The wind is blowing N 35.0 degrees W at 1.60 * 10^2 mph. A plane has an engine speed of 3.20 * 10^2 mph. Where should the pilot
point the plane in order to fly straight W?
1 answer:
Answer: 24.2° SouthWest
<u>Step-by-step explanation:</u>
First step: DRAW A PICTURE of the vectors from head to tail <em>(see image)</em>
I created a perpendicular from the resultant vector to the vertex of the given vectors so I could use Pythagorean Theorem to find the length of the perpendicular. Then I used that value to find the angle of the plane.
<u>Perpendicular (x):</u>
cos 35° = adjacent/hypotenuse
cos 35° = x/160
→ x = 160 cos 35°
<u>Angle (θ):</u>
sin θ = opposite/hypotenuse
sin θ = x/320
sin θ = 160 cos 35°/320
θ = arcsin (160 cos 35°/320)
θ = 24.2°
Direction is down (south) and left (west)
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Answer:
2
Step-by-step explanation:
We take the equation
and substitute the values for each individual variable in the problem. It looks like this:
Now we can solve the equation.
When solved, it equals 2.
Answer:
a. two-tailed test
b. reject H0 if Z>1.96 or Z<-1.96
c. Z = 1.73
d. we have failed to reject the null hypothesis
e. P-value = 0.0418
Step-by-step explanation:
We will use a Z test to resolve this, an it will be a two-tailed test because the hypothesis statements are not indicating a specific direction for the significant difference (H0 : μ1 = μ2 ; H1 : μ1 ≠ μ2), this also means that the significanclevel will be divided between the both tails (2.5% en each tail for the rejection regions). See attached drawing for reference.
We need to find our critical value:
Zα/2 = Z(0.05/2) = 0.025
If we look for 0.025 in a Z table we will find that the critical value is 1.96 to the right, and by symmetry -1.96 to the left. So our decision rule will be to reject H0 if Z>1.96 or Z<-1.96
The Z test will be done using the next equation:
Z = (x⁻1 - x⁻2) - (μ1 - μ2) / √( σ²1/n1 + σ²2/n2
Because we are testing the null hypothesis we know that μ1 - μ2 must be zero if they are supposed to be equal (H0 : μ1 = μ2), so we calculate as follows:
Z = (100.5 - 98.8) - (0) / √( (3.4)²/38 + (5.8)²/51 = 1.7/0.9817 = 1.73
Z<1.96, therefore we have failed to reject the null hypothesis
The P-value for this test would be represented by the probability of Z being greater than 1.73, so we can look for it in any Z table, finding that its value is 0.0418, and because P-value>0.025 we again confirm that we don't have evidence statistically significant to reject the null hypothesis
