Ask question

Ask question

All categories

3 years ago

6

How do you write the standard number 3,500 in scientific notation? A. 3.5 × 101 B. 3.5 × 105 C. 3.5 × 103 D. 3.5 × 104

1 answer:

Svet_ta [14]3 years ago

7 0

Answer:

C 3.5*10^3

Step-by-step explanation:

You might be interested in

. 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

Ron walks 0.5 mile on a track in 10 minutes. Stevie walks 0.25 mile on the track in 6 minutes find the unit rate for each walker

Firlakuza [10]

Answer:

Ron's speed = 3 miles/hour

Stevie's speed = 2.5 miles/hour

On comparing we see Ron is walking faster than Stevie.

Step-by-step explanation:

Given:

Ron takes 10 minutes to walk on a track to cover a distance of 0.5 miles

Stevie takes 6 minutes to walk on a track to cover a distance of 0.25 miles

To find their unit rates in mile per hour and choose the faster one.

Solution:

Unit rate in miles per hour signifies their speeds. Thus, we will find out their speeds.

Ron:

Distance= 0.5 miles

Time = 10 minutes = $10\ min\times \frac{1\ hr}{60\ min}=\frac{1}{6}$ hours

Speed = $\frac{Distance}{Time}=\frac{0.5}{\frac{1}{6}}=0.5\times6=3\ miles/hour$

Stevie

Distance = 0.25 miles

Time = 6 minutes = $6\ min\times \frac{1\ hr}{60\ min}=\frac{1}{10}$ hours

Speed = $\frac{Distance}{Time}=\frac{0.25}{\frac{1}{10}}=0.25\times10=2.5\ miles/hour$

Thus, we have

Ron's speed = 3 miles/hour

Stevie's speed = 2.5 miles/hour

On comparing we see Ron is walking faster than Stevie.

4 0

3 years ago

The movie theater has 250 seats. 225 seats were sold for the current showing. What percent of seats are empty?

disa [49]

Answer:

25

Step-by-step explanation:

8 0

3 years ago

Sylvie finds the solution to the system of equations by graphing. y = x + 1 and y = x – 1 Which graph shows the solution to Sylv

sesenic [268]

Hey user☺☺

The graph will have no solution.

Hope it works

6 0

3 years ago

Read 2 more answers

Grayson is deciding between two truck rental companies. Company A charges an initial fee of $40 for the rental plus $2 per mile

Alexandra [31]

Answer:

A is 10 dollar cheaper than B

Step-by-step explanation:

A : 40 dollars plus 45*2=90

90+40= 130 dollars

B:100 dollars 45*1=45

100+45= 145 dollars

5 0

3 years ago

Read 2 more answers