Answer:
There are 8 true/false questions and 26 fill-in-the-blank questions.
Step-by-step explanation:
Let "t" be the number of 2-point true/false questions and "f" the number of 5-point fill-in-the-blank questions.
Mrs. Simmons gave a history test worth 92 points. Symbollically,
2 t + 5 f = 92 [1]
There were a total of 34 questions in the test. Symbollicaly,
t + f = 34
t = 34 - f [2]
If we replace [2] in 1, we get
2 (34 - f) + 5 f = 92
68 - 2 f + 5 f = 92
3 f = 24
f = 8
We replace f = 8 in [2],
t = 34 - 8 = 26
There are 8 true/false questions and 26 fill-in-the-blank questions.
since the lengths of all those four sides are in a 3:2:6:7 ratio, and the whole perimeter is 126, what we do is, simply divide the whole by (3+2+6+7) and distribute accordingly.
a. By definition of conditional probability,
P(C | D) = P(C and D) / P(D) ==> P(C and D) = 0.3
b. C and D are mutually exclusive if P(C and D) = 0, but this is clearly not the case, so no.
c. C and D are independent if P(C and D) = P(C) P(D). But P(C) P(D) = 0.2 ≠ 0.3, so no.
d. Using the inclusion/exclusion principle, we have
P(C or D) = P(C) + P(D) - P(C and D) ==> P(C or D) = 0.6
e. Using the definition of conditional probability again, we have
P(D | C) = P(C and D) / P(C) ==> P(D | C) = 0.75
Answer:
6
Step-by-step explanation:
STEP
1
:
1
Simplify —
3
The equation at the end of step
1
:
12 1
—— + (((—)2) • 9) • 3)
4 3
STEP
2
:
Equation at the end of step
2
:
12 1
—— + ((—— • 9) • 3)
4 32
STEP
3
:
Canceling Out:
3.1 Canceling out 32 as it appears on both sides of the fraction line
Equation at the end of step
3
:
12
—— + (1 • 3)
4
STEP
4
:
3
Simplify —
1
Equation at the end of step
4
:
3 + 3
STEP
5
:
Pulling out like terms
5.1 Pull out 3
After pulling out, we are left with :
3 • ( 1 - (-1) ))
Final result :
6
