CubeyThePenguin

fabric required: 2 1/2 + 1 3/4 = 3 + 1/2 + 3/4 = 4 1/4 yards

fabric in possession: 3 yards

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need to purchase 4 1/4 - 3 = 1 1/4 yards

total cost = (1 1/4) * ($7.98) = $9.98 (to the nearest cent)

2x - 5 <= x + 12

Subtract x from both sides to isolate x:

x - 5 <= 12

Add 5 to both sides:

x <= 17

In interval form: \([17, \infty)\)

\(2a_1 - a_2a_0 = (-1)^1 \quad \rightarrow \quad 2(5) - a_2 \cdot 1 = -1 \quad \rightarrow \quad a_2 = 11\)

\(2a_2 - a_3a_1 = (-1)^2 \quad \rightarrow \quad 2(11) - a_3 \cdot 5 = 1 \quad \rightarrow \quad a_3 = \boxed{\frac{21}{5}}\)

To divide a fraction, multiply by the reciprocal.

\(\frac{1}{4} \div \frac{-3}{8} = \frac{1}{4} \cdot \frac{8}{-3} = \frac{8}{-12} = \boxed{-\frac{2}{3}}\)

To divide a fraction, multiply by its reciprocal.

\(\frac{-7}{10} \div \frac{2}{5} = \frac{-7}{10} \cdot \frac{5}{2} = \frac{-35}{20} = \boxed{\frac{-7}{4}}\)

\(3(x-4) - 2(x^2 - x + 7) + 5(x-1) + 3(x+8)\)

\((3x - 12) - (2x^2 - 2x - 14) + (5x - 5) + (3x + 24)\)

\(3x - 12 - 2x^2 + 2x + 14 + 5x - 5 + 3x + 24\)

\(-2x^2 + 13x + 21 \)

constant term = 21

Total number of coin flip configurations: \(2^{10} = 1024\)

(2 choices for each flip: heads or tails, for 10 flips)

heads in 5 flips: \(10 \choose 5\)

(There are 10 choose 5 ways to rearrange the flips in the sequence HHHHHTTTTT.)

heads in 6 flips: \(10 \choose 6\)

heads in 7 flips: \(10 \choose 7\)

etc.

probability = \(\frac{{10 \choose 5} + {10 \choose 6} + {10 \choose 7} + {10 \choose 8} + {10 \choose 9} + {10 \choose 10}}{2^{10}} = \frac{628}{1024} = \boxed{\frac{157}{256}.} \)

best guess: COLLECTS

\(f(x) = y = -5x + 4\)

\(y - 4 = -5x\)

\(\frac{4 - y}{5} = x\)

---> \(\boxed{f^{-1}(x) = \frac{4 - x}{5}}\)

probability of picking blue = \(\frac{4}{13}\)

probability of picking green = \(\frac{5}{13}\)

probability of picking blue OR green = \(\frac{4 + 5}{13} = \boxed{\frac{9}{13}}\)