The difference of 8 and a number X is 36

Thirteen people on a softball team show up for a game. a)How many ways are there to choose 10 players to take the field? b)How m

marishachu [46]

Answer:

a) 286

b) 1,037,836,800

c) 285

Step-by-step explanation:

a) Since order is not important, the total possible number of ways to choose 10 players out of 13 is the following combination:

$C(13,10)=\frac{13!}{(13-10)!10! } \\C(13,10)=\frac{13*12*11*10!}{(3*2*1)10! }\\C(13,10) = 286$

b) The total number of possibilities to assign positions by the selecting 10 players is the permutation of 13 players for 10 positions:

$P(13,10) = \frac{13!}{(13-10)!}\\P(13,10) = 13*12*11*10*9*8*7*6*5*4\\P(13,10) =1,037,836,800$

c) The number of ways to pick 10 players including at least one woman is equal to the total number of ways to pick 10 players (found in item a) minus the the number of ways to pick 10 players without picking a single woman.

Since there 10 male players for 10 positions, there is only one possible way to pick a team without women, therefore:

$P=286-1 =285$

6 0

3 years ago

Given the circle with the equation (x - 3)2 + y2 = 49, determine the location of each point with respect to the graph of the cir

Bas_tet [7]

To find out if a point is inside, on, or outside a circle, we need to substitute the ordered pair into the equation of the circle:
(x-xc)^2+(y-yc)^2=r^2
where (xc,yc) is the centre of the circle, and r=radius of the circle.

If the left-hand side [(x-xc)^2+(y-yc)^2] is less than r^2, then point (x,y) is INSIDE the circle. If the left-hand side is equal to r^2, the point is ON the circle.
Finally, if the left-hand side is greater than r^2, the point is OUTSIDE the circle.

For the given problem, we have xc=3, yc=0, or centre at (3,0), r=sqrt(49)=7
(x-xc)^2+(y-yc)^2=r^2 => (x-3)^2+y^2=7^2

A. (-1,1),
(x-3)^2+y^2=7^2 => (-1-3)^2+1^2=16+1=17 <49 [inside circle]

B. (10,0)
(x-3)^2+y^2=7^2 => (10-3)^2+0^2=49+0=49 [on circle]

C. (4,-8)
(x-3)^2+y^2=7^2 => (4-3)^2+(-8)^2=1+64=65 > 49 [outside circle]

5 0

3 years ago

I need help with all of them

olga nikolaevna [1]

7. Is 45
10. is 15
8.32

6 0

3 years ago

Read 2 more answers

Four tanks each had 54 litres and 750ml. what is their total capacity in litres

Furkat [3]

Answer: 219 I beleive

Step-by-step explanation: 54(4)+(.750)4=219

5 0

3 years ago

Read 2 more answers

Explain why their are no solutions to the system of inequalities y ≤2x-5 y ≥2x+1

rosijanka [135]

Answer:

Sorry this is late and I think this is right.

They are both parallel, they have the same slope, and do not intersect. If you were to draw a slope out for it, you would find this to be true.

For example: Say the question called for you to explain why there aren't any solutions to these system of inequalities:

y < - 1/2x -3

y > 1/2x + 2

y= -x/2 -3 and y= -x/2 + 2 have the same exact slope, are parallel, and never intersect. The first line is 5 units below the second line when x = 0. Because the lines are parallel, it is always below the second line. The solutions of y < - x/2 -3 are the points in the plane below the first line. The solutions of y > 1/2 + 2 are points above the second line.

I hope this helps you. Good luck on whatever you're working on and stay safe! Please let me know if this helped you or didn't.

7 0

4 years ago