Mathematics Questions & Answers

Write the function whose graph is the graph of \( y=x^{2} \), but is shifted up 6 units.

Consider the Standard Normal distribution. The mean is always \( \square \) and the standard deviation is always

Consider the following function. \( f(x)=\left\{\begin{array}{rrr}5 x-4 & \text { if } & x<3 \\ x^{2}+3 & \text { if } & 3 \leq x<10 \\ 3 & \text { if } & x \geq 10\end{array}\right. \) Which "piece(s)" should be used to find the \( y \)-intercept? Select all that apply. \( \square \) A. 3 \( \square \) B. \( 5 x-4 \) \( \square \) C. \( x^{2}+3 \)

Which of the following functions has a graph that is the graph of \( y=\sqrt{x} \) shifted up 1 unit? Choose the correct answer below. \( y=\sqrt{x}-1 \) \( y=\sqrt{x}+1 \) \( y=\sqrt{x-1} \) \( y=\sqrt{x+1} \)

Let \( f(x)=x^{2}+a x+b \) and \( g(x)=x^{2}-2 b x-a \), where \( a \) and \( b \) are constants. Given that the H.C.F. of \( f(x) \) and \( g(x) \) is \( x-1 \), find the values of \( a \) and \( b \). A. \( \quad a=5, b=-2 \) B. \( \quad a=3, b=2 \) C. \( \quad a=-3, b=2 \) D. \( \quad a=-5, b=-2 \)

\( ( e ^ { x } - \sin y ) d x + ( \cos y ) d y \)

A telephone company offers a monthly cellular phone plan for \( \$ 34.99 \). It includes 350 anytime minutes plus \( \$ 0.25 \) per minute for additional minutes. The following function is used to compute the monthly cost for a subscriber, where \( x \) is the number of anytime minutes used. \( C(x)=\left\{\begin{array}{ll}34.99 & \text { if } 0<x \leq 350 \\ 0.25 x-52.51 & \text { if } x>350\end{array}\right. \) Compute the monthly cost of the cellular phone for use of the following anytime minutes. \( \begin{array}{ll}\text { (a) } 225 & \text { (b) } 395 \\ \text { (a) } C(225)=\$ \square \text { (Round to the nearest cent as needed.) } \\ \text { (b) } C(395)=\$ \square \text { (Round to the nearest cent as needed.) } \\ \text { (c) } C(351)=\$ \square \text { (Round to the nearest cent as needed.) }\end{array} \)

Which of the following functions has a graph that is symmetric about the \( y \)-axis? Select all that apply. \( \square \) A. \( y=|x| \) \( \square \) B. \( y=\sqrt{x} \) \( \square \) C. \( y=\frac{1}{x} \) \( \square \) D. \( y=x^{3} \)

En una bolsa hay cuatro tarjetas, con los números \( 1,2,3 \) y 4 respectivamente. Si se sacan dos tarjetas de la bolsa, una tras otra y con reposición, ¿cuál es la probabilidad de que la suma de los números obtenidos sea 7 ? A. \( \frac{1}{4} \) B. \( \frac{7}{16} \) C. \( \frac{1}{16} \)

2) Dato un punto \( P(-2 ;-1) \) e una rette II \( y=2 x-3 \) deterninare retto per il punto \( P \) ! Fare grefico