Find the slope, if it exists, of the line containing the points (-4,0) and (-5,3)

Mrs.Steﬀen’s third grade class has 30 students in it. The students are divided into three groups(numbered 1, 2,and 3),each havin

qaws [65]

Answer:

a. $\\ 10! = 3628800$ ;

b. $\\ 10!*10!*10! = 47784725839872000000 = 4.7784725839872*10^{19}$

Step-by-step explanation:

We need here to apply the Multiplication Principle or the Fundamental Principle of Counting for each answer. Answer b needs an extra reasoning for being completed.

The Multiplication Principle states that if there are n ways of doing something and m ways of doing another thing, then there are n x m ways of doing both (Rule of product (2020), in Wikipedia).

<h3>In how many ways can ten students line up? </h3>

There are ten students. When one is selected, there is no other way to select it again. So, no repetition is allowed.

Then, in the beginning, there are 10 possibilities for 10 students; when one is selected, there are nine possibilities left. When another is selected, eight possibilities are left to form the file, and so on.

Thus, we need to multiply the possibilities after each selection: that is why the Multiplication Principle is important here.

This could be expressed mathematically using n!:

$\\ n! = n * (n-1)! * (n-2)! *...* 2*1.$

For instance, $\\ 5! = 5 * (5-1)! * (5-2)! *...*2*1 = 5 * 4 * 3 * 2 * 1 = 120.$

So, for the case in question, the ten students can line up in:

$\\ 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800$ ways to line up in a single file.

<h3>Second Question</h3>

For this question, we need to consider the former reasoning with extra consideration in mind.

The members of Group 1 can occupy only the following places in forming the file:

$\\ G1 = \{ 1, 4, 7, 10, 13, 16, 19, 22, 25, 28\}^{th}$ places.

The members of Group 2 only:

$\\ G2 = \{ 2, 5, 8, 11, 14, 17, 20, 23, 26, 29\}^{th}$ places.

And the members of Group 3, the following only ones:

$\\ G3 = \{ 3, 6, 9, 12, 15, 18, 21, 24, 27, 30\}^{th}$ places.

Well, having into account these possible places for each member of G1, G2 and G3, there are: 10! ways for lining up members of G1; 10! ways for lining up members of G2 and, also, 10! ways for lining up members of G3.

After using the Multiplication Principle, we have, thus:

$\\ 10! * 10! * 10! = 47784725839872000000 = 4.7784725839872 *10^{19}$ ways the students can line up to come in from recess.

3 0

1 year ago

Kelly blends coffee. She mixes brand A costing $6 per kilogram with brand B costing $8 per kilogram. How many kilograms of each

sukhopar [10]

Step-by-step explanation:

Let

x

be the kg of coffee of brand A in the mix and

y

be the kg of coffee of brand B in the mix.

The total kg must be

50

.

x

+

y

=

50

The cost per kg of the mix must br

$

7.20

. For this, the total cost of the mix will be

6

x

+

8

y

, so the total cost per kg of the mix will be

6

x

+

8

y

50

.

6

x

+

8

y

50

=

7.20

Now that we have our two equations, we can solve.

6

x

+

8

y

=

7.20

⋅

50

6

x

+

8

y

=

360

From the first equation, we can multiply both sides by

6

to get:

6

x

+

6

y

=

300

Subtracting, we get:

2

y

=

60

y

=

30

Thus, we need

30

kg of brand B in our mix. This means that

50

−

30

=

20

kg will be of brand A.

6 0

1 year ago

Romeo paid $380.75 in car repairs. The sales Tax rate is 7.5% . Which of the following is a responsible estimate for the total R

rusak2 [61]

Answer: $380.75x0.075=28.55625

28.55625+380.75=409.30625

$409.30625~$409.31

Answer: $409.31

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Which numbers are irrational? Check all that apply.

SVETLANKA909090 [29]

Answer:

D, E, F are correct

Step-by-step explanation:

I know this because the square root of 196 is 14, the square root of 80 is 8.94427191 and if you square that you'll get 80. The square root of 16 is 4. So that is why A, B, C are wrong because they are all rational. Pi is infinite so it is irrational, the square root of 12 cannot be multiplied by itself to make 12 so it is irrational, and 7 divided by 18 is 3.8 and the 8 goes on for infinity.

6 0

1 year ago

Read 2 more answers

During the 2010 baseball season, the number of wins for three teams was three consecutive integers. Of these three teams, the

uysha [10]

Answer:

76075, 76076, 76077

Step-by-step explanation:

There are 3 teams; Team A, Team B and Team C

Team A has most wins

Team C has least wins

Team B is in between

All these will be consecutive numbers.

Team B: x

Team A: x + 1 (most wins)

Team C: x - 1 (least wins)

Team A + Team B + Team C = Total number of wins

x + x + 1 + x - 1 = 228228

3x = 228228

x = 76076

Wins of Team B : x = 76076

Wins of Team A : x + 1 = 76076 + 1 = 76077

Wins of Team C : x - 1 = 76076 - 1 = 76075

Therefore, in the 2010 season, Team A had 76077 wins, Team B had 76076 wins and Team C had 76075 wins.

!!

6 0

1 year ago