Answer:
Step-by-step explanation:
let the number be x
(x+6)/3 =21
x+6=21*3
x+6=63
x=57
Answer:
3.72769
Step-by-step explanation:
Use tangent - tan74 = 13/x
Solving for x gives you 3.72769
I'm not sure how many decimal places you need, so there are most of them
Hopefully this helps- let me know if you have any questions
Answer:
Step-by-step explanation:
<u>a)</u>
- Given that ; X ~ N ( µ = 65 , σ = 4 )
From application of normal distribution ;
- Z = ( X - µ ) / σ, Z = ( 64 - 65 ) / 4, Z = -0.25
- Z = ( 66 - 65 ) / 4, Z = 0.25
Hence, P ( -0.25 < Z < 0.25 ) = P ( 64 < X < 66 ) = P ( Z < 0.25 ) - P ( Z < -0.25 ) P ( 64 < X < 66 ) = 0.5987 - 0.4013
- P ( 64 < X < 66 ) = 0.1974
b) X ~ N ( µ = 65 , σ = 4 )
From normal distribution application ;
- Z = ( X - µ ) / ( σ / √(n)), plugging in the values,
- Z = ( 64 - 65 ) / ( 4 / √(12)) = Z = -0.866
- Z = ( 66 - 65 ) / ( 4 / √(12)) = Z = 0.866
P ( -0.87 < Z < 0.87 )
- P ( 64 < X < 66 ) = P ( Z < 0.87 ) - P ( Z < -0.87 )
- P ( 64 < X < 66 ) = 0.8068 - 0.1932
- P ( 64 < X < 66 ) = 0.6135
c) From the values gotten for (a) and (b), it is indicative that the probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
Reasons:
1. Because, MO cuts Angle PMN in two equal parts.
2.As ∠PMN is cut in to equal parts thus:
∠PMN = ∠NMO + ∠PMO, where these two parts (∠NMO, ∠PMO) are equal.
3. Both are the same, common you can say..
4. Because, MO cuts Angle PON in two equal parts.
5. As ∠PON is cut in to equal parts thus:
∠PON = ∠NOM + ∠POM, where these two parts (∠NOM , ∠POM) are equal.
6. From the above statements, we have:
= ∠NMO + ∠PMO (Proved)
= ∠NOM + ∠POM (Proved)
= MO = MO (Proved)
Thus, ∆PMO ≅ ∆NMO, by AAS rule
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As simpoool as that!
Answer:
Step-by-step explanation:
I used logic and took the easy way around this as opposed to the long, drawn-out algebraic way. I noticed right off that at x = -3 and x = -1 the y values were the same. In the middle of those two x-values is -2, which is the vertex of the parabola with coordinates (-2, 4). That's the h and k in the formula I'm going to use. Then I picked a point from the table to use as my x and y in the formula I'm going to use. I chose (0, 3) because it's easy. The formula for a quadratic is
and I have everything I need to solve for a. Filling in my h, k, x, and y:
and
and
-1 = 4a so
In work/vertex form the equation for the quadratic is
In standard form it's:
