Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

7 0

3 years ago

In a restaurant, Chad tracked the number of children and adults that came in over an hour. During that time, 16 children and 40

Pepsi [2]

You have 40/16
simplified by 8 and you have 5:2
so the answer is d. 5:2

4 0

3 years ago

The clearance between a pin and the collar around it is important for the proper performance of a disc drive for small computers

hichkok12 [17]

Answer:

(a) The distribution of (Y - X) is N (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 X is defined as the diameter of the pin and the random variable Y is defined as the diameter of the collar.

The distribution of X and Y is:

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

The random variables X and Y 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 N (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 z-table for the probability value.

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

8 0

3 years ago