Liam is a tyre fitter. it takes him 56 minutes to fit 4 tyres to a van.

Mathematics

2 answers:

Inessa [12.5K]1 month ago

7 0

Answer:

a. Multiplying 12 by 14 yields 168 minutes.

b. Dividing 42 by 14 gives 3 tires.

Detailed solution:

There are various ways to approach this problem.

Considering the two problem types, calculate minutes per tire first.

a. 56 divided by 4 results in 14 minutes per tire.

Since 3 vans have 12 tires,

a. 12 times 14 equals 168 minutes.

Divide 42 minutes by 14 minutes per tire to determine how many tires fit in that time.

b. 42 divided by 14 equals 3 tires.

PIT_PIT [12.4K]1 month ago

4 0

Answer:

a) 168 b) 12

Stepwise explanation:

a) 56 divided by 4 is 14; multiplying 14 by 12 results in 168

b) 504 divided by 42 equals 12

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The life of a manufacturer's compact fluorescent light bulbs is normal, with mean 12,000 hours and standard deviation 2,000 hour

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Mean = 12000
Standard Deviation = 2000

Our task is to determine how many standard deviations 14,500 is from the mean.
This requires us to compute the z-score

A z-score indicates how far a sample value is from the mean in terms of standard deviations. A positive z-score signifies that the sample value exceeds the mean.

The formula for calculating the z-score is = (Sample Value - Mean) / Standard Deviation
Thus,
Z-score = $\frac{14500-12000}{2000} =1.25$

This indicates that 14,500 is 1.25 standard deviations higher than the mean of 12,000.

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An electronic product contains 40 integrated circuits. The probability that any integrated circuit is defective is 0.01, and the

Zina [12379]

Answer:

The chance that there is one or more defective integrated circuits is 33.10%.

Detailed solution:

Each integrated circuit can be either defective or not, which provides only two possible outcomes. As a result, this scenario is well-suited to be analyzed using the binomial probability distribution.

About the binomial distribution

This distribution calculates the likelihood of exactly x successes in n repeated trials where each trial has two possible results.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

Here, $C_{n,x}$ represents the count of combinations of x items selected from n elements, described by the formula:

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

And $\pi$ is the probability of the event X occurring.

Applying it to the problem

The product contains 40 integrated circuits, so $n = 40$ .

The probability that an individual integrated circuit is defective is 0.01, so $\pi = 0.01$ .

Finding the probability of at least one defective circuit

There are two cases: either at least one integrated circuit is defective (probability $P(X > 0)$ ) or none are defective (probability $P(X = 0)$ ). Since probabilities sum to 1, we want to determine $P(X>0)$ .