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Problem 4. (10 points) Prove that $\frac{1}{4}n^2 + 3 \in \Omega(n)$ by giving a direct proof based on the definition of big-? involving the inequalities and absolute values, as given in the Perusall textbook Section 10.5. To do so, first write out what $\frac{1}{4}n^2 + 3 \in \Omega(n)$ means according to the definition. Then, you need to find a positive real constant $c$ and a positive integer $n_0$ that satisfy the definition.

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Researchers use the ____ to determine the answer to a question over a longer period of time with multiple assessment points on the same individuals over the years. Multiple Choice cross-sectional approach correlational method descriptive method longitudinal approach

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Assuming it is a SAMPLE, what is the standard deviation of the following data set (margin of error = 1.0). X: 105, 93, 99, 110, 53, 108, 102, 103, 109, 125

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Need help with questions 6-10: 6. If the neutral form of a weak base (NH3 = ammonia, with a pKa value of 4.745, is titrated with a strong acid (HCl = hydrochloric acid), until the conjugate acid (NH4+ = the ammonium ion) is present at a concentration of 0.75 M, and the weak base (NH3 = ammonia) is present at a concentration of 0.25 M so that the initial NH3 becomes 75% protonated), then what is the expected pOH of this solution? A. pOH = 5.347 B. pOH = 5.222 C. pOH = 4.745 D. pOH = 4.268 E. pOH = 4.143 7. What is the expected pH of the above solution (containing both ammonia and ammonium ions)? A. pH = 9.857 B. pH = 9.732 C. pH = 9.255 D. pH = 8.778 E. pH = 8.653 8. If the fully-protonated phosphoric acid (H3PO4 with pKa values of 2.15, 7.20, and 12.4, respectively) is titrated with 2.5 molar equivalents of KOH, which ionic species of H3PO4 will be most abundant? A. H2PO4- and HPO4^2- will be the two most abundant ionic species of phosphoric acid at this titration B. H2PO4- and H3PO4 will be the two most abundant ionic species of phosphoric acid at this titration C. HPO4^2- and PO4^3- will be the two most abundant ionic species of phosphoric acid at this titration D. H3PO4 will be the most abundant ionic species of phosphoric acid at this titration E. PO4^3- will be the most abundant ionic species of phosphoric acid at this titration 9. Which ionic species of phosphoric acid is most abundant at extremely alkaline conditions (pH > 13)? A. H2PO4- B. HPO4^2- C. HPO4^3- D. H3PO4 E. PO4^3- 10. The amino acid histidine (His) in a water solution contains how many neutral zwitterion species? A. one: the His species B. two: the His and His+ species C. three: the His, His+, and His- species D. four: the His, His+, His-, and His2+ species E. five: the His, His+, His-, His2+, and His2- species

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File Edit View Data Transform Analyze G cost perc_profit var 1 256 53 2 281 71 3 131 38 4 95 51 5 329 64 6 358 50 7 291 65 8 153 54 9 205 45 10 485 72 11 183 39 12 201 67 13 H0: There is not a significant relationship between cost and perc_ profit Ha: There is a significant relationship between cost and perc_profit 1. Can you reject or accept the Null Hypothesis? What hypothesis test informs your result, and what is the result? 2. How to visualize the relationship between cost to clients and organizational profitability.

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Question Enrique borrowed $23,500 to buy a car. He pays his uncle 2% interest on the $4,500 he borrowed from him, and he pays the bank 11.5% interest on the rest. What average interest rate does he pay on the total $23,500? • Assume Enrique pays both his uncle and the bank in one lump sum. • Round your answer to the nearest tenth of a percent.

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The amount of mRNA produced from a gene is sometimes used as a measure of the rate of transcription. This is not 100% accurate because the amount of mRNA also depends on ______.

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For each of the pairs below, use an example to show how the first term in each pair affects or is related to the second. Definitions alone without examples will not score. • Serial-position effect.. recall • Functional fixedness.. problem solving • Operational definition.. replication • Double-blind research.. bias • Operant conditioning.. superstition • Reinforcement.. overjustification effect • Myelin sheath.. neural impulse

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Rank the following C-H bonds in the order of INCREASING bond dissociation energy. Ha < Hb < Hc (largest) Hc < Ha < Hb (largest) Hb < Ha < Hc (largest) Hc < Hb < Ha (largest) Ha < Hc < Hb (largest)

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Alice has collected N data samples from several patients. Note that superscript is just the sample index. Each data sample r is a D-dimensional column vector. Let's assume that the average is already removed in the above dataset, i.e. = 0. Alice has two students, Bob and Susan, who each performed dimensionality reduction via PCA. Bob performed note L < D eigenvalues A^2 of the covariance matrix of data that Bob used. Susan, however, first scaled the vectors by a non-zero constant and then performed the PCA. In other words, Susan used the dataset {xr}. Let vectors U be the eigenvectors associated with the top L eigenvalues of the covariance matrix of the dataset that Susan used. Which of the following statements is correct about comparing Bob's PCA with that? a) The top L principal components (i.e., the eigenvectors that Bob has found) have no relation with the top L principal components that Susan obtained. b) The top L principal components (i.e., the eigenvectors that Bob and Susan found) are NOT identical, i.e. for i = 1,..L if is a negative scalar. c) The top L principal components (i.e., the eigenvectors that Bob and Susan found) are identical regardless of the value of , but the corresponding variances along each principal component will be smaller for Susan's case if is larger than L. d) The top L principal components (i.e., the eigenvectors that Bob and Susan found) are identical regardless of the value of , but the corresponding variances along each principal component will be larger for Susan's case if is larger than 1. e) The top L principal components (i.e., the eigenvectors that Bob and Susan found) are identical if is a positive scalar, but no relation exists regarding the corresponding variances along each principal component.

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andrea h.