Here are summary statistics for randomly selected weights of newborn girls: \( \mathrm{n}=36, \overline{\mathrm{x}}=3180.6 \mathrm{~g}, \mathrm{~s}=700.5 \mathrm{~g} \). Use a confidence level of \( 90 \% \) to complete parts (a) through (d) below. (Round to two decimal places as needed.) b. Find the margin of error. \( \mathrm{E}=197.3 \mathrm{~g} \) (Round to one decimal place as needed.) c. Find the confidence interval estimate of \( \mu \). \( 2983.1 \mathrm{~g}<\mu<3378.1 \mathrm{~g} \) (Round to one decimal place as needed.) d. Write a brief statement that interprets the confidence interval. Choose the correct answer below. A. There is a \( 90 \% \) chance that the true value of the population mean weight of newborn girls will fall between the lower bound and the upper bound. B. One has \( 90 \% \) confidence that the sample mean weight of newborn girls is equal to the population mean weight of newborn girls. C. One has \( 90 \% \) confidence that the interval from the lower bound to the upper bound contains the true value of the population mean weight of newborn girls. D. Approximately \( 90 \% \) of sample mean weights of newborn girls will fall between the lower bound and the upper bound.

Factor the binomial completely. \[ x^{7}-x^{3} \]

Solve the inequality: \( y^{2} \geq-7 y-12 \) Give your answer in interval notation. Enter DNE if there is no solution.

5. Dados \( \vec{u} \) y \( \vec{v} \) vectores de \( \mathbb{R}^{n} \) tales que \( \|\vec{u}\|=13,\|\vec{v}\|=19,\|\vec{u}+\vec{v}\|=24 \), calcular: \( \|\vec{u}-\vec{v}\| \) 6. Demostrar que si \( \vec{v} \) es ortogonal a \( \vec{w}_{1} \) y a \( \vec{w}_{2} \),'eentonces \( \vec{v} \) es ortogonal a \( k_{1} \overrightarrow{w_{1}}+k_{2} \overrightarrow{w_{2}} \) cualesquiera sean \( k_{1}, k_{2} \) reales. 7. Dados los siguientes pares de vectores, hallar gráfica y algebraicamente, la proyección escalar y vectorial de \( \vec{u} \) sobre \( \vec{v} \) y de \( \vec{v} \) sobre \( \vec{u} \). a) \( \vec{u}=\breve{i}+\breve{j}, \vec{v}=\breve{i}-\breve{j} \) b) \( \vec{u}=(2 ;-3), \vec{v}=(1 ; 1) \) c) \( \vec{u}=-5 \breve{i}+4 \breve{j}, \vec{v}=-\breve{i} \) 8. Sean \( P=(2 ; 3), Q=(5 ; 7), R=(2 ;-3) \) y \( S=(1 ; 2) \). Calcular la proyección de \( \overrightarrow{R S} \) sobre \( \overrightarrow{P Q} \) y la proyección de \( \overrightarrow{P Q} \) sobre \( \overrightarrow{R S} \)

Previous Problem Problem List Next Problem (1 point) Solve the equation by identifying the quadratic form. Use a substitute variable and find all real solution by factoring. If there is more than one answer, enter a comma separated list. \( (x+1)^{2}-5(x+1)-24=0 \) \( x=\square \) help (numbers)

Determine the inverse function of \( f(x)=-8\left(5^{x}\right)+8 \). Question Help: \( { }^{\text {- Read }} \)