Given data, cos(A - B) = cosAcosB + sinAsinB
<span>let, A=60' and B=30' ( here the ' sign bears degree) </span>
<span>L.H.S = cos(A - B) </span>
<span>=cos (60'-30) ( using value of A and B ) </span>
<span>=cos30' </span>
<span>= sqrt3/2 </span>
<span>R.H.S= cosAcosB + sinAsinB </span>
<span>=cos60' cos30' + sin60' sin30' </span>
<span>= 1/2* sqrt3/2+ sqrt3/2*1/2 </span>
<span>= sqrt3/4 + sqrt3/4 </span>
<span>=2 sqrt3/4 </span>
<span>= sqrt3/2 </span>
<span>so L.H.S =R.H.S or cos(A - B) = cosAcosB + sinAsinB</span>
Answer:
The length of the missing piece is 2 ft 3 inches
Step-by-step explanation:
Here in this question, we are interested in calculating the length of the remaining piece of the board given that we have the total length of the board and two other pieces.
Mathematically, the remaining piece length can be calculated by subtracting the lengths of the known pieces
That would be;
10 ft - 4 ft 7 inches - 3 ft 2 inches
In a foot there are 12 inches
Thus
10 ft = 10 * 12 = 120 inches
4 ft 7 inches = 4(12) + 7 = 55 inches
3 ft 2 inches = 3(12) + 2 = 36 + 2 = 38 inches
Thus the length of the remaining piece would now be;
120 -55 -38 = 27 inches
That is same as 24 + 3 inches
24 inches = 2 ft
So 27 inches = 2 ft 3 inches
The correct answer is choice D. If you put choice D into words, it is saying 30% (0.3) of the total is 12 minutes.
To solve this, use inverse operations.
<span><u>0.3m</u> = <u>12</u>
</span>0.3 0.3
m = 40
It will take Beck 40 minutes.
Answer:
There is no significant evidence which shows that there is a difference in the driving ability of students from West University and East University, <em>assuming a significance level 0.1</em>
Step-by-step explanation:
Let p1 be the proportion of West University students who involved in a car accident within the past year
Let p2 be the proportion of East University students who involved in a car accident within the past year
Then
p1=p2
p1≠p2
The formula for the test statistic is given as:
z=
where
- p1 is the <em>sample</em> proportion of West University students who involved in a car accident within the past year (0.15)
- p2 is the <em>sample</em> proportion of East University students who involved in a car accident within the past year (0.12)
- p is the pool proportion of p1 and p2 (
) - n1 is the sample size of the students from West University (100)
- n2 is the sample size ofthe students from East University (100)
Then we have z=
≈ 0.6208
Since this is a two tailed test, corresponding p-value for the test statistic is ≈ 0.5347.
<em>Assuming significance level 0.1</em>, The result is not significant since 0.5347>0.1. Therefore we fail to reject the null hypothesis at 0.1 significance
Answer: l and ll only
Step-by-step explanation:
Those are necessary.