A professor at a university wants to estimate the average number of hours of sleep the students get during exam week. The professor wants to find a sample mean that is within 4.266 hours of the true average for all college students at the university with 99% conconfidence. If the professor knows the standard deviation of the sleep times for all college students is 2.539, what sample size will need to be taken

The sample size is

Step-by-step explanation:

From the question we are told that

   The margin of error is  E =4.266

    The standard deviation is  

From the question we are told the confidence level is  99% , hence the level of significance is    

=>  

Generally from the normal distribution table the critical value  of   is  

Generally the sample size is mathematically represented as  

=>  

=>  

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

(w – 2.5)(w + 2.5)

(–4v – 9)(–4v + 9)

step-by-step explanation: