What is the range of this function?

Answer:

(a)

[tex]Pr(x = 0) = \frac{^7C_2}{45}[/tex]            [tex]Pr(x = 1) = \frac{^7C_1 * ^3C_1}{45}[/tex]            [tex]Pr(x = 2) = \frac{^3C_2}{45}[/tex]

(b)

[tex]E(x) = \frac{3}{5}[/tex]

Step-by-step explanation:

Given

[tex]n = 10[/tex] --- flashbulbs

[tex]k = 3[/tex] --- defective bulbs

[tex]r = 2[/tex] --- selected

Solving (a): The distribution of x

The total outcome is: [tex]^nC_r[/tex]

This gives:

[tex]^{10}C_2 = 45[/tex]

Having 3 defective bulbs means 7 are not.

When there is no defective bulb among the selected, the probability is:

[tex]Pr(x = 0) = \frac{^7C_2}{45}[/tex]

When 1 is defective:

[tex]Pr(x = 1) = \frac{^7C_1 * ^3C_2}{45}[/tex]

When both are defective

[tex]Pr(x = 2) = \frac{^3C_2}{45}[/tex]

So, the distribution is:

[tex]Pr(x = 0) = \frac{^7C_2}{45}[/tex]

[tex]Pr(x = 1) = \frac{^7C_1 * ^3C_1}{45}[/tex]

[tex]Pr(x = 2) = \frac{^3C_2}{45}[/tex]

Solving (b): The expected value

This is calculated as:

[tex]E(x) = \sum x * Pr(x)[/tex]

So, we have:

[tex]E(x) = x_1 * Pr(x_1) +x_2 * Pr(x_2) + ............... + x_n * Pr(x_n)[/tex]

The equation becomes:

[tex]E(x) = 0* Pr(x=0) +1* Pr(x=1) + 2 * Pr(x=2)[/tex]

[tex]E(x) = 1* Pr(x=1) + 2 * Pr(x=2)[/tex]

[tex]E(x) = Pr(x=1) + 2 * Pr(x=2)[/tex]

From the distribution in (a), we have:

[tex]E(x) = \frac{^7C_1 * ^3C_1}{45} + 2 * \frac{^3C_2}{45}[/tex]

[tex]E(x) = \frac{7 * 3}{45} + 2 * \frac{3}{45}[/tex]

[tex]E(x) = \frac{21}{45} + \frac{6}{45}[/tex]

[tex]E(x) = \frac{21+6}{45}[/tex]

[tex]E(x) = \frac{27}{45}[/tex]

Simplify

[tex]E(x) = \frac{3}{5}[/tex]

Answer:

The time-mean speed of the minivans is of 105.8 seconds.

Step-by-step explanation:

Mean of a data-set:

The mean of a data-set is the sum of all values in the data-set divided by the number of values.

Five minivans, times of: 98.0, 108.0, 113.0, 108.0, 102.0, in seconds.

Thus, the mean is:

[tex]M = \frac{98 + 108 + 113 + 108 + 102}{5} = 105.8[/tex]

The time-mean speed of the minivans is of 105.8 seconds.

Answer:

y=2/3

Step-by-step explanation:

Since y is in the denominator, we take it to the other side to make it the numerator. And 6 also changed sides which results in y=4/6. Reducing to lowest terms we get, y=2/3.

Answer:

the volume of the solid is 1024/3 cubic unit

Step-by-step explanation:

Given the data in the question,

radius of the circular disk = 4

Now if the center is at ( 0,0 ), the equation of the circle will be;

x² + y² = 4²

x² + y² = 16

we solve for y

y² = 16 - x²

y = ±√( 16 - x² )

{ positive is for the top while the negative is for the bottom position }

A = b²

b = 2√( 16 - x² )           { parallel cross section }

A = [2√( 16 - x² )]²

A = 4( 16 - x² )

Now,

VOLUME = [tex]\int\limits^r -rA dx[/tex]

= [tex]\int\limits^4_4 {-4(16-x^2)} \, dx[/tex]

= 4[ 16x - (x³)/3 ]           { from -4 to 4 }

= 4[ ( 64 - 64/3 ) - (-64 = 64/3 0 ]

