Answer: 0.05
Step-by-step explanation:
Let M = Event of getting an A in Marketing class.
S = Event of getting an A in Spanish class,
i.e. P(M) = 0.80 , P(S) = 0.60 and P(M∩S)=0.45
Required probability = P(neither M nor S)
= P(M'∩S')
= P(M∪S)' [∵P(A'∩B')=P(A∪B)']
=1- P(M∪S) [∵P(A')=1-P(A)]
= 1- (P(M)+P(S)- P(M∩S)) [∵P(A∪B)=P(A)+P(B)-P(A∩B)]
= 1- (0.80+0.60-0.45)
= 1- 0.95
= 0.05
hence, the probability that Helen does not get an A in either class= 0.05
<h3>Answer:</h3>
Area of DEFG = (1/2)a²
<h3>Explanation:</h3>
See the attached diagram.
Line FB ║ EG and line GA ║DF. ∆GFA ≅ ∆FGX, and ∆EXF ≅ ∆BAG. Then the area of ∆BFG is equal to the area of ∆EGF and, by symmetry, the area of ∆FDE.
This means the area of DEFG is the same as the area of ∆DFB.
The problem statement tells us ∠FDG = 45°. By symmetry, ∠EGD = 45° and by corresponding angles related to parallel lines ∠FBD = 45°. Then ∠DFB = 90° and the area of ∆DFB = (1/2)(DF)(FB) = (1/2)a².
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<em>Alternate approach</em>
Recognize that ∠EGD = ∠FDG = 45°, so ∠DXG = 90°. This means all the triangles internal to DEFG are right triangles. Designate the distance XF with the variable <em>b</em>. Then DX = (a-b) and the area of the trapezoid is ...
... Area(DEFG) = Area(DXG) + Area(DXE) + Area(GXF) + Area(FXE)
... = (1/2)(a-b)² +(1/2)(a-b)(b) +(1/2)(a-b)(b) +(1/2)b²
... = (1/2)(a² -2ab +b² +ab -b² +ab -b² +b²)
... = (1/2)(a² +ab(-2+1+1) +b²(1-1-1+1))
... Area(DEFG) = (1/2)a²
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A) The number 0.66666667 as fraction is =
B) 32 students prefer granola bars over muffins.
The total number of classmates = 48
The probability that a student says yes = 0.66666667
Note that 0.66666667 can also be written as
To convert 0.66666667 to fraction, multiply both the numerator and the denominator by 100000000
The probability that a student says yes =
Therefore, the number 0.66666667 as fraction is =
Number of students that prefer granola bars over muffins = 0.66666667 x 48
Number of students that prefer granola bars over muffins = 32
Therefore, 32 students prefer granola bars over muffins.
Learn more on decimal to fraction conversion here: brainly.com/question/23038