PART I
Angular size of the minor arc .
Half of the chord an the radius makes a right angled triangle with the radius as the hypotenuse and half of the chord as one of the shorter side.
Therefore, using trigonometric ratio, sine = opp/hyp
sine θ = 8/10 where θ is half the minor angle
θ = 53.13
Therefore, the angular size of the minor arc will be 53.13 × 2 = 106.26°
PART II
The length of an arc is given by (θ/360 )× 2πr
where θ is the angle subtended by the arc to the center of the circle and r is the radius of the circle.
Therefore, length = (106.26/360) × 3.142 × 2×10
= 18.548 Inches
Answer:
percentage change in weight ≈ 10%
Step-by-step explanation:
The dog weighed 48 kg after a diet and after an exercise program the dog had a weight of 43 kg. This means the dog loss weight since the dog weight decreased from an initial value of 48 kg to 43 kg. The decrease in weight can be calculate as
decrease in weight = original weight - new weight
original weight = 48 kg
new weight = 43 kg
decrease in weight = 48 - 43 = 5 kg
Since the weight decrease their will be a percentage decrease in weight.
% decrease = decrease in weight/original weight × 100
% decrease = 5/48 × 100
% decrease = 500/48
% decrease = 10. 42666666667
percentage change in weight ≈ 10%
The "meter" is a larger unit than the "centimeter." Every time you need to convert a larger metric unit to a smaller one, you must multiply to find a greater value.
Answer:
The probability that it will take more than 10 minutes for the next student to arrive at the library parking lot is 0.0821.
Step-by-step explanation:
The random variable <em>X</em> is defined as the amount of time until the next student will arrive in the library parking lot at the university.
The random variable <em>X</em> follows an Exponential distribution with mean, <em>μ</em> = 4 minutes.
The probability density function of <em>X</em> is:

The parameter of the exponential distribution is:

Compute the value of P (X > 10) as follows:


Thus, the probability that it will take more than 10 minutes for the next student to arrive at the library parking lot is 0.0821.