Answer:
450 m²
Step-by-step explanation:
Let x = length of rectangle and y = width of the rectangle.
Therefore,
2x + y = 60...............(1)
Making y subject of the formula, we have:
y = 60 - 2x............... (2)
We know area of a rectangle is length * width i.e A = x*y
Let's substitute (60-2x) for y,
A = x * (60-2x)
= 60x - 2(x)²
= -2x² + 60x
-4x + 60 = 0
-4x = -60
Let's substitute 15 for x in equation 2, we have:
y = 60 - 2(15)
= 60 - 30
y = 30
Since x = 15 & y = 30, the area would be:
A = xy
A = 15 * 30
A = 450 m²
The maximum area of the dog pen is 450m²
Match the mean, median, mode, and range for the data set below.<br>
19, 18, 16, 6, 8, 18, 14, 14, 13
Shalnov [3]
Answer: the mean is 13.4
Step-by-step explanation:
Answer:
The hat weight = 81.166 g
Step-by-step explanation:
∵The figure formed by a rectangle and two identical semi-circle
∵ The length of the rectangle = 52 cm = 0.52 m
∴ The length of the two diameter = 52 cm = 0.52 m
∴ The radius of the semi-circle = 52 ÷ 4 = 13 cm = 0.13 m
∴ The width of the rectangle = 36 - 13 = 23 cm = 0.23 m
∴ The area of the rectangle = 0.52 × 0.23 = 0.1196 m²
∴ The area of the semi-circles = π (0.13)² = 0.0531 m²
∴ The area of the hat = 0.1196 + 0.0531 = 0.17269292 m²
∵ 1 m² = 470 g
∴ The weight of the hat = 0.17269292 × 470 = 81.16567 ≅ 81.166 g
Answer:
The percentage of the bag that should have popped 96 kernels or more is 2.1%.
Step-by-step explanation:
The random variable <em>X</em> can be defined as the number of popcorn kernels that popped out of a mini bag.
The mean is, <em>μ</em> = 72 and the standard deviation is, <em>σ</em> = 12.
Assume that the population of the number of popcorn kernels that popped out of a mini bag follows a Normal distribution.
Compute the probability that a bag popped 96 kernels or more as follows:
Apply continuity correction:
*Use a <em>z</em>-table.
The probability that a bag popped 96 kernels or more is 0.021.
The percentage is, 0.021 × 100 = 2.1%.
Thus, the percentage of the bag that should have popped 96 kernels or more is 2.1%.
