Make q the subject of the formula 2(q+p)=1+5q
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Step-by-step explanation:
Answer:
(a) P(0 ≤ Z ≤ 2.87)=0.498
(b) P(0 ≤ Z ≤ 2)=0.477
(c) P(−2.20 ≤ Z ≤ 0)=0.486
(d) P(−2.20 ≤ Z ≤ 2.20)=0.972
(e) P(Z ≤ 1.01)=0.844
(f) P(−1.95 ≤ Z)=0.974
(g) P(−1.20 ≤ Z ≤ 2.00)=0.862
(h) P(1.01 ≤ Z ≤ 2.50)=0.150
(i) P(1.20 ≤ Z)=0.115
(j) P(|Z| ≤ 2.50)=0.988
Step-by-step explanation:
(a) P(0 ≤ Z ≤ 2.87)
In this case, this is equal to the difference between P(z<2.87) and P(z<0). The last term is substracting because is the area under the curve that is included in P(z<2.87) but does not correspond because the other condition is that z>0.
(b) P(0 ≤ Z ≤ 2)
This is the same case as point a.
(c) P(−2.20 ≤ Z ≤ 0)
This is the same case as point a.
(d) P(−2.20 ≤ Z ≤ 2.20)
This is the same case as point a.
(e) P(Z ≤ 1.01)
This can be calculated simply as the area under the curve for z from -infinity to z=1.01.
(f) P(−1.95 ≤ Z)
This is best expressed as P(z≥-1.95), and is calculated as the area under the curve that goes from z=-1.95 to infininity.
It also can be calculated, thanks to the symmetry in z=0 of the standard normal distribution, as P(z≥-1.95)=P(z≤1.95).
(g) P(−1.20 ≤ Z ≤ 2.00)
This is the same case as point a.
(h) P(1.01 ≤ Z ≤ 2.50)
This is the same case as point a.
(i) P(1.20 ≤ Z)
This is the same case as point f.
(j) P(|Z| ≤ 2.50)
In this case, the z is expressed in absolute value. If z is positive, it has to be under 2.5. If z is negative, it means it has to be over -2.5. So this probability is translated to P|Z| < 2.50)=P(-2.5<z<2.5) and then solved from there like in point a.
The question was incomplete. Below you will find the missing content.
In the figure below, BL, AM, and CK are medians of △ABC. If KC = 108 and OC = 2n + 10, then n=
The picture is attached below.
The value of n is 31.
The median is the line connecting the vertex and its midpoint on the opposite side of the triangle.
The intersection of all 3 medians of the triangle is called the centroid.
As we know centroid divides the median in the ratio of 2:1.
In the given picture,
Medians of triangle △ABC are AM, BL, and CK.
So the centroid of the triangle is O.
Given that KC= 108
As the centroid O divides the line KC in 2:1.
Let OC=2x
KO= X
As KC= KO+OC
⇒ 108= x+2x
⇒ 3x=108
⇒ x=108/3
⇒ x=36
Then OC= 2x= 2*36= 72
As given in the question OC= 2n+10
putting the value of OC in above equation
⇒ 72= 2n+10
⇒ 2n= 72-10
⇒ 2n=62
⇒ n=62/2
⇒n=31
Therefore the value of n is 31.
Learn more about the median of the triangle
here: brainly.com/question/2264495
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