Question

1. there are 40 houses in a neighborhood. - company x provides electricity to \\(\frac{1}{8}\\) of the houses. - company y provides electricity to \\(\frac{2}{5}\\) of the houses. - company z provides electricity to the remaining houses. in this neighborhood, company z provides electricity to— a. 21 houses b. 24 houses c. 16 houses d. 19 houses 7th grade fall semester final review

Explanation:

Step1: Calculate houses for Company X

Total houses = 40, Company X serves $\frac{1}{8}$ of 40. So, $40\times\frac{1}{8} = 5$ houses.

Step2: Calculate houses for Company Y

Company Y serves $\frac{2}{5}$ of 40. So, $40\times\frac{2}{5} = 16$ houses.

Step3: Calculate remaining houses for Company Z

Total houses - (X + Y) = $40 - (5 + 16) = 40 - 21 = 19$? Wait, no, wait: Wait, 5 + 16 is 21? Wait, 40 - 21 is 19? Wait, no, wait, let's recalculate. Wait, 40(1/8)=5, 40(2/5)=16. Then total served by X and Y is 5 + 16 = 21. Then remaining is 40 - 21 = 19? Wait, but let's check again. Wait, 1/8 of 40: 40 divided by 8 is 5. 2/5 of 40: 40 divided by 5 is 8, times 2 is 16. So 5 + 16 = 21. 40 - 21 = 19. Wait, but the options have D as 19. Wait, but let me check again. Wait, maybe I made a mistake. Wait, 1 - 1/8 - 2/5 = (40/40 - 5/40 - 16/40) = (40 - 5 - 16)/40 = 19/40. Then 40*(19/40)=19. Yes, so Company Z serves 19 houses.

Answer:

D. 19 houses