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3 years ago

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An oak tree, elm tree, and maple tree are standing in a park. The three trees are non-collinear. If the oak is 2 feet from the e

lm, the elm is 10 feet from the maple and the oak is 4 feet from the maple, do these three trees form a triangle?

1 answer:

crimeas [40]3 years ago

6 0

No they do not form a triangle because 2×2=4 and 4×4=16 16+4=20 it must equal 10 to form a triangle

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Find the dimensions of a rectangle with perimeter 84 m whose area is as large as possible.

Slav-nsk [51]

21 and 21
(it's a square)
and yes, a square is a rectangle

8 0

2 years ago

Suppose that a box contains r red balls and w white balls. Suppose also that balls are drawn from the box one at a time, at rand

dybincka [34]

Answer: Part a) $P(a)=\frac{1}{\binom{r+w}{r}}$

part b) $P(b)=\frac{1}{\binom{r+w}{r}}+\frac{r}{\binom{r+w}{r}}$

Step-by-step explanation:

The probability is calculated as follows:

We have proability of any event E = $P(E)=\frac{Favourablecases}{TotalCases}$

For part a)

Probability that a red ball is drawn in first attempt = $P(E_{1})=\frac{r}{r+w}$

Probability that a red ball is drawn in second attempt= $P(E_{2})=\frac{r-1}{r+w-1}$

Probability that a red ball is drawn in third attempt = $P(E_{3})=\frac{r-2}{r+w-1}$

Generalising this result

Probability that a red ball is drawn in [tex}i^{th}[/tex] attempt = $P(E_{i})=\frac{r-i}{r+w-i}$

Thus the probability that events $E_{1},E_{2}....E_{i}$ occur in succession is

$P(E)=P(E_{1})\times P(E_{2})\times P(E_{3})\times ...$

Thus $P(E)$ = $\frac{r}{r+w}\times \frac{r-1}{r+w-1}\times \frac{r-2}{r+w-2}\times ...\times \frac{1}{w}\\\\P(E)=\frac{r!}{(r+w)!}\times (w-1)!$

Thus our probability becomes

$P(E)=\frac{1}{\binom{r+w}{r}}$

Part b)

The event " r red balls are drawn before 2 whites are drawn" can happen in 2 ways

1) 'r' red balls are drawn before 2 white balls are drawn with probability same as calculated for part a.

2) exactly 1 white ball is drawn in between 'r' draws then a red ball again at $(r+1)^{th}$ draw

We have to calculate probability of part 2 as we have already calculated probability of part 1.

For part 2 we have to figure out how many ways are there to draw a white ball among (r) red balls which is obtained by permutations of 1 white ball among (r) red balls which equals $\binom{r}{r-1}$

Thus the probability becomes $P(E_i)=\frac{\binom{r}{r-1}}{\binom{r+w}{r}}=\frac{r}{\binom{r+w}{r}}$

Thus required probability of case b becomes $P(E)+ P(E_{i})$

= $P(b)=\frac{1}{\binom{r+w}{r}}+\frac{r}{\binom{r+w}{r}}\\\\$

7 0

2 years ago

What are the coordinates of the midpoint of the segment whose endpoints are A (-1, -2) and B (6, 12)

Klio2033 [76]

<u>Answer:</u>

Mid point = $(\frac{5}{2} ,5)$

<u>Step-by-step explanation:</u>

We are given the coordinates of the end points of a line segment AB and we are to find the coordinates of its mid point.

The coordinates of the end points are: A (-1, -2) and B (6, 12).

We know the formula of the mid point:

Mid point = $(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )$

So putting in the given values to find the mid point of line segment AB:

Mid point = $(\frac{-1+6}{2} ,\frac{-2+12}{2} )$ = $(\frac{5}{2} ,5)$

5 0

2 years ago

9x - 4y? +72x–24y— 36–0

earnstyle [38]

Not is posible because no exist a igualty

3 0

2 years ago

Help on this ik it’s easy but I gotta do other hw rn

ddd [48]

Answer:

2: addition

3: subtraction

4: division

5: subtraction

6: division (I think)

7: addition

8: subtraction

9: multiplication

10: addition

12: n/10

13: n+6

14: 9x(n-5)

15: 4n-1

16: 50+40h

Step-by-step explanation:

you said its easy so i assume you know how to do it

6 0

1 year ago

Read 2 more answers