Answer:
Option (B)
Step-by-step explanation:
If the probabilities of two events A and B are P(A) and P(B) then the conditional probability of an event that can be derived by the formula,
P(B | A) = 
P(A ∩ B) = P(B|A) × P(A)
P(A ∩ B) = (0.8) × (0.4)
= 0.32
Therefore, Option (B) will be the correct option.
Answer:
59 to 66
Step-by-step explanation:
Mean test scores = u = 74.2
Standard Deviation =
= 9.6
According to the given data, following is the range of grades:
Grade A: 85% to 100%
Grade B: 55% to 85%
Grade C: 19% to 55%
Grade D: 6% to 19%
Grade F: 0% to 6%
So, the grade D will be given to the students from 6% to 19% scores. We can convert these percentages to numerical limits using the z scores. First we need to to identify the corresponding z scores of these limits.
6% to 19% in decimal form would be 0.06 to 0.19. Corresponding z score for 0.06 is -1.56 and that for 0.19 is -0.88 (From the z table)
The formula for z score is:

For z = -1.56, we get:

For z = -0.88, we get:

Therefore, a numerical limits for a D grade would be from 59 to 66 (rounded to nearest whole numbers)
Question:
Solve each calculation. Be sure to report your answer with the correct number of significant figures.
5.61000 dg × 1.1010 dg
12.0 m ÷ 3.1415 m
Answer:
1.
=
2. 
Step-by-step explanation:
1. 5.61000 dg × 1.1010 dg
We start by representing each digit using scientific notation


Then, Multiply both numbers

First, rearrange


From law of indices,
;
So, we have

Because 5.61000 is given in 3 significant figures and 1.1010 is given in 4 significant figures, we approximate the result to 4 significant figures
This gives
Hence,
=
2.
12.0 m ÷ 3.1415 m
Using proper notation
12.0 m ÷ 3.1415 m = 
We start by representing 3.1415 using scientific notation

By substitution;

Take
to the numerator

From law of indices,
= 10000

Multiply

Divide

Because 12.0 is given in 2 significant figures and 3.1415 is given in 5 significant figures, we approximate the result to 5 significant figures

No, the first choice equals 190 and the second 144.