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3 years ago

11

8 is 20% of what number?

1 answer:

AnnyKZ [126]3 years ago

5 0

8 is 20% of 40
(8*5=40)

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

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

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 <em>the events are disjoint</em>, 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, <em>supposing there is no replacement</em>, 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

Please hurry i neeeed this fast!!!

lina2011 [118]

Answer:

consecutive interior angles

Step-by-step explanation:

inside of the angle and consecutive to each other

5 0

3 years ago

Read 2 more answers

Maggie needs to spend at least six hours each week practicing the piano. She has already practiced 3

grandymaker [24]

Answer:

t ≥ 1.5

Step-by-step explanation:

Lets take time for practicing the piano to be t

The number of hours to practice per week should be at least 6 hours

This is written as t ≥ 6

She already practiced 3 hours this week, thus the remaining hours to practice should be

t ≥ 3

The minimum remaining hours to practice for the remaining 2 days should be

t=3

If these hours are evenly divided, then in a single day she should practice

for t ≥ 1.5

8 0

3 years ago

Logariths, please help

Valentin [98]

Answer:

<em>{ - 2 , 8 } </em>

Step-by-step explanation:

$log_{4}$ ( x² - 6x ) = 2

4² = ( x² - 6x )

x² - 6x - 16 = 0

- 6 = - 8 + 2

- 16 = - 8 * 2

( x - 8 )( x + 2 ) = 0 ⇒ $x_{1}$ = - 2 , $x_{2}$ = 8

<em>{ - 2 , 8 }</em>

3 0

2 years ago

Find the distance between the pair of points.

SVEN [57.7K]

Answer:

Distance is $\sqrt{290}$ units

Step-by-step explanation:

Use the distance formula which is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ where $d$ is the distance between points $(x_1,y_1)$ and $(x_2,y_2)$

We are given that $(x_1,y_1)$ is $(-6,-23)$ and $(x_2,y_2)$ is $(-23,-24)$ , therefore the distance between the two points is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$d=\sqrt{(-23-(-6))^2+(-24-(-23))^2}$

$d=\sqrt{(-23+6))^2+(-24+23))^2}$

$d=\sqrt{(-17)^2+(-1)^2}$

$d=\sqrt{289+1}$

$d=\sqrt{290}$

Therefore, the distance between $(-6,-23)$ and $(-23,-24)$ is $\sqrt{290}$ units.

3 0

2 years ago