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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.)

Rebecca decided to solve 18 + 29 by rounding both numbers up to friendly numbers. Show what her first step might look like, then finish the problem in the way you expect that she would finish it.

Ellery and Sofia were discussing when you must trade groups of base ten blocks for the next largest block. Ellery says she repackages when she has 9 of a block. Sofia disagrees, she says you don’t need to repackage when you have 9. Do you agree or disagree with Ellery and Sofia? Explain.

Firefighters connect a fire hose to a hydrant and lift the other end of the hose into the air to attack a fire in an upper floor. Just below the hydrant the gauge water pressure is 148 kPa, the pipe has a diameter of 6.0 cm, and the volume flow rate through the pipe is 0.04 m3/s. If the gauge water pressure is zero at the high end of the hose, which has a diameter of 5.0 cm, to what height did the firefighters lift the hose?