Asprinkler manufacturer claims that the average activating temperatures is at least 135 degrees. to test this claim, you randomly select a sample of 32 systems and find the mean activation temperature to be 133 degrees. assume the population standard deviation is 3.3 degrees. find the standardized test statistic and the corresponding p-value.

z-value = -3.4283

p-value = 0.0003

Step-by-step explanation:

To find the standardized test statistic or z-value, we use the formula

where

N = size of the sample.

So,

As your sampling suggests that the real mean could be less than the manufacturer's mean, then you are interested in the area under the normal curve to the left of -3.4283 and this would be your p-value.

We compute the area of the normal curve for values to the left of -3.4283 either with a table or with a computer and find that this area is equal to 0.0003.

So the p-value is  

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'.

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.