A tire company claims that the lifetimes of its tires average 50750 miles. The standard deviation of tire lifetimes is known to be 5750 miles. You sample 175 tires and will test the hypothesis that the mean tire lifetime is at least 50750 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 50250 miles. A) It is decided to reject H0 if the sample mean is less than 50150. Find the level and power of this test.
B) If the test is made at the 5% level, what is the power?
C) At what level should the test be conducted so that the power is 0.87?
D) You are given the opportunity to sample more tires. How many tires should be sampled in total so that the power is 0.87 if the test is made at the 5% level?

Yoku is putting on sunscreen. he uses 2\text{ ml}2 ml to cover 50\text{ cm}^250 cm 2 of his skin. he wants to know how many milliliters of sunscreen (c)(c) he needs to cover 325\text{ cm}^2325 cm 2 of his skin. how many milliliters of sunscreen does yoku need to cover 325 \text{ cm}^2325 cm 2 of his skin?

He mass of a single atom of carbon can be found by dividing the atomic mass (12.01 g) by 6.022 x 10^23. which is the mass of a single carbon atom, correctly written in scientific notation with the correct number of significant figures?

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)