True or false: all animals have adaptations.

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:

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

Answer:

The first and last one!!

Step-by-step explanation:

Was it correct?? Hope this helps!!(¬_¬ )

Answer:

1. 40

2. -25

Step-by-step explanation:

I'm sure this is the answer

Answer:

1

Hope this helps!!!!

Answer:

(y-9)(2y^2 +9)

Answer:

5x-15 = 2x+21

x=12

Step-by-step explanation:

Vertical and Corresponding Angles can be used to prove so.

Step-by-step explanation:

[tex]f(\pi) = - 3 \\ f( \frac{\pi}{2} ) = 0 \\ f( - \frac{3\pi}{2} ) = 0 \\ \: \: = 3 \cos(theta) [/tex]

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

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.

Answer:

-9/5 is the slope

Step-by-step explanation:

5-(-4)=9

1-6=-5

Answer:

Step-by-step explanation:

From the first image attached below, we will see the sketch of the curve x = y² & x = 2y

In the picture connected underneath, the concealed locale(shaded region) is bounded by the given curves. Now, we discover the marks of the crossing point of the curves. These curves will cross, when:

[tex]y^2 =2 y \\ \\ or y^2 -2y = 0 \\ \\ y(y-2) = 0 \\ \\ y = 0 \ \ or \ \ y = 2[/tex]

Thus, the shaded region fall within the interval 0 ≤ y ≤ 2

Now, from the subsequent picture appended we sketch the solid acquired by turning the concealed region about the y-axis.

For the cross-sectional area of the washer:

[tex]A (y) = \pi (outer \ radius)^2 - \pi ( inner \ radius )^2 \\ \\ A(y) = \pi (2y^)2- \pi (y^)^2 \\ \\ A(y) = 4 \pi y^2 - \pi y^4 \\ \\ A(y) = \pi( 4 y^2 -y^4)[/tex]

Finally, the volume of (solid) is:

[tex]V = \int^2_0 A(y) \ dy \\ \\ V = \int^2_0 \pi (4y^2 -y^4) \ dy \\ \\ V = \pi \int^2_0 (4y^2 -y^4) \ dy \\ \\ V = \pi \Big[\dfrac{4}{3}y^3 - \dfrac{y^5}{5} \big ] ^2_0 \\ \\ V = \pi \Big [ \dfrac{4}{3}(2)^3-\dfrac{2^3}{5} \Big ] \\ \\ V = \dfrac{64}{15}\pi \\ \\ V = (4.27 ) \pi[/tex]

Answer:

Yes.

Step-by-step explanation:

Answer:

a= x= 3, -1

b= x=1

c= (1, -8)

Step-by-by-step explanation:

For the show your work, you have to create the graph of the parabola. (attached image)

Answer:

8 × (1/2)²

8 × 0.25

2 Answer!

Hope this helps, thank you :) !!

Answer:

Step-by-step explanation:

The answer is : 2

Simplify

I added image with explation! Hope this helps!

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:

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:

The area is 113.1

Step-by-step explanation:

Hope this helped Mark BRAINLEST!!!

Answer:

( x +1 ) ( x + 3 )

Answer:

x is 21. dccxpxpdpdpdpdp

Answer:

Mutual

Step-by-step explanation:

33° +2x-15 =90

2x =90+15-33

2x=72

X=36

Answer:

Option A : The system has two solutions, and both are viable because they result in positive values of time.

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

The system has two solutions, and both are viable because they result in positive values of time.

Answer:

y = -5x + 12

Step-by-step explanation:

slope intercept form is where you simplify it and get the y by itself, so:

[tex]y-2 = -5(x-2)\\y-2 = -5x+10\\y = -5x+ 12[/tex]

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:

q = 114

Step-by-step explanation:

q/19 > 5

q > 19 * 5 = 95

==> q = 114 works

Answer:

rrerer

Step-by-step explanation:erewqwdqwdqd noo hlp me

Answer:

10/20

Step-by-step explanation:

$15 for 10 hours and $20 for 10 hours

Answer:

$9.90

Step-by-step explanation:

$2.97 divided by 3 equal 0.99 cents

0.99 multiplied by 10 equal 9.90

Answer:

y=x-4

Step-by-step explanation:

Answer:

P'(4,4)

Step-by-step explanation:

P(8,-3) T(x,y) = (x-4, y+7)

P'(8-4,-3+7)=P'(4,4)