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Construct a K-map for F(x, y, z) = xz + yz + xyz. Use this K-map to find the implicants, prime implicants, and essential prime implicants of F(x, y, z).


Find the volume in the first octant bounded by x+y+z=9, and the inside cylinder 3y=27-x^3



The average hospitality girls working in a certain area is 19 years old. A civic oriented group made a recent survey on the age of the hospitality girls working in the same locality. A random sample of 20 respondents showed an average of 15.4 years old with a standard deviation of 2.14 years old. Using a 0.05 level of significance, has the hospitality girls gone lower?


Cereal boxes are filled at a factory. Through extensive sampling, it is found that their equipment fills the boxes to a mean of 502 grams, with a standard deviation of 3.1 grams.

10,000 boxes of cereal are produced each day. 

In a daily run, how many cereal boxes are expected to weigh between 500 and 504 grams?



if the side of triangle are 16,20 and 27 respectivly,what is the lenght of the bisector of the largest angle?


29. Let f be the function given by ( ) 2 x f x xe− = . From the values of x given below, find a value of x so that the slope of the line tangent to the graph of f at ( xfx , ( )) is equal to 0.2?


The graph of(x²+y²)²=4(x²-y²) shown in the figure is called lemnicate find the points on the graph that correspond to x=1 find the equation of the tangent line to the graph at each point found in point a find the points on the graph at which the tangent is horizontal

A company’s dividend growth rate is 10% the discount rate is 8%, there are 20 years of dividend to be paid and the current dividend is $10. What is the value of the stock based on the constant growth model?






The probability of getting a 4G internet connection in rural areas is 0.8 Calculate the probability of getting 7 connections in 10 attempts.


The average waiting time in a doctor’s office varies. The standard deviation of waiting times in a doctor’s office is 3.4 minutes. A random sample of 30 patients in the doctor’s office has a standard deviation of waiting times of 4.1 minutes. One doctor believes the variance of waiting times is greater than originally thought. a) What is the test statistic? b) What is the p-value? c) What can you conclude at the 5% significance level?


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