1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vera_Pavlovna [14]
3 years ago
13

A certain lot consisting of ten items has three defective items and seven nondefective items. How many possible subsets of 2 ite

ms can be chosen from this lot?
21
45
90
Mathematics
1 answer:
Charra [1.4K]3 years ago
4 0

Answer:

45

Step-by-step explanation:

The order in which the items are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

How many possible subsets of 2 items can be chosen from this lot?

Combinations of 2 from a set of 10. So

C_{10,2} = \frac{10!}{2!(10-2)!} = 45

You might be interested in
PLEASE HELP FAST!!!!
nevsk [136]
A8
b0
c3.
d4
e 1 this is it
4 0
2 years ago
Find the area of the shaded portion. Show all work for full credit.
andre [41]
Alright, so first of all, you need to find the area of the circle that is part of the cone-shaped area so you can remove it. You need the formula:
 Area =  \pi  r^{2} ( \frac{c}{360} )where c = angle.

Now plug in the answers, and you get:
A =  \pi 6^{2} ( \frac{120}{360} ).

This would then equal to 12 \pi.


now, essentially, the shape of this ENTIRE area is of 2 right triangles. Divide 120 by 2, you get 60 degrees. You have 2 60/30/90 triangles (shown in the bottom)


Now, what you need to do is to find the area of the entire thing by using the formula to calculate the right triangle area (A = (1/2)bh). You have b, which is 6. To find the h, you use tan(60) = x/6, which gives you 6 \sqrt{3}.

The area of one right triangle of this size would be = 18 \sqrt{3}

Because 2 right triangles, multiply the area by 2 and get: 36 \sqrt{3}

Now, remember the area of that circle in that total area? subtract it from the total area (36 \sqrt{3}) by 12pi and you get 24.65.

The final answer is 24.65

7 0
3 years ago
Read 2 more answers
Whats 30% out of 720,000
Anarel [89]
Percent means parts out of 100
30%=30/100=3/10
3/10 out of 720000 means 3/10 times 720,000=2160000/10=216,000
the answer is 216,000
6 0
3 years ago
Is 4/6 greater than 5/10
Brut [27]
If you convert both fractions so that they both have the same denominator, you will get 20/30 (which is equivalent to 4/6) and 15/30 (which is equivalent to 5/10). 
20/30 > 15/30, so 4/6 is greater than 5/10.
6 0
3 years ago
Read 2 more answers
Xsquared+1/20x-1/20 so I need that to be solved any way possible
VARVARA [1.3K]
Hallo ^_^

Quadratic Equation :
ax² + bx + c = 0

From the task :
x² + 1/20 x = 1/20

Switch sides :
x² + 1/20x - 1/20 = 0

Multiple each sides by 20
20(x² + 1/20x - 1/20) = 0(20)
⇒ 20x² + x - 1 = 0

From that :
a = 20, b = 1 and c = - 1

Solve x using quadratic formula :

x_1x_2 = \frac{-b\pm\sqrt{b^2-4ac}}{2a}

Substitution using the formula :

x_1x_2 = \frac{-1 \pm \sqrt{1^2-4(20)(-1)}}{2(20)} \\\\
x_1x_2 = \frac{-1 \pm \sqrt{81}}{40} \\\\
x_1x_2 = \frac{-1 \pm 9}{40} \\\\

x_1 =  \frac{- 1 + 9}{40} \\\\
x_1 =  \frac{8}{40} \\\\
x_1 =  \frac{1}{5} \\\\

x_2 =  \frac{- 1 - 9}{40} \\\\
x_2 =  \frac{-10}{40} \\\\
x_2 = -  \frac{1}{4} \\\\

\therefore \boxed{x = \frac{1}{5} \ or \ x =-  \frac{1}{4}}

Sorry for my bad english :)
5 0
3 years ago
Other questions:
  • Raise 7 to the 5th power, subtract the result from 9, then multiply what you have by c
    11·1 answer
  • 50 POINTS AGAIN y=2x+5 Complete the missing value in the solution to the equation. (2,__) (I didn't mess up on the number this t
    11·2 answers
  • Isaac wants to buy tomatoes and a loaf of bread. Tomatoes are $1.20 a pound, and a loaf of bread is $2.00. He has $8.00 to spend
    10·1 answer
  • Please help!! I need the answer!!
    14·1 answer
  • Solve the equation:<br> (2x^3+5x^2)(1−2x)=0<br> Its says there are two solutions, please explain
    15·1 answer
  • Fill in the blanks:<br> V=___W=___x=___y=___z=___
    9·1 answer
  • 1. Identify and explain one way in which the movie portrays historical facts accurately in the movie (History vs. Hollywood).
    10·1 answer
  • A rectangular balcony is 14 feet long and 6 feet wide. What is its area?
    6·2 answers
  • Which of the following numbers are integers?<br> 8, -4.1, -9, 1.75, 22, 1/6
    11·2 answers
  • In the diagram below, if AB = 25, AC = 15, and BD = 5, then find the length of DC.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!