Sovi.AI - AI Math Tutor

Scan to solve math questions
ENFRDEESJAZH-CNZH-TW

QUESTION IMAGE

Question was provided via image upload.

Question

Question was provided via image upload.

Explanation:

Solve Question 23

We need to find a possible perimeter of a rectangle with an area of \(24\text{ cm}^2\).
Let the side lengths of the rectangle be \(a\) and \(b\), where \(a \times b = 24\).
The perimeter is given by \(P = 2(a + b)\).
If \(a\) and \(b\) are integers, the possible factor pairs of \(24\) are:

  • \(1 \times 24 \implies P = 2(1 + 24) = 50\text{ cm}\)
  • \(2 \times 12 \implies P = 2(2 + 12) = 28\text{ cm}\)
  • \(3 \times 8 \implies P = 2(3 + 8) = 22\text{ cm}\)
  • \(4 \times 6 \implies P = 2(4 + 6) = 20\text{ cm}\)

Looking at the options:
A. \(20\text{ cm}\)
B. \(23\text{ cm}\)
C. \(21\text{ cm}\)
D. \(44\text{ cm}\)
E. \(30\text{ cm}\)

The value \(20\text{ cm}\) is a possible perimeter.

Solve Question 24

We need to find the sum of the digits of the number \(10^{50} - 23\) when written in decimal notation.
The number \(10^{50}\) is \(1\) followed by \(50\) zeros.
When we subtract \(23\) from \(10^{50}\):

$$ 10^{50} - 23 = \underbrace{999\dots99}_{48\text{ nines}}77 $$

The number of digits is \(50\). The first \(48\) digits are \(9\), and the last two digits are \(7\) and \(7\).
The sum of the digits is:

$$ 48 \times 9 + 7 + 7 = 432 + 14 = 446 $$

Let's check the options:
A. \(210\)
B. \(443\)
C. \(432\)
D. \(453\)
E. none of these

Since \(446\) is not listed, the correct option is E.

Solve Question 25

We need to find the area of the shaded shape.
The outer shape is a rectangle with dimensions \(20\text{ cm}\) by \(12\text{ cm}\).
The area of the outer rectangle is:

$$ A_{\text{outer}} = 20 \times 12 = 240\text{ cm}^2 $$

The inner unshaded shape is a parallelogram with a base of \(8\text{ cm}\) and a height of \(4\text{ cm}\).
The area of the parallelogram is:

$$ A_{\text{inner}} = 8 \times 4 = 32\text{ cm}^2 $$

The area of the shaded region is:

$$ A_{\text{shaded}} = A_{\text{outer}} - A_{\text{inner}} = 240 - 32 = 208\text{ cm}^2 $$

Looking at the options:
A. \(208\)
B. \(212\)
C. \(224\)
D. \(240\)
E. none of these

The correct option is A.

Solve Question 26

We need to find the concentration in \(\text{g/L}\) if there are \(5\text{ g}\) of salt in \(100\text{ mL}\) of water.
First, convert the volume from milliliters to liters:

$$ 100\text{ mL} = 0.1\text{ L} $$

Now, calculate the concentration:

$$ \text{Concentration} = \frac{5\text{ g}}{0.1\text{ L}} = 50\text{ g/L} $$

Looking at the options:
A. \(50\text{ g/L}\)
B. \(5\text{ g/L}\)
C. \(500\text{ g/L}\)
D. \(50\text{ kg/L}\)
E. \(5\text{ g/mL}\)

The correct option is A.

Solve Question 27

Julia was born in \(1980\). In \(2025\) she will be \(45\) years old because \(45^2 = 2025\).
Julia's great-grandmother was \(x\) years old in the year \(x^2\).
For a person to be alive in a reasonable historical timeframe relative to \(1980\), we look for a perfect square \(x^2\) representing a year in the 19th or 20th century.
Let's test values for \(x\):

  • If \(x = 43\), \(x^2 = 1849\). Born in \(1849 - 43 = 1806\).
  • If \(x = 44\), \(x^2 = 1936\). Born in \(1936 - 44 = 1892\).

If she was born in \(1892\), her age in \(2025\) would be:

$$ 2025 - 1892 = 133\text{ years old} $$

This is…

Answer:

Question 23

  • (A) 20cm (Correct answer)
  • (B) 23cm
  • (C) 21cm
  • (D) 44cm
  • (E) 30cm

Question 24

  • (A) 210
  • (B) 443
  • (C) 432
  • (D) 453
  • (E) none of these (Correct answer)

Question 25

  • (A) 208 (Correct answer)
  • (B) 212
  • (C) 224
  • (D) 240
  • (E) none of these

Question 26

  • (A) 50g/L (Correct answer)
  • (B) 5g/L
  • (C) 500g/L
  • (D) 50kg/L
  • (E) 5g/mL

Question 27

  • (A) 100
  • (B) 121
  • (C) 88
  • (D) 97
  • (E) 133 (Correct answer)

Question 28

  • (A) 5000
  • (B) 5555
  • (C) 1001
  • (D) 5151
  • (E) 5050 (Correct answer)