In general, the eigenvalues of an upper triangular matrix are given by the entries on the diagonal. the same is true for a lower triangular matrix. verify this for 2 × 2 and 3 × 3 matrices.

He graph of f(x) = |x| is stretched by a factor of 0.3 and translated down 4 units. which statement about the domain and range of each function is correct? the range of the transformed function and the parent function are both all real numbers greater than or equal to 4. the domain of the transformed function is all real numbers and is, therefore, different from that of the parent function. the range of the transformed function is all real numbers greater than or equal to 0 and is, therefore, different from that of the parent function. the domain of the transformed function and the parent function are both all real numbers.

Identify the statement below as either descriptive or inferential statistics. upper a certain website sold an average of 117 books per day last week. is the statement an example of descriptive or inferential statistics? a. it is an example of descriptive statistics because it uses a sample to make a claim about a population. b. it is an example of inferential statistics because it uses a sample to make a claim about a population. c. it is an example of inferential statistics because it summarizes the information in a sample. d. it is an example of descriptive statistics because it summarizes the information in a sample.

Atest of sobriety involves measuring the subject's motor skills. a sample of 31 randomly selected sober subjects take the test and produce a mean score of 64.4 with a standard deviation of 2. a claim is made that the true mean score for all sober subjects is equal to 65. for each part below, enter only a numeric value in the answer box. for example, do not type "z =" or "t =" before your answers. round each of your answers to 3 places after the decimal point. (a) calculate the value of the test statistic used in this test. test statistic's value = (b) use your calculator to find the p-value of this test. p-value = (c) use your calculator to find the critical value(s) used to test this claim at the 0.2 significance level. if there are two critical values, then list them both with a comma between them. critical value(s) =