Let A= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose an element of A is randomly selected. What is the probability that it belongs to {1, 2}U{2, 6, 7, 9}U{5, 6, 7).​

Answer:

0.0242 = 2.42% probability that all three are UCR shirts.

Step-by-step explanation:

The shirts are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

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

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

4 + 7 = 11 shirts mean that [tex]N = 11[/tex]

4 UCR shirts mean that [tex]k = 4[/tex]

3 are pulled, which means that [tex]n = 3[/tex]

What is the probability that all three are UCR shirts?

This is [tex]P(X = 3)[/tex]. So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,11,3,4) = \frac{C_{4,3}*C_{7,0}}{C_{11,3}} = 0.0242[/tex]

0.0242 = 2.42% probability that all three are UCR shirts.

The probability that all three are UCR shirts is 0.0242 or 2.42%.

Given that,

Suppose you have 4 UCR shirts and 7 shirts from other universities that you got when trying to decide where to go to college.

Whilst packing for a weekend of camping with friends, you reach into your drawer full of university shirts and pull three out at random.

We have to determine,

What is the probability that all three are UCR shirts.

According to the question,

The probability of x successes is given by the following formula:

[tex]P (X=x) = \ (h,k,x,N) = \ \dfrac{^kC_x \ \times \ ^{N-k} C_n_-_k} {^NC_n}[/tex]

Where, x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Then,

N = 4 + 7 = 11 shirts  , k =4 UCR shirts , n = 3 are pulled random

Therefore,

Substitute the values in the formula,

[tex]P (X=x) = \ (n,k,x,N) = \ \dfrac{^kC_x \ \times \ ^{N-k} C_n_-_k} {^NC_n}\\\\P (X=x) = \ (3,4,3,11) = \ \dfrac{^4C_3 \ \times \ ^{11-4} C_3_-_k} {^11C_3}\\\\P (X=3) = \ (3,4,3,11) = \ \dfrac{^4C_3 \ \times \ ^{7} C__0} {^{11}C_3}\\\\P(X=3) = P (X=3) = \ (3,4,3,11) = \dfrac{4}{1320}\\\\P (X=3) = \ (3,4,3,11) = 0.0242[/tex]

Hence, The probability that all three are UCR shirts is 0.0242 or 2.42%.

To know more about Probability click the link given below.

https://brainly.com/question/20912064

Step-by-step explanation:

x = (7±√193)/18

Answer:

x=3

Step-by-step explanation:

2 triangles are proportional so we have

4/6=x/4,5

--> x=(4.4,5)/6=3

You can also use sin cos but this way is faster

Answer:

Step-by-step explanation:

First term = a =4

Common difference = d = 2nd term - first term

d = 8 - 4 = 4

Last term = l = 400

First we have to fin the number of terms 'n'

l = a + (n-1)d

4 + (n-1)*4 = 400

4 + 4n- 4 = 400

      4n = 400     {Divide both sides by 4}

         n = 400/4

n = 100

[tex]S_{n}=\frac{n}{2}(a + l)\\\\ = \frac{100}{2}*(4+400)\\\\=50 * 404\\\\= 20200[/tex]

Answer:

20200

Step-by-step explanation:

a=1  ×  4=4

a=2  ×  4=8

a=3  ×  4=12

a = 4  × 4 = 16

400 = 4 + ( n - 1 ) 4]

400 = 4 + 4n - 4

4n = 400

400 / 4n

n = 100

100 / 2 [ 4 + 400 ]

50 [ 404 ]

50 × 404

= 20200

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

x ≥6

Step-by-step explanation:

Given the product:

√(x-6)*√(x+3)

The function has to be defined if x ≥0

Hence;

√(x-6)*√(x+3)≥0

Find the product

√(x-6)(x+3)≥0

Square both sides

(x-6)(x+3)≥0

x-6≥0 and x+3≥0

x≥0+6 and x ≥0 - 3

x ≥6 and x ≥-3

Hence the required inequality is x ≥6

Answer:

The correct answer is 0.13

Answer:

ya

Step-by-step explanation:

Answer:

[tex]f(12) = 323.02[/tex]

