We have two equations from the two clues respectively. (1) L = 2W - 2 (2) 2L + 2W = 80 Rewrite (1) as 2W = L + 2 Now substitute into (2) 2L + L + 2 = 80 3L...
We have two equations from the two clues respectively. (1) L = 2W - 2 (2) 2L + 2W = 80 Rewrite (1) as 2W = L + 2 Now substitute into (2) 2L + L + 2 = 80 3L...
Let's Use three events. H: Heads tossed T: Tails tossed W: White marble chosen Note that Pr(W|H) = 2 / (5+2+6) = 2/13 Pr(W|T) = 3 / (9 + 3 + 0) = 3/12 = 1/4 We can now...
Let D be the number of daffodils and R be the number of roses he bought. The clue of number of flowers bought and amount of money he spent gives two equations. (1) D + R = 35 (2) 4D...
Since the trains are moving towards each other, each train's speed relative to the other train is 108 + 96 = 204 mph Therefore they will crash in 51 miles / 204 mph = 1/4 hours = 15 minutes. The hero has 15 minutes to save the...
Let X be the amount of the cheaper candy and 8-X be the amount of the more expensive candy. This totals 8 lb. of candy. The mixture costs a total $ [0.71X+1.25(8-X)] and this must be (8 lb)($0.91/lb) = $7.28. Now equate and solve for X. 0.71X...
If each of the days has a 40% chance of rain, there is a 60% chance of dry weather on each day, or p = 0.6 If all days are independent, then the probability of dry weather on all 3 days is p3 = 0.216 So it will rain on at least one day with probability 1...
The second question is easier, so let's get it out of the way first. The total size of the class we choose from when flipping heads is 12+15 = 27 and 15 of them are girls. Therefore Pr[Girl | H] = 15/27 = 5/9 Now for the first question. Here you use...
Note that for a circular orbit, the gravity force matches the centripetal force which is F = mv2/r. For the given satellite it is F = mv2/r = (1120 kg)(3960 m/s)2 / (3.80×106 m) ≈ 4600 N Note that the final units are Newtons and that I only...
Note that if a function f(x) is period p, then af(x) still has period p for a≠0 because you are just rescaling the values of the function, and f(ax) has period p/a because the value of f(x) at x = k is the same as that of f(x) at x = k/a, so the graph is scaled...
Since E and F are independent, the probabilities of E and E' are invariant under whether F happened or not. (1) Pr(E'|F) = Pr(E') = 1 - Pr(E) = 1 - 0.45 = 0.55 (2) Pr(E|F') = Pr(E) = 0.45
The number subscribing to New York Times only is 17 - 5 = 12. The number subscribing to Wall Street Journal only is 14 - 5 = 9. The number that subscribe to exactly one of the two is therefore 12 + 9 = 21. This gives a probability 21/43 ≈ 0.488
Remember that Scientific notation for a real number is R = a × 10b where |a|<10 and b is an integer. Start by writing 74 × 106 using the definition of a million. Now notice how |74| > 10. However 7.4 × 101 where 1 ≤ |7.4| < 10. Rewrite...
Prime-factor the right side: 612 = 212312 Now we know that x = ±2a3b and y = 2c3d for some integers a,b,c,d ≥ 0 (±2a3b)2 (2c3d)3 212 312 22a+3c 32b+3d = 212 312 2a + 3c = 12 2b + d = 12 For...
67 and 73 inches are 1 standard deviation. The empirical (68-95-99.7) rule says that 68% of the population of 10th grade boys have heights in this range.
f(x) = x2 - 1/x + 1 and g(x) = x - 1 so a. f(2) = 22 - 1/2 + 1 = 5 - 1/2 = 9/2 = 4.5 g(2) = 2 - 1 = 1 b. f(7) = 72 - 1/7 + 1 = 50 - 1/7 = 349/7 = 49.857142... g(7) = 7 - 1 = 6 c...
5 hours and 48 minutes is 5 + 4/5 = 29/5 hours. Let x be the length of the trip measured in kilometers. Use t = x/v It takes him x/25 hours to travel to the post office and x/4 hours to walk back and that should sum to 5.8 hours x/25...
Since the train has 5/6 it's usual speed, it will take 6/5 times as long as usual. We are told that this is 10 minutes longer. We can set up an equation for this. (6/5)t = t + 10 t + t/5 = t + 10 t/5 = 10 t = 50 Therefore,...
Start by marking the stationary points. Method 1: Next, get the gradient vector field ∇z = 〈 ∂z/∂x , ∂z/∂y 〉 = ∇z = 〈 3x2 - 12x , -2y 〉 The gradient is the zero vector at the two stationary points. At any other point...
There are 11! ways to arrange 11 people overall. Since permuting just the women has no effect on the arrangement in the problem, you must divide by 6! Similarly for men, you must divide by 5! There are 11! / (5! 6!) = 462 arrangements...
The probability is a number. For example, the probability of getting heads in one flip of a fair coin is 1/2 A probability distribution, is a function that assigns a probability to every possible event. Usually, we only define a distribution by specifying the PMF (discrete distributions)...