A homeowner uses a $10 bill to pay a neighbor for cutting his lawn. The

According to a Pew Research survey, about 27% of American adults are pessimistic about the future of marriage and the family. Th

IgorLugansk [536]

Answer:

P(X≤5)=0.5357

Step-by-step explanation:

Using the binomial model, the probability that x adults from the sample, are pessimistic about the future is calculated as:

$P(x)=\frac{n!}{x!(n-x)!} *p^{x}*(1-p)^{n-x}$

Where n is the size of the sample and p is the probability that an adult is pessimistic about the future of marriage and family. So, replacing n by 20 and p by 0.27, we get:

$P(x)=\frac{20!}{x!(20-x)!}*0.27^{x}*(1-0.27)^{20-x}$

Now, 25% of 20 people is equal to 5 people, so the probability that, in a sample of 20 American adults, 25% or fewer of the people are pessimistic about the future of marriage and family is equal to calculated the probability that in the sample of 20 adults, 5 people of fewer are pessimistic about the future of marriage and family.

Then, that probability is calculated as:

P(X≤5)= P(1) + P(2) + P(3) + P(4) + P(5)

Where:

$P(0)=\frac{20!}{0!(20-0)!}*0.27^{0}*(1-0.27)^{20-0}=0.0018$

$P(1)=\frac{20!}{1!(20-1)!}*0.27^{1}*(1-0.27)^{20-1}=0.0137$

$P(2)=\frac{20!}{2!(20-2)!}*0.27^{2}*(1-0.27)^{20-2}=0.0480\\P(3)=\frac{20!}{3!(20-3)!}*0.27^{3}*(1-0.27)^{20-3}=0.1065\\P(4)=\frac{20!}{4!(20-4)!}*0.27^{4}*(1-0.27)^{20-4}=0.1675\\P(5)=\frac{20!}{5!(20-5)!}*0.27^{5}*(1-0.27)^{20-5}=0.1982$

Finally, P(X≤5) is equal to:

P(X≤5) = 0.0018+0.0137 + 0.0480 + 0.1065 + 0.1675 + 0.1982

P(X≤5) = 0.5357

3 0

2 years ago

4 and 5 are complements, and 1 and 5 are complements. By the congruent complements theorem, which angle is congruent to 4? 1 2 3

Zepler [3.9K]

The theorem tells you angles complementary to the same angle are congruent. Both 4 and 1 are complementary to 5, so 4 and 1 are congruent.

The angle congruent to 4 is 1.

8 0

2 years ago

Read 2 more answers

Jenny is eight years older then twice her cousin sues age. The sum of their ages is less then 32. What is the greatest age that

maw [93]

Answer:

The age of Sue could be 7 years

Step-by-step explanation:

Jenny is 8 years older than twice her cousin Sue's age.

The first equation will be :

J = 8 + 2S ---------(1)

The sum of their ages is less than 32.

The second equation will be :

J + S < 32 ----------------(2)

Now rearrange both equations :

8 + 2S + S < 32

3S < 32 - 8

3S < 24

S < 24/3

S < 8

S = 7

The age of Sue could be 7 years.

3 0

2 years ago

James wants to invest $12,000. He can invest the money at 7.2% simple interest for 30 yr or he can invest at 6.8% with interest

Sever21 [200]

Over time, compound interest at any rate will outperform simple interest. When the rates are nearly equal to start with, compound interest will be greater in very short order. Here, it takes less than 1 year for compound interest to give a larger account balance.

In 30 years, the simple interest will be

... I = P·r·t = 12,000·0.07·30 = 25,200

In 30 years, the compound interest will be

... I = P·(e^(rt) -1) = 12,000·(e^(.068·30) -1) ≈ 80,287.31

_____

6.8% compounded continuously results in more total interest

4 0

1 year ago

The length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58° to 3

viva [34]

Answer:

119.45 m

Step-by-step explanation:

Given:

When angle of elevation of the sun changes from 58° to 36° the length of shadow of a pole increases by 90 m.

To find:

Length of pole = ?

Solution:

Kindly refer to the attached image.

$\triangle ABC$ represents the 1st angle of elevation of sun i.e. 58°

$\triangle ABD$ represents the 2nd angle of elevation of sun i.e. 36°

Change in shadow is represented by CD = 90 m

Let height of pole, AB = $h$ m

Let side BC = $x$ m

Now, let us apply tangent rules in $\triangle ABC, \triangle ABD$ one by one:

$tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan58^\circ=\dfrac{AB}{BC}\\\Rightarrow tan58^\circ=\dfrac{h}{x}\\\Rightarrow x = 0.624h ..... (1)$

$tan36^\circ = \dfrac{h}{x+90}$

Putting value of $x$ using equation (1):

$tan36^\circ = \dfrac{h}{0.624h+90}\\\Rightarrow 0.726\times 0.624h+0.726\times 90 = h\\\Rightarrow h-0.453h =65.34\\\Rightarrow \bold{h = 119.45\ m}$

119.45 m is the height of pole.

7 0

2 years ago