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Questions in mathematics

📝 Answered - 6. There are 4 arithmetic means between 5 and 20. (a) Write the formula to calculate arithmetic mean between [tex]$a$[/tex] and [tex]$b$[/tex]. (b) What is the 4th mean of the given sequence? Find it. (c) Show that the second middle number is 11.

📝 Answered - Tanaya (T) is 10 years older than her sister Filita (F) who is 2 years younger than her brother Mario(M). If T, F, M denote their ages, which one of the following represents the given information? a. $\left{\begin{array}{l}T=F+10 \\ F=M-2\end{array}\right.$ b. $\left{\begin{array}{l}T=F+10 \\ M=F-2\end{array}\right.$ c. $\left{\begin{array}{l}F=T-10 \\ M=F+2\end{array}\right.$ d. $\left{\begin{array}{l}F=T+10 \\ M=F-2\end{array}\right.$

📝 Answered - The function $f(x)=2.15\left(2 x^2-4 x-6\right)$ models the cost, in dollars, of a rug with width $x$ feet. What is the cost of a rug that is 9 feet wide? A. $120 B. $258 C. $606 D. $655

📝 Answered - If the following series continues the same pattern, what is the next number in the series 1, 10, 7, 16?

📝 Answered - Find the decimal equivalent to $\frac{4}{15}$. A. 0.26 B. $0.2 \overline{6}$ C. 2.6 D. $\overline{0.26}$

📝 Answered - Find $x$ in $10-2 x=-18$

📝 Answered - An equation for the depreciation of a car is given by $y=A(1-r)^t$, where $y=$ current value of the car, $A=$ original cost, $r=$ rate of depreciation, and $t=$ time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10\%. Approximately how old is the car? A. 3.3 years B. 5.0 years C. 5.6 years D. 6.6 years

📝 Answered - Which linear equation can be derived from this proportion? [tex]\frac{12}{x+8}=\frac{7}{x+1}[/tex] A. [tex]$12 x+96=7 x+7$[/tex] B. [tex]$12 x+1=7 x+8$[/tex] C. [tex]$12 x+12=7 x+56$[/tex] D. [tex]$12 x+8=7 x+1$[/tex]

📝 Answered - Use the laws of exponents to simplify. $5^{\frac{3}{5}} \cdot 5^{\frac{1}{10}}$

📝 Answered - Solve the logarithmic equation. $\log _4 x=3$ $x=$ (Simplify your answer. Type an exact answer, using $e$ as needed.)