Answer:
Part A: Option 2, A: Anna’s answer is incorrect. She correctly factored out 5x, but incorrectly identified a and b, so her answer cannot be correct.
Part B: Option 3, B: 5x(x+2)(x^2−2x+4)
Step-by-step explanation:
p(x) = 5x^4 + 40x
p(x) = 5x(x^3 + 8)
p(x) = 5x(x + 2)(x^2 - 2x + 4)
Part A: Option 2, A: Anna’s answer is incorrect. She correctly factored out 5x, but incorrectly identified a and b, so her answer cannot be correct.
Part B: Option 3, B: 5x(x+2)(x^2−2x+4)
Answer:
The coordinates of point B are (6,7).
Step-by-step explanation:
Given points are
Blue = A(-4,8)
Purple = M(1,7.5)
Green = B
It is given that point M is the midpoint of point A and B.
Let coordinates of points are (a,b).
Midpoint of two points is
Coordinates of midpoint are (1,7.5).
On comparing both sides we get
Therefore, the coordinates of point B are (6,7).
Answer:
The variance of the temperatures of the 10 day period must be at least zero.
Step-by-step explanation:
The variance is the expectation of the squared deviation of a random variable from its mean. It measures how far a set of numbers are spread out from their average value.
Its unit of measure corresponding to the square of the unit of measure of the variable. In this case, the variance of the temperatures is expressed in (°C)². The variance has a minimum value of 0.
Since the variance is squared, it will always have values greater than zero.
The formula for finding the surface area of a cube is A=6y^2 where y is the side length. we know a=96. so we just isolate y.
96/6= 6y^2 / 6
16=y^2
sqrt (16) = sqrt(y^2)
4=y
So y is 4
Answer:
a. The probability that a customer purchase none of these items is 0.49
b. The probability that a customer purchase exactly 1 of these items would be of 0.28
Step-by-step explanation:
a. In order to calculate the probability that a customer purchase none of these items we would have to make the following:
let A represents suit
B represents shirt
C represents tie
P(A) = 0.22
P(B) = 0.30
P(C) = 0.28
P(A∩B) = 0.11
P(C∩B) = 0.10
P(A∩C) = 0.14
P(A∩B∩C) = 0.06
Therefore, the probability that a customer purchase none of these items we would have to calculate the following:
1 - P(A∪B∪C)
P(A∪B∪C) =P(A) + P(B) + P(C) − P(A ∩ B) − P(A ∩ C) − P(B ∩ C) + P(A ∩ B ∩ C)
= 0.22+0.28+0.30-0.11-0.10-0.14+0.06
= 0.51
Hence, 1 - P(A∪B∪C) = 1-0.51 = 0.49
The probability that a customer purchase none of these items is 0.49
b.To calculate the probability that a customer purchase exactly 1 of these items we would have to make the following calculation:
= P(A∪B∪C) - ( P(A∩B) +P(C∩B) +P(A∩C) - 2 P(A ∩ B ∩ C))
=0.51 -0.23 = 0.28
The probability that a customer purchase exactly 1 of these items would be of 0.28
