Answer and explanation:
Null hypothesis(H0) says sentiment for increasing speed limit in the two populations is the same
Alternative hypothesis(Ha) says sentiment for increasing speed limit in the two populations is different
Where p1 is the first population proportion =65/297= 0.22
And p2 is the second population proportion = 78/189= 0.41
P= p1+p2/n1+n2= 65+78/297+189= 0.29
Hence H0= p1-p2=0
Ha=p1-p2≠0
Test statistic= p1-p2/√p(1-p) (1/n1+1/n2)
= 0.22-0.41/√0.29(1-0.29)(1/297+1/189)
= -4.49
Critical value at 95% significance level= 1.96( from tables)
We therefore reject null hypothesis as critical value is greater than test statistic
Therefore the sentiment for increasing speed limit in the two populations is different
b. at proportions of 0.24 and 0.40 for p1 and p2 respectively
Test statistic = 0.24-0.40/0.29(1-0.29)(1/297+1/189)
= -3.78
P value is 0.0002 at 0.05 significance level
Hence probability =0.4998
Answer:
A = 1.0 L
B = 0.50 atm
C = 0.60 atm
D = 4.0 L
Step-by-step explanation:
According to the Boyle's law, the volume of a gas is inversely proportional to its volume. If we consider an initial state (1) and a final state (2):
P₁ × V₁ = P₂ × V₂
A
P₁ × V₁ = P₂ × V₂
1.5 atm × 2.0 L = 3.0 atm × A
A = 1.0 L
B
P₁ × V₁ = P₂ × V₂
1.5 atm × 2.0 L = B × 6.0 L
B = 0.50 atm
C
P₁ × V₁ = P₂ × V₂
1.5 atm × 2.0 L = C × 5.0 L
C = 0.60 atm
D
P₁ × V₁ = P₂ × V₂
1.5 atm × 2.0 L = 0.75 atm × D
D = 4.0 L
Answer:
When we have something like:
![\sqrt[n]{x}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D)
It is called the n-th root of x.
Where x is called the radicand, and n is called the index.
Then the term:
![\sqrt[4]{16}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B16%7D)
is called the fourth root of 16.
And in this case, we can see that the index is 4, and the radicand is 16.
At the end, we have the question: what is the 4th root of 16?
this is:
![\sqrt[4]{16} = \sqrt[4]{4*4} = \sqrt[4]{2*2*2*2} = 2](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B16%7D%20%3D%20%5Csqrt%5B4%5D%7B4%2A4%7D%20%20%3D%20%5Csqrt%5B4%5D%7B2%2A2%2A2%2A2%7D%20%3D%202)
The 4th root of 16 is equal to 2.
Answer:
6 : 1
Step-by-step explanation:
b - 3a / 9 = a /3
Cross multiply
3(b - 3a) = 9a
Expand
3b - 9a = 9a
Add 9a to both sides
3b = 9a + 9a
3b = 18a
Divide both sides by 3
b = 6a
Ratio of a : b
6 : 1
