Answer:
A)82.02 mi
B) 18.7° SE
Step-by-step explanation:
From the image attached, we can see the angles and distance depicted as given in the question. Using parallel angles, we have been able to establish that the internal angle at egg island is 100°.
A) Thus, we can find the distance between the home port and forrest island using law of cosines which is that;
a² = b² + c² - 2bc Cos A
Thus, let the distance between the home port and forrest island be x.
So,
x² = 40² + 65² - 2(40 × 65)cos 100
x² = 1600 + 4225 - (2 × 2600 × -0.1736)
x² = 6727.72
x = √6727.72
x = 82.02 mi
B) To find the bearing from Forrest Island back to his home port, we will make use of law of sines which is that;
A/sinA = b/sinB = c/sinC
82.02/sin 100 = 40/sinθ
Cross multiply to get;
sinθ = (40 × sin 100)/82.02
sin θ = 0.4803
θ = sin^(-1) 0.4803
θ = 28.7°
From the diagram we can see that from parallel angles, 10° is part of the total angle θ.
Thus, the bearing from Forrest Island back to his home port is;
28.7 - 10 = 18.7° SE
20 total marbles....7 are green
probability on first draw is 7/20...and since the marble was not replaced, the probability on the second draw is 6/19. And since they cant happen at the same time, we multiply
7/20 * 6/19 = 42/380 which reduces to 21/190
I=prt
I=26,000×0.08×3
I=6,240
<span>The correct answer is 216x</span>⁶<span>y</span>⁵<span>.
Explanation:
The first thing we do is raise the last monomial to the third power.
(4xy)(2x</span>²<span>y)(3xy)</span>³
<span>=(4xy)(2x</span>²<span>y)(3</span>³<span>x</span>³<span>y</span>³<span>)
=4xy(2x</span>²<span>y)(27x</span>³<span>y</span>³<span>).
Now we can multiply the first two monomials. When we multiply powers with the same base, we add the exponents:
8x</span>³<span>y</span>²<span>(27x</span>³<span>y</span>³<span>).
We multiply these last two monomials, again adding the exponents:
216x</span>⁶<span>y</span>⁵<span>.</span>
Answer:
1. rational number
2. a positive rational number
Step-by-step explanation:
A rational number is a number that can be expressed as a simple fraction. When two rational numbers are multiplied together, the only logical answer would be for the outcome/product to also be rational.
The reciprocal of a positive rational number is also a positive rational number because if the original number was negative, the reciprocal would also be negative since the signs wouldn't change (in this case, the original number is positive). Since the original number is already a rational number, just by flipping it (the reciprocal), it would not change to an irrational, but instead stay the same.
