Let's call our estimate x. It will be the average of n IQ scores. Our average won't usually exactly equal the mean 97. But if we repeated averages over different sets of tests, the mean of our estimate the average would be the same as the mean of a single test,
μ = 97
Variances add, so the standard deviations add in quadrature, like the Pythagorean Theorem in n dimensions. This means the standard deviation of the average x is
σ = 17/√n
We want to be 95% certain
97 - 5 ≤ x ≤ 97 + 5
By the 68-95-99.7 rule, 95% certain means within two standard deviations. That means we're 95% sure that
μ - 2σ ≤ x ≤ μ + 2σ
Comparing to what we want, that's means we have to solve
2σ = 5
2 (17/√n) = 5
√n = 2 (17/5)
n = (34/5)² = 46.24
We better round up.
Answer: We need a sample size of 47 to be 95% certain of being within 5 points of the mean
P = 4
13 + 3 = 16
16/4 = 4
These questions require reverse order, you have to work backwards
For example 4 * P you would do 4/P instead
Answer:
center of mass
X = 
Y = 
Step-by-step explanation:
y = x and x = 0
parabola ; y = 20 - x^2
attached below is the detailed solution
M =
б
Mx =
б
My =
б
X = 
Y = 
For the first one, you just need to divide the amount of feet by 3 to get the amount of yards (there are three feet in a yard).
1431 / 3 = 476 2/3
The 102nd floor of the Sears Tower is 476 2/3 yards from the ground.
Second, you just need to multiply the amount of centimeters by 10 (there are 10 millimeters in a centimeter).
16 * 10 = 160
The butterfly has a wingspan of 160mm.
Third, the measurements are indeed
7. =
8. =
9. <
10. >
11. >
12. =
Fourth, you just need to know your conversion factors.
1. There are 3 feet in a yard. 42 / 3 = 14 yards
2. There are 1000 meters in a kilometer. 2350 / 1000 = 2.35 km
3. 12 inches in a foot. 18 * 12 = 216 inches
4. 10 decimeters in a meter. 289 * 10 = 2890 dm
5. 1760 yards in a mile. 1760 * 5 = 8800 yds
6. 10 millimeters in a centimeter. 35 * 10 = 350 mm
Hope that was helpful =)