If the police have 8 suspects, how many different ways can they select 5 for a lineup?

Answers

Answer 1

Answer:

Answer:

56 different ways

Step-by-step explanation:

This is a combination question since it deals with selection. For example, if n objects is to be selected from a pool of r objects, this can be done in nCr different ways.

nCr = n!/(n-r)!r!

According to the question, If the police have 8 suspects, the different number of ways 5 can be selected for a line up is expressed as 8C5

8C5 = 8!/(8-5)!5!

8C5 = 8!/(3!)!5!

8C5 = 8*7*6*5!/3*2*5!

8C5 = 8*7*6/3*2

8C5 = 8*7

8C5 = 56 different ways

Hence, the selection of picking 5 for a line up out of 8 suspects can be done in 56 different ways.

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The half-life of a radioactive substance is 200 years. There are 8000 grams of the substance initially. How many grams of the substance are left after 300 years?

Answers

Answer:

There are 2,000 grams left after 300 years.

Step-by-step explanation:

Giving the following information:

The half-life of a radioactive substance is 200 years. There are 8000 grams of the substance initially.

First, we need to calculate the reduction of the substance each year:

Yearly reduction= 8,000/400= 20 grams per year

Now, for 300 years:

300 year reduction= 20*300= 6,000

There are 2,000 grams left after 300 years.

In Exercise, expand the logarithmic expression.
ln(x + 1)2

Answers

Answer:

In(x^2+2x+1)

Step-by-step explanation:

In(x+1)^2 = In(x+1)(x+1) = In(x^2+x+x+1) = In(x^2+2x+1)

use the given endpoint R and the midpoint M to find the coordinates of the other endpoint S. r(3,0) and m(0,5)

Answers

Answer:

s= (-3, 10)

Step-by-step explanation:

x= 0-3=-3

y=5+5=10

Divide write the quotient in lowest term 1 1/3 divided by 1 3/4

Answers

Answer:

7/3 or 2 1/3

Step-by-step explanation:

1 1/3 ÷ 1 3/4

Change to improper fractions

(3*1+1)/3 ÷ (4*1+3)/4

4/3 ÷ 7/4

Copy dot flip

4/3 * 7/4

Rewriting

4/4 * 7/3

7/3

As a mixed number

2 1/3

Answer:

11/3÷13/4

11/3×4/13

44/39=

1.1282

Find the slope given A(1, -1) B(-2, 1)

Answers

Answer:-2 /3

Step-by-step explanation: 1-(-1)/-2-1

1+1/-3

2/-3

-2/3

Carl is balancing his checking account. After comparing the bank statement to his register, he notices an outstanding debit of $58.00.Which shows the correct amount in Carl’s checking account?
$51.75
$109.75
$167.75
$221.87