9. Observing the pattern, the decimal digit at position n is 9 when n is even and 0 when n is odd. Because 44 is an even number, the 44th digit after the decimal point is 9.
Answer: y = 2/5 --> y = 0.4
Step-by-step explanation:
The equation 5y = 2 represents a horizontal line at y = 2/5.
This means that the y-coordinate holds the value of 2/5 = 0.4 for any x-coordinate.
1. Selected Case B. 2. 9 cm³. 3. 20 cm. 4. 4.5 m³. Explanation: In question 1, we need to fit a drum with a volume of 14,000 cm³. The volume of a cylinder can be calculated via the formula πr²h. For Case A, with r = 100 mm (10 cm) and h = 300 mm (30 cm), the total volume is approximately 9424.78 cm³, insufficient for the given drum. Case B, with r = 200 mm (20 cm) and h = 30 cm, gives a volume of approximately 37699.11 cm³. Case C with r = 32 cm and h = 250 mm (25 cm) results in a volume of about 80424.77 cm³. The smallest volume among Cases B and C is Case B at 37699.11 cm³, thus it is the correct choice. For question 2, the dimensions of the speaker are Length = 45 cm = 0.45 m, Width = 0.4 m, Height = 50 cm = 0.5 m, leading to a volume of 0.09 m³ or 9 cm³. Question 3 involves a speaker with a volume of 30,000 cm³ with Length = 30 cm = 0.45 m and Height = 500 mm = 50 cm, requiring to find its Width: 30,000 = 30 × W × 50, hence W = 20 cm. For question 4, with dimensions of Base = 2 m, Length = 3 m, Height =1.5 m, the volume of the prism is calculated as 4.5 m³.
Triangle XYZ is an equilateral triangle, meaning the sector's central angle measures 120 degrees, which is equivalent to 2π/3 radians. To find the area of a sector corresponding to a central angle β, we use the formula A = (1/2)r²*β, where β is expressed in radians. For this sector, the area calculation is A = (1/2)*2²*(2π/3) = 4π/3 square units.
Answer:
The scale factor is measured to be 2.5.
Step-by-step explanation:
The triangles are depicted below.
In triangle ΔABC,
the side lengths are AB = 2 units, BC = 2 units
In triangle ΔA'B'C',
the side lengths are A'B' = 5 units, B'C' = 5 units.
The formula for the scale factor in a dilation is given by:
Scale factor = 
Thus, the scale factor is 2.5.
