What is the temperature change from 7°C to -13°C? Evaluate 2/3(2 1/5 - 1 1/2) + 1 1/5 * 3/4 + 1 2/5

Here are the answers to your math questions: 1. Step 1: Identify the initial and final temperatures. Initial temperature = 7^ Final temperature = -13^ Step 2: Calculate the drop in temperature. The drop in temperature is the initial temperature minus the final temperature. Drop = 7^ - (-13^) Drop = 7^ + 13^ Drop = 20^ The drop in temperature was A. 20^. 2. Step 1: Convert all mixed numbers to improper fractions. 2(1)/(5) = (11)/(5) 1(1)/(2) = (3)/(2) 1(1)/(5) = (6)/(5) 1(2)/(5) = (7)/(5) Step 2: Substitute the improper fractions into the expression. (2)/(3)((11)/(5) - (3)/(2)) + (6)/(5) × (3)/(4) + (7)/(5) Step 3: Perform the subtraction inside the parentheses. Find a common denominator for (11)/(5) and (3)/(2), which is 10. (11)/(5) - (3)/(2) = (11 × 2)/(5 × 2) - (3 × 5)/(2 × 5) = (22)/(10) - (15)/(10) = (7)/(10) Step 4: Substitute this back into the expression. (2)/(3)((7)/(10)) + (6)/(5) × (3)/(4) + (7)/(5) Step 5: Perform the multiplications. (2)/(3) × (7)/(10) = (14)/(30) = (7)/(15) (6)/(5) × (3)/(4) = (18)/(20) = (9)/(10) Step 6: Substitute these results back into the expression. (7)/(15) + (9)/(10) + (7)/(5) Step 7: Find a common denominator for 15, 10, and 5, which is 30. (7 × 2)/(15 × 2) + (9 × 3)/(10 × 3) + (7 × 6)/(5 × 6) (14)/(30) + (27)/(30) + (42)/(30) Step 8: Add the fractions. (14 + 27 + 42)/(30) = (41 + 42)/(30) = (83)/(30) Step 9: Convert the improper fraction to a mixed number. (83)/(30) = 2(23)/(30) The possible answer is D. 2(23)/(30). 3. Step 1: Write the given number. 0.000461 m^2 Step 2: Move the decimal point to the right until there is only one non-zero digit to its left. The first non-zero digit is 4. So, we move the decimal point after 4. 0.000461 4.61 Step 3: Count the number of places the decimal point was moved. The decimal point moved 4 places to the right. Step 4: Since the decimal point was moved to the right, the exponent of 10 will be negative. 4.61 × 10^-4 The area expressed in standard form is B. 4.61 × 10^-4. 4. Step 1: Identify the given area of the square farm. Area (A) = 12.96 m^2 Step 2: Find the length of one side (s) of the square. For a square, A = s^2. So, s = sqrt(A). s = sqrt(12.96) s = 3.6 m Step 3: Calculate the perimeter of the square farm. The perimeter (P) of a square is 4 × s. P = 4 × 3.6 m P = 14.4 m The perimeter of the farm is A. 14.4 m. 5. Step 1: Define the width and length of the rectangular field. Let the width be X meters. The length is 5 m more than its width, so Length = (X + 5) meters. Step 2: Write the formula for the perimeter of a rectangle. Perimeter (P) = 2(Length + Width) Step 3: Substitute the given values and expressions into the formula. 52 = 2((X + 5) + X) Step 4: Simplify the expression inside the parentheses. 52 = 2(2X + 5) Step 5: Distribute the 2. 52 = 4X + 10 This equation represents the given information. The correct option is C. 4X + 10 = 52. 6. Step 1: Analyze the number line. The number line shows a closed circle at 9. This means 9 is included in the solution. The arrow points to the left from 9. This means all numbers less than 9 are included. Step 2: Combine these observations into an inequality. The values are less than or equal to 9. X 9 The inequality that represents the above information is A. X 9. 7. Step 1: Determine the dimensions of the floor. From the diagram, the floor is a rectangle with length 15 m and width 10 m. Step 2: Calculate the area of the floor. Area of floor = Length × Width Area_floor = 15 m × 10 m = 150 m^2 Step 3: Determine the dimensions of the carpet. The carpet leaves a uniform margin of 1 m from the wall on all sides. Carpet length = Floor length - 2 × margin Carpet length = 15 m - (2 × 1 m) = 15 m - 2 m = 13 m Carpet width = Floor width - 2 × margin Carpet width = 10 m - (2 × 1 m) = 10 m - 2 m = 8 m Step 4: Calculate the area of the carpet. Area of carpet = Carpet length × Carpet width Area_carpet = 13 m × 8 m = 104 m^2 Step 5: Calculate the area of the space not covered by the carpet. Area not covered = Area of floor - Area of carpet Area_not covered = 150 m^2 - 104 m^2 = 46 m^2 There seems to be a mismatch with the provided options (A. 170m², B. 144cm², C. 50m², D. 120cm²). Let me re-check the question and my calculations. The question asks for the area of the space not covered by the carpet. My calculation is 46 m^2. None of the options match this. Let's re-examine the image for any misinterpretation. The diagram shows the floor as 15m by 10m. The carpet is placed with a 1m margin. Floor area = 15 * 10 = 150 m^2. Carpet length = 15 - 1 - 1 = 13m. Carpet width = 10 - 1 - 1 = 8m. Carpet area = 13 * 8 = 104 m^2. Area not covered = 150 - 104 = 46 m^2. It's possible there's an error in the question's options or the diagram's labels. However, based on the information given, 46 m^2 is the correct answer. Since I must select from the given options, and none of them are 46 m^2, I cannot provide a definitive answer from the options. I will state the calculated answer. The area of the space not covered by the carpet is 46 m^2. (Note: This answer is not among the provided options.) 3 done, 2 left today. You're making progress.