Answer:
(a) 1024 ways
(b) 243 ways
Step-by-step explanation:
When answers are independent, the total number of ways all questions can be answered is the product of the number of ways each question can be answered.
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<h3>(a)</h3>
The first question can have one answer 4 ways. The second question can be answered 4 ways for each of the ways the first question was answered. That is, the two questions can be answered 4×4 = 16 ways. Similarly, each additional question multiplies the number of ways the questions can be answered by 4.
The 5 questions can be answered 4×4×4×4×4 = 4^5 = 1024 ways.
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<h3>(b)</h3>
There are 3 ways to answer the first question incorrectly. Each additional question can be answered incorrectly 3 ways for each of the ways previous questions were answered. The total number of ways all questions can be answered incorrectly is ...
3^5 = 243
A student can answer all questions wrong in 243 different ways.
5.25
%
Convert the percentage to a fraction by placing the expression over
100
100
. Percentage means 'out of
100
100
'.
5.25
100
5.25
100
Convert the decimal number to a fraction by shifting the decimal point in both the numerator and denominator. Since there are
2
2
numbers to the right of the decimal point, move the decimal point
2
2
places to the right.
525
10000
525
10000
Reduce the expression by cancelling the common factors.
Factor
25
25
out of
10000
10000
.
25
⋅
21
25
⋅
400
25
⋅
21
25
⋅
400
Cancel the common factor.
25
⋅
21
25
⋅
400
25
⋅
21
25
⋅
400
Rewrite the expression.
21
400
21
400
Convert the fraction to a decimal by dividing the numerator by the denominator.
0.0525
0.0525
Hope that help! :)
-2/3, -0.3, 1/4, 0.75, 0.8