GuideFoot - Learn Together, Grow Smarter. Logo

Questions in mathematics

📝 Answered - Use a horizontal format to find the sum: $(7 x^2-x)+7 x^3+(-6 x^3+x^2-6)$

📝 Answered - [tex]\frac{3}{4} x-9=27[/tex]

📝 Answered - Use the IVT to determine if there is a solution to [tex]f(x)=-9[/tex] in the interval between -2 and 4. If so, find the value of [tex]c[/tex] in the interval such that [tex]f(c)=-9[/tex]. * [tex]f(x)[/tex] is continuous on [-2,4] * -9 is not between -2 and 4 so the IVT does not apply * [tex]f(x)[/tex] is continuous on [-2,4] * -9 is between [tex]f(-2)=24[/tex] and [tex]f(4)=-24[/tex] * [tex]c=1[/tex] * [tex]f(x)[/tex] is continuous on [-2,4] * -9 is between [tex]f(-2)=24[/tex] and [tex]f(4)=-24[/tex] * [tex]c=9[/tex] * [tex]f(x)[/tex] is continuous on [-2,4] * -9 is between [tex]f(-2)=24[/tex] and [tex]f(4)=-24[/tex] * [tex]c=1, c=9[/tex]

📝 Answered - A family is canoeing downstream (with the current). Their speed relative to the banks of the river averages $2.75 mi / h$. During the return trip, they paddle upstream (against the current), averaging $1.5 mi / h$ relative to the riverbank. Write and solve a system of equations to find the family's paddling speed in still water. Let s equal the families paddling speed and c represent the current. A. $s + c =2.75$ $s-c=1.5$ B. $2.75 s= c$ $1.5 s=c$ C. $s + c =2.75$ $c-s=1.5$ D. $2.75 c=s$ $1.5 c=s$

📝 Answered - Find the 11th term of the geometric sequence [tex]$1,3,9, \ldots$[/tex]

📝 Answered - What numbers make the comparison true? 260, 960

📝 Answered - Match each inequality to its solution. a. b. c. d. 1. [tex]$-3 x\ \textgreater \ -36$[/tex] 2. [tex]$b+5\ \textgreater \ 23$[/tex] 3. [tex]$1+7 n \geq-90$[/tex]

📝 Answered - A sequence of numbers follows this rule: Multiply the previous number by -2 and add 3. The fourth term in the sequence is -7. a. Give the next 3 terms in the sequence. b. Give the 3 terms that came before -7 in the sequence.

📝 Answered - The discrete random variable X has the probability function given by [tex]P(X=x)=\left\{\begin{array}{ll} k x & x=2,4,6 \\ k(x-2) & x=8 \\ 0 & \text { Otherwise } \end{array}, \text { Where } k\right.\text { is a constant. }[/tex] (a) Find [tex]$k$[/tex] (b) Find [tex]$F(5)$[/tex] (c) Find [tex]$E[X]$[/tex] (d) Find [tex]$\operatorname{Var}[3-4 X]$[/tex] Let X be a discrete random variable with the following probability mass function. [tex]P_X(x)=\left\{\begin{array}{ll} 0.1 & \text { for } \quad x=0.2 \\ 0.2 & \text { for } \quad x=0.4 \\ 0.2 & \text { for } \quad x=0.5 \\ 0.3 & \text { for } \quad x=0.8 \\ 0.2 & \text { for } \quad x=1.0 \\ 0 & \text { otherwise } \end{array}\right.[/tex] Find [tex]$P(X=0.2 \mid X\ \textless \ 0.6)$[/tex] According to the population and housing census conducted by the National Statistical Office, 40% of the Malawians population, 25 years old or above, have completed a bachelor's degree. Given a random sample of 50 Malawians, 25 years old or above. (a) Mention with reasons the probability distribution to model number of people who have completed bachelor's degree among the 50 people who are 25 years old or above. (b) What is the expected number of people who have completed a bachelor's degree. (c) What is the standard deviation of the number of people who have completed a bachelor's degree? An electronic scale in an automated filling operation stops the manufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.001 and each fill is independent. (a) What is the mean number of fills before the line is stopped? (b) What is the standard deviation of the number of fills before the line is stopped? The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a mean of 0.02 failures per hour. What is the probability that the instrument does not fail in an eight-hour shift? Hint: [tex]$P(x)=\frac{\theta^x e^{-\theta}}{x!}$[/tex] The length of stay at specific emergency department has a mean of 4.6 hours with standard deviation of 2.9. Assume that the length of stay is normally distributed. (a) What is the probability of length of stay greater than 10 hours? (b) What length of stay is exceeded by 25% of the visits?

📝 Answered - Simplify the following: (a) $[7-3 x+10 y-(x-2 y)]-[5 x+2 y-10]$ (b) $\left(y^2-y-1\right)-\left[\frac{1}{2}\left(x-1+2 x^2\right)\right]$ (c) $a b^2+4 a^2 b-3 a^2 b+8 a b^2+5 a b^2+3 a b^2$ (d) $\left(a^2+b^2-2 a b\right)+\left(2 a^2-b^2+a b\right)-\left(a^2-2 b^2+a b\right)$ (e) $\left(3 p^2-2 p-\frac{1}{2}\right)+\left(1-p^2\right)+\left(p^2-6 p\right)+\left(2 p-\frac{5}{2}\right)$ (f) $\left(2 x^2+2 y^2+2 z^2+3 x u z\right)-\left(x^2+y^2+2 x y z+z^2\right)$ (g) $(3 x+5 y-x+2 y)+(5 x+3 y)-(2 y-x+5 x-3 y)$ (h) $(3 x+2 y-9)+(2 x-6 y+2)-[(4 x-9 y-1)+(-3 x+8 y+7)]$