Related questions with answers

A random sample of 300 electronic components manufactured by a certain process are tested, and 25 are found to be defective. Let p represent the proportion of components manufactured by this process that are defective. The process engineer claims that $p \leq 0.05$ . Does the sample provide enough evidence to reject the claim?

Use this information: A function f (x, y) is said to be homogeneous of degree n if $f ( t x , t y ) = t ^ { n } f ( x , y )$ . For all homogeneous functions of degree n, the following equation is true: $x \frac { \partial f } { \partial x } + y \frac { \partial f } { \partial y } = n f ( x , y )$ . Show that the given function is homogeneous and verify that $x \frac { \partial f } { \partial x } + y \frac { \partial f } { \partial y } = n f ( x , y )$ . $f ( x , y ) = x ^ { 2 } y - 2 y ^ { 3 }$

Use the information provided to solve the problem. If $w = 5 x ^ { 2 } + 2 y ^ { 2 } , x = - 3 s + t$ , and $y = s - 4 t$ , find $\frac { \partial w } { \partial s }$ and $\frac { \partial w } { \partial t }$ .