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A pilot flew a jet from City A to City B, a distance of 1700 miles. On the return trip, the average speed was 20% faster than th

ArbitrLikvidat [17]

The answer is about 650 mi/h

8 0

4 years ago

Read 2 more answers

Each item produced by a certain manufacturer is independently of acceptable quality with probability 0.95. Approximate the proba

Diano4ka-milaya [45]

Answer:

The probability that at most 10 of the next 150 items produced are unacceptable is 0.8315.

Step-by-step explanation:

Let X = number of items with unacceptable quality.

The probability of an item being unacceptable is, P (X) = p = 0.05.

The sample of items selected is of size, n = 150.

The random variable X follows a Binomial distribution with parameters n = 150 and p = 0.05.

According to the Central limit theorem, if a sample of large size (n > 30) is selected from an unknown population then the sampling distribution of sample mean can be approximated by the Normal distribution.

The mean of this sampling distribution is: $\mu_{\hat p}= p=0.05$

The standard deviation of this sampling distribution is: $\sigma_{\hat p}=\sqrt{\frac{ p(1-p)}{n}}=\sqrt{\frac{0.05(1-.0.05)}{150} }=0.0178$

If 10 of the 150 items produced are unacceptable then the probability of this event is:

$\hat p=\frac{10}{150}=0.067$

Compute the value of $P(\hat p\leq 0.067)$ as follows:

$P(\hat p\leq 0.067)=P(\frac{\hat p-\mu_{p}}{\sigma_{p}} \leq\frac{0.067-0.05}{0.0178})=P(Z\leq 0.96)=0.8315$

*Use a z-table for the probability.

Thus, the probability that at most 10 of the next 150 items produced are unacceptable is 0.8315.

5 0

3 years ago

Clock #2: A clock has a radius of 6 inches. The center is 14.5 inches below the ceiling. Record the distance as you did for Cloc

Whitepunk [10]

Answer:

The question is incomplete, I assume that we want to write an equation that defines the position (or distance) between the tip of the second hand of the clock and the ceiling.

We know that:

The center of the clock is 14.5 in below the ceiling.

The radius of the clock is 6 inches.

So, a general cosine equation is written as:

f(x) = A*sin(w*t) + M

where:

A = amplitude, in this case, is equal to the radius of the clock

w = angular frequency

t = time in seconds

M = midline (the oscillation is around this point), in this case, would be the distance between the center of the clock and the ceiling, because the clock is 14.5 inches below the ceiling, we can write this as M = -14.5 in

Replacing these two in the equation we have:

f(t) = 6in*cos(w*t) - 14,5in

Now, we know that at t = 0s the tip of the second hand of the clock is in its most high point, so at t = 0 we have the maximum, this is why we used a cosine function, because the maximum of the cosine function is at:

cos(0) = 1

We also know that the minimum will be at t = 30 seconds (when the tip of the second hand is in the bottom part of the clock)

then we need to have:

cos(w*30s) = -1

Remember that:

cos(pi) = -1

then:

w*30s = pi

solving for w, we get:

w = pi/30s

Then the equation for the distance between the tip of the second hand of the clock and the ceiling is:

f(t) = 6in*cos(t*pi/30s) - 14.5 in