[tex]f(12) = 16.7 * 1.28^{12[/tex]

Step-by-step explanation:

Given

[tex]f(-2.5) = 9[/tex]

[tex]f(7) = 91[/tex]

[tex]f(12) = 16.7 * 1.28^{12[/tex]

Required

[tex]f(12)[/tex]

An exponential function is:

[tex]f(x) = ab^x[/tex]

[tex]f(-2.5) = 9[/tex] implies that:

[tex]9 = ab^{-2.5}[/tex]

[tex]f(7) = 91[/tex] implies that:

[tex]91 = ab^7[/tex]

Divide both equations

[tex]91/9 = ab^7/ab^{-2.5}[/tex]

[tex]91/9 = b^7/b^{-2.5}[/tex]

Apply law of indices

[tex]91/9 = b^{7+2.5}[/tex]

[tex]10.11 = b^{9.5}[/tex]

Take 9,5th root of both sides

[tex]b = 1.28[/tex]

So, we have:

[tex]9 = ab^{-2.5}[/tex]

[tex]9 = a * 1.28^{-2.5}[/tex]

[tex]9 = a * 0.54[/tex]

[tex]a = 9/0.54[/tex]

[tex]a = 16.7[/tex]

f(12) is calculated as:

[tex]f(x) = ab^x[/tex]

[tex]f(12) = 16.7 * 1.28^{12[/tex]

[tex]f(12) = 323.02[/tex]

Answer:

Step-by-step explanation:

In a parallelogram, opposite angles are equal.

∠G = ∠E

5x - 9 = 3x + 11

Add 9 to both sides

5x = 3x + 11 + 9

5x = 3x + 20

Subtract 3x from both sides

5x-  3x = 20

2x = 20

Divide both sides by 2

x = 10

∠G = 5x - 9

     = 5*10 - 9

     = 50 - 9

∠G = 41°

∠G = ∠E = 41°

In parallelogram, adjacent angles are supplementary.

∠G + ∠D = 180

41 + ∠D = 180

     ∠D = 180 - 41

   ∠D = 139

∠D = ∠F = 139°

Answer:

[tex]Apple \to 4[/tex]

[tex]Banana \to 4[/tex]

[tex]Cherry \to 5[/tex]

Step-by-step explanation:

Given

[tex]A \to Apple[/tex]

[tex]B \to Banana[/tex]

[tex]C \to Cherry[/tex]

From the rows, the equation is:

[tex]B + 2A =12[/tex] --- (1)

[tex]2B + C = 13[/tex] --- (2)

[tex]A + 2C = 14[/tex] --- (3)

Make A the subject in: [tex]A + 2C = 14[/tex]

[tex]A = 14 -2C[/tex]

Substitute [tex]A = 14 -2C[/tex] in [tex]B + 2A =12[/tex]

[tex]B + 2(14 - 2C ) = 12[/tex]

[tex]B + 28 - 4C = 12[/tex]

Make B the subject

[tex]B = 4C - 28 +12[/tex]

[tex]B = 4C -16[/tex]

Substitute [tex]B = 4C -16[/tex] in [tex]2B + C = 13[/tex]

[tex]2(4C - 16) + C = 13[/tex]

[tex]8C - 32 + C = 13[/tex]

Collect like terms

[tex]8C + C = 13+32[/tex]

[tex]9C = 45[/tex]

Divide by 9

[tex]C = 5[/tex]

Recall that:

[tex]B = 4C -16[/tex]

[tex]B =4*5-16[/tex]

[tex]B =20-16[/tex]

[tex]B =4[/tex]

Recall that:

[tex]A = 14 -2C[/tex]

[tex]A= 14 -2*5[/tex]

[tex]A= 14 -10[/tex]

[tex]A =4[/tex]

Hence:

[tex]Apple \to 4[/tex]

[tex]Banana \to 4[/tex]

[tex]Cherry \to 5[/tex]

Answer: 1,6         2,2       5,0    These are the correct answers.

Step-by-step explanation:

Answer:

8.58

Step-by-step explanation:

the length of minor arc XZ

= 82/360 × 2 × 3.14 × 6

= 8.58 in

Answer:

11

Step-by-step explanation:

D+16/3=17 the steps?

