Given:
250 sheep in a 40-acre pasture.
Number of sheep grazing in each acre.
250/40 = 6.25 or 6 sheep per acre
n = 6
sample proportion: signified by ρ
Sample 1: 4 → 4/6 = 0.67
Sample 2: 1 → 1/6 = 0.17
Sample 3: 9 → 9/6 = 1.50
multiply the sample proportion by 1-ρ
Sample 1: 0.67(1-0.67) = 0.67(0.33) = 0.2211
Sample 2: 0.17(1-0.17) = 0.17(0.83) = 0.1411
Sample 3: 1.50(1-1.5) = 1.5(-0.5) = -0.75
divide the result by n. n = 6
Sample 1: 0.2211/6 = 0.03685
Sample 2: 0.1411/6 = 0.02352
Sample 3: -0.75/6 = -0.125
square root of the quotient to get the standard error.
Sample 1: √0.03685 = 0.1919
Sample 2: √0.02352 = 0.1534
Sample 3: √-0.125 = invalid
z value 95% confidence 1.96.
Sample 1: 1.96 * 0.1919 = 0.3761 or 37.61% margin of error
Sample 2: 1.96 * 0.1534 = 0.3007 or 30.07% margin of error
Answer:
<h3>C. They are both perfect squares and perfect cubes.</h3>
Step-by-step explanation:
Perfect squares are numbers that their square root can be found easily without any remainder.
Given the following patterns;
1*1 = 1 and 1*1*1 = 1
It can be seen that 1 is 1 perfect square since 1*1 = 1² = 1
Also 1 is perfect cube since 1*1*1 = 1³ = 1 (cube of the value gives 1)
Similarly for the expression;
8*8 = 64
8² = 64 (since the square of 8 gives 64, then 64 is known to be a perfect square)
Also 4*4*4 = 64
i.e 4³ = 64 (This shows that the cube root of 64 is 4 making it a perfect cube since we can get a whole number for the cube root of 64)
The same is applicable for other expressions 729 = 27 × 27, and 9 × 9 × 9, 4,096 = 64 × 64, and 16 × 16 × 16
This values are easily expressed as a constant multiple of a number showing that they are both perfect squares and perfect cubes.
Triangle ABC and triangle DCE are congruent, so line DE = line AB
Use the cosine rule to find angle ACB
Angle ACB = 48.1°
Answer:
31.99 sorry if wrong
Step-by-step explanation:
You should subtract the powers when they are divided and add them when they are multiplied this rule is so important for now you just have to subtract them and you will get the answer
Hope it helps :)
