Use Lagrange multipliers to minimize the function f(x, y,z)=x2 +y2 +z2 subject to the following constraint: x+y+z-24=0
Assume that x, y, and z are positive

Ms. sutton recorded the word counts and scores of the top ten essays in a timed writing contest. the table shows her data. how does the word count of an essay relate to its score in the contest? word count tends to decrease as the score decreases. word count tends to increase as the score decreases. word count tends to remain constant as the score decreases. word count has no apparent relationship to the score of the essay.

Weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of $50. find the probability that a worker selected at random makes between $450 and $500

Formulate the indicated conclusion in nontechnical terms. be sure to address the original claim. the foundation chair for a hospital claims that the mean number of filled overnight beds is over 523, and she is therefore justified starting a funding campaign to add a wing to the hospital. assuming that a hypothesis test has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.