Henry constructed circle A with a radius of 4 units. He then created a sector
as shown in the figure below. Which of the following expressions would help
him find the area of the shaded sector?

Answer:

a) 0.3087 = 30.87% probability that exactly two iPhones will end up being serviced under warranty.

b) 0.4718 = 47.18% probability that at least two iPhones will end up being serviced under warranty

c) The expected number of iPhones in the family that require service is 1.5.

d) The standard deviation of the number of iPhones in the family that requires service is 1.0247.

Step-by-step explanation:

For each iPhone, there are only two possible outcomes. Either they have battery issues under warranty, or they do not. iPhones are independent. This means that we use the binomial probability distribution 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.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Thirty percent of such iPhones will need battery service while under warranty.

This means that [tex]p = 0.3[/tex]

A family owns 5 iPhones produced within the time frame of potential faulty production.

This means that [tex]n = 5[/tex]

(a) What is the probability that exactly two iPhones will end up being serviced under warranty?

This is P(X = 2).

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

[tex]P(X = 2) = C_{5,2}.(0.3)^{2}.(0.7)^{3} = 0.3087[/tex]

0.3087 = 30.87% probability that exactly two iPhones will end up being serviced under warranty.

(b) What is the probability that at least two iPhones will end up being serviced under warranty?

This is:

[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]

So

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

[tex]P(X = 2) = C_{5,2}.(0.3)^{2}.(0.7)^{3} = 0.3087[/tex]

[tex]P(X = 3) = C_{5,3}.(0.3)^{3}.(0.7)^{2} = 0.1323[/tex]

[tex]P(X = 4) = C_{5,4}.(0.3)^{4}.(0.7)^{1} = 0.0284[/tex]

[tex]P(X = 5) = C_{5,5}.(0.3)^{5}.(0.7)^{0} = 0.0024[/tex]

[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.3087 + 0.1323 + 0.0284 + 0.0024 = 0.4718[/tex]

0.4718 = 47.18% probability that at least two iPhones will end up being serviced under warranty.

(c) What is the expected number of iPhones in the family that require service?

[tex]E(X) = np = 5*0.3 = 1.5[/tex]

The expected number of iPhones in the family that require service is 1.5.

(d) What is the standard deviation of the number of iPhones in the family that requires service?

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{5*0.3*0.7} = 1.0247[/tex]

The standard deviation of the number of iPhones in the family that requires service is 1.0247.

Answer:

132 feet

Step-by-step explanation:

Volume = 11×3×4 = 132 feet

Answer:

No

Step-by-step explanation:

In order for the shapes to be congruent, corresponding parts must be congruent.  The corresponding angles are NOT congruent, so the shapes are not congruent.

9514 1404 393

Answer:

  A, C, B

Step-by-step explanation:

It is helpful to remember the trig identities ...

  sin = 1/csc

  cos = 1/sec

  tan = 1/cot

__

1. sin(θ)cos(θ)sec(θ)csc(θ) = (sin(θ)csc(θ))(cos(θ)sec(θ)) = (1)(1) = 1 . . . matches A

2. 1/cot²(θ)·sec(θ)cos(θ) = 1/(1/tan²(θ))·(1) = tan²(θ) . . . matches C

3. tan(θ)/cot(θ) = tan(θ)/(1/tan(θ)) = tan²(θ) . . . matches B

Answer:

1.sin Θ cos Θ sec Θ csc Θ

sinocoso×1/coso ×1/sino=1

1. is the required answer

2.1/(cot^2Θ) * sec Θ cos Θ

=sin²o/cos²o×1/coso×coso

=sin²o/cos²o

tan²o is answer

3.tan Θ/ cot Θ

sino/coso/(coso/sino)

sin²o/cos²o

tan²ois answer here o = theta

Answer:

Check pdf

Step-by-step explanation:

Answer:

( x +1 ) ( x + 3 )

Answer:

The lines will never intersect.Step-by-step

explanation:

The slope of the cups is the same, 1.5.  The y-intercept of the small cups is 6The y-intercept of the big cups is 9. This means that the lines will never intersect because they are parallel lines and have the same slope but different y-intercepts.

I hope this helps :)   Please give brainliest! :)

Answer:

It gains 8 cm

Step-by-step explanation:

Answer:

We know that all the sides of a square are equal. Perimeter of a square is 4 times of s side. Perimeter of a square = 4 × length of a side.

Step-by-step explanation:

Answer:

10/20

Step-by-step explanation:

$15 for 10 hours and $20 for 10 hours

9514 1404 393

Answer:

  divide by x

Step-by-step explanation:

To answer your question, you can get from A to B by dividing by x:

  [tex]5x=3x\\\\\dfrac{5x}{x}=\dfrac{3x}{x}\qquad\text{only if $x\ne0$}\\\\5=3[/tex]

However, this is only a valid operation if x ≠ 0. In this equation, x = 0, so that division is not valid.

