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Olenka [21]
3 years ago
10

In a random sample of 20 ​people, the mean commute time to work was 33.5 minutes and the standard deviation was

Mathematics
1 answer:
STALIN [3.7K]3 years ago
6 0
Construct<span> the </span>confidence interval<span> for the </span>population mean<span> it </span>using<span> a </span>t-distribution<span>. ... In a </span>random sample<span> of eight </span>people<span>, the </span>mean commute time<span> to </span>work<span> was 35.5 </span>minutes<span> and the sample </span>standard deviation<span> was. </span>7.2 minutes<span>. ... </span>Use<span> a </span>t-distribution<span> to find the margin of error and </span>construct<span> a 95% ...</span>Assume normal<span> distribution.</span>
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Let $P$ and $Q$ be constants. The graphs of the lines $x + 5y = 7$ and $15x + Py = Q$ are perpendicular and intersect at the poi
Marta_Voda [28]

Answer:

<em>(-3, -129)</em>

<em></em>

Step-by-step explanation:

Given

Two lines:

$x + 5y = 7$

$15x + Py = Q$

are perpendicular to each other and intersect at point (-8,3).

To find: (P, Q)

Solution:

The two lines intersect at (-8,3).

It means, the equation of line will be satisfied when we put value of x = -8 and y = 3

Putting in the second equation, we will get an equation in P and Q:

15\times (-8) + P \times 3 = Q\\\Rightarrow 3P = Q +120 ..... (1)

Given that two lines are perpendicular.

It means the product of their slopes will be equal to -1.

i.e. m_1\times m_2=-1

Slope of a line of the form ax+by+c=0 is given as:

m=-\dfrac{a}{b}

So, slopes of given lines are:

m_1=-\dfrac{1}{5}\\m_2=-\dfrac{15}{P}

Using the condition:

-\dfrac{1}{5}\times \dfrac{-15}{P}=-1\\\Rightarrow P = -3

Putting the value of P in equation (1):

\Rightarrow 3\times (-3) = Q +120 \\\Rightarrow Q = -9-120 = -129

So, answer is <em>(-3, -129)</em>

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Company B. Its kinda commen sense.
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