How many ways are there to arrange the letters a, b, c, and d such that a is not followed immediately by b?

1 answer:

4 0

First, let's determine how many combinations there are without any restrictions. There are 4 letters, so we have 4 options to choose from for the first letter. For the second letter, there are only 3 options, for the third there are only 2 options, and finally for the last letter there is just 1 option. Therefore, we have:

$4! = 4 \times 3 \times 2 \times 1 = 24$ options

Now we can subtract the number of combinations in which a is immediately followed by b.

Instead of having 4 options to choose from, we now only have 3:

ab, c, or d

So using the same logic as before, we have:

$3! = 3 \times 2 \times 1 = 6$ options

Now just subtract the 6 combinations that don't work from the total:

24 - 6 = 18

The answer is 18.

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A company employs two shifts of workers. Each shift produces a type of gasket where the thickness is the critical dimension. The

Oksanka [162]

Answer:

a) $[-0.134,0.034]$

b) We are uncertain

c) It will change significantly

Step-by-step explanation:

a) Since the variances are unknown, we use the t-test with 95% confidence interval, that is the significance level = 1-0.05 = 0.025.

Since we assume that the variances are equal, we use the pooled variance given as

$s_p^2 = \frac{ (n_1 -1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}$ ,

where $n_1 = 40, n_2 = 30, s_1 = 0.16, s_2 = 0.19$ .

The mean difference $\mu_1 - \mu_2 = 10.85 - 10.90 = -0.05$ .

The confidence interval is

$(\mu_1 - \mu_2) \pm t_{n_1+n_2-2,\alpha/2} \sqrt{\frac{s_p^2}{n_1} + \frac{s_p^2}{n_2}} = (-0.05) \pm t_{68,0.025} \sqrt{\frac{0.03}{40} + \frac{0.03}{30}}$

$= -0.05\pm 1.995 \times 0.042 = -0.05 \pm 0.084 = [-0.134,0.034]$

b) With 95% confidence, we can say that it is possible that the gaskets from shift 2 are, on average, wider than the gaskets from shift 1, because the mean difference extends to the negative interval or that the gaskets from shift 1 are wider, because the confidence interval extends to the positive interval.

c) Increasing the sample sizes results in a smaller margin of error, which gives us a narrower confidence interval, thus giving us a good idea of what the true mean difference is.

6 0

4 years ago

Who wants a brainist whats the how do you convert ratios

iren2701 [21]

Answer: