consider X-axis along the east-west direction and north-south direction along Y-axis
A = magnitude of distance traveled by hiker in north-east direction = 30 kilometer
θ = angle of direction of displacement of the hiker relative to x-axis or east direction = 45 degree counterclockwise
A' = component of distance traveled by the hiker along the east direction.
Since the angle is given with the x-axis, the Sin provides the component in Y-direction. hence
Using the equation
A' = A Sinθ
Inserting the values
A' = (30) Sin45
A' = 21.2 km
Answer:
Explained below.
Step-by-step explanation:
The information provided is as follows:

(1)
A single mean test is to be performed in this case.
As the population standard deviation is not provided, a one-sample <em>t</em>-test will be used.
The correct option is b.
(2)
The null hypothesis is:
<em>H</em>₀: The average temperature in the population is 98.6°F, i.e. <em>μ </em>= 98.6°F.
The correct option is b.
(3)
The alternative hypothesis is:
<em>Hₐ</em>: The average temperature in the population is less than 98.6°F, i.e. <em>μ </em>< 98.6°F.
The correct option is c.
(4)
The standard deviation of the sample mean is as follows:

Thus, the value of SD is 0.3°F.
(5)
Compute the value of test statistic as follows:


Thus, the value of test statistic is -1.67.
(6)
The degrees of freedom of the test are:
df = n - 1
= 9 - 1
= 8
Thus, the degrees of freedom of the test is 8.
Answer: 0.2pi
Step-by-step explanation:
1. Find the area of the entire circle
2. Set up a proportion that compares the relationship of the Area of sector and the Area of circle to the Arc measure and the circle measure
3. Solve!
QUESTION 3
The sum of the interior angles of a kite is
.
.
.
.
.
But the two remaining opposite angles of the kite are congruent.

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.
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QUESTION 4
RH is the hypotenuse of the right triangle formed by the triangle with side lengths, RH,12, and 20.
Using the Pythagoras Theorem, we obtain;





QUESTION 5
The given figure is an isosceles trapezium.
The base angles of an isosceles trapezium are equal.
Therefore
QUESTION 6
The measure of angle Y and Z are supplementary angles.
The two angles form a pair of co-interior angles of the trapezium.
This implies that;



QUESTION 7
The sum of the interior angles of a kite is
.
.
.
.
.
But the two remaining opposite angles are congruent.

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.
.
.
QUESTION 8
The diagonals of the kite meet at right angles.
The length of BC can also be found using Pythagoras Theorem;




QUESTION 9.
The sum of the interior angles of a trapezium is
.
.
.
But the measure of angle M and K are congruent.
.
.
.
.