• rearrange into the form y = mx + c to find the gradient:
5x -3y = 2
-3y = 2 -5x
y = (-5/-3x) + (2/-3)
y = 5/3x - 2/3
gradient of line m is 5/3

• use formula to find perpendicular gradient, m1 X m2 = -1, and rearrange:
5/3 X m2 = -1
m2 = -3/5 is the slope of the perpendicular line :)

7 0

3 years ago

The bursting strength of bottles of a certain type is normally distributed with μ=250 psi and σ= 30 psi. If these bottles are sh

sweet [91]

Answer:

4.75% of the bottles are succesful.

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:

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

The Z-score measures how many standard deviations the measure is from the mean. 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, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 250, \sigma = 30$ .

If these bottles are shipped 12 to a carton, in what proportion of cartons will at least one of the bottles have a bursting strength exceeding 300 psi?

This proportion is the percentage of the bootles that exceed 300 psi. This is 1 subtracted by the pvalue of Z when $X = 300$ .

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

$Z = \frac{300 - 250}{30}$

$Z = 1.67$

$Z = 1.67$ has a pvalue of 0.9525.

This means that the proportion of sucesses is 1-0.9525 = 0.0475 = 4.75% of the bottles.

8 0

2 years ago