Live practice

Form the required totals explicitly and divide by the full number of observations.

The variance is nonnegative and the reported standard deviation is its positive square root.

Simplify the expression before substitution and preserve one-sided information.

Substitution into the original expression verifies the stated domain and final value.

Use rectangular-coordinate definitions and keep corresponding coordinates aligned.

The final relation satisfies the original coordinate or distance condition, completing the verification.

Translate every condition into an equation and retain exact values throughout the conic calculation.

The last line satisfies the original conditions and supplies every requested part.

Proceed from the given expression and keep every transformation explicit.

The last line satisfies the required domain and establishes the result.

Proceed from the given expression and keep every transformation explicit.

The last line satisfies the required domain and establishes the result.

(i) \(B\cap C=\varnothing\), so the left side is \(\varnothing\). The second coordinates in \(A\times B\) lie in \(B\), while those in \(A\times C\) lie in disjoint \(C\); hence their intersection is also \(\varnothing\).

(ii) Since \(A\subset B\) and \(C\subset D\), every \((a,c)\in A\times C\) has \(a\in B,c\in D\). Thus \(A\times C\subset B\times D\).

Reconnect the carbonyl carbons of propanal and pentan-3-one by C=C, retaining their alkyl substituents.

Expand each name from the parent chain and then mark each characteristic group.

Choose familiar hydrides, oxides, oxyanions and interhalogen compounds whose usual atom charges give the required values.