Question 7 In a sales campaign, a petrol company gives a each motorist who buys their petrol a card with a picture of a film star on it. There are 10 different pictures, one each of 10 different film stars, and any motorist who collects a complete set of all 10 pictures gets a free gift. On any occasion when a motorist buys petrol, the card received is equally likely to carry any one of the 10 pictures in the set. (i) Find the probability that the first four cards the motorist receives all carry different pictures. (ii) Find the probability that the first four cards received result in the motorist having exactly three different pictures. (iii) Two of the ten film stars in the set are X and Y. Find the probability that the first four cards received result in the motorist having a picture of X or Y (or both). (iv) At a certain stage the motorist has collected nine of the ten pictures. Find the least value of n such that P(at most n more cards are needed to complete the set) > 0.99. (UCLES)

Determine the effective annual yield for $1 invested for 1 year at 7.5% compounded quarterly. The effective annual yield is %. (Round to the nearest hundredth.)

Please write each number in front of the resultthank you. Shelly and Kelly Macdonald met up with Sarah and Tara MacNeill to go fishing in Cape Breton. They found two pools in a stream containing speckled trout (assume equal variance), with the Macdonalds at one pool and the MacNeills at the other, and at the end of the day each team had caught (and released unharmed) 5 fish. For each fish they recorded the length and weight, and the data on length (in cm) is summarized below (Give the answers to 2 places past decimal) Team Mean Sed. Dev Macdonald 19 1.4 MacNeill 2141 2 a.) To test whether or not the fish have the same mean size in the two pools, the null hypothesis will be: HO: 11-42 -2.41 HO: -2 -2.41 HO: 12-0 HO: -20 Tries 0/1 b.) The alternative hypothesis for this test will be: Ha: 1-2.-241 Ha1.22.41 Ma120 Hai 1-120 Tres 0/1 c.) What in the pooled estimate of the variance? ** Trys d.) Compute the value of the test statistic WOH Tries 0/5 e) Find bounds on the value for the test. P<.001 01 <P < .05 05 P1 P>.1 f) Is there statistically significant evidence against HO at a = 0.05 ? Yes No Not enough information to decide #*** Tries 0/1 g.) Calculate the 95% confidence interval for the difference in mean length Lower: Upper:

1.The Longest Common Subsequence Problem implement the Longest Common Subsequence (LCS) problem using dynamic programming. Input: two DNA sequences Adenine (A), Guanine (G), Cytosine (C) and Thymine (T) Output: the Longest Common Subsequence (LCS) of the input sequences Test data example) S1=ACCGGTCGAGTGCGCGGAAGCCGGCCGAA S2=GTCGTTCGGAATGCCGTTGCTCTGTAAA S3=GTCGTCGGAAGCCGGCCGAA programming language is c or java

Shelly and Kelly Macdonald met up with Sarah and Tara MacNeill to go fishing in Cape Breton. They found two pools in a stream containing speckled trout (assume equal variance), with the Macdonalds at one pool and the MacNeills at the other, and at the end of the day each team had caught (and released unharmed) 5 fish. For each fish they recorded the length and weight, and the data on length (in cm) is summarized below (Give the answers to 2 places past decimal) Team Macdonald MacNeill Mean 18.1 20.35 Std.Dev 1.4 1.9 a.) To test whether or not the fish have the same mean size in the two pools, the null hypothesis will be: HO: 1-X 2 = -2.25 HO: p1-y2 = -2.25 HO: X 1-8 2 = 0 HO: 1-2 = 0 # Tries 0/1 b.) The alternative hypothesis for this test will be: Ha: * 1- 2 = -2.25 Ha: p1-12 + -2.25 Ha: 81-X 2 = 0 Ha: p1-42 = 0 1236 Tries 0/1 c.) What is the pooled estimate of the variance? 1202 Tries 0/5 d.) Compute the value of the test statistic. 1 Tries 0/5

A 50-g weight is hung at the 20-cm mark of a meterstick and a 100-g weight is hung at the 70-cm mark. At what point must the meterstick be supported for it to be in rotational equilibrium? The weight of the meterstick is negligible. O at the 56.67-cm mark. at the 46.67 cm mark. O at the 53.33-cm mark. O at the 43.33 cm mark.

Part A The post is made of Douglas fir and has a diameter of 100 mm (Figure 1) It is subjected to the load of 20 kN and the soil provides a frictional resistance distributed around the post that is triangular along its sides that is, it varies from w=0 kN/mat y=0 m to w= 15 kN/m at y = 2 m. Neglect the weight of the post Determine the force at its bottom needed for equilibrium Express your answer to three significant figures and include appropriate units. HÅ ? Value Units Submit Request Answer Figure 1 of 1 Part B 20KN What is the displacement of the top of the post with respect to a bottom B? Express your answer to three significant figures and include appropriato unito, ? 2 m 0 = Value Units 12 kN/m Submit Request Answer