__

A better approach to the solution is to put the equation in standard form:

  f(x) = 0

You can get there by subtracting 3x from both sides.

  5x -3x = 3x -3x

  2x = 0

Now, you can legitimately divide by 2 to find ...

  x = 0 . . . . . . . . the reason why dividing by x is not allowed

Answer:

I just did it its 1/3n - 5

Step-by-step explanation:

Answer:

Statistic

Step-by-step explanation:

A statistic is a sample of the whole mean like

E.x( how many pink doughnuts are in the dozen pack of doughnuts.

A parameter represent the whole mean

E.x( how many donuts were made at 7:00)

Since they are sampling 25 cars, it is a statistic.

Answer:

The maximum rent each will pay is $1,333.

Step-by-step explanation:

They want the monthly rent to be no more than $3,999.

It will be split evenly between all of them, with each contributing with x.

This means that the maximum rent each will pay is given by:

[tex]3x = 3999[/tex]

[tex]x = \frac{3999}{3}[/tex]

[tex]x = 1333[/tex]

The maximum rent each will pay is $1,333.

Answer:

(3.5, 2)

Step-by-step explanation:

From the attachment, we have:

[tex]H = (1,1)[/tex]

[tex]J= (2,3)[/tex]

[tex]K=(6,3)[/tex]

[tex]L = (5,1)[/tex]

Required

Determine the point of intersection

To do this, we simply calculate the midpoints of the diagonals; which are:

HK and JL

Midpoint is calculated as:

[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]

For HK:

[tex]M = \frac{1}{2}(1+6,1+3)[/tex]

[tex]M = \frac{1}{2}(7,4)[/tex]

[tex]M = (3.5,2)[/tex]

For JL:

[tex]M = \frac{1}{2}(2+5,3+1)[/tex]

[tex]M = \frac{1}{2}(7,4)[/tex]

[tex]M = (3.5,2)[/tex]

For both diagonals, the coordinate of the midpoint is (3.5, 2).

Hence, the point of intersection is: (3.5, 2)

Answer:

the answer is y=21

Step-by-step explanation:

hope this helps:)

Answer:

y=21

Step-by-step explanation:

92 = 5y - 13

92 + 13 = 5y - 13 + 13

105 = 5y

105/5 = 5y/5

21 = y

Hope this helps!

Please consider giving me brainliest, I only need 5 more to become an expert rank, so your kindness is appreciated!

Answer:

I think

A:(2,1)

B:(4,-2)

C:(4,-6)

D:(1,-3)

Answer:

1

Step-by-step explanation:

Answer:

270

Step-by-step explanation:

bc if he does 9 miles for 3 days every week thats already 27 miles. for 10 weeks that would be 270 bc 10*27 is 270.

Answer:

I cannot see the question clearly. But I know how to do .

Answer:

the domain and range are all real numbers

Step-by-step explanation:

Answer:

x= 7y+14  /2

y= 2/ 7 x−2

Step-by-step explanation:

Answer:

x is 21. dccxpxpdpdpdpdp

Answer:

Mutual

Step-by-step explanation:

33° +2x-15 =90

2x =90+15-33

2x=72

X=36

Answer:

4800 1 x 24 x 25 x 8

Step-by-step explanation: 1 x 24 x 25 x 8

Answer:6

Step-by-step explanation:

Angle 2, angle 6, angle 4, and angle 8 have the same measure that is 78 degrees and this can be determined by using the corresponding angle property.

GIven :

The following steps can be used in order to determine the other angles whose measure is 78 degrees:

Step 1 - The corresponding angle property is used in order to determine the other angles whose measure is 78 degrees.

Step 2 - According to the given figure, angle 2 and angle 6 are corresponding angles. Therefore, the measure of angle 6 is also 78 degrees.

Step 3 - Angle 8 is the opposite angle of angle 6 therefore, the measure of angle 8 is 78 degrees.

Step 4 - Angle 4 is the opposite angle of angle 2 therefore, the measure of angle 2 is 78 degrees.

Therefore, the correct options are B), D), and F).

For more information, refer to the link given below:

https://brainly.com/question/10714897

Answer:

95

Step-by-step explanation:

3x + x = 380

4x = 380

x= 95

proof

3*95 = 285

Your share of 285 plus that of your friend shares of 95 will give you the total shares of 380

Answer:

5²+1×2 - 4(4) = 11

Step-by-step explanation:

up top when it says a = 4

and b = 5 that's means b and a are those numbers.

then while 4 is touching a that means to multiply. And the 2 up top of b means 5×5, then do order of operations to find the answer. If you dont you'll get it WRONG.

Order of operations is this

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction