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 and standard deviation , the zscore of a measure X is given by
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 .
What is the probability that a line width is greater than 0.62 micrometer?
That is
So
Z = 2.4 has a pvalue of 0.99180.
This means that P(X \leq 0.62) = 0.99180.
We also have that
There is a 0.82% probability that a line width is greater than 0.62 micrometer.
Answer:
<h2>-x²+4x +6</h2>
Step-by-step explanation:
Given f(x)=4x+1 and g(x)=x²-5
(f-g)(x) is derived by taking the difference of both functions
(f-g)(x) = f(x)-g(x)
(f-g)(x) = 4x+1 - (x²-5)
(f-g)(x) = 4x+1-x²+5
(f-g)(x) = -x²+4x +6
This gives the requires expression
Answer:
Step-by-step explanation:
We can break down this problem by first realizing different parts of the circle.
- The line which is 8 units long is a chord of the circle.
- The line that is 3.6 is <em>almost</em> the radius of the circle
- The line that x sits on is the radius.
With this, we can find out if we find the radius of the circle, we have our answer.
We should also note that the angle formed by the 3.6 units long line and the chord is a right angle.
<em>What we need is a way to find the radius of the circle</em><em>. This will get us x</em>. The radius of a circle will be the length of any line that starts from point O and ends at the circle edge.
If we draw a line connecting the end of the 3.6 line at point O to the end of the 8 unit long chord, we get a triangle! (Image attached for reference).
We can solve for the hypotenuse using the Pythagorean Theorem. This theorem states that:
Since we know one side is 3.6, we can use that as A. The second side will be 4 since the 3.6 line lies directly in the center of the chord = 8/2 = 4!
Therefore, since this is the radius of the circle (also the hypotenuse), this can be said for any line that comes from point O onto the edge of the circle.
The line X does just that. Therefore, the value of x is also 5.4.
Hope this helped!
Answer:
SSS, SAS, ASA, AAS, HL
Step-by-step explanation:
1. SSS (side side side) says if 3 sides of one triangle are congruent to 3 sides of another triangle, then the 2 triangles are congruent.
2. SAS (side angle side) says if 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the 2 triangles are congruent.
3. ASA (angle side angle) says if 2 angles and the included side of a triangle are congruent to 2 angles and the included side of another triangle, then the 2 triangles are congruent.
4. AAS (angle angle side) says if 2 angles and the none included side of one triangle are congruent to the corresponding parts of another triangle, then the 2 triangles are congruent.
5 HL (hypotenuse leg) says if 2 right triangles that have a congruent hypotenuse and a corresponding congruent leg, then the 2 triangles are congruent.
Because it is a rectangle, the sides are equal, and they share the same hypotenuse.
Answer:
Step-by-step explanation:
if f(x)=3x-1 and g(x)=2x+5 then
f(x)-g(x)=3x-1-(2x+5)
f(x)-g(x)=3x-1-2x-5
f(x)-g(x)=x-6