Express 16% percent as a fraction in the simplest form

. A box in a certain supply room contains four 40-W lightbulbs, five 60-W bulbs, and six 75-W bulbs. Suppose that three bulbs ar

yaroslaw [1]

Answer:

a) 59.34%

b) 44.82%

c) 26.37%

d) 4.19%

Step-by-step explanation:

(a)

There are in total 4+5+6 = 15 bulbs. If we want to select 3 randomly there are K ways of doing this, where K is the combination of 15 elements taken 3 at a time

$K=\binom{15}{3}=\frac{15!}{3!(15-3)!}=\frac{15!}{3!12!}=\frac{15.14.13}{6}=455$

As there are 9 non 75-W bulbs, by the fundamental rule of counting, there are 6*5*9 = 270 ways of selecting 3 bulbs with exactly two 75-W bulbs.

So, the probability of selecting exactly 2 bulbs of 75 W is

$\frac{270}{455}=0.5934=59.34\%$

(b)

The probability of selecting three 40-W bulbs is

$\frac{4*3*2}{455}=0.0527=5.27\%$

The probability of selecting three 60-W bulbs is

$\frac{5*4*3}{455}=0.1318=13.18\%$

The probability of selecting three 75-W bulbs is

$\frac{6*5*4}{455}=0.2637=26.37\%$

Since the events are disjoint, the probability of taking 3 bulbs of the same kind is the sum 0.0527+0.1318+0.2637 = 0.4482 = 44.82%

(c)

There are 6*5*4 ways of selecting one bulb of each type, so the probability of selecting 3 bulbs of each type is

$\frac{6*5*4}{455}=0.2637=26.37\%$

(d)

The probability that it is necessary to examine at least six bulbs until a 75-W bulb is found, supposing there is no replacement, is the same as the probability of taking 5 bulbs one after another without replacement and none of them is 75-W.

As there are 15 bulbs and 9 of them are not 75-W, the probability a non 75-W bulb is $\frac{9}{15}=0.6$

Since there are no replacement, the probability of taking a second non 75-W bulb is now $\frac{8}{14}=0.5714$

Following this procedure 5 times, we find the probabilities

$\frac{9}{15},\frac{8}{14},\frac{7}{13},\frac{6}{12},\frac{5}{11}$

which are

0.6, 0.5714, 0.5384, 0.5, 0.4545

As the events are independent, the probability of choosing 5 non 75-W bulbs is the product

0.6*0.5714*0.5384*0.5*0.4545 = 0.0419 = 4.19%

3 0

3 years ago

0.1x + 9 ≤ 45 what is x?

soldi70 [24.7K]

Hi Robles928518,

0,1x + 9 ≤ 45
0,1x ≤ 45 - 9
0,1x ≤ 36
x ≤ 360

x ∈ ] - ∞ ; 360 ]

5 0

3 years ago

Read 2 more answers

5.1436 rounded to the nearest hundredth

tatiyna

Answer:

5.14

Step-by-step explanation:

ones.tenths hundredths

8 0

3 years ago

Read 2 more answers

A cylinder has a radius of 5cm and a height of 9cm find its total area

Sauron [17]

Answer: 706.5

Step-by-step explanation:

First you have to square the radius. So for this question you multiply 5x5. That makes 25. Then you multiply that with pi ( 3.14 ) and that makes 78.50. Next you multiply it by 9, that makes 706.5.

7 0

3 years ago

Rewrite -4/15 as an equivalent fraction

timofeeve [1]

$(\frac{-4}{5} )$ in the form of Equivalent Fraction can be written as $\frac{-4x}{15x}$ , where "x" is any integer.

As per the question statement, we are provided with a fraction, $(\frac{-4}{5} )$ .

We are required to rewrite the above mentioned fraction in the form of a general Equivalent Fraction.

To solve this question, we need to know what an equivalent fraction is.

Equivalent fractions are those fractions that have different numerators and denominators but are equal to the same value, when simplified.

For example, $(\frac{1}{2}, \frac{2}{4}, \frac{3}{6}, \frac{4}{8})$ all equate to $\frac{1}{2}$ when simplified.

Now, for this case, equivalent fractions of $(\frac{-4}{5} )$ are $(\frac{-8}{30}, \frac{-12}{45}, \frac{-16}{60},...)$ , where

$\frac{-8}{30}=\frac{(-4)*2}{15*2}\\\frac{-12}{45}=\frac{(-4)*3}{15*3}\\ \frac{-16}{60}=\frac{(-4)*4}{15*4}$

i.e., the equivalent fractions of $(\frac{-4}{5} )$ are in the form of $\frac{-4x}{15x}$ , where "x" can be any integer, (...-6, -5, -4, -3, -2, -1, 2, 3, 4, 5, 6...)

Fractions: In mathematics, a fraction is a numerical entity that is not a whole number.

To learn more about fractions, click on the link below.

brainly.com/question/17912

#SPJ9

5 0

1 year ago