Questions in mathematics

Questions in mathematics

📝 Answered - A machine manufactures 2,825 screws per day. How many screws did it produce in the year 2004, assuming that the machine works on all days of the year? Hint: 2004 was a leap year.

📝 Answered - Nyamboke walked from her home to the market. She walked at a speed of 4 km/hr and took 30 minutes to reach the market. On her way back, she took 40 minutes to reach home. What was Nyamboke's speed on her way back?

📝 Answered - A group of choir members decided to raise 3600/= to buy a guitar. Each member was to contribute an equal amount. In the preparation process, five members transferred to another church, which meant the remaining contributors had to pay more to achieve the target. a. Show that the increase in the contribution per member was: Sh. 18,000 / (n(n-5)) if n is the initial number of members. b. If the increase in the contribution per member was Sh. 24, what was the original contribution before the other members left? c. Calculate the percentage increase in the contribution after the others left.

📝 Answered - 2. Write the first six terms of the following sequence: f(n) = (-3)^{n-1} 3. Find the 5th term and the 15th term of the sequence given by: a_n = 3 - n^2

📝 Answered - 1. \( \frac{1}{5} \times \frac{1}{5} = \) 2. \( \frac{2}{3} \times 1 \frac{3}{5} = \) 3. \( 3 \frac{1}{5} \times 2 \frac{1}{3} = \) 4. \( 4 \frac{1}{8} \times \frac{1}{5} = \) 5. \( 5 \frac{1}{5} \times 1 \frac{1}{4} = \)

📝 Answered - The park owners want to put an information booth halfway between the roller coaster and the water slide. If the roller coaster is located on the map at $(7,6)$ and the water slide is located at $(-3,-4)$, at which coordinates should the information booth be placed? A. $(1,1)$ B. $(2,1)$ C. $(2,-1)$ D. $(4,2)

📝 Answered - The total cost of gasoline varies directly with the number of gallons purchased. Gas costs $1.77 per gallon. Write a direct variation to model the total cost [tex]$c$[/tex] for [tex]$g$[/tex] gallons of gas. [tex]$g=1.77 c$[/tex] [tex]$c=1.77 g$[/tex] [tex]$c=\frac{8}{177}g$[/tex]

📝 Answered - Fill in the missing column of the following truth table. \begin{tabular}{|c|c|c|c|} \hline$p$ & $q$ & $\neg p$ & $\neg q$ \\ \hline$T$ & $T$ & $F$ & $F$ \\ \hline$F$ & $T$ & $T$ & $F$ \\ \hline$T$ & $F$ & $F$ & $T$ \\ \hline$F$ & $F$ & $T$ & $T$ \\ \hline \end{tabular} a) \begin{tabular}{|c|} \hline$\neg p \vee \neg q$ \\ \hline$F$ \\ \hline$T$ \\ \hline$T$ \\ \hline$T$ \\ \hline \end{tabular} b) \begin{tabular}{|c|c|} \hline$\rho \vee \neg q$ \\ \hline$\sigma$ & \\ \hline$T$ & \\ \hline$F$ & \\ \hline$T$ & \\ \hline \end{tabular}

📝 Answered - (A) 2 (B) 4 (C) 6 (D) 8 (E) 10 (A) % (B) % (C) [tex]$1 / 3$[/tex] (D) [tex]$1 / 2$[/tex] (E) [tex]$2 / 1$[/tex]

📝 Answered - Multiply each pair of factors. Type the product in the space provided. [tex]\begin{array}{l} (6+3 i)(6-3 i)=\square \\ (4-5 i)(4+5 i)=\square \\ (-3+8 i)(-3-8 i)=\square \end{array}[/tex]