Answer:
4.99 units
Step-by-step explanation:
Considering ∆ABD in the figure given, <ABD = <ABC = 90° (angle on a straight line)
Therefore, we would consider ∆ABD as a right angled triangle having side AB = 3 units, and angle D = 31°
==>Use trigonometric function to solve for the length of side BD
Side BD is the adjacent side to the angle given, while side AB is the opposite side to the angle given.
Thus,
tan D = opposite/adjacent
tan 31 = 3/BD
0.6009 = 3/BD
multiply both sides by BD
0.6009*BD = 3
Divide both sides by 0.6009 to make BD the subject of formula
BD = 3/0.6009
BD ≈ 4.99 units
Answer:
a) 230300 ways
b) Check Explanation
Step-by-step explanation:
a) This is a combination problem,
We require how many ways 4 factories be placed among 50 states.
Mathematically, that is
⁵⁰C₄ ways = 230300 ways
b) If you have no idea which states will be chosen, what is the probability that all 4 factories will be located in the mid-Atlantic region.
This can be done in two ways
Method 1
The mid Atlantic region is one of 9 geographic divisions in the US
Probability of 1 factory being located in this geographic region = (1/9)
The probability of the 4 factories being in just this region = (probability of locating one factory in this region)⁴ = (1/9)⁴ = 0.0001524
Method 2
The mid Atlantic region contains only 3 out of 50 states. (New York, New Jersey, Pennsylvania)
Probability of 1 factory being located in one of the 3 stares = (3/50)
Probability of locating all four factories in one of the states in this region = (3/50)⁴ = 0.00001296.
24 can go into 217 9 times
Answer:
no
Step-by-step explanation:
4 quarts = 1 gallon, so he would have 1.5 gallons.
8 pints = 1 gallon, he would need 4 pints to have 2 gallons
10,15,20,25,30
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