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# Determine whether the following equation is separable if so solve the given initial value problem

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definition of derivative, determine whether f(t) =1,t≤0 1/2(t+ 5),0< t≤1 is differentiable at t= 1 √t+ 2, t >1 3. FM Corporation is a company that manufactures face masks. For everyxthousand pieces of facemask sold, the company’s revenue (in thousand pesos) isR(x) =x(5 +x),x≥0. a. If the company soldxthousand pieces of face mask, find the company’s marginal revenue.Note: Marginal revenue is the increase in revenue that results from the sale of one additionalunit of output. b. Find the number of face mask sold if the company has a marginal revenue of Php 25,000.
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q → r) and q → (p ∨ r). Q2. Write the converse, inverse and contrapositive of the statement: “I will score marks whenever I will study”. Q3. Convert the following compound propositions into English sentences for given p: It is below freezing. q: It is snowing. (i) ¬q → ¬p (ii) ¬q ∨ (¬p ∧ q ) (iii) p ↔ ¬q (iv) p ∨ q (v) ¬q ∧ ¬p Q4. Determine whether each of the statements is true or false. (i) If 1 + 1 = 2, then 2 + 2 = 5. (ii) If 1 + 1 = 3, then 2 + 2 = 4. (iii) If 1 + 1 = 3, then dogs can fly. (iv) Monkeys can fly if and only if 1 + 1 = 3. (v) A number is prime if and only if it is divisible by 1 and itself.
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two objects and recorded whether or not the dog being tested correctly chose the object indicated. A four-year-old male beagle named Augie participated in this study. He chose the correct object 42 out of 70 times when the experimenter leaned towards the correct object. (a) (2 points) Let the parameter of interest, π, represent the probability that the long-run probability that Augie chooses correctly. Researches are interested to see if Augie understands human body cues (better than gussing). Fill in the blanks for the null and alternative hypotheses. H0 : Ha : (b) (6 points) Based on the above context, conduct a test of significance to determine the p-value to investigate if domestic dogs understand human body cues. What conclusion will you draw with significance level of 10%? (If you use an applet, please specify which applet you use, and the inputs.) (c) (5 points) Based on the above context, conduct a test of significance to determine the p-value to investigate if domestic dogs understand human body cues. What conclusion will you draw with significance level of 5%? (If you use an applet, please specify which applet you use, and the inputs.) (d) (2 points) Are your conclusions from part (b) and (c) the same? If they are different, please provide an explanation. (e) (5 points) Shown below is a dotplot from a simulation of 100 sample proportions under the assump- tion that the long-run probability that Augie chooses correct is 0.50. Based on this dotplot, would a 90% confidence interval for π contain the value 0.5? Explain your answer. (f) (4 points) Compute the standard error of the sample proportion of times that Augie chose the object correctly. 1 (g) (5 points) (h) (3 points) question? (i) (4 points) (j) (4 points) A. B. C. Construct an approximate 95% confidence interval for π using the 2SD method. What is the margin of error of the confidence interval that you found in the previous How would you interpret the confidence interval that you found in part (g)? Which of the following is a correct interpretation of the 95% confidence level? If Augie repeats this process many times, then about 95% of the intervals produced will capture the true proportion of times of choosing the correct objective. About 95% times Augie chooses the correct objective. If Augie repeats this process and constructs 20 intervals from separate independent sam- ples, we can expect about 19 of those intervals to contain the true proportion Augie chooses the correct objective. (k) (4 points) object 21 out of 35 times. Conjecture how, if at all, the center and the width of a 99% confidence interval would change with these data, compared to the original 2SD 95% confidence interval. The center of the confidence interval would . The width of the confidence interval would . (l) (4 points) Suppose that we repeated the same study with Augie, and this time he chose the correct object 17 out of 35 times, and we also change the confidence level from 95% to 99%. Conjecture how, if at all, the center and the width of a 99% confidence interval would change with these data, compared to the original 2SD 95% confidence interval. Suppose that we repeated the same study with Augie, and this time he chose the correct The center of the confidence interval would The width of the confidence interval would . .
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eople experienced a group-based behavioral intervention, which involved weekly meetings with a trained interventionist for a period of six months. The following data are the numbers of pounds lost for 14 people, based on means and standard deviations given in the article. Assume the population is approximately normal. Perform a hypothesis test to determine whether the mean weight loss is greater than 20 pounds. Use the =α0.10 level of significance and the critical value method. 22.5 28.5 7.6 24.1 21.5 12.9 17.3 21.2 37.6 33.8 12.1 36.3 24.1 19.4
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