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4 years ago

Using point-slope form, write the equation of the line that passes through the point

Mathematics

1 answer:

liraira [26]4 years ago

4 0

Hey sorry i was eating. The answer is b

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Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backu

JulsSmile [24]

Answer:

a) There is a 10.24% probability that both generators fail during a power outage.

b) There is an 89.76% probability of having a working generator in the event of a power outage, which is not high enough for the hospital.

Step-by-step explanation:

For each emergency backup generator, there are only two possible outcomes. Either they work correctly, or they fail. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

Assume that emergency backup generators fail 32% of the times when they are needed. So they work correctly 100-32 = 68% of the time. So $p = 0.68$

There are two generators, so $n = 2$

a. Find the probability that both generators fail during a power outage

This is $P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{2,0}.(0.68)^{0}.(0.32)^{2} = 0.1024$

There is a 10.24% probability that both generators fail during a power outage.

b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital? Assume the hospital needs both generators to fail less than 1% of the time when needed.

Either there are no working generators, or there is at least one working generator. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ . So

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1024 = 0.8976$

There is an 89.76% probability of having a working generator in the event of a power outage, which is not high enough for the hospital.

To be high enough for the hospital, this probability should be at least of 99%.

7 0

4 years ago

When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What do Upper P (Upper A )P(A) and U

bezimeni [28]

Answer:

P(A): It is the probability of selecting someone with blue eyes.

$P(\bar{A})$ : It is the probability of selecting someone who does not have blue eyes

Step-by-step explanation:

We are given the following in the question:

A: event of selecting someone with blue eyes.

Probability:

The probability of an event tells the chances of happening of that event.

It is mathematically defined as:

$\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

Complement of an event:

It is the event that consist of all outcomes not happening in A.

It is represented by $\bar{A}$

$P(A) + P(\bar{A}) = 1$

We have to explain the representation:

a) P(A): It is the probability of selecting someone with blue eyes.

It gives us the chances of someone having blue eyes.

b) $P(\bar{A})$ : It is the probability of selecting someone who does not have blue eyes

It is the chances of selecting someone who does not have blue eyes.

4 0

4 years ago

Please Help T(-5,-5) N(3,7) What is the distance

umka21 [38]

Answer:

a=(x1,y1)

Step-by-step explanation:

7 0

3 years ago

Can someone help me please ? Thanks!

White raven [17]

Answer: Choice A) x = 15; y = 17

---------------------

Explanation:

The "7x+7" angle and the "112 degree" angle are congruent. They are vertical angles. So
7x+7 = 112
7x+7-7 = 112-7
7x = 105
7x/7 = 105/7
x = 15

We technically have enough to stop here, but let's keep going to find y

The "4y" angle and the "112 degree" angle are supplementary. They form a single straight line. They add to 180 degrees

So,
4y+112 = 180
4y+112-112 = 180-112
4y = 68
4y/4 = 68/4
y = 17

4 0

3 years ago

What sine function represents an amplitude of 1, a period of 2π, a horizontal shift of π, and a vertical shift of −4?

Gwar [14]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\
% function transformations for trigonometric functions
\begin{array}{rllll}
% left side templates
f(x)=&{{ A}}sin({{ B}}x+{{ C}})+{{ D}}
\\\\
f(x)=&{{ A}}cos({{ B}}x+{{ C}})+{{ D}}\\\\
f(x)=&{{ A}}tan({{ B}}x+{{ C}})+{{ D}}
\end{array}
\\\\
-------------------\\\\$

$\bf % template detailing
\bullet \textit{ stretches or shrinks}\\
\quad \textit{horizontally by amplitude } |{{ A}}|\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\$

$\bf \bullet \textit{vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{function period or frequency}\\
\left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\
\left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)$

with that template in mind, let's see

the period of 2π, well, for that, you have to do nothing, because that's sine original period

Amplitude of 1, well, that's also sine's original amplitude

horizontal shift/phase... ok, that means C/B = π, now, it doesn't say if to the left or the right, so I gather either is ok, so...let's do the right

you could use then, C = -π and B = 1, that gives you -π/1 or -π

vertical shift of -4, well, that simply means D = -4

f(θ) = sin(θ - π) - 4 <-- will do

5 0

4 years ago