There are 8 runners in a race. What is the probability that Abby, Becca, and Carmen place first, second, and third in any order?

2 answers:

8 0

Well there are equally 8 runners in the race , and abby and becca and carmen are three of them . now the chances of them getting first , second , and third would be 3 out of 8 or 3 over 8 .

Mkey [24]1 year ago

3 0

$|\Omega|=8!\\
|A|=3!\cdot5!\\\\
P(A)=\dfrac{3!5!}{8!}=\dfrac{2\cdot3}{6\cdot7\cdot8}=\dfrac{1}{56}\approx1,8\%$

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A karate center has 120 students. The director wants to set a goal to motivate her instructors to increase student enrollment. U

iVinArrow [24]

A) Plan A requires for a percentage increase of a number of students. This means that year after year the number of new students will increase. Plan B requires for a constant number of new students each year. This means that year after year the percentage increase would get smaller.

B) To solve this problem we will use formula for a growth of population:
$final = initial * (1+percentage)^{t}$
Where:
final = final number of students
initial = initial number of students
percentage = requested percentage increase
t = number of years

We can insert numbers and solve for t:
$240= 120* (1+0.12)^{t} \\ 2=1.12^{t} \\ log2=log(1.12^{t} ) \\ log2=t*log1.12 \\ t= \frac{log2}{log1.12} \\ t=6.12years$

For Plan B we can use simple formula
increase = 120
increase per year = 20
number of years = increase / (increase per year) = 120 / 20 = 6 years

Plan B is better to double the enrollment.

C)We use same steps as in B) to solve this.


$360= 120* (1+0.12)^{t} \\ 3=1.12^{t} \\ log3=log(1.12^{t} ) \\ log3=t*log1.12 \\ t= \frac{log3}{log1.12} \\ t=9.69years$

For Plan B we can use simple formula
increase = 240
increase per year = 20
number of years = increase / (increase per year) = 240 / 20 = 12 years

Plan A is better to triple the enrollment.

3 0

2 years ago

A circle is divided into 9 uneven "pie" shaped pieces. Each section is labeled 1, 2, ... , 9. The circle is then spun and the nu

8_murik_8 [283]

There are three outcomes of 4 out of eighteen outcomes, so the fraction of angle of spinner numbered 4 is $\frac{3}{8}$

7 0

2 years ago

Read 2 more answers

A company that is selling computer tablets has determined that it regularly makes a net profit of $180 for each computer tablet

Gekata [30.6K]

Answer:

Considering the prediction of people who will fill out the form and receive the refund, the company should expect its net profit to drop to:

$174.6 per computer tablet.

Step-by-step explanation:

The benefit per tablet before the rebate program is $180 per computer tablet, however, once the rebate program is implemented, 18% of people who purchase their computer tablet are expected to complete the form and obtain the VISA card, which would reduce the benefit as shown below:

18% benefit from computer tablets = original benefit - refund value.
18% benefit from computer tablets = $180 - $30 = $150

With this we identify that 18% of computer tablets will have a benefit reduced to $150, however, as the remaining percentage of tablets (82%) will still have the benefit of $180, the general benefit must be calculated to have a single value, as it's shown in the following:

Overall benefit = Percentage of tablets with reimbursement * Benefit of tablets with reimbursement + Percentage of tablets without reimbursement * Benefit of tablets without reimbursement.
General profit = 18% * 150 + 82% * 180
General profit = $ 174.6

By having a $ 30 rebate on 18% of the tablets, the overall benefit drops to $174.6.

6 0

2 years ago

a rectangular piece of paper 71 cm long and 10m wide . a cylinder is formed by rolling the paper along its length , find volume

natka813 [3]

Answer:

Volume=355 cm³

Step-by-step explanation:

I assume it should be 10 cm, not 10 m. If it is 10 m, everything will have to be adjusted.

Circumference = 2 $\pi$ r