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3 years ago

The perimeter of a bedroom is 88 feet. The ratio of the width to the length is 5:6. What are the dimensions of the bedroom?

Mathematics

1 answer:

Elza [17]3 years ago

7 0

Answer:

20 feet wide, 24 feet long

Step-by-step explanation:

Let x - width, y - length.

The perimeter is given by the formula:

P = 2*(width + length) or using x, y

P = 2*(x + y) = 88

x + y = 44

And we know that the ratio between the sides is 5/6:

x/y = 5/6. x is on top because the length is bigger than the width

x = 5y/6

Plug this in the first expression:

y + 5y/6 = 44. Muliply by 6

6y + 5y = 264

11y = 264

y = 264/11 = 24.

So x = 5(24)/6 = 20

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Teams A and B are playing a series of games. The series is over as soon as a team wins a total of three games. Team A is two tim

Alexus [3.1K]

Answer:

The probability that A wins the series is:

$P(x=3) = \frac{n!}{(n-3)!3!}(2p)^{3}(1-2p)^{n-3}$

Step-by-step explanation:

Since team A and B are playing a series of games, let n be the total number of games played. Since there is a probability that either A or B will win if any of the two teams wins three games, then this experiment follows a binomial distribution. Binomial, because the experiment(i.e games played) is carried out n number of times.

Now, if the probability that team B wins the series is p, then the probability that team A wins the series is 2p(from the question).

Since our aim is to know the probability of A winning the series, then the probability of success is 2p and probability of failure is 1-2p

The probability density function for binomial distribution is given as:

$P(x) = \frac{n!}{(n-x)!x!}p^{x}q^{n-x}$

Where:

n = total number of trials

x = total number of successes

p = probability of success

q = probability of failure

Therefore, we have, after substituting:

$P(x=3) = \frac{n!}{(n-3)!3!}(2p)^{3}(1-2p)^{n-3}$

Which is the required answer.

4 0

3 years ago

Bill has some counter in a bag.

andrew11 [14]

9514 1404 393

Answer:

Step-by-step explanation:

The 10 non-yellow counters in the bag represent 5/7 of the total number of counters, c.

10 = (5/7)c

10(7/5) = c = 14

There are 14 counters in the bag, of which 14-10 = 4 are yellow.

_____

<em>Alternate solution</em>

Let y represent the number of yellow counters in the bag. The probability of drawing a yellow counter is the number of yellow counters divided by the total number of counters:

y/(y +3 +7) = 2/7

Multiply both sides of this equation by 7(y+10) to get ...

7y = 2(y +10)

7y = 2y +20 . . . . eliminate parentheses

5y = 20 . . . . . . . . subtract 2y

y = 20/5 = 4 . . . . divide by the coefficient of y

There are 4 yellow counters in the bag before any are taken.

<em>Another alternate solution</em>

If the probability of yellow is 2/7, the ratio of yellow (y) to non-yellow is ...

yellow : non-yellow = 2 : (7-2) = 2 : 5 = y : (3+7) = y : 10 = 4 : 10

⇒ y = 4

There are 4 yellow counters in the bag.

8 0

3 years ago

Ron has a bag containing 3 green pears and 4 red pears he randomly selects a lead then randomly selects another pear without rep

Alborosie

First pear    Second pear probability

green (3/7)---------green (2/6)    (3/7)*(2/6) = 1/7
      ---------red (4/6)    (3/7) *(4/6) = 2/7

red (4/7)-------------green (3/6) (4/7)*(3/6) = 2/7
   -------------red (3/6)    (4/7)*(3/6) = 2/7
   -------------------------
   1/7 + 2/7 + 2/7 + 2/7 = 1

The probailities that two are green are: 1/7

The probabilities that one is green and the other is red are:2 /7 + 2/7 = 4/7

The probabilities that two are red are: 2/7

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3 years ago

Which two days will Jack work half of his salary if: Monday he gets $36 Tuesday he gets $60 Wednesday he gets $72 Thursday he ge

Mumz [18]

Answer:

it is Tuesday and can you answer my question in my profile PLEASE

5 0

2 years ago

Read 2 more answers

Hola chicos, soy nuevo en brainly, y estoy teniendo algunos problemas con el curso de ecuaciones diferenciales, podrían por favo

weqwewe [10]

Answer:

hi!!

Step-by-step explanation:

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3 years ago