I would convert them to improper fractions and then multiply. The improper fractions would be 35/4*13/6, and then you multiply across, 455/24, and that doesn't reduce, but you can convert it back to a mixed number, which is 18 23/24.
Given:
Population proportion,
![\mu _{p}](https://tex.z-dn.net/?f=%5Cmu%20_%7Bp%7D)
= 57% = 0.57
Population standard deviation, σ = 3.5% = 0.035
Sample size, n = 40
Confidence level = 95%
The standard error is
![SE_{p} = \sqrt{ \frac{p(1-p)}{n} } = \sqrt{ \frac{0.57*0.43}{40} } =0.0783](https://tex.z-dn.net/?f=SE_%7Bp%7D%20%3D%20%20%5Csqrt%7B%20%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%20%7D%20%3D%20%5Csqrt%7B%20%5Cfrac%7B0.57%2A0.43%7D%7B40%7D%20%7D%20%3D0.0783)
The confidence interval is
![\hat{p} \pm z^{*}SE_{p}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%20%5Cpm%20z%5E%7B%2A%7DSE_%7Bp%7D)
where
![\hat{p}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D)
= sample proportion
z* = 1.96 at the 95% confidence lvvel
The sample proportion lies in the interval
(0.57-1.96*0.0783, 0.57+1.96*0.0783) = (0.4165, 0.7235)
Answer: Between 0.417 and 72.4), or between (41% and 72%)
Answer:
b. complementary
Step-by-step explanation:
-Complementary angles are angles that add up to 90°.
-These are usually the two acute angles in the right triangle.
#To verify, lets take the two angles 30° and 60°:
![Cos \ 60\textdegree=0.5\\\\Sin \ 30\textdegree=0.5\\\\\therefore Sin \ 30\textdegree=Cos \ 60 \textdegree=0.5](https://tex.z-dn.net/?f=Cos%20%5C%2060%5Ctextdegree%3D0.5%5C%5C%5C%5CSin%20%5C%2030%5Ctextdegree%3D0.5%5C%5C%5C%5C%5Ctherefore%20Sin%20%5C%2030%5Ctextdegree%3DCos%20%5C%2060%20%5Ctextdegree%3D0.5)
#We can reverse as:
![Sin \ 60\textdegree=0.86603\\\\Cos \ 30\textdegree=0.86603\\\\\therefore Sin \ 60\textdegree=Cos \ 30\textdegree=0.86603](https://tex.z-dn.net/?f=Sin%20%5C%2060%5Ctextdegree%3D0.86603%5C%5C%5C%5CCos%20%5C%2030%5Ctextdegree%3D0.86603%5C%5C%5C%5C%5Ctherefore%20Sin%20%5C%2060%5Ctextdegree%3DCos%20%5C%2030%5Ctextdegree%3D0.86603)
Hence, two angles are said to be complimentary if they sum up to 90°.
Answer:
10. 1/9
11. 1 1/6
12. 1/8
Step-by-step explanation:
10.
He spent 2/3 of 1/6 of the day.
In math, "of" means multiplication, so 2/3 of 1/6 means 2/3 * 1/6.
2/3 * 1/6 = 2/18 = 1/9
He spent 1/9 of the day adding mulch.
11.
He spent 2/3 of 1 3/4 hours.
In math, "of" means multiplication, so 2/3 of 1 3/4 means 2/3 * 1 3/4.
2/3 * 1 3/4 = 2/3 * 7/4 = 14/12 = 7/6 = 1 1/6
He spent 1 1/6 hours working on the project.
12.
She planted 1/6 of 3/4 of the area.
In math, "of" means multiplication, so 1/6 of 3/4 means 1/6 * 3/4.
1/6 * 3/4 = 3/24 = 1/8
She planted carrots in 1/8 of the garden.