= 4[ 64 - 64/3 + 64 - 64/3 ]

= 4[ (192 - 64 + 192 - 64 ) / 3 ]

= 4[ 256 / 3 ]

= 1024/3 cubic unit

Therefore,  the volume of the solid is 1024/3 cubic unit

Answer:

x =35

Step-by-step explanation:

The sum of the angles of a triangle add to 180

x+10 +x + 3x-5 = 180

Combine like terms

5x+5 = 180

Subtract 5 from each side

5x+5-5 =180-5

5x = 175

Divide by 5

5x/5 =175/5

x =35

Answer:

c is equal to e

Step-by-step explanation: a

Answer:

-46

Step-by-step explanation:

To find your score, take Bill's score which is -17 and if it is 29 less than, you subtract 29

So, - 17 - 29 is -46

Answer:

Step-by-step explanation:

Answer:

0.3164 = 31.64% probability the team wins all its conference games

Step-by-step explanation:

For each conference game, there are only two possible outcomes. Either the team wins it, or they lose. The probability of winning a game is independent of any other game. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [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]

And p is the probability of X happening.

A football team has a probability of .75 of winning when playing any of the other four teams in its conference.

The probability means that [tex]p = 0.75[/tex], and four games means that [tex]n = 4[/tex]

If the games are independent, what is the probability the team wins all its conference games?

This is P(X = 4). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{4,4}.(0.75)^{4}.(0.25)^{0} = 0.3164[/tex]

0.3164 = 31.64% probability the team wins all its conference games

Answer:

to put the equation into standard for we must multiply the terms on the right side of the equation. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

Step-by-step explanation:

y

=

(

x

−

13

)

(

x

−

12

)

becomes:

y

=

(

x

×

x

)

−

(

x

×

12

)

−

(

13

×

x

)

+

(

13

×

12

)

y

=

x

2

−

12

x

−

13

x

+

156

We can now combine like terms:

y

=

x

2

+

(

−

12

−

13

)

x

+

156

y

=

x

2

+

(

−

25

)

x

+

156

y

=

x

2

−

25

x

+

156

Answer:

B. π = 8C/5

Step-by-step explanation:

Given the following data;

Diameter = ⅝

To find the ratio;

Mathematically, the circumference of a circle is given by the formula;

C = πD

Where;

C is the circumference of a circle.

D is the diameter of a circle.

Substituting the value of D, we have;

C = π * ⅝

Cross-multiplying, we have;

8C = 5π

π = 8C/5

Answer:

I think it might be SAS. (side angle side)

Answer:

Option D (There is no solution) is the correct answer.

Step-by-step explanation:

According to the question, the matrix is:

⇒ [tex]\left[\begin{array}{ccc}1&-5&-4\\0&0&7\end{array}\right][/tex]

The linear equation will be:

⇒ [tex]x-5y=-4[/tex]

and

⇒ [tex]0.x+0.y=7[/tex]

i.e,

                [tex]0=7[/tex] (Not possible)

Thus the above given matrix has no solution. So the above is the correct option.

Answer:

C) f(x) = 1500(2.15)x

Step-by-step explanation:

Got it right on Edge :)

Answer:

B. 4/3pi (7^3)

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

We know the radius is 7

V = 4/3 pi 7^3

Answer:19.82

Step-by-step explanation:

Got it right i did it on a test

Answer:

Thirty rounded to the nearest whole number percent is 30% (%=percent)

Step-by-step explanation:

Well, you see that if you have 30 out of one hundred then that's when all you have to do is go with the same number and just add percent or % to the end.

Please Mark as Brainliest

Hope this Helps

This is just evidence

Answer:

the image is very blurry...

but the answer is 4 ^ (three numbers multiplied together)

I think they are (1/3)(6)(1/2) = 1

so that would be [tex]4^{1}[/tex] = 4

if that last number is an 1/5 ???

