Answer:
a). L=53+3 D.... equation
b). Total length of the road after the crew has worked 31 days=146 miles
Step-by-step explanation:
Step 1
Find an expression for calculating the total length of a the road as follows;
L=F+(M×D)
where;
L=total length of the road in miles
F=starting length of the road in miles
M=number of miles per day added
D=number of days the crew has worked
In our case;
L=unknown
F=53 miles
M=3 miles per day
D=unknown
L=53+(3×D)
L=53+3 D.... equation
Solve for L when D=31 days
L=53+(3×31)
L=53+93=146
Total length of the road after the crew has worked 31 days=146 miles
AB = 30 in and BC = 50 in.
We use Pythagorean theorem to solve this. Since AN is an altitude, this means that it is perpendicular to BC. This means BN and AN are the legs of one right triangle, with AB being the hypotenuse:
18²+24² = AB²
324 + 576 = AB²
900 = AB²
Take the square root of both sides:
√900 = √AB²
30 = AB
NC and AN form the legs of the other right triangle, with AC being the hypotenuse:
24²+NC² = 40²
576 + NC² = 1600
Subtract 576 from both sides:
576 + NC² - 576 = 1600 - 576
NC² = 1024
Take the square root of both sides:
√NC² = √1024
NC = 32
BC = BN + NC = 18 + 32 = 50
Answer:
2/7
then 2/14
Step-by-step explanation:
Let P(H)=p be the probability of one head. In many scenarios, this probability is assumed to be p=12 for an unbiased coin. In this instance, P(H)=3P(T) so that p=3(1−p)⟹4p=3 or p=34.
You are interested in the event that out of three coin tosses, at least 2 of them are Heads, or equivalently, at most one of them is tails. So you are interested in finding the likelihood of zero tails, or one tails.
The probability of zero tails would be the case where you only received heads. Since each coin toss is independent, you can multiply these three tosses together: P(H)P(H)P(H)=p3 or in your case, (34)3=2764.
Now we must consider the case where one of your coin flips is a tails. Since you have three flips, you have three independent opportunities for tails. The likelihood of two heads and one tails is 3(p2)(1−p). The reason for the 3 coefficient is the fact that there are three possible events which include two heads and one tails: HHT,HTH,THH. In your case (where the coin is 3 times more likely to have heads): 3(34)2(14)=2764.
Adding those events together you get p3+3(p2)(1−p)=5464. Note that the 3 coefficient
Answer: See below
Step-by-step explanation:
- Both will use the straight edge to make segments and use the compass to take measurements.
- They will draw a line with a straight edge and will find a starting point, then with a compass:
- Annie will take the measurement of the segment and, from the starting point of the line, will put in the other point to obtain the congruent segment.
- But in Jaymie's case, she will need to do a little more work with a compass because to build congruent angles, she will need to make a semi-circle in the original angle and transfer this measurement to the new line to construct the angle.
