Jack is a college athlete who has been weighing himself weekly on the same scale in the athletic center for the past few years. Jack’s mean weight over the last nine weeks is 180 lbs. Over a period of a few months, Jack’s weight measurements are approximately normal, with a standard deviation of about 3 lbs. Assume that 3 lbs is the true standard deviation in Jack’s weight. Suppose that Jack asks you to compute a 90% confidence interval for his true mean weight. First, identify the positive critical value, , for a 90% level of confidence using software or a table of critical values. Then, derive the standard error of the mean, SE. Finally, compute the margin of error, , for the 90% confidence interval for Jack’s mean weight. Please enter all values to three decimal places.

Find the pattern and use it to list the nth term in the sequence. 6, 12, 20, 30, 42, 56, the nth term of the sequence is

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)

Ihonestly have no clue if it's each or none.