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Assume two Events A and B are mutually exclusive and, furthermore, P(A) = 0.6 and P(B) = 0.25. (a) Find P(A ∩ B). (b) Find P(A ∪ B).

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8. Consider the two topological subspaces of (R, U) ((a,b), U$_{(a,b)}$) and ((c, d), U$_{(c,d)}$) (i) Show that the linear function f: ((a, b), U$_{(a,b)}$) $\rightarrow$ ((c, d), U$_{(c,d)}$) x $\mapsto$ ($\frac{d-c}{b-a}$)x + $\frac{bc-ad}{b-a}$ is a bijection by writing down its inverse function. (ii) Show that the function f is a homeomorpism.

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A statistical power of $ 95 \% $ implies that the chance that the alternative hypothesis is true is $ 95 \% $. it is vepy likely that $ H_{0} $ will be rejected if it is not true. the p-value for the study will be $ 5 \% $. $ H_{0} $ is probably false.

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2 pts Object A has a temperature of 5000K while object B's temperature is 500K. Which object has its blackbody spectrum peak at a shorter wavelength? Object A Object A in the winter and Object B in the summer Both have the same peak wavelength Object A in the summer and Object B in the winter Object B

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Current Attempt in Progress The financial statement which summarizes the operating, investing, and financing activities of an entity for a period of time is the Oretained earnings statement. income statement. statement of financial position. statement of cash flows.

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Which of the following statements about exercise injury prevention are not true? Group of answer choices Keep moving throught the pain, It will go away on its' own. Dehydration can kill your performance, so stay well hydrated. Try to drink 16 oz. of water in the two hours before your workout and then take in water during your workout to replace any lost fluids. While you don't want to exercise immediately after eating a large meal, eating about 2 hours before exercise can help fuel your exercise and help you avoid bonking during your workout. In addition to helping reduce workout boredom, cross-training allows you to get a full body workout without overstressing certain muscle groups.

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30 P MC1 ut of 390 330 270 210 150 90 30 MC2 MC1 0 40 120 200 280 360 440 520 600 The figure above shows the demand and cost conditions for a monopoly with two plants. In order to maximize profit the firm should produce units. The profit-maximizing price is $ The firm will produce: in plant 1 units. in plant 2 units. Time left 1:29:58 Demand Q 680 760 840 920

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1. From the following particulars, prepare a Statement of profit and loss for the year ending March 2023, showing a profit before tax as per Schedule III of the Companies Act - 2013. PARTICULARS (?.) (?.) Plant and Machinery 1,60,000 Land 6,74,000 Depreciation on Plant and Machinery 16,000 Purchases (Adjusted) 4,00,000 Closing stock 1,50,000 Wages 1,20,000 Sales (Net) 10,00,000 Salaries 80,000 Bank overdraft 2,00,000 10% debentures (issued on 1st April, 2022) 1,00,000 Equity share capital - shares of Rs. 100 each (fully paid) 2,00,000 Preference share capital - 1,000; 6% shares of Rs. 100 each (fully paid) 1,00,000 16,00,000 16,00,000

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In a population distributed according to the normal distribution with a standard deviation of 15, we randomly extract a sample of 9 observations. We want to test whether the mean is 55 or 60. Calculate the power of the test at a significance level of 5%.

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is the prefix expression of the postfix expression [A BC*DE*++F +]. ? [+A++*BCD*EF] ? [++A+*BC*DEF] ? [+A++*BC*DEF] ? [++A+*BCD*EF]

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christopher w.