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Serga [27]
3 years ago
7

Our school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can

we choose 6 starters if exactly two of the triplets are in the starting lineup?
Mathematics
1 answer:
KatRina [158]3 years ago
7 0

Answer:

990 ways to choose 6 starters out of 14 with exactly two of the three triplets.

Step-by-step explanation:

Ways to choose 2 of the triplets

= C(3,2) = 3! / (2!1!) = 3

Ways to choose the remaining 4 starters out of 11 players left

= C(11,4) = 11! / (4!7!) = 330

Total number of ways to choose 6 starters

= 3*330 = 990

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Error Analysis: Describe the error in the way the difference of the two polynomials is set up and/or
maria [59]

Answer:

  The distributive property is not properly applied to the second polynomial.

Step-by-step explanation:

For whatever reason, it is a common mistake to say that ...

  -(a +b +c) = -a +b +c . . . . WRONG!

Rather, it should be ...

  -(a +b +c) = -a -b -c . . . . CORRECT

6 0
3 years ago
I really Need help solving this problem!
Paraphin [41]

Answer:

Hello,

Answer A : 11.2 ≤ X ≤ 29.2

Step-by-step explanation:

Z=\dfrac{X-20.2}{4.5} \\\\X=4.5*Z+20.2\\\\For\ Z=-2,  \ X=4.5*(-2)+20.2=11.2\\For\ Z=2,  \ X=4.5*2+20.2=29.2\\

8 0
3 years ago
The following table shows a portion of a five-year amortization schedule. A 5-year amortization schedule. Loan amount or princip
kogti [31]

The percentage of the payments made were due to interest is 32.6 %. Then the correct option is B.

<h3>What is the percentage?</h3>

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

The following table shows a portion of a five-year amortization schedule.

A 5-year amortization schedule.

Loan amount or principal: 10,900 dollars.

The interest rate on loan: 10. 95 percent.

The table will be

Month         Payment         Principal         Interest         Balance

  15               236.72            155.87            80.85           8704.27

  16               236.72            157.29            79.43           8546.98

  17               236.72            158.73            77.99            8388.25

  18               236.72            160.18            76.54            8228.07

  19               236.72            161.64            75.08            80.66.43

  20              236.72            163.11             73.61             7903.32

Total payment = 6 × 236.72 = $ 1420.32

Total interest = 80.85 + 79.43 + 77.99 + 76.56 + 75.08 + 73.61

Total interest = $ 463.38

Then the percentage will be

\rm Percentage = \dfrac{463.38}{1420.32}*100\\\\Percentage = 32.625 \approx  32.6\ \%

More about the percentage link is given below.

brainly.com/question/8011401

7 0
3 years ago
Show that the points (0.-1).(2, 1).(0.3) and (-2, 1) are the vertices of a square ABCD.
Inessa05 [86]

The diagram is below

  • A = (0,-1)
  • B = (2,1)
  • C = (0,3)
  • D = (-2,1)

Let's find the distance from A to B using the distance formula.

d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-2)^2 + (-1-1)^2}\\\\d = \sqrt{(-2)^2 + (-2)^2}\\\\d = \sqrt{4 + 4}\\\\d = \sqrt{8}\\\\d \approx 2.828\\\\

The distance from A to B is exactly \sqrt{8} units or approximately 2.828 units. This is the length of side AB.

Through very similar steps, you should find that the other side lengths of BC, CD and AD are all the same.

Since AB = BC = CD = AD, this means we have a rhombus. Recall a rhombus is any quadrilateral with all four sides the same length.

-----------------------------

Let's find the slope of line AB

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{1 - (-1)}{2 - 0}\\\\m = \frac{1 + 1}{2 - 0}\\\\m = \frac{2}{2}\\\\m = 1\\\\

Line AB has a slope of 1.

Through similar steps, you should find the slope of line BC is -1.

Rule: Whenever two slopes multiply to -1, then their corresponding lines are perpendicular.

Based on that rule, lines AB and BC are perpendicular. This means they meet up at a right angle (aka 90 degree angle).

You should find that line CD has a slope of 1, so BC and CD are perpendicular. Lastly, line AD has a slope of -1. So all the slopes mentioned are either +1 or -1. The slopes alternate as you move around the figure. This all shows that any two adjacent sides meet at a 90 degree angle.

Therefore, this figure is a rectangle. Any rectangle has all four angles of 90 degrees.

-----------------------------

The first section showed that we have a rhombus. The second section afterward showed that we also have a rectangle. The combination of a rhombus and a rectangle at the same time leads to a square.

Therefore, quadrilateral ABCD is a square.

5 0
3 years ago
A person leaves her camp at 7:00 a.m. to hike back to her car. The distance from the car in kilometers y after x hours of hiking
FromTheMoon [43]

Answer:

The x axis in the function represents, the number of hours after 7:00 A.M. , the person reaches her car. The person reaches the car at 1:00 P.M.

Step-by-step explanation:

The x axis denotes the no. of hours and and the y axis denotes the distance from the car.

X Intercept is a point where the line intersects the X axis, we can easily notice the fact that at that point, y=0 ie. The person has reached his/her respective car.

The line intersects x at 6.

Therefore, a total of 6 hours are taken from the beginning of the hike.

Thus, the person reaches the car at 1:00 P.M.

6 0
3 years ago
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