Answer:
(i) The radius of the scale model of the Earth is 12.7 cm and its volume is 8580.25 cm³ (ii)
Step-by-step explanation:
First you have to find the ratio between the radius of the Moon and the radius of its model (3.4 cm/1700km) and then multiply it for the radius of the Earth model.
Radius of the scale model of the Earth = 6350 km x (3.4 cm/1700 km)
⇒Radius of the scale model of the Earth = 12.7 cm.
Finally, to find the volume of the scale model of the Earth you have to use the formula for the volume of a sphere.
V= 4πr³/3 ⇒ V= 4π(12.7 cm)³/3⇒ V= 8580.25 cm³
Answer:
2
Step-by-step explanation:
If two shapes are similar, this means the ratio of similar sides to each other are the same.
So, in the green shape, the long side length is 5 mm. In the purple shape, the long side length is 10 mm in length. The ratio is therefore 5 to 10, which can be simplified to 1 to 2 (which is basically saying that the side lengths of the purple shape are double the length of the sides of the green shape).
Using the same 1 to 2 ratio, you know that the short side length on the green shape is 1. The short side length on the purple shape (j) must therefore be double, which is 2.
Answer:
- 66
Step-by-step explanation:
Evaluate g(- 4) then substitute the value obtained into f(x) , that is
g(- 4) = - 2(- 4)² = - 2 × 16 = - 32, then
f(- 32) = 2(- 32 - 1) = 2 × - 33 = - 66
9514 1404 393
Answer:
45. (8√2)∠π/4
46. (7√2)∠3π/4
Step-by-step explanation:
The polar form of a+bi is ...
a +bi ⇔ (√(a²+b²))∠arctan(b/a)
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45. 8 +8i = (√(8² +8²))∠arctan(8/8) = (8√2)∠π/4
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46. -7 +7i = (√((-7)² +7²))∠arctan(7/-7) = (7√2)∠3π/4
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<em>Additional comment</em>
The arctan function usually returns a value in the range -π/2 to π/2. The quadrant of the desired result can be determined by the signs of the components of the vector. For negative real parts, π needs to be added to the value that is usually returned by the arctan function.
Answer:
Confidence Interval =-0.76,+1.56
Step-by-step explanation:
The confidence interval can be determined by
(x1`- x2`) ± z∝/2 √s1²/n1 + s2²/n2
z∝/2 for 93% is 1.81
The mean and the standard deviations can be calculated using the calculator.
The mean x1`= ∑x/ n= 5+ 5+ 6+ 6+ 6+ 3+ 4+ 6+ 6+ 6
= 53/10= 5.3
Standard deviation = s1`= 1.0049= 1.005
The mean x2`= ∑x/ n= 7+ 3+ 4 +7+ 4+ 7+ 3+ 3+ 7+ 4/10
= 49/10= 4.9
Standard Deviation = s2= 1.75783= 1.76
Putting the values
(x1`- x2`) ± z∝/2 √s1²/n1 + s2²/n2
(5.3-4.9 ) ± 1.81 √1.005²/10 +1.76²/10
0.4 ± 1.81 √ 1.010025/10 + 3.0976/10
-0.76,+1.56
The confidence interval for 93% two tailed test is [-0.76,+1.56]