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Give five decimals that are between 1.45 and 1.46. Each decimal must have a different number of digits.

Show your scratch paper to the camera and upload to the Canvas once you are done with the midterm. 

Consider Eva’s work and verbal explanation of the standard algorithm for computing 389 + 475. a)  What does each “carried 1” in Eva’s work represent? b)  Eva’s teacher said “I agree with you that we start with 9 + 5. But are we adding 1 + 8 + 7 ones? What do you think Eva’s teacher is trying to help Eva understand? c)  Educators suggest using the language of “carried” in addition computations may confuse students. Why? What term should be used that is more descriptive of the mathematical ideas? d)  Add 159 + 76 using the US standard algorithm like Eva did, and write an accompanying explanation of the steps that avoids the term “carried” and more clearly addresses what is being added each time.

Consider the following word problem: Rachael has 14 puppies. Donna has 8 puppies. How many more puppies does Rachael have than Donna? a)  Grace and Hannah disagree on how to solve this problem. Grace writes 14 – 8 = ☐as her number equation, but Hannah claims that 8 + ☐= 14 is the correct equation to use. Whose number equation better directly models the situation? b)  Consider the following problem: Petra has 14 carrot sticks in her lunch box. She eats 8 carrot sticks for lunch. How many carrot sticks does Petra have left to eat? Whose number equation from part (a) better directly models the situation presented in this problem? Explain your choice.

How would you solve 359+296 by using partial sum algorithm. Explain each of your step. 

Imagine you are using the base ten blocks to represent values. You decide to model each number using only one type of block at a time. How could you model each of the following? a) 260 with tensb) 15,400 with hundreds c) 6,000 with tensd) 13,000 with hundreds

11.  Find the Radius of Convergence and the Interval of Convergence of the power series

In the figure, a cylindrical L-shaped pipe is connected to a cylindrical tank in the atmosphere near the surface of the Earth. The absolute pressure at point B is 150 kPa, and the density of the oil is 900 kg/m3. What is the mass of the piston? (The figure shows the system which is filled with oil and consists of a hollow closed vertical cylinder and an L-shaped pipe connected to the middle of its lateral surface. The cylinder has a height of 60 centimeters and a base diameter of 20 centimeters. The top base of the cylinder is marked A. The bottom base of the cylinder is marked B. The pipe has a diameter of 4.0 centimeters. The vertical part of the pipe has the oil column of 100 centimeters with a piston on it.)

8. Use the definition of a Taylor series to find the terms of the series for f(x) = 2×3 – 4x + 1 centered at 2. Please, record the series in the Canvas answer box.    

In the figure, a cylindrical L-shaped pipe is connected to a cylindrical tank in the atmosphere near the surface of the Earth. The absolute pressure at point B is 180 kPa, and the density of the oil is 900 kg/m3. What is the mass of the piston? (The figure shows the system which is filled with oil and consists of a hollow closed vertical cylinder and an L-shaped pipe connected to the middle of its lateral surface. The cylinder has a height of 60 centimeters and a base diameter of 20 centimeters. The top base of the cylinder is marked A. The bottom base of the cylinder is marked B. The pipe has a diameter of 4.0 centimeters. The vertical part of the pipe has the oil column of 100 centimeters with a piston on it.)