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3 years ago

How many different three-person relay teams can be chosen from six students?

1 answer:

5 0

The first person can be any one of 6.
   For each of those . . .
The second person can be any one of the remaining 5.
   For each of those . . .
The third person can be any one of the remaining 4.

Total number of ways to pick 3 people out of 6 = (6 x 5 x 4) = 120 ways.

BUT . . .

For each 3-person team, there are (3 x 2 x 1) = 6 ways to pick
the same three people.

In the 120 ways to pick 3 people, you'll find each different
group of 3 people picked 6 times, in a different order.

The number of different 3-person teams is

   120 / 6 = 20 teams .

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Zena needs a salesperson. Salesperson A is offering his services for an initial $100 in addition to $5 per hour. Salesperson B i

77julia77 [94]

Answer:

Step-by-step explanation:

The correct question is

Zena needs a salesperson. Salesperson A is offering his services for an initial $50 in addition to $5 per hour. salesperson B is offering her services for an initial $40 in addition to $7 per hour. When will the two coaches charge the same amount of money?

Let

x ----> the number of hours

y ----> the total charge

we know that

Salesperson A

------> equation A

Salesperson B

------> equation B

To find out when the two coaches charge the same amount of money, equate equation A and equation B and solve for x

7x+40=5x+50

7x-5x=50-40

2x=10

<h2>x=5 hours i think just im not sure but i tried</h2>

7 0

3 years ago

Read 2 more answers

The smiths plan to recarpet their family room, which measures 15 ft. by 20 ft. how many square yards of carpet are needed? 30 33

BaLLatris [955]

15x20=300
300 square feet is 33.33333333333333333333333333333333333 square yards (divide by 9)
the answer is 33

6 0

3 years ago

Read 2 more answers

Write an algebraic expression: 4 groups of y.

Dvinal [7]

4y is your answer because ffor is the mathmatical term for multiplying in any word problem.

8 0

3 years ago

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According to a recent Catalyst Census, 16% of executive officers were women with companies that have company headquarters in the

Elanso [62]

Answer: 0.0885

Step-by-step explanation:

Given : According to a recent Catalyst Census, 16% of executive officers were women with companies that have company headquarters in the Midwest.

i.e. p= 0.16

Sample size : n= 154

Now, the probability that more than 20% of this sample is comprised of female employees is given by :-

$P(p>0.20)=P(z>\dfrac{0.20-0.16}{\sqrt{\dfrac{0.16(1-0.16)}{154}}})$

[∵ $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$ ]

$=P(z>1.35)\approx1-P(z\leq1.35)=1-0.9115=0.0885$ [Using the standard z-value table]

Hence, the required probability = 0.0885

6 0

3 years ago

3. How many solutions does the system of equations have? 2x=-10y+ 6 and x+5y=3

ozzi

Answer:

<h2>3. Infinitely many</h2>

Step-by-step explanation:

$\left\{\begin{array}{ccc}ax+by=c\\dx+ey=f\end{array}\right\\\\(1)\\\text{if}\ a=d,\ b=e,\ c=f,\ \text{then the system of equations has infinitely many solutions}\\Example:\\\left\{\begin{array}{ccc}2x-3y=5\\2x-3y=5\end{array}\right\\(2)\\\text{if}\ a=d,\ b=e,\ c\neq f,\ \text{then the system of equations has no solution}\\Example:\\\left\{\begin{array}{ccc}2x-3y=5\\2x-3y=-5\end{array}\right$

$(3)\\\text{if}\ a\neq d\ \text{or}\ b\neq e,\ \text{then the system of equations has infinitely many solutions}\\Example:\\\left\{\begin{array}{ccc}x-3y=5\\2x-3y=5\end{array}\right$

$\text{We have:}\\\\\left\{\begin{array}{ccc}2x=-10y+6&\text{add 10y to both sides}\\x+5y=3\end{array}\right\\\left\{\begin{array}{ccc}2x+10y=6&\text{divide both sides by 2}\\x+5y=3\end{array}\right\\\left\{\begin{array}{ccc}x+5y=3\\x+5y=3\end{array}\right$

4 0

3 years ago