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meriva
2 years ago
12

What is the slope of a line perpendicular to the line whose equation is 3y + 2x = -5?

Mathematics
1 answer:
konstantin123 [22]2 years ago
4 0

Answer:

I think the slope of the line is -2/3

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Kelly took 12 pictures at school on Tuesday. She took 7 pictures at lunch and 5 pictures at recess. If she randomly selects a pi
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Read 2 more answers
A survey on British Social Attitudes asked respondents if they had ever boycotted goods for ethical reasons (Statesman, January
Blababa [14]

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.

5 0
3 years ago
The distance, y, in centimeters, of an ant from a hole in the tree for a certain amount of time, x, in seconds, is shown in the
Alenkasestr [34]

Answer:

<h3>Part A</h3>

The graph is non-linear as it is not a continuous straight line (with only one slope).

<h3>Part B</h3>

<u>Increasing</u>:  the y-value increases as the x-value increases

<u>Constant</u>:  the y-value stays the same as the x-value changes

<u>Decreasing</u>:  the y-value decreases as the x-value increases

Therefore,

  • Increasing segment:  Between 0 and 2 seconds
  • Constant segment: Between 2 and 3 seconds
  • Decreasing segment: Between 3 and 5 seconds

<h3>Part C</h3>

For the first 2 seconds, the ant moves 6 cm from a hole in the tree at a steady speed of 3 cm per second. For the next second, the ant is at rest then turns around. For the next 2 seconds, the ant moves 6 cm back to the hole at a steady speed of 3 cm per second.  The ant then stops.

4 0
2 years ago
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