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2 years ago

Which is an equation of the line passing through (-2,3) and perpendicular to the line 5x-y=12?

Mathematics

1 answer:

user100 [1]2 years ago

7 0

Answer:

y = -1/5x + 2.6

Step-by-step explanation:

Put the equation into slope intercept form:

5x - y = 12

-y = -5x + 12

y = 5x - 12

The slope of a perpendicular line will be the opposite reciprocal.

So, the slope of the new line will be -1/5

Then, plug this slope and the given point into the equation y = mx + b to find b

y = mx + b

3 = -1/5(-2) + b

3 = 0.4 + b

2.6 = b

So, the equation will be y = -1/5x + 2.6

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A real estate agent has 14 properties that she shows. She feels that there is a 50% chance of selling any one property during a

Ratling [72]

Answer:

91.02% probability of selling more than 4 properties in one week.

Step-by-step explanation:

For each property, there are only two possible outcomes. Either it is sold, or it is not. The chance of selling any one property is independent of selling another property. 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.

In this problem we have that:

$n = 14, p = 0.5$

Compute the probability of selling more than 4 properties in one week.

Either you sell 4 or less properties in one week, or you sell more. The sum of the probabilities of these events is decimal 1. So

$P(X \leq 4) + P(X > 4) = 1$

We want to find $P(X > 4)$ . So

$P(X > 4) = 1 - P(X \leq 4)$

In which

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

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

$P(X = 0) = C_{14,0}.(0.5)^{0}.(0.5)^{14} = 0.000061$

$P(X = 1) = C_{14,1}.(0.5)^{1}.(0.5)^{13} = 0.000854$

$P(X = 2) = C_{14,2}.(0.5)^{2}.(0.5)^{12} = 0.0056$

$P(X = 3) = C_{14,3}.(0.5)^{3}.(0.5)^{11} = 0.0222$

$P(X = 4) = C_{14,4}.(0.5)^{4}.(0.5)^{10} = 0.0611$

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.000061 + 0.000854 + 0.0056 + 0.0222 + 0.0611 = 0.0898$

Finally

$P(X > 4) = 1 - P(X \leq 4) = 1 - 0.0898 = 0.9102$

91.02% probability of selling more than 4 properties in one week.

8 0

3 years ago

Brian and Colin are marking exam papers. Each set takes Brian 40 minutes and Colin 1 hour. Express the times Brian and Colin tak

NeTakaya

Answer:

2:3 in the simplest form

Step-by-step explanation:

40/60

2/3=2:3

3 0

3 years ago

Read 2 more answers

There are 130 people in a sport centre. 61 people use the gym. 68 people use the swimming pool. 60 people use the track. 25 peop

yKpoI14uk [10]

Answer:

25+30+19= 74

74/130

Step-by-step explanation:

4 0

3 years ago

Give the quadratic sequence 2,3,10,23,........<br>write down the next term of the sequence.

Nataly_w [17]

Answer:

The next term of the sequence is 42

3 0

3 years ago

What are the x-intercepts of the quadratic function? y = x2 – 3x + 2

makkiz [27]

y = x² - 3x + 2

The x-intercepts can be take by matching the equation to 0, so,

x² - 3x + 2 = 0

Δ = b² - 4.a.c

Δ = -3² - 4 . 1 . 2

Δ = 9 - 4. 1 . 2

Δ = 1

There 2 real roots.

x = (-b +- √Δ)/2a

x' = (--3 + √1)/2.1

x'' = (--3 - √1)/2.1

x' = 4 / 2

x'' = 2 / 2

x' = 2

x'' = 1

Alternative A.

8 0

3 years ago