This figure shows the nose cone of a rocket used for launching satellites. The nose cone houses the satellite until the satellit

Solution/Step-by-step breakdown:

Information provided:

m<9 = 97°

m<12 = 114°

a. m<1 = m<9 because they are corresponding angles, which are equal.

m<1 = 97° (using substitution)

b. m<2 + m<1 = 180° (since they form a linear pair)

m<2 + 97° = 180° (substitute the value)

m<2 = 180 - 97 (subtracting 97 from both sides)

m<2 = 83°

c. m<3 = m<11 (as they are corresponding angles)

m<11 + m<12 = 180° (linear pair)

m<11 + 114° = 180° (substituting the known angle)

m<11 = 180 - 114

m<11 = 66°

m<3 = m<11 = 66°

d. m<4 + m<3 = 180° (linear pair)

m<4 + 66° = 180° (substituting the known angle)

m<4 = 180 - 66

m<4 = 114°

e. m<5 = m<2 as vertical angles are equal.

m<5 = 83° (using substitution)

f. m<6 = m<1 (vertical angles are equal)

m<6 = 97° (using substitution)

g. m<7 = m<4 (as vertical angles are equal)

m<7 = 114° (using substitution)

h. m<8 = m<3 (due to vertical angles being equal)

m<8 = 66° (using substitution)

i. m<10 = m<2 (corresponding angles are equal)

m<10 = 83° (using substitution)

j. m<11 = m<3 (because they are vertical angles)

m<11 = 66° (using substitution)

k. m<13 = m<5 (corresponding angles)

m<13 = 83° (applying substitution)

l. m<14 = m<9 (as vertical angles)

m<14 = 97° (applying substitution)

m. m<15 = m<12 (as vertical angles)

m<15 = 114° (applying substitution)

n. m<16 = m<11 (because they are vertical angles)

m<16 = 66° (applying substitution)

Starting with the equation Y - 4x = 7, we can express y as y = 4x + 7. Now, substitute this expression into the second equation 2y + 4x = 2: 2(4x + 7) + 4x = 2, which simplifies to 8x + 14 + 4x = 2. After that, we gather like terms: 12x = 2 - 14, yielding 12x = -12, hence x = -1. Plugging x into the equation y - 4(-1) = 7 also reveals: y + 4 = 7, which gives y = 3. Thus, the solution arrives at (-1, 3).

Answer:

a) The outlier is the point located at the bottom right of the graph

b) The plotted points resemble a line that has a positive gradient

c) By conducting correlation analysis, we can determine the strength of the correlation

Step-by-step explanation:

a) The problem presents a scenario where Igor, who has recently moved, is experienced but needs to retrain medically to practice in the UK

Thus, he corresponds to the outlier situated nearest to the graph's bottom right

b) According to the scatter graph, there's a direct relationship showing that as a doctor's age increases, their annual salary tends to climb as well

Referencing the graph:

Age      Salary

22        £28000

26        £30000

34        £44000

38        £42000

42        £30000

42        £46000

50        £55000

The data points follow a line demonstrating the proportional increase of salary with age.

c) To reinforce this conclusion's reliability, correlation analysis should be conducted to ascertain the relationship between age and annual incomes.