On the $xy$-plane, the origin is labeled with an $M$. The points $(1,0)$, $(-1,0)$, $(0,1)$, and $(0,-1)$ are labeled with $A$'s. The points $(2,0)$, $(1,1)$, $(0,2)$, $(-1, 1)$, $(-2, 0)$, $(-1, -1)$, $(0, -2)$, and $(1, -1)$ are labeled with $T$'s. The points $(3,0)$, $(2,1)$, $(1,2)$, $(0, 3)$, $(-1, 2)$, $(-2, 1)$, $(-3, 0)$, $(-2,-1)$, $(-1,-2)$, $(0, -3)$, $(1, -2)$, and $(2, -1)$ are labeled with $H$'s. If you are only allowed to move up, down, left, and right, starting from the origin, how many distinct paths can be followed to spell the word MATH?

In a recent basketball game between the storm and the chargers, the number of points scored by the storm in the first half was equal to the number of points scored by the chargers in the second half of the game. in the first half, the storm scored 64 points, which is one - third of the total points that were scored during the game. during the second half, the chargers scored 16 points more than one - fourth the points scored in the game. you want to know how many total points that were scored during the game. 1. write an equation that models this situation. then, solve the equation. 2. how many total points were scored during the game? explain your reasoning. 3. does your answer make sense? justify your reasoning.

Arestaurant gives out a scratch-off card to every customer. the probability that a customer will win a prize from a scratch-off card is 25%. design and conduct a simulation using random numbers to find the experimental probability that a customer will need more than 3 cards in order to win a prize. justify the model for your simulation, and conduct at least 10 trials.

Circle a has a diameter of 7 inches, a circumference of 21.98 inches, and an area of 38.465 square inches. the diameter of circle b is 6 inches, the circumference is 18.84 inches, and the area is 28.26 square inches. part a: using the formula for circumference, solve for the value of pi for each circle. (4 points) part b: use the formula for area and solve for the value of pi for each circle. (4 points)