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miskamm [114]
3 years ago
7

If a line with a slope of -2 crosses the y-axis at (0, 3), what is the equation of the line in slope intercept form

Mathematics
1 answer:
aleksley [76]3 years ago
6 0

Answer:

y=-2x+3

Step-by-step explanation:

Slope intercept form is y = mx + b where m is the slope, b is the y-intercept, and y and x are their respective coordinates.

The questions gives us a coordinate pair and a slope so all we need to find is the y-intercept to find the equation.

Begin by plugging in what we know.

(3) = (-2)(0) + b

3 = 0 + b

3 = b

Plug in the y-intercept (b) and slope (m)

y=-2x+3

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A committee of 15 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the pr
Igoryamba

Answer:

0.006% probability that the final vote count is unanimous.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So 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.

Random voting:

So 50% of voting yes, 50% no, so p = 0.5

15 members:

This means that n = 15

What is the probability that the final vote count is unanimous?

Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So

p = P(X = 0) + P(X = 15)

In which

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

P(X = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003

P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003

So

p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006

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