The minimum point of the graph y = 2x^2 + 2x +1 is located at:

Mathematics

1 answer:

slega [8]3 years ago

8 0

Answer:

Step-by-step explanation:

By completing the square, y = 2x^2 + 2x +1 will be y=2(x+1/2)^2+(1/2) the minimum point is the vertex of the parabola which is (-1/2, 1/2)

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The line width used for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.5 micrometer and a st

Alinara [238K]

Answer:

There is a 0.82% probability that a line width is greater than 0.62 micrometer.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

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

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

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. The sum of the probabilities is decimal 1. So 1-pvalue is the probability that the value of the measure is larger than X.

In this problem

The line width used for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.5 micrometer and a standard deviation of 0.05 micrometer, so $\mu = 0.5, \sigma = 0.05$ .

What is the probability that a line width is greater than 0.62 micrometer?

That is $P(X > 0.62)$

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

$Z = \frac{0.62 - 0.5}{0.05}$

$Z = 2.4$

Z = 2.4 has a pvalue of 0.99180.

This means that P(X \leq 0.62) = 0.99180.

We also have that

$P(X \leq 0.62) + P(X > 0.62) = 1$

$P(X > 0.62) = 1 - 0.99180 = 0.0082$

There is a 0.82% probability that a line width is greater than 0.62 micrometer.

3 0

3 years ago

to avoid a large shallow reef a ship set a course from point a and traveled 24 miles east to point b . the ship them turn and tr

Sever21 [200]

First, we are going to find the distance traveled by the ship adding the tow distances:
Distance traveled= 24 mi +33 mi=57 mi

Next, we are going to use the Pythagorean theorem to find the distance from $a$ to $c$ :
$d^2=24^2+33^2$
$d^2=576+1089$
d^2=1665
$d= \sqrt{1665}$
$d=40.8$ mi

Finally, we are going to subtract the two distances:
57 mi -40.8 mi= 16.2 mi

We can conclude that <span>if the ship could have traveled in a straight lime from point a to point c, it could have saved 16.2 miles.</span>