Direct Variation<span>. Directly Proportional. A relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first. If b is directly proportional to a, the equation is of the form b = ka (where k is a constant).</span>
Answer:
- A) The radius of the sphere is 3 millimeters.
- B) The circumference of the sphere is 6π millimeters.
Step-by-step explanation:
Based on the answer selections, it appears we need to find the radius and circumference of the sphere. We can start with the volume formula in terms of the radius:
V = (4/3)πr³
36π = (4/3)πr³
(36π)(3/(4π)) = r³ = 27 . . . . . . mm³
r = ∛27 = 3 . . . . mm³
Then the circumference is ...
C = 2πr = 2π(3 mm) = 6π mm
The radius is 3 mm; the circumference is 6π mm.
Answer:
Option C is right
Step-by-step explanation:
Given are two samples
I group has sample size 90, mean = 9.2 and std dev =0,.37
II group has sample size 70, mean = 7.3 and std dev = 0.58
we find that mean difference i.e. difference between mean hours of sleep between two groups
= 9.2-7.3 = 1.9
Std error for difference = 0.0620
Since sample size is sufficiently large we can use Z critical for 99%
i.e. 2.58
Margin of error =±2.58(0.062)
=0.16
Hence confidence interval 99% for difference in hours of sleep
= (1.9-0.16,1.9+0.16)
=(1.74, 2.06)
Answer:
1. Area of the garden = 84 inch²
2. Diameter = 12 ft
Step-by-step explanation:
1 The area of the garden can be computed when you separate the composite shape into simpler ones. The shape can be separated into a trapezium and a rectangle.
The area of the garden will be the area of the rectangle plus the area of the trapezium.
area of rectangle = length × width
length = 10 inches
width = 5 inches
area of the rectangle = 10 × 5 = 50 inches²
Area of the trapezium = 1/2(a + b)h
a = 7 inch
b = 15 - 5 = 10 inch
h = 4 inch
area of the trapezium = 1/2 (7 + 10)4
area = 1/2(17)4
area = 68/2
area of the trapezium= 34 inch²
Area of the garden = 34 inch² + 50 inch² = 84 inch²
2. volume of a cylinder = πr²h
volume = 252π ft³
h = 7 ft
252π = π × r² × 7
252π = 7πr²
divide both sides by 7π
r² = 252π/7π
r² = 36
square root both sides
r = √36
r = 6 ft
Diameter = 2 × radius
Diameter = 2 × 6
Diameter = 12 ft