Answer:
m∠A = 20°
Step-by-step explanation:
Given that the sum of the angles of any triangle is 180°, adding the expressions of each angle and setting them equal to 180° will give the value of 'x' and allow you to evaluate the angles.
2x + 5x + 11x = 180
18x = 180
18x/18 = 180/18 or x = 10
m∠A = 2x or 2(10) = 20°
m∠B = 5x or 5(10) = 50°
m∠C = 11x or 11(10) = 110°
Out of the choices given, the only one that is true is that m∠A = 20°.
Answer:
x-intercepts are (0, 0) and (-6, 0)
Step-by-step explanation:
equation of a parabola in vertex form: y = a(x - h)² + k
where (h, k) is the vertex
Substituting the given vertex (-3, -18) into the equation:
y = a(x + 3)² - 18
If the y-intercept is (0, 0) then substitute x=0 and y=0 into the equation and solve for a:
0 = a(0 + 3)² - 18
⇒ 0 = a(3)² - 18
⇒ 0 = 9a - 18
⇒ 9a = 18
⇒ a = 2
Therefore, y = 2(x + 3)² - 18
To find the x-intercepts, set the equation to 0 and solve for x:
2(x + 3)² - 18 = 0
Add 18 to both sides: 2(x + 3)² = 18
Divide both sides by 2: (x + 3)² = 9
Square root both sides: x + 3 = ±3
Subtract 3 from both sides: x = ±3 - 3
so x = 3 - 3 = 0
and x = -3 - 3 = -6
So x-intercepts are (0, 0) and (-6, 0)
Answer:
The country's population for the year 2030 is 368.8 million.
Step-by-step explanation:
The differential equation is:
Integrate the differential equation to determine the equation of P in terms of <em>t</em> as follows:
![\int\limits {\frac{1}{P(600-P)} } \, dP =k\int\limits {1} \, dt \\(\frac{1}{600} )[(\int\limits {\frac{1}{P} } \, dP) - (\int\limits {\frac{}{600-P} } \, dP)]=k\int\limits {1} \, dt\\\ln P-\ln (600-P)=600kt+C\\\ln (\frac{P}{600-P} )=600kt+C\\\frac{P}{600-P} = Ce^{600kt}](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7B%5Cfrac%7B1%7D%7BP%28600-P%29%7D%20%7D%20%5C%2C%20dP%20%3Dk%5Cint%5Climits%20%7B1%7D%20%5C%2C%20dt%20%5C%5C%28%5Cfrac%7B1%7D%7B600%7D%20%29%5B%28%5Cint%5Climits%20%7B%5Cfrac%7B1%7D%7BP%7D%20%7D%20%5C%2C%20dP%29%20-%20%28%5Cint%5Climits%20%7B%5Cfrac%7B%7D%7B600-P%7D%20%7D%20%5C%2C%20dP%29%5D%3Dk%5Cint%5Climits%20%7B1%7D%20%5C%2C%20dt%5C%5C%5Cln%20P-%5Cln%20%28600-P%29%3D600kt%2BC%5C%5C%5Cln%20%28%5Cfrac%7BP%7D%7B600-P%7D%20%29%3D600kt%2BC%5C%5C%5Cfrac%7BP%7D%7B600-P%7D%20%3D%20Ce%5E%7B600kt%7D)
At <em>t</em> = 0 the value of <em>P</em> is 300 million.
Determine the value of constant C as follows:
It is provided that the population growth rate is 1 million per year.
Then for the year 1961, the population is: P (1) = 301
Then 
.
Determine <em>k</em> as follows:
For the year 2030, P (2030) = P (70).
Determine the value of P (70) as follows:
Thus, the country's population for the year 2030 is 368.8 million.
Answer:
The correct answer is "0.0842".
Step-by-step explanation:
Given:
X = 5
By using the Poisson's distribution formula, we get
The probability will be:
⇒ 
By substituting values, we get
Answer:
Half-Life uses the formula N () = Noe # No = Initial Amount time h = length of half-life. Ifyou start with 65 milligrams of Chromium 51,used to track red blood cells, which has half-life of 27.7 days: How long will it take for 80% ofthe material to decay? t= (27.7) h5 (65) (h3) 4= (27.7) h; (05)
Step-by-step explanation:
