Answer:
CI = 21 ± 0.365
Step-by-step explanation:
The confidence interval is:
CI = x ± SE * CV
where x is the sample mean, SE is the standard error, and CV is the critical value (either t score or z score).
Here, x = 21.
The standard error for a sample mean is:
SE = σ / √n
SE = 3.2 / √510
SE = 0.142
The critical value is looked up in a table or found with a calculator. But first, we must find the alpha level and the critical probability.
α = 1 - 0.99 = 0.01
p* = 1 - (α/2) = 1 - (0.01/2) = 0.995
Using a calculator or a z-score table:
P(x<z) = 0.995
z = 2.576
Therefore:
CI = 21 ± 0.142 × 2.576
CI = 21 ± 0.365
Round as needed.
Answer:
D
Step-by-step explanation:
The area of a circle can be found using:
a=πr^2
We know that the radius is 10 meters. Therefore, we can substitute 10 in for r.
a=π*10^2
Evaluate the exponent
a=π*100
Multiply pi and 100
a=314.159265359
Round to the nearest tenth: there is a 5 in the hundreth place, which indicates we round up the 1 in the tenths place to a 2.
a=314.2
The area is 314.2 square meters, or choice D
Answer:
20% decrease in value.
Step-by-step explanation:
Do 650,000 divided by 100 to find what 1% of the original price is:
650,000 divided by 100 = 6,500
To find what percentage of the original price 520,000 is, we divide it by 1% of the original cost (6,500):
520,000 divided by 6,500 = 80 (percent)
So if 520,000 is 80% of 650,000 the car has decreased in value by 20%.
Answer:
The leg measures 14.14 cm
Step-by-step explanation:
The "40 - 40 - 90" special right triangle is an isosceles right triangle because two angles measures the same. (Check the picture)
The legs are the same.
The hypotenuse is:
a × √2
From the question, the length of the hypotenuse is 20 cm.
20 = a × √2
20 ÷ √2 = a
a = 10√2 ≈ 14.14 cm
