Mathematics help please

Is y=-3x^2 +10 a function

Sever21 [200]

Answer:

YES

Step-by-step explanation:

3 0

3 years ago

The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 28 mm and standard d

Misha Larkins [42]

Answer:

14.69% probability that defect length is at most 20 mm

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:

$\mu = 28, \sigma = 7.6$

What is the probability that defect length is at most 20 mm

This is the pvalue of Z when X = 20. So

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

$Z = \frac{20 - 28}{7.6}$

$Z = -1.05$

$Z = -1.05$ has a pvalue of 0.1469

14.69% probability that defect length is at most 20 mm

5 0

4 years ago

Find the nth term of the sequence 7,25,51,85,127

olya-2409 [2.1K]

Let a (n) denote the n-th term of the given sequence.

Check the forward differences, and denote the n-th difference by b (n). That is,

b (n) = a (n + 1) - a (n)

These so-called first differences are

b (1) = a (2) - a (1) = 25 - 7 = 18

b (2) = a (3) - a (2) = 51 - 25 = 26

b (3) = a (4) - a (3) = 85 - 51 = 34

b (4) = a (5) - a (4) = 127 - 85 = 42

Now consider this sequence of differences,

18, 26, 34, 42, …

and notice that the difference between consecutive terms in this sequence b is 8:

26 - 18 = 8

34 - 26 = 8

42 - 34 = 8

and so on. This means b is an arithmetic sequence, and in particular follows the rule

b (n) = 18 + 8 (n - 1) = 8n + 10

for n ≥ 1.

So we have

a (n + 1) - a (n) = 8n + 10

or, replacing n + 1 with n,

a (n) = a (n - 1) + 8 (n - 1) + 10

a (n) = a (n - 1) + 8n + 2

We can solve for a (n) by iteratively substituting:

a (n) = [a (n - 2) + 8 (n - 1) + 2] + 8n + 2

a (n) = a (n - 2) + 8 (n + (n - 1)) + 2×2

a (n) = [a (n - 3) + 8 (n - 2) + 2] + 8 (n + (n - 1)) + 2×2

a (n) = a (n - 3) + 8 (n + (n - 1) + (n - 2)) + 3×2

and so on. The pattern should be clear; we end up with

a (n) = a (1) + 8 (n + (n - 1) + … + 3 + 2) + (n - 1)×2

The middle group is the sum,

$\displaystyle 8\sum_{k=2}^nk=8\sum_{k=1}^nk-8=\frac{8n(n+1)}2-8=4n^2+4n-8$

so that

a (n) = a (1) + (4n ² + 4n - 8) + 2 (n - 1)

a (n) = 4n ² + 6n - 3

4 0

3 years ago

Enter the answer to the problem below, using the correct number of

Lena [83]

Answer:

‬80.796,64‬

Step-by-step explanation:

7 0

3 years ago

Rewrite the equation by completing the square. x^2 −16x+63=0 (x +{ })^2={ }

Elina [12.6K]

Answer:

(x + 4) ^{2} + 47 = 0

Step-by-step explanation:

$(x ^{2} + 4 ^{2} ) - 4 ^{2} + 63 = 0 \\ (x + 4) ^{2} + 47 = 0$

When completing squares, basing on our equation in the question:

First square the half of 16 e.g (16÷2)^2 = 4^2

Add the result to x^2 and subtract it with 63 e.g the second equation

7 0

4 years ago