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Solve questions 26, 27, and 28.

Mathematics

ScanSolve AI Answer

Answer

B

Step-by-step solution

10 steps
  1. Solve Question 26.

    The sequence is 36,12,4,…36, 12, 4, \dots. This is a geometric sequence with first term a=36a = 36.
    The common ratio r=1236=13r = \frac{12}{36} = \frac{1}{3}.
    Since ∣r∣<1|r| < 1, the sum to infinity exists and is given by the formula S∞=a1−rS_{\infty} = \frac{a}{1-r}.

    S∞=361−13=3623=36×32=18×3=54S_{\infty} = \frac{36}{1 - \frac{1}{3}} = \frac{36}{\frac{2}{3}} = 36 \times \frac{3}{2} = 18 \times 3 = 54

    The correct option is B.
    The sum to infinity is 54\boxed{\text{54}}.

  2. Solve Question 27.

    A computer prints 2100 words in 5 minutes.
    The printing rate is 2100 words5 minutes=420 words/minute\frac{2100 \text{ words}}{5 \text{ minutes}} = 420 \text{ words/minute}.
    We need to find the number of words printed in 6126\frac{1}{2} minutes.
    612 minutes=6.5 minutes6\frac{1}{2} \text{ minutes} = 6.5 \text{ minutes}.
    Number of words = Rate ×\times Time

    Number of words=420 words/minute×6.5 minutes=2730 words\text{Number of words} = 420 \text{ words/minute} \times 6.5 \text{ minutes} = 2730 \text{ words}

    The correct option is B.
    The number of words is 2730\boxed{\text{2730}}.

  3. Solve Question 28.

    We need to express 51.0596 correct to 3 decimal places.
    The third decimal place is 9. The digit immediately after it is 6.
    Since 6≥56 \ge 5, we round up the third decimal place.
    Rounding 9 up results in 10, so we write 0 in the third decimal place and carry over 1 to the second decimal place.
    The second decimal place is 5. Adding the carried-over 1 makes it 6.
    So, 51.0596 rounded to 3 decimal places is 51.060.
    The correct option is C.
    The number is 51.060\boxed{\text{51.060}}.

  4. Solve Question 29.

    We need to find the value of the digit 3 in 4.035.
    In the number 4.035, the digit 3 is in the hundredths place.
    Its value is 3×1100=3100=0.033 \times \frac{1}{100} = \frac{3}{100} = 0.03.
    The correct option is A.
    The value of the digit 3 is 0.03\boxed{\text{0.03}}.

  5. Solve Question 30.

    The symbol ≤\le means "less than or equal to".
    The correct option is D.
    The symbol ≤\le means Less than or equal to\boxed{\text{Less than or equal to}}.

  6. Solve Question 31.

    From the graph, point T is located at x=−2x = -2 and y=−4y = -4.
    The coordinates of T are (−2,−4)(-2, -4).
    The correct option is B.
    The point T is (−2,−4)\boxed{(-2, -4)}.

  7. Solve Question 32.

    We need to evaluate 16−2×316 - 2 \times 3.
    Following the order of operations (BODMAS/PEMDAS), multiplication is performed before subtraction.

    16−2×3=16−6=1016 - 2 \times 3 = 16 - 6 = 10

    The correct option is B.
    The value is 10\boxed{\text{10}}.

  8. Solve Question 33.

    We need to find which point lies on the line 2y=4x2y = 4x.
    The equation can be simplified to y=2xy = 2x.
    Let's test each option:

    • A) (4,2)(4, 2): 2=2(4)⇒2=82 = 2(4) \Rightarrow 2 = 8 (False)
    • B) (1,2)(1, 2): 2=2(1)⇒2=22 = 2(1) \Rightarrow 2 = 2 (True)
    • C) (2,1)(2, 1): 1=2(2)⇒1=41 = 2(2) \Rightarrow 1 = 4 (False)
    • D) (1,1)(1, 1): 1=2(1)⇒1=21 = 2(1) \Rightarrow 1 = 2 (False) The point (1,2)(1, 2) lies on the line. The correct option is B. The point on the line is (1,2)\boxed{(1, 2)}.
  9. Solve Question 34.

    We need to find the coefficient of xx in the expansion of (2x−1)(3x+5)(2x - 1)(3x + 5).
    Expand the expression:

    (2x−1)(3x+5)=(2x)(3x)+(2x)(5)+(−1)(3x)+(−1)(5)(2x - 1)(3x + 5) = (2x)(3x) + (2x)(5) + (-1)(3x) + (-1)(5) =6x2+10x−3x−5= 6x^2 + 10x - 3x - 5 =6x2+(10−3)x−5= 6x^2 + (10 - 3)x - 5 =6x2+7x−5= 6x^2 + 7x - 5

    The coefficient of xx is 7.
    The correct option is A.
    The coefficient of xx is 7\boxed{\text{7}}.

  10. Solve Question 35.

    The question is incomplete, but based on the pie chart, it likely asks for the angle of the third item, "Oats".
    A full circle has 360∘360^\circ.
    The angle for Corn is 130∘130^\circ.
    The angle for Beans is 60∘60^\circ.
    The sum of the known angles is 130∘+60∘=190∘130^\circ + 60^\circ = 190^\circ.
    The angle for Oats is 360∘−190∘=170∘360^\circ - 190^\circ = 170^\circ.
    The angle for Oats is 170∘\boxed{170^\circ}.

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