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Questions in mathematics

[Done] Simplify [tex]\frac{5^5 \cdot 6^3 \cdot 8^{10}}{5^3 \cdot 6 \cdot 8^9}[/tex].

[Done] Given [tex]f(x)=x^2-2 x[/tex], identify the axis of symmetry, vertex, [tex]x[/tex]-intercepts, [tex]y[/tex]-intercept, and the range of the function. Axis of Symmetry Vertex [tex]x[/tex]-intercepts [tex]y[/tex]-intercept Range

[Done] The frequency table was made using a bag containing slips of paper that are numbered [tex]$1,2,3,4$[/tex], or 5. | [tex]x[/tex] | [tex]f[/tex] | |---|---| | 1 | 4 | | 2 | 12 | | 3 | 20 | | 4 | 32 | | 5 | 12 |

[Done] In the final round of the Western Baking Challenge, Max and Colette must each create a display of iced cookies. Colette's cookies cooled off first, and she begins icing them at a rate of 3 cookies per minute. After Collette has iced 12 cookies, Max starts icing his cookies at a rate of 5 cookies per minute. Soon, he will catch up to Colette and the two will have iced the same number of cookies. Which equation can you use to find [tex]$m$[/tex], the number of minutes it will take Max to catch up to Colette? [tex]$3 m+12=5 m$[/tex] [tex]$5 m+3=12 m$[/tex] How long will it take Max to catch up to Colette? Simplify any fractions. $\square$ minutes

[Done] $1 \frac{3}{5}-1 \frac{3}{5}$

[Done] Simplify each expression. 1. [tex]3^8 \cdot 3=[/tex]

[Done] At his school's spring carnival, Porter is in charge of the balloon-launcher contest. In this contest, each team builds a catapult to launch water balloons at a target. Porter gives a bucket of 14 water balloons to each team in the contest. In all, he gives out 70 water balloons. Which equation can you use to find the number of teams [tex]$t$[/tex] in the contest? [tex]$t-14=70$[/tex] [tex]$t+14=70$[/tex] [tex]$\frac{t}{14}=70$[/tex] [tex]$14 t=70$[/tex] Solve this equation for [tex]$t$[/tex] to find the number of teams in the contest. $\square$ teams

[Done] Solve the equation. $5 x+4=-8+2 x+18$

[Done] Write expressions to represent the length and width of Melissa's vegetable garden.

[Done] There are 6 tiles numbered 1 to 6 in a box. Two tiles are selected at random without replacement to form a 2-digit number where the first number picked is the tens digit and the second number picked is the ones digit. Jeffrey found the probability that the number selected is 16 as shown. Explain his error. The number of ways to select 1 and 6 is given by ${ }_6 c_2=15$ $P(16)=\frac{1}{{ }_6 C_2}=\frac{1}{15}$