The line through (4,-1) and (k,5) is parallel to the line y=-3x+5. FInd the value of k.

Mathematics

1 answer:

Tema [17]3 years ago

3 0

Answer:

k = 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 5 ← is in slope- intercept form

with slope m = - 3

Parallel lines have equal slopes, thus the 2 points have a slope of - 3

calculate the slope using the slope formula and equate to - 3

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (4, - 1) and (x₂, y₂ ) = (k, 5)

m = $\frac{5+1}{k-4}$ = $\frac{6}{k-4}$ = - 3 ( multiply both sides by (k - 4) )

- 3(k - 4) = 6 ( divide both sides by - 3 )

k - 4 = - 2 ( add 4 to both sides )

k = 2

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Among all monthly bills from a certain credit card company, the mean amount billed was $465 and the standard deviation was $300.

Fynjy0 [20]

Answer:

0.02% probability that the average amount billed on the sample bills is greater than $500.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

Normal probability distribution

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:

$\mu = 465, \sigma = 300, n = 900, s = \frac{300}{\sqrt{900}} = 10$ .