Numerade

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Show that the following number is rational by writing it as a ratio of two integers. 4/7 + 2/9

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What is the smallest possible capacitance of a parallel plate capacitor with the plate area 2500 cm squared separatzd by a distnce of 0.10mm

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$\boxed{\text{First Order Differential Equations}}$ Solve the following initial value problem $t(1+t)y' + ty = \ln t$, $y(1) = 2$, $t > 0$.

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A researcher reports that the average salary of a professor is more than P₄₂,₀₀₀. A sample of 30 professors has a mean salary of P₄₃,₂₆₀. At d=0.05, test the claim that professors earn more than P₄₂,₀₀₀ a month. The standard deviation of the population is P₅,₂₃₀.

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*5. You own an ice-cream van and sell each ice-cream for $2. How many ice-creams you can sell depends on the hours of opening as indicated in the table below. For each hour the stall is open, your opportunity cost is $15. For how many hours should you open your stall? Hours of opening Total sales of ice creams 0 1 2 3 4 5 0 20 35 45 50 50

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Among the literature on quitting smoking are data detailing the relative successfulness of people of different ages in quitting smoking. A study of 400 adults who began various smoking-cessation programs produced the data in the table below. In the table, each participant is classified according to two variables: length of their smoking cessation period ("Less than two weeks", "Between two weeks and one year", or "At least one year") and age ("21-34", or "35 and over"). In the table, "less than two weeks" means that the individual returned to smoking within two weeks of beginning the program; "between two weeks and one year" means that the individual lasted the first two weeks without smoking but retuned to smoking within a year; and "at least one year" means that the individual has not smoked for at least a year since beginning the program. The table is a contingency table whose cells contain the respective observed frequencies of classifications of the 400 smokers. In addition, three of the cells have blanks beneath the observed frequencies. Fill in these blanks with the frequencies expected if the two variables, age and length of the smoking cessation period, are independent. Round your answers to two or more decimal places. Send data to Excel Length of smoking cessation period Less than two weeks Between two wecks and one year At least one year Total 57 131 67 21-34 255 42 65 38 Age 35 and over 145 Total 99 196 105 400

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Figure 16.7 The outcome of clustering in K-means depends on the initial seeds. For seeds $d_2$ and $d_5$, K-means converges to {\{$d_1, d_2, d_3\}, \{$d_4, d_5, d_6\}$}, a suboptimal clustering. For seeds $d_2$ and $d_3$, it converges to {\{$d_1, d_2, d_4, d_5\}, \{$d_3, d_6\}$}, the global optimum for K = 2.

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The points A (1, 2, 3), B(-1, 3, 2), and C (3, -2, -1) are given. a. Determine a vector equation of the line that passes through A and that is parallel to the segment BC.

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Which of the following are intermediates in the following reaction? HO H3O+ OH a. OH HO H b. +OH2 c. +H2O d.OH c and d a and b a and c b and c a and d H

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Cansino and her colleagues (2013) studied age differences in adults' abilities to remember the context in which an event or experience occurred. This is how they described their research method: "A total of 1,500 healthy adults between the ages of 21 and 80 participated in this study. An equal number of men and women were evenly distributed among the six decades in the age range (250 adults per decade)" (p. 975). The research design used in the study by Cansino et al. (2013) is most likely: a. Longitudinal b. Non-developmental c. Sequential (or cross-lag) d. Cross-sectional The neurosensitivity hypothesis of the mechanism driving sensory processing sensitivity suggests that highly sensitive sensory processing is driven by a _____________ instead of __________. a. A highly sensitive central nervous system; three distinct sensitivity factors stemming from psychology, physiology, and genetic influences. b. Three distinct sensitivity factors stemming from psychology, physiology, and genetic influences; a highly sensitive central nervous system. c. Autonomic adrenocortical activity; brain circuitry. d. Temperament and behavior; genes and epigenome. Liz and Allen have looked up a wide range of books to identify the various developmental milestones that their newborn daughter will experience over the next few years, such as when she might start to roll onto her stomach, then crawl, then walk. Their focus on such milestones most emphasizes the concept of: a. Critical periods b. Nurture c. Sensitive periods d. Maturation Leary & Baumeister argue that self-esteem is an internal gauge of a. Belonging b. Fear of loss c. A global feeling of success d. Physical attractiveness

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ronald b.