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Debora [2.8K]
1 year ago
7

a starting lineup in a basketball consists of two guards, two forwards, and a center. a. a certain college team has on its roste

r 4 centers, 5 guards, 5 forwards, and one individual (x) who can play either guard or forward. how many different starting lineups can be created? (hint: consider lineups without x, then lineups with x as guard, then lineups with x as foward.)
Mathematics
1 answer:
AURORKA [14]1 year ago
3 0

Different starting lineups can be created - 120+60+120=300. A certain college team has on its roster 4 centers, 5 guards, 5 forwards, and one individual (x) who can play either guard or forward.

1. A lineup without x is an example. You must decide.

  • 5 quards, 2 guards;
  • two of the three forwards;
  • from 4 centers, 1 center.

It can be made as -

2C5 × 2C3× 1C4 = 10× 3×4 = 120 ways

2. Consider starting lineups with guard x. You must decide.

  • 2 guards chosen from 6 quards (at least one of them must be x);
  • two of the three forwards;
  • from 4 centers, 1 center.

1C5×2C3×1C4 = 5×3×4 = 60 ways

3. Think about lineups where x is the forward. You must decide.

  • 5 quards, 2 guards;
  • 2 forwards from 4 forwards (x must be one of them);
  • from 4 centers, 1 center.

2C5×1C3×1C4 = 10×3×4 = 120 ways.

Therefore, total number different lineups is - 120+60+120=300.

To learn more about combinations from given link

brainly.com/question/8781187

#SPJ4

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Arada [10]

The Solution:

Given:

Center = (0,0)

Point A = (-5,2) being a point on the circle.

We are required to check if point P = (2,-5) is on the circle.

Solving the given problem graphically, we have:

From the above graph, it is clear that point P(2,-5) is a point on the circle.

8 0
10 months ago
The little Mexican restaurant sells only two kinds of beef burritos mucho beef sandwich Lucho beef last week the restaurant orde
Finger [1]

Answer:

Cost of a single Mucho beef burrito: \$5.5

Cost of a double Mucho beef burrito: \$6.5

Step-by-step explanation:

<h3> The exercise is: "The Little Mexican restaurant sells only two kinds of beef burritos: Mucho beef and Mucho Mucho beef. Last week in the restaurant sold 16 orders of the single Mucho variety and 22 orders of the double Mucho. If the restaurant sold $231 Worth of beef burritos last week and the single neutral kind cost $1 Less than the double Mucho, how much did each type of burrito cost?"</h3>

Let be "x" the the cost in dollars of a single Mucho beef burrito and "y" the cost in dollars of a double Mucho burrito.

Set a system of equations:

\left \{ {{16x+22y=231} \atop {x=y-1}} \right.

To solve this system you can apply the Substitution Method:

1. Substitute the second equation into the first equation and solve for "y":

16(y-1)+22y=231\\\\16y-16+22y=231\\\\38y=231+16\\\\y=\frac{247}{38}\\\\y=6.5

2. Substitute the value of "y" into the second equation and evaluate in order to find the value of "x":

x=6.5-1\\\\x=5.5

5 0
3 years ago
Change the equation of the circle x^2+14x+y^2-10y=14x 2 + 14 x + y 2 − 10 y = 14 into center-radius form of a circle.
jonny [76]

Answer:

The answer to your question is      (x + 7)² + (y - 5)² = 88

Step-by-step explanation:

Equation

                     x²  +  14x  +  y²  - 10y   =  14

Complete perfect trinomial squares

                     x² + 14x + (7)² + y² - 10y + (5)² = 14 + (7)² + (5)²

Simplify

                     x² + 14x + (7)² + y² - 10y + (5)² = 14 + 49 + 25

                     x² + 14x + (7)² + y² - 10y + (5)² = 88

Factor

                     (x + 7)² + (y - 5)² = 88   This is the equation in the form

                     center-radius

7 0
3 years ago
Don’t know the answer to this?
Vaselesa [24]

Answer:

Step-by-step explanation:

The first one.

3 0
3 years ago
X^2 + 8x + c<br> What is c ?
katrin [286]

Answer:

C is a constant ( a value that doesn't change)

Step-by-step explanation:

for example (X^2), here x is a variable with an exponent. (8x), here 8 is a coefficient. making c a constant.

8 0
3 years ago
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