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he0gaubong
31.12.2020 •
Mathematics
Two consecutive odd integers are such that one-third the smaller is greater than one-seventh of the larger one by 6. Find the numbers.
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Ответ:
the number is 33 and 35 respectively
Step-by-step explanation:
The computation is shown below:
Let us assume X and X + 2 are the two consecutive odd integers
Now the equation is
(X ÷ 3) = ((X + 2) ÷ 7) + 6
(X ÷ 3) = (X + 2 + 6 × 7) ÷ 7
(X ÷ 3) = (X + 2 + 42) ÷ 7
(X ÷ 3) = (X + 44) ÷ 7
Now do the cross multiplication
7X = 3(X + 44)
7X = 3X + 132
4X = 132
X = 33
And, X + 2 = 33 + 2 = 35
hence, the number is 33 and 35 respectively
Ответ:
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.