Answer:
In parallelogram ABCD
FD is perpendicular to BC
BE is perpendicular to CD
Consider triangle BEC and triangle DFC
FC = EC (Given)
Angle BEC = Angle DFC (=90°)
Angle BCE = Angle DCF (common)
Therefore triangle BEC is congruent to triangle DFC (AAS congruency)
DF = BE (CPCT)
Since the altitudes are equal their bases will also be equal
Therefore BC = DC
Therefore BC = DC = AD = AB
Therefore ABCD is a rhombus
Hope this helps!
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Answer:
a) 0.96
b) 0.016
c) 0.018
d) 0.982
e) x = 2
Step-by-step explanation:
We are given with the Probability density function f(x)= 2/x^3 where x > 1.
<em>Firstly we will calculate the general probability that of P(a < X < b) </em>
P(a < X < b) = 
= 
= ![2[ \frac{x^{-3+1} }{-3+1}]^{b}_a dx](https://tex.z-dn.net/?f=2%5B%20%5Cfrac%7Bx%5E%7B-3%2B1%7D%20%7D%7B-3%2B1%7D%5D%5E%7Bb%7D_a%20%20%20dx)
{ Because ![\int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a](https://tex.z-dn.net/?f=%5Cint_%7Ba%7D%5E%7Bb%7D%20x%5E%7Bn%7D%20dx%20%3D%20%5B%20%5Cfrac%7Bx%5E%7Bn%2B1%7D%20%7D%7Bn%2B1%7D%5D%5E%7Bb%7D_a)
}
= ![2[ \frac{x^{-2} }{-2}]^{b}_a](https://tex.z-dn.net/?f=2%5B%20%5Cfrac%7Bx%5E%7B-2%7D%20%7D%7B-2%7D%5D%5E%7Bb%7D_a)
= ![\frac{2}{-2} [ x^{-2} ]^{b}_a](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B-2%7D%20%5B%20x%5E%7B-2%7D%20%5D%5E%7Bb%7D_a)
= ![-1 [ b^{-2} - a^{-2} ]](https://tex.z-dn.net/?f=-1%20%5B%20b%5E%7B-2%7D%20-%20a%5E%7B-2%7D%20%20%5D)
= 
a) Now P(X < 5) = P(1 < X < 5) {because x > 1 }
Comparing with general probability we get,
P(1 < X < 5) = 
= 
= 0.96 .
b) P(X > 8) = P(8 < X < ∞) = 1/
- 1/∞ = 1/64 - 0 = 0.016
c) P(6 < X < 10) = 
= 
= 0.018 .
d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)
= 
+ (1/
- 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982
e) We have to find x such that P(X < x) = 0.75 ;
⇒ P(1 < X < x) = 0.75
⇒ 
= 0.75
⇒ 
= 1 - 0.75 = 0.25
⇒ 
= 
⇒ = 4 ⇒ x = 
Therefore, value of x such that P(X < x) = 0.75 is 2.
Answer:
Yes it can
Step-by-step explanation:
To check wether it's a right angle triangle we need to apply the Pythagoras theorem
h^2= a^2 +b^2
Hypotenuse is always the longest side so
5^2 = 3^2 + 4^2
This is correct, so the triangle is a right angle triangle
Answer from Gauthmath
Focus on the regression line. Notice how (0,90) and (1,75) are on this line. Compute the slope of the line through those points
Use the slope formula
m = (y2-y1)/(x2-x1)
m = (75-90)/(1-0)
m = -15/1
m = -15
So Matthew's balance is decreasing by approximately 15 dollars each month. The negative slope means "decrease". This is shown by the fact that the line goes downhill as you move from left to right.
Answer: decreases by $15 each month
<span>The ratio of boys to girls is 12 to 16, 12:16 or 12/16 </span>
