Answer:
$69
Step-by-step explanation:
Given the amount of money each girl spent based on the number of hours they were shopping modeled by the function p(x) = 3x4 + 2x3 − 4x2 + 21
To get how much they spend together if each go shopping for 2hours, we will substitute x = 2 into the given function as shown:
p(2) = 3(2)⁴ + 2(2)³ − 4(2)² + 21
p(2) = 3(16) + 2(8) − 4(4) + 21
p(2) = 48 + 16 − 16 + 21
p(2) = 48+21
p(2) = 69
Therefore they spend $69 together
It applies because interest slowly increases the amount of money gained. IF you have any Tolkien related questions, feel free to ask me
so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.
in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.
now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20A%28%5Cstackrel%7Bx_1%7D%7B7%7D~%2C~%5Cstackrel%7By_1%7D%7B4%7D%29%5Cqquad%20M%28%5Cstackrel%7Bx_2%7D%7B%5Cfrac%7B19%7D%7B2%7D%7D~%2C~%5Cstackrel%7By_2%7D%7B%5Cfrac%7B7%7D%7B2%7D%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20AM%3D%5Csqrt%7B%5Cleft%28%20%5Cfrac%7B19%7D%7B2%7D-7%20%5Cright%29%5E2%2B%5Cleft%28%20%5Cfrac%7B7%7D%7B2%7D-4%20%5Cright%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20AM%3D%5Csqrt%7B%5Cleft%28%20%5Cfrac%7B5%7D%7B2%7D%5Cright%29%5E2%2B%5Cleft%28%20-%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29%5E2%7D%5Cimplies%20%5Cboxed%7BAM%5Capprox%202.549509756796392%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
The corrects answers are B and D for this one.
Since you divide the same side for both the the rectangles on both parts and if the division statements are equaled, then they are similar.
For example;
Answer B.
50 / 10 = 5
and
30 / 6 = 5
Answer D.
7.5 / 2.5 = 3
and
4.5 / 1.5 = 3
Since they both equal the same for both of the rectangles for the answers individually, they are similar polygon rectangles.
Hope this helps!
<em>~ ShadowXReaper069</em><em />
Answer:
0.7 ; 0.65 ; 0.115
Step-by-step explanation:
Step-by-step explanation:
P(A) = 0.5 ; P(B) = 0.3
P(not successful) = P(B') = 1 - 0.3 = 0.7 ; P(A') = 1 - 0.5 = 0.5
1.)
Both events are independent events, hence the outcome of one does not depend on the other. That is the failure of the Asian project has nothing to do with the European project.
Probability that European project isn't successful;
P(B') = 1 - P(B) = 1 - 0.3 = 0.7
2.)
Probability that atleast one of the 2 projects is successful :
P(AUB) = P(A) + P(B) - P(AnB)
P(AnB) = P(A) * P(B) = 0.5 * 0.3 = 0.15
P(AUB) = 0.5 + 0.3 - 0.15 = 0.65
3.)
Probability that only the Asian project is successful, given that atleast one of the two projects is successful :
[P(A) - P(AnB)] ÷ P(AuB)
[0.5 * 0.15] ÷ 0.65
= 0.075 ÷ 0.65
= 0.1153846
= 0.115
