For a rectangle, the perimeter can be calculated as P=2l+2w. Assuming the length is horizontal and the width is vertical, the span between the x coordinates will give the length, while the span between the y coordinates will determine the width. Once these measurements are obtained, you can apply them to the perimeter formula. |7 -(-7)| = 14 gives l = 14, |5-(-2)| = 7 gives w=7. Therefore, P=2(14)+2(7), which results in P= 28+14, thus, P= 42.
In the case of an equilateral triangle ABC, each angle measures 60 degrees, as the total angle sum in any triangle is 180 degrees, and dividing that by 3 yields 60. Setting this equal to 3x-12, we have 60 = 3x - 12. After adding 12 to both sides, we get 72 = 3x, and dividing 72 by 3 gives us x = 24.66! I hope this clarifies things for you!
P(S) = Probability of Smash = 0.05 (5%)
P(M) = Probability of Modest = 0.5 (50%)
P(F) = Probability of Flop = 0.45 (45%)
Based on this, we utilize the model for discrete random variables, leading to:
E(X) = (0.05 * 5.2) + (0.5 * 0.9) + (0.45 * 0)
= 0.26 + 0.45 + 0
= 0.71 Mill'
Answer:
Step-by-step explanation:
The world population currently is rising at a yearly rate of 1.35 percent. The nature of the growth is exponential. We will use the exponential growth formula, expressed as
A = P(1 + r)^t
Where:
A indicates the population after t years.
t symbolizes the number of years.
P is the initial population count.
r signifies the growth rate.
<pFrom the given data,
P = 6.1 × 10^9
r = 1.35% = 1.35/100 = 0.0135
t = 1
Hence,
A = 6.1 × 10^9(1 + 0.0135)^1
A = 6.1 × 10^9(1.0135)^1
A = 6182350000
The total number of people added would be
6182350000 - 6100000000
= 82350000
(a) The multiplicative inverse of 1234 (mod 4321) is x so that 1234*x ≡ 1 (mod 4321). We can apply Euclid's algorithm:
4321 = 1234 * 3 + 619
1234 = 619 * 1 + 615
619 = 615 * 1 + 4
615 = 4 * 153 + 3
4 = 3 * 1 + 1
Now we will express 1 as a linear combination of 4321 and 1234:
1 = 4 - 3
1 = 4 - (615 - 4 * 153) = 4 * 154 - 615
1 = 619 * 154 - 155 * (1234 - 619) = 619 * 309 - 155 * 1234
1 = (4321 - 1234 * 3) * 309 - 155 * 1234 = 4321 * 309 - 1082 * 1234
This reduces to
1 ≡ -1082 * 1234 (mod 4321)
Thus, the inverse is
-1082 ≡ 3239 (mod 4321)
(b) Since both 24140 and 40902 are even, their GCD cannot equal 1, indicating no inverse exists.
