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IrinaK [193]
3 years ago
15

Do two triangles with the same base and height have the same area

Mathematics
1 answer:
Stels [109]3 years ago
6 0
Yes.

The area is half the product of base and height. If those dimensions are the same, the area is the same.
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The clearance between a pin and the collar around it is important for the proper performance of a disc drive for small computers
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Answer:

(a) The distribution of (Y - X) is <em>N</em> (0.001, 0.0005).

(b) The probability that the pin will not fit inside the collar is 0.023.

Step-by-step explanation:

The random variable <em>X</em> is defined as the diameter of the pin and the random variable <em>Y</em> is defined as the diameter of the collar.

The distribution of <em>X</em> and <em>Y</em> is:

X\sim N(0.525, 0.0003)\\Y\sim N(0.526, 0.0004)

The random variables <em>X</em> and <em>Y</em> are independent of each other.

(a)

Compute the expected value of (Y - X) as follows:

E(Y-X)=E(Y)-E(X)=0.526-0.525=0.001

The mean of (Y - X) is 0.001.

Compute the variance of (Y - X) as follows:

V(Y-X)=V(Y)+V(X)-2Cov(X,Y)\\=V(Y)+V(X);\ X\ and\ Y\ are\ independent\\=0.0003^{2}+0.0004^{2}\\=0.00000025

SD(Y-X)=\sqrt{0.00000025}=0.0005

The standard deviation of (Y - X) is 0.0005.

Thus, the distribution of (Y - X) is <em>N</em> (0.001, 0.0005).

(b)

Compute the probability of [(Y - X) ≤ 0] as follows:

P(Y-X\leq 0)=P(\frac{(Y-X)-\mu_{Y-X}}{\sigma_{Y-X}}\leq \frac{0-0.001}{0.0005})=P(Z

*Use a <em>z</em>-table for the probability value.

Thus, the probability that the pin will not fit inside the collar is 0.023.

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3 years ago
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