(1/3)(6)(1/5) = 2/5

then the answer would be

[tex]\sqrt[5]{4^{2} }[/tex] = [tex]\sqrt[5]{16}[/tex]

Step-by-step explanation:

Here's an answer! :)

Answer:

1/13

Step-by-step explanation:

there are total no of 52 cards

out of that there are 4 queen

propability = tatal no of favorable outcomes / total no of possible outcomes

=4 / 52

=1/13

Answer:

1/13

Step-by-step explanation:

Total cards = 52

Number of Queen = 4

Probability of the chosen card to be queen

                                                                   [tex]=\frac{Number \ of \ queen}{total \ number \ of \ cards}\\\\=\frac{4}{52} \\\\= \frac{1}{13}[/tex]

Answer:

10

Step-by-step explanation:

5

C

3

5!/(3!(5-3)!)

5!/(3!x2!)

120/12

10

In 10 ways can a supermarket manager display 5 brands of cereals

in 3 spaces on a shelf.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

Given:

Total brands of cereals= 5

Using Combination, C(n, r)

= n!/ r! (n- r)!

So, the number of ways

= C(5, 3)

= 5!/(3!(5-3)!) 5

= 5 x 4 x 3! / 3! x 2!

= 5 x 4 /2

= 10

Thus, the total number of ways is 10.

Learn more about Combination here:

https://brainly.com/question/13387529

#SPJ6

Answer:

sim eu também preciso desta respota

Answer:

1/2( 110+42)

Step-by-step explanation:

Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)

<<XYZ = 1/2( 42+110)

Answer:

(A) 89 (B) 91 (C) 92 (D) 95 4.If |x−2| = p, where x < 2, then x+1 equals (A) −2 (B) 3− p (C) |2p−2| (D) 2p−2 5.A

Step-by-step explanation:

Following are the calculation to the find the value of x:

Given:

Please find the question.

To find:

x=?

Solution:

[tex]\frac{71}{7} <\frac{x}{9} < \frac{113}{11}\\\\10 <\frac{71}{7} < 11 \\\\10< \frac{113}{11}<11\\\\\frac{x}{9} >10\\\\x>90\\\\\text{When}\ x=91 \\\\\frac{71}{7} > \frac{91}{9}\\\\x=92\\\\ \frac{71}{7}< \frac{92}{9} <\frac{113}{11}\\\\[/tex]

so, x= 92 \\\\

by compare score value x= 92

Learn more:

brainly.com/question/3922668

Answer:

Given:

Cost = £ 800

Tax = 20%

To find:

The total cost

Solution:

Total cost = Cost + Tax

Tax = 20 % of cost

20 / 100 * 800

Tax = £ 160

Hence,

Total cost =  £ 800 + £ 160

Total cost = £ 960

Answer:

21%

Step-by-step explanation:

Area of one sprinkler

a = πr²

a = π10²

a = 314.159 ft²

8 sprinklers

a = 8 * 314.159

a = 2,513.272

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

area of field

a = lw

a = 80 * 40

a = 3200

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

area not watered

a = 3200 - 2,513.272

a = 686.728

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

percentage not watered

p = 686.728 / 3200 * 100%

p = 21.46025%

Rounded

21%

The new age of the teacher is 25

Answer:

The age of the new teacher is 35

Answer:

y = -x + 8

Step-by-step explanation:

First, plug in the slope.

y = mx + b

y = -1x + b

y = -x + b

Then, plug in the point.

7 = -(1) + b

7 = -1 + b

8 = b

Answer:

[tex]P(x< 240) = 0.0521[/tex]

Step-by-step explanation:

Given

[tex]\bar x = 266[/tex]

[tex]\sigma = 16[/tex]

Required

[tex]P(x < 240)[/tex] --- pregnancy will last less than 240 days

First, calculate the z score

[tex]z = \frac{x - \bar x}{\sigma}[/tex]

Where:

[tex]x = 240[/tex]

So, we have:

[tex]z = \frac{240 - 266}{16}[/tex]

[tex]z = \frac{-26}{16}[/tex]

[tex]z = -1.625[/tex]

So:

[tex]P(x< 240) = P(z < -1.625)[/tex]

From z probability:

[tex]P(z < -1.625) = 0.052081[/tex]

[tex]P(z < -1.625) = 0.0521[/tex] --- approximated

So:

[tex]P(x< 240) = 0.0521[/tex]