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1.C.1377. How many 6-digit cube-numbers are there? C.1378. Somebody calculated the exact values of and in the decimal system. ...

and in the decimal system. How many digits are there in these two numbers all together? C.1379. Alex and Burt took their rabbits to a whole salesman to sell them to him at once. Each of them got as many dollars for each of their rabbits as many as the rabbits they each took to him. But, because their rabbits were so beautiful, they each got as many extra dollars for their rabbits from the salesman as many as the rabbits they each sold him. This way Alex received $202 more than Burt. How many rabbits did they each sell to the salesman? C.1380. How many {a, b, c} sets are there containing three positive whole elements, where the product of a, b, and c is 2310? C.1381. Let a, b, c, and d be different digits. Find their values so that the following sum has the least possible number of divisors, but the sum itself is the greatest possible. C.1382. Fill in a 25×25 grid by using the numbers +1 and -1. Create the products of the 25 numbers in each column and in each row. Could the sum of these 50 numbers be: a) 0 b) 10 c) 17? C.1383. Is there such a triangle in which the heights are 1, 2, and 3 units long? C.1384. You put a plain on each side of a regular, square-based pyramid. How many sections do these 5 planes divide the space?
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2.1. Find the second-order derivative of the following function:f(x) = log2cosx+ lnπ 2. Using limit definition of derivative, determine whether f(t) =1,t≤0 1/2(t+ ...

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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3.The average amount of time that high school seniors spend studying weekly is 6.5 hours with a standard deviation of ...

rd deviation of 3.2 hours. A sample of 35 high school seniors is selected. Find the following values, if possible. Please round your answers to four decimal places. If you should not find a probability, please write NA for your answer. What is the probability that the sample mean studying time is between 4 and 5 hours? What is the probability that the sample mean studying time is less than 6 hours? What is the probability that the sample mean studying time is more than 8.5 hours?
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4.1. Find a positive integer b that makes the following equation true. (3042)b + (5425)b = (12511)b. b is number ...

is number that can be binary system, decimal system, hexadecimal system. 2. For each of the following pairs of sets, determine if they are disjoint, equal, one is a proper subset of the other, or none of the above. Provide evidence for your answer (i) Q×Z and R×Z (ii) R−ZandQ (iii) {−x|x∈Z}andZ (iv) {x^2 |x∈Z}andZ
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5.1. Find a positive integer b that makes the following equation true. (3042)b + (5425)b = (12511)b. b is ...

b is number that can be binary system, decimal system, hexadecimal system. 2. For each of the following pairs of sets, determine if they are disjoint, equal, one is a proper subset of the other, or none of the above. Provide evidence for your answer (i) Q×Z and R×Z (ii) R−ZandQ (iii) {−x|x∈Z}andZ (iv) {x^2 |x∈Z}andZ
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6. The marketing research department for the company that manufactures and sells “notebook” computers established the following price – demand function: p(x) ...

ters established the following price – demand function: p(x) = 10 – 0,001x, where p(x) is the wholesale price in dollars at which x thousand computers can be sold. Total cost (in dollars) of producing x items is given by C(x) = 7000 + 2x. A) Find the revenue function and state its domain. B) Find the marginal revenue function. Find R´(4000) and R´(6000). Interpret the results. C) Evaluate the approximate revenue and exact revenue of producing 101-th notebook. D) Find the profit function E) Find the marginal profit function. F) Evaluate the approximate profit and exact profit of producing 101-th notebook. G) Find P´(5000) and P´(7000). Interpret the results.
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7.3) Suppose that a piece of equipment produces steel pipes and malfunctions 5% of the time, if the next 4 ...

xt 4 tests are performed, find P(x=0), P(x=1), P(x=2),P(x=3) and P(x=4). SHOW ALL WORK TO GET CREDIT) 4) Use the confidence interval (99%) to solve the following question. A company is trying to establish the number of average amount of funds that are owed by its employees. They collect 1,000 accounts and found the sample average owed is $250 with a standard deviation of 10. Calculate the confidence interval (MUST SHOW ALL WORK TO GET CREDIT) 5) Use the t distribution formula and table to solve the following question. A random sample of 91 with a sample average of 90 and a standard deviation of 4.2 hours, calculate the confidence interval at 98% (MUST SHOW ALL WORK TO GET CREDIT) 6) A poll of 3,000 adults out of 5,500 was collected to found that they did not get a master’s degree. Calculate the confidence interval at 95%. (MUST SHOW ALL WORK TO GET CREDIT)
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics