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s344n2d4d5 [400]

2 years ago

6

Vint is testing ceiling fans in a factory. For one of the tests, he switches the fan on, and after it attains a maximum speed of

500 rotations per minute (rpm), he switches the fan back off, recording the amount of time it takes for the fan to completely stop spinning. The given equation models Vint's test, where x represents time in seconds and y represents the speed in rotations per minute. The equation has been graphed as shown.
Assuming that the test was complete when the fan stopped spinning completely, how long was the test?

A. 100 seconds

B. 10 seconds

C. 20 seconds

D. 500 seconds

2 answers:

Natasha_Volkova [10]2 years ago

8 0

Answer:

20 seconds

Step-by-step explanation:

Given :

$y=-5x^2+100x$

Where x represents time in seconds and y represents the speed in rotations per minute.

To Find : Assuming that the test was complete when the fan stopped spinning completely, how long was the test?

Solution:

Since we are supposed to find how long will it take to stop the fan completely

We assumed that test was complete when the fan stopped spinning completely

i.e. y = Speed = 0

So, Substitute y = 0 in the equation $y=-5x^2+100x$

⇒ $0=-5x^2+100x$

⇒ $5x^2=100x$

⇒ $5x=100$

⇒ $x=\frac{100}{5}$

⇒ $x=20$

Thus it took 20 seconds to stop the fan

Hence the test was 20 seconds long.

Gennadij [26K]2 years ago

5 0

Answer:

C. 20 seconds

Step-by-step explanation:

We want to know when y=0

The first y is when it started and the second y=0 is when it stops

Looking at the graph y=0 at x=0 and y=0 at x=20

The fan started at time 0 and stopped at 20 seconds

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Answer:

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Step-by-step explanation:

First, convert the 70% so that we can use it with the 80 cups. To do this, convert the percent to a decimal by moving the decimal 2 spaces to the left:

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2 years ago

A survey on British Social Attitudes asked respondents if they had ever boycotted goods for ethical reasons (Statesman, January

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Answer:

a) 27.89% probability that two have ever boycotted goods for ethical reasons

b) 41.81% probability that at least two respondents have boycotted goods for ethical reasons

c) 41.16% probability that between 3 and 6 have boycotted goods for ethical reasons

d) The expected number is 2.3 and the standard deviation is 1.33.

Step-by-step explanation:

We use the binomial probability distribution to solve this question.

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.

23% of the respondents have boycotted goods for ethical reasons.

This means that $p = 0.23$

a) In a sample of six British citizens, what is the probability that two have ever boycotted goods for ethical reasons?

This is P(X = 2) when n = 6. So

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

$P(X = 2) = C_{6,2}.(0.23)^{2}.(0.77)^{4} = 0.2789$

27.89% probability that two have ever boycotted goods for ethical reasons

b) In a sample of six British citizens, what is the probability that at least two respondents have boycotted goods for ethical reasons?

Either less than two have, or at least two. The sum of the probabilities of these events is decimal 1. So

$P(X < 2) + P(X \geq 2) = 1$

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1)$

$P(X = 0) = C_{6,0}.(0.23)^{0}.(0.77)^{6} = 0.2084$

$P(X = 1) = C_{6,1}.(0.23)^{1}.(0.77)^{5} = 0.3735$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.2084 + 0.3735 = 0.5819$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.5819 = 0.4181$

41.81% probability that at least two respondents have boycotted goods for ethical reasons

c) In a sample of ten British citizens, what is the probability that between 3 and 6 have boycotted goods for ethical reasons?

Now n = 10.

$P(3 \leq X \leq 6) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)$

$P(X = 3) = C_{10,3}.(0.23)^{3}.(0.77)^{7} = 0.2343$

$P(X = 4) = C_{10,4}.(0.23)^{4}.(0.77)^{6} = 0.1225$

$P(X = 5) = C_{10,5}.(0.23)^{5}.(0.77)^{5} = 0.0439$

$P(X = 6) = C_{10,6}.(0.23)^{6}.(0.77)^{4} = 0.0109$

$P(3 \leq X \leq 6) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.2343 + 0.1225 + 0.0439 + 0.0109 = 0.4116$

41.16% probability that between 3 and 6 have boycotted goods for ethical reasons

d) In a sample of ten British citizens, what is the expected number of people that have boycotted goods for ethical reasons? Also find the standard deviation.

$E(X) = np = 10*0.23 = 2.3$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.23*0.77} = 1.33$

The expected number is 2.3 and the standard deviation is 1.33.

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