AREA, PERIMETER & VOLUME QUESTION

Mathematics

1 answer:

Inessa [12.5K]1 month ago

7 0

1. Selected Case B. 2. 9 cm³. 3. 20 cm. 4. 4.5 m³. Explanation: In question 1, we need to fit a drum with a volume of 14,000 cm³. The volume of a cylinder can be calculated via the formula πr²h. For Case A, with r = 100 mm (10 cm) and h = 300 mm (30 cm), the total volume is approximately 9424.78 cm³, insufficient for the given drum. Case B, with r = 200 mm (20 cm) and h = 30 cm, gives a volume of approximately 37699.11 cm³. Case C with r = 32 cm and h = 250 mm (25 cm) results in a volume of about 80424.77 cm³. The smallest volume among Cases B and C is Case B at 37699.11 cm³, thus it is the correct choice. For question 2, the dimensions of the speaker are Length = 45 cm = 0.45 m, Width = 0.4 m, Height = 50 cm = 0.5 m, leading to a volume of 0.09 m³ or 9 cm³. Question 3 involves a speaker with a volume of 30,000 cm³ with Length = 30 cm = 0.45 m and Height = 500 mm = 50 cm, requiring to find its Width: 30,000 = 30 × W × 50, hence W = 20 cm. For question 4, with dimensions of Base = 2 m, Length = 3 m, Height =1.5 m, the volume of the prism is calculated as 4.5 m³.

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If 6 components are drawn at random from the container, the probability that at least 4 are not defective is . If 8 components a

Svet_ta [12734]

The question is missing some information. It should be phrased as follows:

A container has 50 electronic components, with 10 identified as defective. If 6 components are randomly selected from the container, what is the probability that at least 4 of them are not defective? Additionally, if 8 components are drawn at random from the container, what is the probability that exactly 3 are defective?

Answers
Part 1. 0.02
Part 2. 0.0375

Explanation
Probability denotes the likelihood of an event occurring. It is computed as:
probability = (Number of favorable outcomes)/(Number of total outcomes)

Part 1
When 6 components are chosen, if 4 are confirmed functioning, then 2 must be defective.
P(at least 4 functional) = 4/40× 2/10
= 1/10 × 1/5
= 1/50
= 0.02

Part 2
Choosing 8 components, if 3 are defective, then 5 are functioning.
P(3 defective) = 3/40 × 5/10
= 15/400
= 3/80
= 0.0375

4 0

2 months ago

A 95% confidence interval for the population proportion of professional tennis players who earn more than 2 million dollars a ye

Svet_ta [12734]

Response:

e. 545

Detailed explanation:

In a survey sample containing n individuals, with a success probability of $\pi$ , and a confidence level of $1-\alpha$ , the ensuing confidence interval for proportions is established.