1. D+16/3=17

Divide 16/3.

D+6 = 17

2. subtract 6 from both side.

D = 11.

Answer:

9×9=72

8×8=64

8×7=56

5×4=20

Answer

9x9=81

8x8=64

8x7=56

5x4=20

Step-by-step explanation:

9514 1404 393

Answer:

  20 = 2 + (7 -4) × 6

Step-by-step explanation:

The Order of Operations requires the parentheses be evaluated first, then the multiplication performed. Finally, the addition is performed.

If each of the blanks is filled with a single digit, the result of the multiplication must be a composite number greater than 10. Those are 12, 14, 15, 16, 18, 20. For the expression shown above, we have chosen to make the product be 18. That means the first blank is filled with 2 and the remaining blanks must evaluate to one of the products 2×9 or 3×6.

We have chosen 6 for the last blank, so the two blanks in parentheses must have a difference of 3. The digits 2 and 6 cannot be used, leaving possible choices as (3-0), (4-1), (7-4), (8-5).

Our final expression is chosen to be ...

  20 = 2 +(7 -4)×6

Answer:

10k ÷ 10 + 1 = k + 1

Step-by-step explanation:

LHS

10k ÷ 10 + 1

10(9) ÷ 10 + 1

90 ÷ 10 + 1

10

RHS

k + 1

9 + 1

10

10k ÷ 10 + 1 = 10

Answer:

6.8 ounces

Step-by-step explanation:

1 lb = 16 oz

3.40/8 * 16 = 6.8

The slope should be -1/2, because the line goes down 1 unit and then right 2 units.

Also it would be y = -1/2x+1 in y=mx+b.

Answer:

x = 30.5 degree

Step-by-step explanation:

take angle x as reference angle

using sin rule

sin x = opposite / hypotenuse

sin x = 3.4 / 6.7

sin x = 0.507

x = [tex]sin^{-1} (0.507)[/tex]

x = 30.46

x = 30.5 degree

Answer:

x=-6

Step-by-step explanation:

see the image below:)

Answer:

this is an accurate equation because the square root of 3•3•5•5•7•7 is 105 & 3•5•7 is also 105, making them equal! i’m sorry i also don’t understand what the question is asking, but i hope this helped :/

Answer:

0.333

Step-by-step explanation:

2^4-6(6)+3(6)÷2×3

=16-36+18÷6

=-2÷6=0.333

Answer:

Area = 105.6 square cm

Step-by-step explanation:

[tex]Area \ of \ circle = \pi r^2\\Area \ of \ semi-circle = \frac{1}{2} \pi r^2 = \frac{1}{2} \times 3.142 \times 8.2^2 = 105.6cm^2[/tex]

Answer:

4

Step-by-step explanation:

yes

Answer:

36 green apples

Step-by-step explanation:

Red=40%

Green =x%

40/100 × 60apples

0.4×60

24red apples

so 60-24

36green apples

Answer:

b) 36.

Step-by-step explanation:

Justicemoya35 has an excellent answer, but I will provide a slightly different approach!

According to the word problem, the box contains 60 apples.

If 40% of the apples are red, then 60% of the apples are green.

As I mentioned before, there are 60 apples; 60% of the 60 apples are green.

This means we have the find 60% of 60.

We can find the percentage of a number by using this formula:

60% OF 60

[tex]\frac{is}{of} =\frac{percent}{100}[/tex]

[tex]\frac{x}{60} =\frac{60}{100}[/tex]

Now that I've correctly set up the problem, we cross multiply, then divide the products.

[tex]60*60=3600[/tex]

[tex]100*x=100x[/tex]

[tex]3600/100x=36[/tex]

[tex]x=36.[/tex]

Therefore, 36 apples are red.

Answer:

281

Step-by-step explanation:

(Sorry I'm not sure exactly if that's what you were looking for!!) I may be wrong! The 140 5/10 part messed me up a little bit because I don't know if it was 140 and 5/10 (All as one number) so I solved accordingly! I hope that helps!