1. ## Homework Help

1. A large map of the US uses a scale of 2cm=2.5km. On the map, the distance between two cities is 1 meter. What is the actual distance between the two cities?

2. the ratio of the measures of two complementary angles is 4 to 5. the smallest measure is increased by 10%. By what percent must the larger measure be decreased so that the two angles remain complementary?

3. What is the 25th number in the pattern 1,2,3,5,7,10,13,17,21,26....?

4. The mean of the set of numbers {87,85,80,83,84,x} is 83.5. What is the median of the set of six numbers? Express your answer as a decimal to the nearest tenth.

5. A local ice cream shop carries vanilla ice cream, chocolate ice cream, and strawbarry ice cream, as well as regular and sugar cones. Customers can order a single oe double scoop of their favorite flavor, or they can choose one scoop of one flavor topped with one scoop of another. If chocolate topped with vanilla is not the same as vanilla topped with chocolate, how many different ice cream con orders are possible??

2. 1. A large map of the US uses a scale of 2cm=2.5km. On the map, the distance between two cities is 1 meter. What is the actual distance between the two cities?

1meter = 100cm = 50 * 2 cm

50*2.5km = 125km

3. 3. What is the 25th number in the pattern 1,2,3,5,7,10,13,17,21,26....?

1,2,3, 5,7, 10,13, 17,21, 26,31, 37,43, 50,57, 65,73, 82,91, 101,111,
+1 +2 +3 +4 +5 +6 +7 +8 +9 +10
122,133, 145,157
+11 +12

the 25th number is 157

4. 4) X= 82. To get that value, you just solve the algebraic equation (80+83+84+85+87+x)/6= 83.5 so X=82

so the ordered set is now {80, 82, 83, 84, 85, 87}. Therefore the medium is 83.5 because (83+84)/2 = 83.5

5. 5) Since there are two cones and 3 different flavor and orders matter, then it's simply a permutation problem.

so 2*(3P1 + 3P2)
= 2*(3+9)
= 18

Note: Permutation means: n!/(n-k)!
so 3P1 = 3!/2! = $\frac {3*2*1}{2*1} = 3$

6. can u explain a little more in detail how u reach 18 as the answer?