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Its the start of the New Year! This is where we'll keep with the math problems in 2023. If you want to access the problems from 2022, you can press the button below.

You're getting ready for New Years! You invite 6 friends over and you want to make 3 cookies per every person, including yourself. The recipe calls for 2 cups of flour for 9 cookies. How many cups of flour do you need?

To find the amount of cookies you will need to make, you should multiply the amount of people by the number of cookies you need to make.

(5 friends + 1 yourself) * 3 cookies per person = 18 cookies

Since the recipe accounts for 9 cookies, you would need 2 batches of cookies. This means you need 2 batches * 2 cups of flour per batch = 4 cups of flour.

If a hockey team scores 13% of the time, on average, how many times would they score if they had 307 shots on goal in a season (round to the nearest goal)?

If a team scores 13% of the time, they would score 13/100 shots taken. From here we can set up a proportion:

13/100 = x/307

100x = (13)(307)

x = 3991/100 = 39.91

Since we round to the nearest goal, the answer is 40 goals.

A basketball team averages 14 points per player during a game. There are 6 players on the team who have scored. A player scores a quarter of the points during a game. How many points did they score?

If there are 14 points per player during a game, and there are 6 players who have scored, then there were 84 points scored by that team. Since the player scored a quarter of the points, that means they scored 84/4 points, or, 21 points.

A figure skater does a jump. They are in the air for .63 seconds and complete 4.5 revolutions. About how many rpm is the figure skater spinning? (ignore air resistance and friction)

To find the amount of time it takes to complete one rotation, you would divide the revolutions by the amount of air time:

4.5 revolutions / .63 seconds = 7.143 rev/sec

To convert this to revolutions per minute, one would have to multiply this number by 60.

7.143 rev/sec * 60 sec/min = 428.571 rpm

Someone is standing on the ground 450 feet away from the base of a cell tower. If the person looks towards the top of the cell tower looks up at an angle of 32 degrees, how tall is the tower?

The person makes a right triangle with the cell tower. We know one angle and the adjacent side. From this, we can use trigonometry to determine the height of the tower.

sin(32 degrees) = x/450

x = 238.464

If 74% of a compound dissolves when coming into contact with water, how much of a 251 gram sample would dissolve in water?

In order to solve this problem, you would need to find the percent of 251 grams that will dissolve. Since 74% of the compound dissolves, to find the percent of the compound that dissolves, all you have to do is multiply the mass by the percent that dissolves.

.74 percent * 251 grams = 185.74 grams that dissolves

Someone looks at the top of a skyscraper from 2 different points where the distance between the two points is 60 feet. If the angles of elevation are 30 and 60 degrees, how tall is the skyscraper?

There are a few ways to solve this problem, but I will be using the law of sines.

The law of sines are a set of ratios that can be used to find different sides or angles in any triangle.

sin30/x = sin30/60ft

x=60

sin60 = x/60

x = 103.9 feet

If a boat docked at a pier and travels 12 knots (nautical miles per hour) west for 4 hours and then 10 knots north for 6.4 hours, how far from the start would the boat be?

The shape of the boat’s path would be a right triangle. To find the distances that the boat travelled west and north, you can multiply the speed of the boat by the amount of time it has travelled.

12 knots * 4 hours = 48 nautical miles west

10 knots * 6.4 hours = 64 nautical miles north

These numbers create a 3-4-5 right triangle, meaning the distance from the boat to the port is 80 nautical miles.

A power washer charges a flat rate of $50 in addition to $25/hour of work. Write an equation for the price of the service, P, as a function of hours of work, w.

Since the power washer charges $25/hour, you can assume the price to be 25*hours of work without the flat rate. Since the flat rate of $50 doesn’t change with the amount of time the job takes, you can just add the 50 to the equation.

P = 25w + 50

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