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SpyIntel [72]
2 years ago
6

A candy company plans to hang posters of a new product in supermarkets. The product is a box of premium chocolates. The art team

made a scale drawing of the top of the box using a scale of 3 inches to 1 inch. The length of the scale drawing of the box is 24 inches, and its width is 15 inches. What are the actual dimensions of the top of the chocolate box?
A.) The length is 8 inches, and the width is 5 inches.

B.) The length is 12 inches, and the width is 7.5 inches.

C.) The length is 16 inches, and the width is 10 inches.

D.) The length is 22 inches, and the width is 12 inches.
Mathematics
2 answers:
SashulF [63]2 years ago
8 0
<span>B.) The length is 12 inches, and the width is 7.5 inches</span>
Sloan [31]2 years ago
7 0

Answer:

A) The length is 8 inches, and the width is 5 inches.

Step-by-step explanation:

Given,

The scale in the drawing is,

3 inches to 1 inches,

That is, for 1 inches of measure, the measure of the drawing is 3 inches,

Thus, the original measures of the box will obtained after dividing each measures of the drawing by 3,

Here, the length of the scale drawing of the box is 24 inches and its width is 15 inches,

So, the length of the box = \frac{24}{3} = 8 inches,

And, the width of je box = \frac{15}{3} = 5 inches,

Hence, Option 'A' is correct.

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Every day your friend commutes to school on the subway at 9 AM. If the subway is on time, she will stop for a $3 coffee on the w
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Answer:

1.02% probability of spending 0 dollars on coffee over the course of a five day week

7.68% probability of spending 3 dollars on coffee over the course of a five day week

23.04% probability of spending 6 dollars on coffee over the course of a five day week

34.56% probability of spending 9 dollars on coffee over the course of a five day week

25.92% probability of spending 12 dollars on coffee over the course of a five day week

7.78% probability of spending 12 dollars on coffee over the course of a five day week

Step-by-step explanation:

For each day, there are only two possible outcomes. Either the subway is on time, or it is not. Each day, the probability of the train being on time is independent from other days. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

The probability that the subway is delayed is 40%. 100-40 = 60% of the train being on time, so p = 0.6

The week has 5 days, so n = 5

She spends 3 dollars on coffee each day the train is on time.

Probabability that she spends 0 dollars on coffee:

This is the probability of the train being late all 5 days, so it is P(X = 0).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{5,0}.(0.6)^{0}.(0.4)^{5} = 0.0102

1.02% probability of spending 0 dollars on coffee over the course of a five day week

Probabability that she spends 3 dollars on coffee:

This is the probability of the train being late for 4 days and on time for 1, so it is P(X = 1).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 1) = C_{5,1}.(0.6)^{1}.(0.4)^{4} = 0.0768

7.68% probability of spending 3 dollars on coffee over the course of a five day week

Probabability that she spends 6 dollars on coffee:

This is the probability of the train being late for 3 days and on time for 2, so it is P(X = 2).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{5,2}.(0.6)^{2}.(0.4)^{3} = 0.2304

23.04% probability of spending 6 dollars on coffee over the course of a five day week

Probabability that she spends 9 dollars on coffee:

This is the probability of the train being late for 2 days and on time for 3, so it is P(X = 3).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{5,3}.(0.6)^{3}.(0.4)^{2} = 0.3456

34.56% probability of spending 9 dollars on coffee over the course of a five day week

Probabability that she spends 12 dollars on coffee:

This is the probability of the train being late for 1 day and on time for 4, so it is P(X = 4).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 4) = C_{5,4}.(0.6)^{4}.(0.4)^{1} = 0.2592

25.92% probability of spending 12 dollars on coffee over the course of a five day week

Probabability that she spends 15 dollars on coffee:

Probability that the subway is on time all days of the week, so P(X = 5).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 5) = C_{5,5}.(0.6)^{5}.(0.4)^{0} = 0.0778

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