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Ilya [14]
3 years ago
6

Mathematically derive a set of values for b and c such that the interval [0, 10] represents the solution to the inequality |x−b|

<= c.
Mathematics
1 answer:
Roman55 [17]3 years ago
8 0

Answer: Ix - 5I ≥ 5.

Step-by-step explanation:

We want the set:

[0, 10]

to be the solution of:

Ix - bI ≤ c

So we need to find the values of c and b.

The first step is to find the middle point in our segment.

We can do that by adding the extremes and dividing it by 2.

M = (10 + 0)/2 = 5

And we also want to find half of the difference between the extremes, this is:

D = (10 - 0)/2 = 5.

Now, this set will be the set of solutions of:

Ix - MI ≥ D

Then in our case, we have:

Ix - 5I ≥ 5.

so we have that b = 5, and c = 5.

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A professor gives her 100 students an exam; scores are normally distributed. The section has an average exam score of 80 with a
frozen [14]

Answer:

6.18% of the class has an exam score of A- or higher.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 80, \sigma = 6.5

What percentage of the class has an exam score of A- or higher (defined as at least 90)?

This is 1 subtracted by the pvalue of Z when X = 90. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{90 - 80}{6.5}

Z = 1.54

Z = 1.54 has a pvalue of 0.9382

1 - 0.9382 = 0.0618

6.18% of the class has an exam score of A- or higher.

4 0
3 years ago
Type the correct answer in each box.
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Answer:

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Step-by-step explanation:

3 0
3 years ago
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tiny-mole [99]

Answer:

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—————————————

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Step-by-step explanation:

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shtirl [24]

Answer:

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Step-by-step explanation:

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8 0
3 years ago
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You want to frame a picture that is 5 in by 7 in with a 1 in wide frame. What is the perimeter of the outside edge of the frame?
r-ruslan [8.4K]
94 if your using the whole frame the math is 5×7=35 we have 2 sides do times 35 by 2 35×2=70 then we do 1×7=7 for the outside of the game then do 7 times 2 b/c you have 2 sides the do your final side by doing 5×1=5 then times that by 2 and you get 10 .70+14+10=94
4 0
3 years ago
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