Live practice

Use the sequence definition or geometric-progression formula, keeping the first-term offset explicit.

The displayed substitutions cover every requested part and verify the result against the original data.

Use the binomial theorem and simplify each general term.

The units digit must be one of 2,4,6; the other two places each have six choices.

Divide by −12 and reverse the inequality sign.

Powers of i repeat every four powers.

Use θ° = θ radians × 180/π and convert the decimal parts into minutes and seconds.

Since \(n(B)=3\) and \(n(A\times B)=n(A)n(B)\),

Membership is checked directly against the listed elements of \(A\):

• \(5\in A\)
• \(8\notin A\)
• \(0\notin A\)
• \(4\in A\)
• \(2\in A\)
• \(10\notin A\)

Decomposers such as bacteria and fungi act on dead plants, dead animals and organic wastes. They break complex organic matter into simpler inorganic substances. These mineral nutrients return to the soil and water and can again be absorbed by producers. Decomposition therefore recycles matter, maintains soil fertility and prevents dead organic material from continuously accumulating.

Draw closed curves leaving the north pole and entering the south pole outside the magnet; inside, they continue from south to north. Put arrows N→S outside. Lines are denser near the poles, showing greater field strength.