At the book fair, books were on sale for 15% off the regular price. Hannah bought a book that had a regular price of $6.00. What
1 answer:
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Option B:
It is one-half the area of a square of side length 4 units.
Solution:
Base of the triangle = 4 units
Height of the triangle = 4 units
Area of the triangle =
Area of the triangle = 8 square units
Option A: It is one-half the area of a rectangle of length 4 units and width 2 units.
Area of the rectangle = 4 × 2 = 8 square units
Half of rectangle = square units
It is not true because area of the triangle is 8 square units.
Option B: It is one-half the area of a square of side length 4 units.
Area of the square = 4 × 4 = 16 square units
Half of square = square units
It is true because area of the triangle is 8 square units.
Option C: It is twice the area of a rectangle of length 4 units and width 2 units.
Area of the rectangle = 4 × 2 = 8 square units
Twice of rectangle = 2 × 8 = 16 square units
It is not true because area of the triangle is 8 square units.
Option D: It is twice the area of a square of side length 4 units.
Area of the square = 4 × 4 = 16 square units
Twice of square = 2 × 16 = 32 square units
It is not true because area of the triangle is 8 square units.
Hence Option B is the correct answer.
It is one-half the area of a square of side length 4 units.
This situation has two outcomes: either an invoice is discounted or not. This two outcomes satisfy what we call a binomial distribution (note "bi" in binomial).
The binomial distribution tells us the probability that a randomly selected sample will have the outcome of success. In this case, we consider receiving the discount as the "success" outcome while not receiving it means "failure". The distribution takes the form:
where n is the total number of samples, x is the number of samples you'll expect to have a success outcome, p is the probability of success, q is the probability of failure, and nCx is the combination of n samples taken x at a time.
You have an inconsistency regarding the total number of samples by the way, but I will take the first mentioned sample of 15 as I answer (you can just follow through the same process for another value).
For the next step, let's digest the problem to get the needed variables.
The total number of samples, n, is equal to 15. The probability of success (receiving a discount), p, is 10% or 0.1, and the probability of failure (not receiving a discount) is 90% or 0.9.
For P(X=x), we need to find the probability that less than two of the samples have success outcomes therefore we need to find the probability that NO invoice will receive the discount plus the probability that ONE invoice will receive the discount. This is equivalent to saying
Calculating these probabilities we'll get:
ANSWER: The probability that fewer than 2 sampled invoices will receive the discount is 0.549 or 54.9%.
The binomial distribution tells us the probability that a randomly selected sample will have the outcome of success. In this case, we consider receiving the discount as the "success" outcome while not receiving it means "failure". The distribution takes the form:
where n is the total number of samples, x is the number of samples you'll expect to have a success outcome, p is the probability of success, q is the probability of failure, and nCx is the combination of n samples taken x at a time.
You have an inconsistency regarding the total number of samples by the way, but I will take the first mentioned sample of 15 as I answer (you can just follow through the same process for another value).
For the next step, let's digest the problem to get the needed variables.
The total number of samples, n, is equal to 15. The probability of success (receiving a discount), p, is 10% or 0.1, and the probability of failure (not receiving a discount) is 90% or 0.9.
For P(X=x), we need to find the probability that less than two of the samples have success outcomes therefore we need to find the probability that NO invoice will receive the discount plus the probability that ONE invoice will receive the discount. This is equivalent to saying
Calculating these probabilities we'll get:
ANSWER: The probability that fewer than 2 sampled invoices will receive the discount is 0.549 or 54.9%.