Math Problem Statement

A series of math problems including: calculating the volume of a coffee tin, checking for a Pythagorean triple, and dividing an inheritance according to a ratio.

Solution

Let's go through each question visible in the image:

  1. Q7: "What is each angle size in a triple junction?"
    Answer: 120°.
    A triple junction occurs when three angles meet at a point. Since the sum of angles around a point is 360°, dividing that by 3 gives 120° per angle.

  2. Q8: "6 - 5/8 = 5.375"
    This is a subtraction of a fraction from a whole number. The result, 5.375, is correct. Converting 5/8 to decimal gives 0.625, and subtracting from 6 results in 5.375.

  3. Q9: "Find 400% of $40."
    Answer: $160.
    400% of a number is 4 times the original number. So, 40×4=16040 \times 4 = 160.

  4. Q10: "A quadrilateral with two pairs of congruent adjacent sides is called a kite."
    Answer: Kite.
    A kite is defined as a quadrilateral with two distinct pairs of adjacent sides that are congruent.

  5. Q11: "The volume of a coffee tin 10 cm deep and 20 cm in diameter is ______ cm³."
    To calculate the volume of a cylindrical object:
    Volume = π × r² × h, where r is the radius and h is the height.
    Here, the diameter is 20 cm, so the radius is 10 cm. The height (depth) is 10 cm.
    Volume = π×102×103141.59\pi \times 10^2 \times 10 \approx 3141.59 cm³.

  6. Q12: "Is a triangle with sides of 3, 4, and 5 a Pythagorean triple?"
    Answer: Yes.
    A Pythagorean triple consists of three positive integers that satisfy the equation a2+b2=c2a^2 + b^2 = c^2. For sides 3, 4, and 5:
    32+42=9+16=25=523^2 + 4^2 = 9 + 16 = 25 = 5^2, so the triangle is a Pythagorean triple.

  7. Q13: "Two sisters share an inheritance of $1 million dollars by a ratio of 2:3. How much does each sister inherit?"
    The total ratio parts are 2+3=52 + 3 = 5.
    The first sister receives 25×1,000,000=400,000\frac{2}{5} \times 1,000,000 = 400,000, and the second sister receives 35×1,000,000=600,000\frac{3}{5} \times 1,000,000 = 600,000.


Would you like further details or explanations on any of these answers?

Here are 5 related questions to expand your knowledge:

  1. How do you calculate the interior angles of polygons based on the number of sides?
  2. What is the relationship between percentages and fractions in real-world applications?
  3. What are the properties of different types of quadrilaterals, such as rectangles, rhombuses, and kites?
  4. How can the Pythagorean theorem be applied in three-dimensional geometry?
  5. How can ratios be used to solve real-world problems involving sharing or dividing quantities?

Tip: When calculating volumes of 3D shapes like cylinders, always double-check your units to ensure consistency (e.g., cm for both height and radius).

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Percentage calculations
Pythagorean Theorem
Ratios

Formulas

Volume of a cylinder: V = πr²h
Percentage calculation: (percentage / 100) * amount
Pythagorean triple: a² + b² = c²
Ratio-based division

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-9