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3 years ago

Y=-1/2x+11 that passes through (4,-8)

Mathematics

1 answer:

kompoz [17]3 years ago

8 0

A line in point-slope form has the equation

y = mx + b

where m=slope (increase in y for unit increase in x), and

b=y-intercept (value of y where line cuts y-axis)

The original line is

y=(-1/2)x + 11

slope = m = -1/2

Any line perpendicular to a line with slope m has a slope of m1=-1/m

So the slope m1 of the required line

m1 = -1 / (-1/2) = +2

and the required line therefore has an equation of

y=2x+b

Knowing that the line passes through P1=(x1, y1)=(4,-8), we can find b using the point slope form of a line with slope m : (y-y1) = m(x-x1)

where m=+2 as found above.

Substituting values, m=+2, x1=4, y1= -8

y-(-8) = +2(x--4)

simplify

y+8 = 2x-8

y=2x-16 (in point slope form)

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a ferry boat collects 67 people at pier one. At pier two 36 people get on and 23 people get off. At pier three 18 get on and 29

GREYUIT [131]

Starts off with 67 people.

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2 years ago

4d. Health Survey. In a survey of 1020 adults in the United States, 44% said that they wash their hands after riding public tran

AleksandrR [38]

Answer:

Discrete. See explanation below

Step-by-step explanation:

We need to remember some previous concepts:

We have two types of numerical data: Discrete and Continuous

When we say Discrete data we are refering to data that is countable or can be expressed with integers in a domain.

In the other case when we talk about continuous data we are refering to data that is continuous in a specified domain, it can contain decimals or rational numbers in the Real numbers for example.

For this special case we know that they select a sample size of n=1020 and the sample proportion of people in the United States who wash their hands after riding public transportation was 0.44 or 44% in percentage.

$\hat p = \frac{X}{1020}=0.44$

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But the number of subjects on this survey needs to be Discrete, since the possible values are 0,1,2,3,4,.....,n and never we have decimals or continuous data in order to express this.

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2 years ago

A designer builds a model of a sports car. The finished model is exactly the same shape as the original, but smaller. The scale

lesantik [10]

Answer:

$Ratio = 2 : 15$

Step-by-step explanation:

Given

$k = 2 : 15$ --- scale factor

Required [missing from the question]:

The ratio of width of the model to the original

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The ratio of the width of the model to the original equals the given scale factor i.e.

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2 years ago

Suppose that, after measuring the duration of many telephone calls, a telephone company found their data was well-approximated b

Musya8 [376]

Answer:

a) 7.79%

b) 67.03%

c) Cumulative Distribution Function

$P(t) = \displaystyle\int^{\infty}_{-\infty} 0.1e^{-0.1t}~dt\\\\= \displaystyle\int^{b}_{a} 0.1e^{-0.1t}~dt, ~~a\leq t \leq b$

Step-by-step explanation:

We are given the following in the question:

$p(x) = 0.1 e^{-0.1x}$

where x is the duration of a call, in minutes.

a) P( calls last between 2 and 3 minutes)

$=\displaystyle\int^3_2 p(x)~ dx\\\\= \displaystyle\int^3_20.1e^{-0.1x}~dx\\\\=\Big[-e^{-0.1x}\Big]^3_2\\\\=-\Big[e^{-0.3}-e^{-0.2}\Big]\\\\= 0.0779\\=7.79\%$

b) P(calls last 4 minutes or more)

$=\displaystyle\int^{\infty}_4 p(x)~ dx\\\\= \displaystyle\int^{\infty}_40.1e^{-0.1x}~dx\\\\=\Big[-e^{-0.1x}\Big]^{\infty}_4\\\\=-\Big[e^{\infty}-e^{-0.4}\Big]\\\\=-(0- 0.6703)\\= 0.6703\\=67.03\%$