answer:1. **Apply the constraints and requirements:** - Desserts available: cake, pie, ice cream, pudding. - No dessert is repeated consecutively. - Cake is required on Monday; ice cream is required on Thursday. 2. **Determine the options per day influenced by constraints:** - Sunday: 4 choices (all options available). - Monday: 1 choice (cake must be served). - Tuesday: 3 choices (anything but cake). - Wednesday: 3 choices (pie, pudding, or the dessert not chosen for Tuesday from pie or pudding). - Thursday: 1 choice (ice cream must be served). - Friday: 3 choices (excluded the ice cream served on Thursday). - Saturday: 3 choices (excluding the dessert served on Friday). 3. **Calculate the total combinations for the dessert menus:** - The total number of dessert plans for the week can be calculated as: [ 4 times 1 times 3 times 3 times 1 times 3 times 3 = 324 ] The total number of different dessert menus for the week, according to the specified constraints, is 324. Given the choices, the correct answer is boxed{textbf{(B)} 324}.

answer:We rewrite the expression as: [frac{a}{|a|} + frac{b}{|b|} + frac{c}{|c|} + frac{d}{|d|} + frac{abcd}{|abcd|} = frac{a}{|a|} + frac{b}{|b|} + frac{c}{|c|} + frac{d}{|d|} + frac{a}{|a|}cdotfrac{b}{|b|}cdotfrac{c}{|c|}cdotfrac{d}{|d|}.] Each term frac{x}{|x|} is 1 if x is positive and -1 if x is negative. Let k be the number of variables among a, b, c, d that are positive. - If k = 4 or k = 0: all terms have the same sign: [ text{Sum} = 4 + 1 = 5 quad text{or} quad text{Sum} = -4 + (-1) = -5. ] - If k = 3 or k = 1: three terms are 1 and one is -1, or vice versa; the product term matches the single differing term: [ text{Sum} = 3 - 1 + (-1) = 1 quad text{or} quad text{Sum} = 1 - 3 + 1 = -1. ] - If k = 2: two terms are 1, two are -1; the product is 1: [ text{Sum} = 2 - 2 + 1 = 1. ] Thus, the possible values of the expression are boxed{5, 1, -1, -5}.

answer:To solve this problem, we evaluate each of the given options step by step to see which operation results in 1. **Option A: -3+left(-3right)** We start by adding -3 to -3: begin{align*} -3 + (-3) &= -6 &neq 1 end{align*} Since this does not equal 1, option A does not meet the requirements. **Option B: -3-left(-3right)** Next, we subtract -3 from -3, which is the same as adding 3 to -3: begin{align*} -3 - (-3) &= -3 + 3 &= 0 &neq 1 end{align*} Since this does not equal 1, option B does not meet the requirements. **Option C: -3div left(-3right)** For this option, we divide -3 by -3: begin{align*} -3 div (-3) &= 1 &= 1 end{align*} Since this equals 1, option C meets the requirements. **Option D: -3times left(-3right)** Finally, we multiply -3 by -3: begin{align*} -3 times (-3) &= 9 &neq 1 end{align*} Since this does not equal 1, option D does not meet the requirements. After evaluating all options, we find that only option C results in 1. Therefore, the correct answer is boxed{C}.

answer:To calculate the percentage of the page used by the typist, we first need to determine the area of the entire page and the area of the portion used for typing. The area of the entire page is: Area = length × width Area = 20 cm × 30 cm Area = 600 cm² Now, we need to calculate the area available for typing after leaving the margins. Since a margin of 2 cm is left on each side, the width available for typing is reduced by 4 cm (2 cm on each side). Similarly, since a margin of 3 cm is left on the top and bottom, the length available for typing is reduced by 6 cm (3 cm on the top and 3 cm on the bottom). The width available for typing is: Width = 20 cm - 4 cm (2 cm on each side) Width = 16 cm The length available for typing is: Length = 30 cm - 6 cm (3 cm on the top and bottom) Length = 24 cm The area available for typing is: Area = length × width Area = 16 cm × 24 cm Area = 384 cm² Now, to find the percentage of the page used by the typist, we divide the area available for typing by the total area of the page and multiply by 100: Percentage used = (Area available for typing / Total area of the page) × 100 Percentage used = (384 cm² / 600 cm²) × 100 Percentage used = 0.64 × 100 Percentage used = 64% Therefore, the typist uses boxed{64%} of the page.