Questions in mathematics

Questions in mathematics

📝 Answered - At the start of the day, the rain barrel at Bella Terra Farms held 695 gallons of water. They used 58 gallons to water the herb garden in the morning. In the afternoon, they used another 213 gallons to water the vegetable garden. How much water was left in the rain barrel after they watered the vegetable garden?

📝 Answered - Completely expand the logarithm: $n \log _b \frac{x}{y z}$

📝 Answered - $\lim _{x \rightarrow 0}\left(\frac{2 x^2-x \cdot \sin (x)}{x \cdot \ln (x)-2 \sin ^2(x)}\right)$

📝 Answered - 12. Rationalize the denominator of the following: \( \frac{1}{\sqrt{5} + \sqrt{2}} \) 13. Simplify and find the value of: (a) \( (243)^{\frac{6}{5}} \) (b) \( (21)^{\frac{3}{2}} \times (21)^{\frac{5}{2}} \) 14. Given that \( \sqrt{10} = 3.162 \), find the value of \( \frac{1}{\sqrt{10}} \) 15. Find the product: \( \sqrt{2} \times \sqrt[4]{2} \times \sqrt[12]{32} \)

📝 Answered - All spent half of his June salary on school fees, 1/4 on farming, and 2/5 of the remainder on food. Calculate his June salary if he spent Sh 3200 on food?

📝 Answered - Multiply. [tex](5 x-1)(5 x-1)[/tex]

📝 Answered - Which statement is true considering a significance level of 5%? A. The result is statistically significant, which implies that wearing a watch helps people manage their time better. B. The result is not statistically significant, which implies that wearing a watch does not help people manage their time better. C. The result is statistically significant, which implies that wearing a watch does not help people manage their time better. D. The result is not statistically significant, which implies that this result could be due to random chance.

📝 Answered - Solve each equation. 47. [tex]$x^6+7 x^3-8=0$[/tex]

📝 Answered - How many boxes will fit along the width of the shipping crate? | | Storage Crate Size | Box Dimensions | | :----- | :------------------- | :------------- | | Width | 5 feet | 7 inches | | Height | 5 feet | 5 inches | | Length | 7 feet | 7 inches |

📝 Answered - Divide the polynomials by using long division. 1) $(2p^3 + 4p^2 - 24p + 19) \div (p - 2)$ A) $2p^2 + 8p - 5, R -2$ B) $2p^2 + 8p - 5, R 6$ C) $2p^2 + 8p - 10, R 5$ D) $2p^2 + 8p - 8, R 3$ E) $2p^2 + 8p - 10, R 3$ 2) $\frac{m^4 - m^3 - 6m^2 - 2m + 2}{m + 1}$ A) $m^3 - 2m^2 - 4m + 2$ B) $m^3 - 2m^2 - 4m + 4$ C) $m^3 - 2m^2 - 2m - 1$ D) $m^3 - 2m^2 - 2m$ E) $m^3 - 2m^2 - 4m + 5$