Homework 1.1
Table 1 below shows the number of children per grade in Nu Horizon High school.
TABLE 1: The number of boys and girls in Nu Horizon High school
GRADE
8
BOYS
95
120
99
B
75
GIRLS
102
118
101
95
80
TOTAL
197
238
А
186
C С
10
11
12
Study TABLE 1 and answer the questions that follow:
1.1.1
Determine the value of A, B and C
1.1.2
In which grade are there more boys than girls?
1.1.3
Determine the ratio of boys : girls in Grade 12 in a simplified form.​

x-3y=4

step-by-step e

a

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt