C - (x-3)^2=36
If we expand (x-3)^2=36:
(x-3)(x-3)=36
x^2-3x-3x+9=36
x^2-6x+9=36
Then subtract 36
x^2-6x-27=0
Answer:
28m⁷n⁵
Step-by-step explanation:
You would first multiply 14 by 2. You would then multiply (which is really addition when it comes to exponents) your like-term exponents.
(14m²n⁵)(2m⁵) =28m⁷n⁵
14(2) = 28
m² + m⁵=m⁷
n⁵ + 0 = n⁵
Answer:
The correct answer is third option. 994
Step-by-step explanation:
<u>Points to remember</u>
Volume of cylinder = πr²h
Where 'r' is the radius and 'h' is the height of cylinder
From the given question we get the cylinder height and radius
The height h = 3 times the diameter of one ball
= 3 * 7.5 = 22.5 cm
Radius = half of the diameter of a ball
= 7.5/2 = 3.75 cm
<u>To find the volume of cylinder</u>
Volume of cylinder = πr²h
= 3.14 * 3.75² * 22.5
= 993.515 ≈ 994
The correct answer is third option. 994
Let Xi be the random variable representing the number of units the first worker produces in day i.
Define X = X1 + X2 + X3 + X4 + X5 as the random variable representing the number of units the
first worker produces during the entire week. It is easy to prove that X is normally distributed with mean µx = 5·75 = 375 and standard deviation σx = 20√5.
Similarly, define random variables Y1, Y2,...,Y5 representing the number of units produces by
the second worker during each of the five days and define Y = Y1 + Y2 + Y3 + Y4 + Y5. Again, Y is normally distributed with mean µy = 5·65 = 325 and standard deviation σy = 25√5. Of course, we assume that X and Y are independent. The problem asks for P(X > Y ) or in other words for P(X −Y > 0). It is a quite surprising fact that the random variable U = X−Y , the difference between X and Y , is also normally distributed with mean µU = µx−µy = 375−325 = 50 and standard deviation σU, where σ2 U = σ2 x+σ2 y = 400·5+625·5 = 1025·5 = 5125. It follows that σU = √5125. A reference to the above fact can be found online at http://mathworld.wolfram.com/NormalDifferenceDistribution.html.
Now everything reduces to finding P(U > 0) P(U > 0) = P(U −50 √5125 > − 50 √5125)≈ P(Z > −0.69843) ≈ 0.757546 .
Answer:
D
Step-by-step explanation:
Firstly,
≤ or ≥ means closed circle, and
< or > means open circle
Now, let's solve the compound inequality:
x - 1 ≤ 7
x ≤ 8
and
2x ≥ 22
x ≥ 11
This solution means "everything left of 8 (inclusive and closed circle)" and "everything right of 11 (inclusive and closed circle)"
Looking at the choices, D is right.
