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Home Question Bank Math Archive 2025 February 10

Math Questions from Feb 10,2025

Browse the Math Q&A Archive for Feb 10,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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The dimensions of a rectangular prism are 1.5 feet by 3.5 feet by 2 feet. What is the volume of the rectangular prism in cubic feet? A. \( 7 \mathrm{ft}^{3} \) B. \( 7.25 \mathrm{ft}^{3} \) C \( 8.5 \mathrm{f}^{3} \) D. \( 10.5 \mathrm{ft}^{3} \) 8. A cada dois minutos, um semáforo para pedestres muda de verde para vermelho e de vermelho para verde. Ás 14 horas esse semáforo mudou de verde para vermelho De que cor ele estará às 14 h 25 min ? Lesuelva \( -4 x-5=11 \) \( --7-11 x \) A specific board of supervisors uses the weighted voting system \( [54: 25,23,19,12,9,1] \). Assume that the players are \( \mathrm{P}_{1} \) through \( \mathrm{P}_{6} \). Complete parts (a) through (d) below. (c) List all the five-player winning coalitions and find the critical players in each coalition. A. \( \left\{P_{1}, P_{2}, P_{3}, P_{4}, P_{5}\right\},\left\{P_{1}, P_{2}, P_{3}, P_{4}, P_{6}\right\},\left\{P_{1}, P_{2}, P_{3}, P_{5}, P_{6}\right\},\left\{P_{1}, P_{2}, P_{4}, P_{5}, P_{6}\right\} \), \[ \left\{P_{1}, P_{3}, P_{4}, P_{5}, P_{6}\right\},\left\{P_{2}, P_{3}, P_{4}, P_{5}, P_{6}\right\} \] B. \( \left\{P_{1}, P_{2}, P_{3}, P_{4}, P_{5}\right\},\left\{P_{1}, P_{2}, P_{3}, P_{4}, P_{6}\right\},\left\{P_{1}, P_{2}, P_{3}, P_{5}, P_{6}\right\},\left\{P_{1}, P_{2}, P_{4}, P_{5}, P_{6}\right\} \), \[ \left\{P_{1}, P_{3}, P_{4}, P_{5}, P_{6}\right\},\left\{\overline{P_{2}}, P_{3}, P_{4}, P_{5}, P_{6}\right\} \] C. \( \left\{P_{1}, P_{2}, P_{3}, P_{4}, P_{5}\right\},\left\{P_{1}, P_{2}, P_{3}, P_{4}, P_{6}\right\},\left\{P_{1}, P_{2}, P_{3}, P_{5}, P_{6}\right\},\left\{P_{1}, P_{2}, P_{4}, P_{5}, P_{6}\right\} \), \[ \left\{\overline{P_{1}}, \overline{P_{3}}, P_{4}, P_{5}, P_{6}\right\},\left\{\overline{P_{2}}, \overline{P_{3}}, P_{4}, P_{5}, P_{6}\right\} \] D. \( \left\{P_{1}, P_{2}, P_{3}, P_{4}, P_{5}\right\} \cdot\left\{P_{1}, P_{2}, P_{3}, P_{4}, P_{6}\right\},\left\{P_{1}, P_{2}, P_{3}, P_{5}, P_{6}\right\},\left\{P_{1}, P_{2}, P_{4}, P_{5}, P_{6}\right\} \), \( \left\{\overline{P_{1}}, P_{3}, P_{4}, P_{5}, P_{6}\right\} \cdot\left\{\overline{P_{2}}, \overline{P_{3}}, P_{4}, P_{5}, P_{6}\right\} \) F7. On donne deux termes du carre d'un binome. Trouvez le troisieme : \( \begin{array}{lll}\text { a) } x^{2}+4 x+\ldots & -10 x+1+\ldots & 4 x^{2}+a^{2}-\ldots \\ \text { b) } 16+x^{2}+\ldots & m^{2}+2 m n \ldots & 4 a^{2}+12 a b \ldots \\ \text { c) } p^{2}-8 p \ldots & x^{2}+p x \ldots & 25 m^{2}-40 m n \ldots \\ \text { d) } 1+4 x^{2} \ldots & 1-2 m \ldots & 4 a^{2} x^{2}+4 a b x \ldots \\ \text { e) } 9 y^{2}+6 y \ldots & 4 y^{2}+20 y \ldots & 9 m^{2}+12 m n \ldots \\ \text { f) } x^{2}+4 y^{2} \ldots & 4 c^{2}+a^{2} \ldots & 16 a^{2}-16 a b \ldots\end{array} \) (3) Convertir a grados a) \( \frac{5}{6} \pi \mathrm{rad} \) b) \( \frac{11}{9} \pi \mathrm{rad} \) Dado el triángulo dado por los vértices \( \mathrm{A}(-1,8), \mathrm{B}(6,1) \) y \( \mathrm{C}(-5,-2) \). Hallar la pendiente de la recta que pasa por el punto \( \mathrm{T}(11,7) \) y que está a una distancia de 1 unidades del centro de gravedad del triángulo ABC \( f ( x ) = \sin ^ { - 1 } ( \frac { 2 x } { 1 + x ^ { 2 } } ) + \cos ^ { - 1 } ( \frac { 1 - x ^ { 2 } } { 1 + x ^ { 2 } } ) = 0 \) Jame: Agesha Score : HW cher: Date: \( \qquad \) Equivalent Fractions 1) \( \frac{7}{56}=\frac{6}{48}=\frac{1}{8}=\frac{5}{40}=\frac{2}{16}=\frac{4}{32}=\frac{3}{} \). 2). \( \frac{5}{10}=\frac{35}{}=\frac{30}{}=\frac{10}{}=\frac{20}{}=\frac{25}{}=\frac{15}{3} \) 3) \( \frac{1}{6}=\frac{7}{24}=\frac{}{36}=\frac{2}{30}=\frac{3}{3}=\frac{1}{3} \) Example 3: The Shell Station has 21 gallons of gas for \( \$ 70 \) or Wawa has 15 gallons for \( \$ 50.00 \) pay less per gallon The Better Deals is \( \qquad \) Example 4: A Hummer that gets 300 miles on 20 gallons of gas or a Camry that gets 495 miles on 15 gallons of gas. more miles per qallen \[ \begin{array}{l} \text { hamner }=\frac{300}{20}=15 \text { miles per gallon } \\ \text { camery }=\frac{495}{18}=83 \text { miles Per gallon } \\ \text { The Better Deats is } \end{array} \] \( \qquad \) camry Auswer each question and round your answer to the nearest whole number. 13) A map has a scale of \( 1 \mathrm{~cm}: 17 \mathrm{~km} \). If 14) A model train has a scale of 2 in: 1 ft . If Jobnstown and San Jose are 204 kmapart, . then they are how far apart on the map? 15) Find the distance between Oak Grove and Victoria on a map with a scale of 1 in :3 mi if they are actually 36 mi apart. \[ \frac{1}{3}-\frac{x}{96}=12 \text { in } \] 17) A mgp, has a scale of \( 3 \mathrm{~cm}: 5 \mathrm{~km} \). If Brisbane and Rockville are 6 cm apart on tho map, then how far apart are the real the real train is 24 ft tall, then how tall is the model train? 16) Smifhville and Fairview are 26 km from each other. How far apart would the cities be on a map that has a scale of \( 5 \mathrm{~cm}: 13 \) km ? 18) A particular satellito is 24 ft wide. A model of it was built with a scale of 4 in: 3 ift. How wide is the model? 1. Grafique al triángulo acutángulo \( A B C \) y marque el ortocentro \( { }^{n} H^{n} \). Si la \( m \angle A H B \) es el triple de la \( m \angle C \), calcular la \( m \angle A H B \).
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