimal places that it takes for Bob to run a complete lap around the circular track.A tortoise and hare are competing in a 400-meter race. The arrogant hare gives the tortoise a 220-meter head start. When the start gun is fired, the hare begins running at a constant speed of 3.5 meters per second and the tortoise begins crawling at constant speed of 1.5 meters per second. Take out a piece of paper and read the above problem context again. You will prepare your written work and solutions on your own paper and upload it and the end of this question. Complete the problem solving process by: i. reading and re-reading the problem to identify the quantities in the situation; ii. making a drawing to represent the relevant quantities in the situation; iii. and defining the variable t to represent the number of seconds since the start of the race. a. Define a function f to determine the distance of the tortoise from the finish line in terms of the number of seconds, t, since the start of the race. Preview Solve f(t) = 0 and describe what your solution represents. t = Preview…
