Answer:
Step-by-step explanation:
It is given that:
And we have to find the value of 
As per trigonometric identities, the relation between 
can represented as:
Putting 
in place of 
Because we are given
Putting value of cosine:
It is given that is in 2nd quadrant and value of sine is always positive in 2nd quadrant. So, the answer is.
Answer:
<h2>33</h2>
Step-by-step explanation:
Given the average low temperature by month in Nashville is represented by the function f(x)=-1.4x² + 19x +1.7, where x is the month, the average rate of change is expressed as d[f(x)]/dx = 2(1.4x) + 19
d[f(x)]/dx = 2.8x + 19
Since the number of months between March and August is 5 months and x is in months, hence we will substitute x = 5 into the resulting function to get the average rate of change from March to August as shown;
d[f(x)]/dx at x = 5
= 2.8(5)+ 19
= 14 + 19
= 33
<em>Hence the average rate of change from March to August is 33</em>
Total men is 12 + 86 = 98
If 200 people were surveyed, that means the number of women should be 200 - 98 = 102.
Table B is the only one with 102 total women.
Answer:
0.9256
Step-by-step explanation:
Given that a convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit
Let X be the number of customers who buy from her store, on a certain day of the week, buy coffee during their visit
X is Binomial (35, 0.55)
since each customer is independent of the other and there are two outcomes.
By approximation to normal we find that both np and nq are >5.
So X can be approximated to normal with mean = np = 19.25
and std dev = 
Required probability = prob that fewer than 24 customers in the sample buy coffee during their visit on that certain day of the week
= 
(after effecting continuity correction)
= 0.9256
Answer:
212m
Step-by-step explanation:
The set up will be equivalent to a right angled triangle where the height is the opposite side facing the 45° angle directly. The length of the rope will be the slant side which is the hypotenuse.
Using the SOH, CAH, TOA trigonometry identity to solve for the length of the rope;
Since we have the angle theta = 45° and opposite = 150m
According to SOH;
Sin theta = opposite/hypotenuse.
Sin45° = 150/hyp
hyp = 150/sin45°
hyp = 150/(1/√2)
hyp = 150×√2
hyp = 150√2 m
hyp = 212.13m
Hence the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertical height of 150 m is approximately 212m
