The school band is comprised of middle school students

if there are 7 HS students for every 2 MS students and there are 18 MS students...

18/2 = 9

9(7) = 63

So, there are 18 + 63 = 81 total students.

Since we had 9 parts last year also (1:8), 81/9 = 9 students are in each part. 8 students in each part are HS and one is MS.

8(9) = 72 HS students last year.

72 - 63 = 9 fewer HS students than last year.

Hope this helps!

Part A:

Linear function

Part B:

House 1; f(x) = 7595.3·x + 178515

House 2; f(x) = 11,000·x + 179000

Part C:

Yes, there will be a significance difference

The value of house 1 after 30 years is $406,374

The value of house 2 after 30 years is $509,000

Step-by-step explanation:

The given values are

               House 1

Year 1,    186,160

Year 2,   193606.40

Year 3,   201350.66

We see that the prices of the houses have a common difference given as follows;

201,350.66 - 193606.40 = 7744.26,

193,606.40 - 186,160 = 7446.4

Which is fairly constant giving a linear function of the house after a fixed number of years

               House 2

Year 1,    190,000

Year 2,   201,000

Year 3,   212,000

We see that the prices of the houses have a common difference given as follows;

212,000 - 201,000 = 11,000,

201,000 - 190,000 = 11,000

Which is fairly constant

Which is fairly constant giving a linear function of the house after a fixed number of years

Part B:

The function for the first house  is given by the regression formula from regression analysis

Y = a + b·X

Where:

X = Value of the house at Year Y

Y = The year

Which gives;

f(x) = 7595.3·x + 178515

The function for the first house  is given by the arithmetic progression also by regression analysis as follows;

f(x) = 11,000·x + 179000

Part C

The value of house 1 after 30 years = 7595.3×30 + 178515 = $406,374

The value of house 2 after 30 years = 11,000×30 + 179000 = $509,000

Yes, there will be a significance difference between house 2 and house 1 to about 509,000 - 406,374 = $102,626.