The graph below shows Lisa's distance from her home (y), in miles, after a certain amount of time (x), in minutes:

Mathematics

2 answers:

steposvetlana [31]2 years ago

7 0

Answer:

Step-by-step explanation:

aleksandrvk [35]2 years ago

4 0

Answer:

Greg

Step-by-step explanation:

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The life in hours of a 75-watt light bulb is known to be normally distributed with standard deviation σ = 25 hours. A random sam

irina [24]

Answer: a) (1008.34,1019.658) b) (1009.24,1018.76)

Step-by-step explanation:

Since we have given that

n = 75

mean = 1014 hours

Standard deviation = 25 hours

At 95% two sided , z = 1.96

So, confidence interval would be

$\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=1014\pm 1.96\dfrac{25}{\sqrt{75}}\\\\=1014\pm 5.658\\\\=(1014-5.658,1014+5.658)\\\\=(1008.34,1019.658)$

(b) Construct a 95% lower confidence bound on the mean life.

z = 1.65

So, confidence interval would be

$\bar{x}\pm z\times \dfrac{\sigma}{\sqrt{n}}\\\\=1014\pm 1.65\times \dfrac{25}{\sqrt{75}}\\\\=1014\pm 4.76\\\\=(1014-4.76,1014+4.76)\\\\=(1009.24,1018.76)$

Hence, a) (1008.34,1019.658) b) (1009.24,1018.76)

4 0

3 years ago

What is the equation of a line that contains the point (2,-5) and is parallel to the line y=3x-4

aev [14]

Answer:

$\large\boxed{y=3x-11}$

Step-by-step explanation:

$\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\y=3x-4\to m_1=3\\\\\text{Therefore}\ m_2=3.\\\\\text{We have the equation:}\ y=3x+b.\\\\\text{Put the coorsdinates of the point (2, -5) to the equation of the line}\\\\-5=3(2)+b\\-5=6+b\qquad\text{subtract 6 from both sides}\\-11=b\to b=-11$