answer:To find the width of the plot of land in front of Jill's house, we need to calculate the total area of the yard and then subtract the areas of the sidewalk and flower beds. First, let's calculate the area of the sidewalk: Sidewalk area = Sidewalk width x Sidewalk length Sidewalk area = 3 feet x 50 feet Sidewalk area = 150 square feet Next, let's calculate the area of each flower bed: Flower bed 1 area = 4 feet x 25 feet (since there are two of these, we multiply by 2) Flower bed 1 total area = 4 feet x 25 feet x 2 Flower bed 1 total area = 200 square feet Flower bed 2 area = 10 feet x 12 feet Flower bed 2 area = 120 square feet Flower bed 3 area = 7 feet x 8 feet Flower bed 3 area = 56 square feet Now, let's add up the areas of the sidewalk and flower beds: Total non-sodded area = Sidewalk area + Flower bed 1 total area + Flower bed 2 area + Flower bed 3 area Total non-sodded area = 150 square feet + 200 square feet + 120 square feet + 56 square feet Total non-sodded area = 526 square feet Jill needs 9474 square feet of sod for the yard, so we subtract the non-sodded area to find the sodded area: Sodded area = Total yard area - Total non-sodded area Sodded area = 9474 square feet - 526 square feet Sodded area = 8948 square feet We know the length of the plot is 50 feet, so we can find the width by dividing the sodded area by the length: Width of the plot = Sodded area / Length of the plot Width of the plot = 8948 square feet / 50 feet Width of the plot = 178.96 feet Therefore, the width of the plot of land in front of Jill's house is approximately boxed{178.96} feet.

answer:1. **Variables and Initial Conditions:** Let the length of the track be x meters. They start frac{x}{2} meters apart because they are diametrically opposite. 2. **First Meeting Analysis:** At their first meeting, Brenda has run 120 meters. Thus, Sally has run frac{x}{2} - 120 meters (since combined they have covered frac{x}{2} meters). 3. **Second Meeting Analysis:** After the first meeting, they next meet when Sally runs an additional 180 meters, so Sally's total running distance by their second meeting is frac{x}{2} - 120 + 180 = frac{x}{2} + 60 meters. Brenda would have run x - (frac{x}{2} + 60) = frac{x}{2} - 60 meters at the second meeting. 4. **Equating Ratios of Speeds:** [ frac{120}{frac{x}{2} - 120} = frac{frac{x}{2} - 60}{frac{x}{2} + 60} ] 5. **Solving the Equation:** [ 120 left(frac{x}{2} + 60right) = left(frac{x}{2} - 60right) left(frac{x}{2} - 120right) ] [ 60x + 7200 = frac{x^2}{4} - 90x + 7200 ] [ frac{x^2}{4} - 150x = 0 ] [ frac{x}{4}(x - 600) = 0 ] [ x - 600 = 0 implies x = 600 ] 6. **Verification and Conclusion:** 600 meters is the total track length. Brenda and Sally's distances by their first and second meetings align proportionally with their speeds. boxed{The final answer is B) 600 meters.}

answer:To find out how many laborers were present, we need to calculate 38.5% of 26. 38.5% of 26 = (38.5/100) * 26 First, convert the percentage to a decimal by dividing by 100: 38.5/100 = 0.385 Then multiply this decimal by the total number of laborers: 0.385 * 26 = 10.01 Since the number of laborers present cannot be a fraction, we round to the nearest whole number. Therefore, boxed{10} laborers were present on that day.

answer:1. **Determine Coordinates of E**: First, we need to find the coordinates of the intersection point E. We can use the equations of the lines AB and CD. The slope of line AB is frac{1-4}{7-0} = -frac{3}{7}, and the slope of line CD is frac{3-1}{5-3} = 1. Equation of line AB: y - 4 = -frac{3}{7}(x - 0) Equation of line CD: y - 1 = 1(x - 3) Setting these two equations equal to find x: [ -frac{3}{7}x + 4 = x - 2 ] [ frac{10}{7}x = 6 ] [ x = frac{42}{10} = 4.2 ] Plugging x = 4.2 back into the equation of line CD: [ y = 4.2 - 2 + 1 = 3.2 ] Thus, E = (4.2, 3.2). 2. **Calculate BE**: With B = (7,1) and E = (4.2, 3.2), [ BE = sqrt{(4.2-7)^2 + (3.2-1)^2} = sqrt{(-2.8)^2 + (2.2)^2} = sqrt{7.84 + 4.84} = sqrt{12.68} ] Thus, BE = sqrt{12.68}. boxed{BE = sqrt{12.68}}