Exercise 2.11

1 answer:

5 0

$\int 8\, dx=8x+C\\\\
0=8\cdot1+C\\
C=-8\\
f'(x)=8x-8\\\\
\int 8x-8\, dx=4x^2-8x+C\\\\
3=4\cdot1^2-8\cdot1+C\\
3=4-8+C\\
C=7\\\\
\boxed{f(x)=4x^2-8x+7}
$

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Stella [2.4K]

Given:

4 relations in the options.

To find:

The relation which represents a function.

Solution:

We know that, a relation is a function if there exist a unique output value for each input value.

In option A, we have two output values y=-5 and y=1 for single input value x=-1. So, it is not a function.

In option B, we have two output values y=2 and y=4 for single input value x=3. So, it is not a function.

In option C, we have two output values y=1 and y=7 for single input value x=-1. So, it is not a function.

In option D, we have unique output value for each input value. So, it is a function.

Therefore, the correct option is D.

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3 years ago

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.71 millimeters and a standard deviat

Harlamova29_29 [7]

Answer:

The bolts with diameter less than 5.57 millimeters and with diameter greater than 5.85 millimeters should be rejected.

Step-by-step explanation:

We have been given that the diameters of bolts produced in a machine shop are normally distributed with a mean of 5.71 millimeters and a standard deviation of 0.08 millimeters.

Let us find the sample score that corresponds to z-score of bottom 4%.

From normal distribution table we got z-score corresponding to bottom 4% is -1.75 and z-score corresponding to top 4% or data above 96% is 1.75.

Upon substituting these values in z-score formula we will get our sample scores (x) as:

$z=\frac{x-\mu}{\sigma}$