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joja [24]
2 years ago
8

Point AAA is at {(6,1)}(6,1)left parenthesis, 6, comma, 1, right parenthesis and point CCC is at {(2,-7)}(2,−7)left parenthesis,

2, comma, minus, 7, right parenthesis. Find the coordinates of point BBB on \overline{AC} AC start overline, A, C, end overline such that AB=\dfrac13BCAB= 3 1 ​ BCA, B, equals, start fraction, 1, divided by, 3, end fraction, B, C.
Mathematics
2 answers:
Citrus2011 [14]2 years ago
6 0

Answer:

5,-1

Step-by-step explanation:

pychu [463]2 years ago
4 0

Answer:

The coordinates of B is (3, - 5)

Step-by-step explanation:

A(6, 1)

C(2, -7)

Coordinates of point B such that AB = 1/3 × BC

Hence we have;

AC = AB + BC = BC + \dfrac{1}{3} \times BC =  \dfrac{4}{3} \times BC

Therefore BC = 3/4 × AC

Hence, AB = 1/3 × BC = 1/3 × 3/4 × AC = 1/4 × AC

AC = √((6 - 2)² + (1 - (-7))²) = √(16 + 64) = √80 = 4·√5

AB = 1/4 × 4·√5 = √5

Therefore;

AB² = (x - 6)² + (y - 1)² = 5

Slope = (1 - (-7))/(6 - 2) = 2

Hence the y coordinate of B = -7 + sin(tan⁻¹(2)) ×√5 = -5

The x coordinate of B = 2 + cos(tan⁻¹(2)) ×√5 = 3

The coordinates of B = (3, - 5)

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Recent homebuyers from a local developer allege that 30% of the houses this developer constructs have some major defect that wil
umka21 [38]

Answer:

3.54% probability of observing at most two defective homes out of a random sample of 20

Step-by-step explanation:

For each house that this developer constructs, there are only two possible outcomes. Either there are some major defect that will require substantial repairs, or there is not. The probability of a house having some major defect that will require substantial repairs is independent of other houses. 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.

30% of the houses this developer constructs have some major defect that will require substantial repairs.

This means that p = 0.3

If the allegation is correct, what is the probability of observing at most two defective homes out of a random sample of 20

This is P(X \leq 2) when n = 20. So

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)

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

P(X = 0) = C_{20,0}.(0.3)^{0}.(0.7)^{20} = 0.0008

P(X = 1) = C_{20,1}.(0.3)^{1}.(0.7)^{19} = 0.0068

P(X = 2) = C_{20,2}.(0.3)^{2}.(0.7)^{18} = 0.0278

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0008 + 0.0068 + 0.0278 = 0.0354

3.54% probability of observing at most two defective homes out of a random sample of 20

5 0
1 year ago
After drawing the line y = 2x − 1 and marking the point A = (−2, 7), Kendall is trying to decide which point on the line is clos
igor_vitrenko [27]

Answer:

Step-by-step explanation:

Having drawn the line, Kendall must verify that the point P belongs to the line y = 2x-1 and then calculate the distance between A-P  and verify if it is the closest to A or there is another one of the line

Having the point P(3,5) substitue x to verify y

y=2*(3)-1=6-1=5 (3,5)

Now if the angle formed by A and P is 90º it means that it is the closest point, otherwise that point must be found

d_{AP}=\sqrt{(y_{2}-y_{1})^{2}+(x_{2}-x_{1})^{2}}=\sqrt{(5-7)^{2}+(3-(-2}))^{2}}=\\\sqrt{(-2)^{2}+(5)^{2}}=\sqrt{29}

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1 year ago
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7 0
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lora16 [44]
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jarptica [38.1K]

Answer:the total discounted price for two dogs to be groomed is 22.75

Step-by-step explanation:

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If you decide to take your two furry friends to be groomed,

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3 0
1 year ago
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