This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Alright angelkaylee17 — let's do this. 21. Step 1: Start at -3 on the number line. Step 2: Subtracting 4 means moving 4 units to the left from -3. -3 - 4 = -7 The final position on the number line is -7. The integer is -7. 22. Step 1: Convert all mixed numbers to improper fractions. Initial sugar: 3(1)/(2) = (3 × 2 + 1)/(2) = (7)/(2) kg Sugar used: 1(1)/(4) = (1 × 4 + 1)/(4) = (5)/(4) kg Additional sugar bought: 2(1)/(2) = (2 × 2 + 1)/(2) = (5)/(2) kg Step 2: Calculate the remaining sugar. Remaining sugar = Initial sugar - Sugar used + Additional sugar bought Remaining = (7)/(2) - (5)/(4) + (5)/(2) Step 3: Find a common denominator, which is 4. Remaining = (7 × 2)/(2 × 2) - (5)/(4) + (5 × 2)/(2 × 2) Remaining = (14)/(4) - (5)/(4) + (10)/(4) Step 4: Perform the addition and subtraction. Remaining = (14 - 5 + 10)/(4) Remaining = (9 + 10)/(4) Remaining = (19)/(4) kg Step 5: Convert the improper fraction back to a mixed number. (19)/(4) = 4(3)/(4) kg Joshua finally remained with 4(3)/(4) kg of sugar. 23. Step 1: Let x be the given repeating decimal. x = 0.18 = 0.1888... (1) Step 2: Multiply by 10 to move the non-repeating digit past the decimal point. 10x = 1.888... (2) Step 3: Multiply by 100 to move one full repeating block past the decimal point. 100x = 18.888... (3) Step 4: Subtract equation (2) from equation (3) to eliminate the repeating part. 100x - 10x = 18.888... - 1.888... 90x = 17 Step 5: Solve for x. x = (17)/(90) The number 0.18 as a fraction is (17)/(90). 24. The problem asks to calculate the distance covered, but the image of the athletic field does not provide any dimensions (e.g., length of straight sections, radius of semicircles). Without these dimensions, it is impossible to calculate the perimeter of the track or the total distance covered. 25. Step 1: Identify the dimensions of the rectangular tin. Height (h) = 30 cm Base length (l) = 20 cm (since it's a square base) Base width (w) = 20 cm Step 2: Calculate the volume of the tin in cubic centimeters. The formula for the volume of a rectangular prism is V = l × w × h. V = 20 cm × 20 cm × 30 cm V = 400 cm^2 × 30 cm V = 12000 cm^3 Step 3: Convert the volume from cubic centimeters to cubic meters. We know that 1 m = 100 cm. Therefore, 1 m^3 = (100 cm)^3 = 100 × 100 × 100 cm^3 = 1,000,000 cm^3. V = 12000 cm^3 × 1 m^31,000,000 cm^3 V = (12000)/(1000000) m^3 V = (12)/(1000) m^3 V = 0.012 m^3 The volume of the paint that can fit in the container is 0.012 m^3. 26. Step 1: Identify the given distance and time. Distance (D) = 432 Km Time (T) = 6 hours Step 2: Convert the distance from kilometers to meters. 1 Km = 1000 m D = 432 Km × 1000 m1 Km = 432000 m Step 3: Convert the time from hours to seconds. 1 hour = 60 minutes 1 minute = 60 seconds T = 6 hours × 60 minutes1 hour × 60 seconds1 minute T = 6 × 3600 seconds = 21600 seconds Step 4: Calculate the average speed using the formula Speed = DistanceTime. Speed = 432000 m21600 s Speed = (4320)/(216) m/s Speed = 20 m/s Wangina's average speed is 20 m/s. Send me the next one 📸