At a party, i play a coin-tossing game with a friend. each time the coin lands heads, i pay my friend $2.50, and each time it lands tails, he pays me $3.50. in this problem, you may ignore continuity corrections. (a) i believe that my net gain after 100 tosses should be around $50, give or take $30. fill in the blanks, and don't forget the units. (4 points) since i gain $3.50 for every tail and lose $2.50 for every head, the box for the net gain is | -2.5 +3.5|l. the box average is $0.5, and the se is $3. therefore, the expected gain in 100 tosses is $(100x0.5)=$50, give or take one se, which will be $(10x3)=$30.

An optical inspection system is used to distinguish among different part types. the probability of a correct classification of any part is 0.92. suppose that three parts are inspected and that the classifications are independent. let the random variable x denote the number of parts that are correctly classified. determine the probability mass function of x. round your answers to four decimal places (e.g. 98.7654). x f(x) 0 1 2 3

Sue's average score for three bowling games was 162. in the second game, sue scored 10 less than in the first game. in the third game, she scored 13 less than in the second game. what was her score in the first game?

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).