SOMEONE HELP

Consider three events A, B and C with following properties.

lisov135 [29]

By the inclusion/exclusion principle,

$\mathbb P(D)=\mathbb P(A\cup B\cup C)$
$\mathbb P(D)=\mathbb P(A)+\mathbb P(B)+\mathbb P(C)-\bigg(\mathbb P(A\cap B)+\mathbb P(A\cap C)+\mathbb P(B\cap C)\bigg)+\mathbb P(A\cap B\cap C)$
$\mathbb P(D)=\dfrac14+\dfrac16+\dfrac14-\dfrac39+\dfrac1{13}$
$\mathbb P(D)=\dfrac{16}{39}\neq1$

So the union of A, B, and C does not constitute the entire sample space.

5 0

4 years ago

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midni

Alex17521 [72]

Answer: It is believed that exactly 20% of Evergreen Valley college students attended the opening night midnight showing of the latest harry potter movie.

Step-by-step explanation:

Since we have given that

n = 84

x = 11

So, $\hat{p}=\dfrac{x}{n}=\dfrac{11}{84}=0.13$

p = 0.20

So, hypothesis:

$H_0:p=\hat{p}\\\\H_a:\hat{p}$

so, test statistic value would be

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.13-0.20}{\sqrt{\dfrac{0.2\times 0.8}{84}}}\\\\z=-1.604$

At 1% level of significance, critical value would be

z= 2.58

Since 2.58>-1.604

So, We will accept the null hypothesis.

Hence, It is believed that exactly 20% of Evergreen Valley college students attended the opening night midnight showing of the latest harry potter movie.

4 0

3 years ago

Read 2 more answers

Pirate Kenny washes his trousers every five months. He washes his hat every seven months. He washes both his trousers and his ha

Ipatiy [6.2K]

Answer:

If you're going by washes, <u>6 washes </u>

Step-by-step explanation:

h: 7, 2, 9, 4, 11, 6, 1, 8

t : 5,10,3,8,1,6

6 0

3 years ago

Please help me, thank you!

dlinn [17]

Answer:

a. The first four terms are -4 , -4/3, -4/9 , -4/27

b. The series is converge

c. The series has sum to ∞ , the sum of the series is -6

Step-by-step explanation:

* Lets revise the geometric series

- Geometric series:

- There is a constant ratio between each two consecutive numbers

- Ex:

# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)

# 5000 , 1000 , 200 , 40 , …………………………(÷5)

* General term (nth term) of a Geometric Progression:

- U1 = a , U2 = ar , U3 = ar2 , U4 = ar3 , U5 = ar4

- Un = ar^n-1, where a is the first term , r is the constant ratio

between each two consecutive terms and n is the position of the

number in the sequence

* In the problem

∵ The Un = -4(1/3)^n-1

∴ a = -4

∴ r = 1/3

a) To find the first four numbers use n = 1, 2 , 3 , 4

∴ U1 = a = -4

∴ U2 = -4(1/3)^(2 - 1) = -4(1/3) = -4/3

∴ U3 = -4(1/3)^(3 - 1) = -4(1/3)^2 = -4(1/9) = -4/9

∴ U4 = -4(1/3)^(4 - 1) = -4(1/3)^3 = -4(1/27) = -4/27

* The first four terms are -4 , -4/3, -4/9 , -4/27

b) If IrI < 1 then the geometric series is converge and if IrI > 1

then the geometric series is diverge

∵ r = 1/3

∴ The series is converge

c. The convergent series has sum to ∞

- The rule is: S∞ = a/(1 - r)

∴ S∞ = -4/(1 - 1/3) = -4/(2/3) = -4 × 3/2 = -6

* The sum of the series is -6

7 0

3 years ago

If g(x) = 8-2 (3x-4) what is the value of g(-5)

Ugo [173]

Answer: 46

Step-by-step explanation: g(-5)= 8-2 (3(-5)-4), equals 46! Hope this helps :)

3 0

3 years ago