I believe the correct answer from the choices listed above is the last option. The measure of an exterior angle at the vertex of a polygon never equals the measure of the adjacent interior angle. Rather, they are always supplementary angles.
Hope this answers the question. Have a nice day.
Answer:
In the figure ∠ABO and ∠BCO have measures equal to 35°.
Step-by-step explanation:
Measure of arc AD = 180-measure of arc CD= 180-125 =55
m<AOB= 55 ( measure of central angle is equal to intercepted arc)
<OAB= 90 degrees (Tangent makes an angle of 90 degrees with the radius)
In triangle AOB ,
< AB0 = 180-(90+55)= 35 degrees( angle sum property of triangle)
In triange BOC ,< BOC=125 ,
m<, BCO=35 degrees
Answer:
a. E(x) = 3.730
b. c = 3.8475
c. 0.4308
Step-by-step explanation:
a.
Given
0 x < 3
F(x) = (x-3)/1.13, 3 < x < 4.13
1 x > 4.13
Calculating E(x)
First, we'll calculate the pdf, f(x).
f(x) is the derivative of F(x)
So, if F(x) = (x-3)/1.13
f(x) = F'(x) = 1/1.13, 3 < x < 4.13
E(x) is the integral of xf(x)
xf(x) = x * 1/1.3 = x/1.3
Integrating x/1.3
E(x) = x²/(2*1.13)
E(x) = x²/2.26 , 3 < x < 4.13
E(x) = (4.13²-3²)/2.16
E(x) = 3.730046296296296
E(x) = 3.730 (approximated)
b.
What is the value c such that P(X < c) = 0.75
First, we'll solve F(c)
F(c) = P(x<c)
F(c) = (c-3)/1.13= 0.75
c - 3 = 1.13 * 0.75
c - 3 = 0.8475
c = 3 + 0.8475
c = 3.8475
c.
What is the probability that X falls within 0.28 minutes of its mean?
Here we'll solve for
P(3.73 - 0.28 < X < 3.73 + 0.28)
= F(3.73 + 0.28) - F(3.73 + 0.28)
= 2*0.28/1.3 = 0.430769
= 0.4308 -- Approximated
322miles=14g
To find the unit rate, divide
322/14=23
The unit rate is 23miles per gallon