A manufacturer claims that the mean lifetime, μ, of its light bulbs is 45 months. The standard deviation of these lifetimes is 7 months. Thirty-one bulbs are selected at random, and their mean lifetime is found to be 48 months. Assume that the population is normally distributed. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 45 months? Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table
the null hypothesis
the alternative hypothesis
the type of test statistic
the value of the test statistic
the two critical values at the .1 level of significance
(round to at least three decimal places)
can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 50 months

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing im pretty sure that is the right answer

step-by-step explanation:

i believe the answer is 68cm

step-by-step explanation:

i just took 34 x 2 because the space between v and y is the same as y to k.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

-2 is the right