We read your photo as:

Solve 2(x + 4) ext >= 5x - 1, graph the solution, change 111012 to base ten, and find the time when three machines produce packages simultaneously.

Mathematics

ScanSolve AI Answer

Step-by-step solution

12 steps

Here are the solutions to the questions:

4a. Solve 2(x+4)≥5x−12(x + 4) \ge 5x - 1 and graph the solution.

  1. Distribute the 2 on the left side.

    2x+8≥5x−12x + 8 \ge 5x - 1
  2. Subtract $2x$ from both sides.

    8≥5x−2x−18 \ge 5x - 2x - 1 8≥3x−18 \ge 3x - 1
  3. Add 1 to both sides.

    8+1≥3x8 + 1 \ge 3x 9≥3x9 \ge 3x
  4. Divide by 3.

    93≥x\frac{9}{3} \ge x 3≥x3 \ge x

    This can also be written as x≤3x \le 3.

  5. Graph the solution.

    The solution x≤3x \le 3 means all numbers less than or equal to 3. On a number line, this is represented by a closed circle at 3 and an arrow extending to the left.

    <------------------•--------------------->
       -1   0   1   2   3   4   5
                  <----- (closed circle at 3, arrow to the left)
    

    The solution is x≤3\boxed{x \le 3}.

    4b. Change 11101211101_2 to base ten numeral.

    To convert a binary number to base ten, multiply each digit by the corresponding power of 2.

    111012=(1×24)+(1×23)+(1×22)+(0×21)+(1×20)11101_2 = (1 \times 2^4) + (1 \times 2^3) + (1 \times 2^2) + (0 \times 2^1) + (1 \times 2^0) =(1×16)+(1×8)+(1×4)+(0×2)+(1×1)= (1 \times 16) + (1 \times 8) + (1 \times 4) + (0 \times 2) + (1 \times 1) =16+8+4+0+1= 16 + 8 + 4 + 0 + 1 =29= 29

    So, 111012=291011101_2 = \boxed{29_{10}}.

    5a. Three machines in a factory produce packages. Machine A every 12 minutes, Machine B every 18 minutes, and Machine C every 24 minutes. Find the time (in minutes) when all three machines will produce a package at the same time.

    This problem requires finding the Least Common Multiple (LCM) of 12, 18, and 24.

  6. Find the prime factorization of each number.

    12=22×3112 = 2^2 \times 3^1 18=21×3218 = 2^1 \times 3^2 24=23×3124 = 2^3 \times 3^1
  7. Identify the highest power of each prime factor present in any of the numbers.

    For prime factor 2: The highest power is 232^3 (from 24).
    For prime factor 3: The highest power is 323^2 (from 18).

  8. Multiply these highest powers to find the LCM.

    LCM(12,18,24)=23×32=8×9=72\text{LCM}(12, 18, 24) = 2^3 \times 3^2 = 8 \times 9 = 72

    All three machines will produce a package at the same time after 72 minutes\boxed{72 \text{ minutes}}.

    5b. If an item is sold at a 20% profit for GH¢60, find the cost price.

    Let the cost price be CC.
    The selling price (SP) is GH¢60.
    The profit percentage is 20%.

    The selling price is the cost price plus the profit.

    SP=Cost Price+Profit\text{SP} = \text{Cost Price} + \text{Profit} Profit=20% of Cost Price=0.20C\text{Profit} = 20\% \text{ of Cost Price} = 0.20C

    So,

    60=C+0.20C60 = C + 0.20C 60=1.20C60 = 1.20C

    To find CC, divide the selling price by 1.20.

    C=601.20C = \frac{60}{1.20} C=60120100C = \frac{60}{\frac{120}{100}} C=60×100120C = \frac{60 \times 100}{120} C=6000120C = \frac{6000}{120} C=50C = 50

    The cost price is GH¢50\boxed{\text{GH¢}50}.

    5c. Arrange the numbers −20,15,−2,0,56,4-20, 15, -2, 0, 56, 4 in ascending order.

    Ascending order means arranging numbers from the smallest to the largest.
    The given numbers are: −20,15,−2,0,56,4-20, 15, -2, 0, 56, 4.

  9. Identify the negative numbers and arrange them.

    −20-20 is smaller than −2-2. So, −20,−2-20, -2.

  10. Place zero.

    0 comes after the negative numbers. So, −20,−2,0-20, -2, 0.

  11. Identify the positive numbers and arrange them.

    The positive numbers are $15, 56, 4$.
    Arranging them: $4, 15, 56$.

  12. Combine all numbers in ascending order.

    −20,−2,0,4,15,56\boxed{-20, -2, 0, 4, 15, 56}
Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question