In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonable) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).

In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 27% with a margin of error of 1.6%. Describe the conclusion about p using an absolute value inequality.

The answer field below uses the symbolic entry option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in < and then =, the symbolic entry option will automatically convert that too ≤ . In the same way, if you type in > and then =, the symbolic entry option will automatically convert that to ≥.

Be sure to use decimal numbers in your answer (such as using 0.40 for 40%).

Answer:

The probability is  [tex]P( p < 435.82 ) = 0.54094[/tex]

Step-by-step explanation:

From the question we are told that

   The population proportion is  p =  54% = 0.54

    The sample size is  n  =  808

Generally the distribution of the population with college degree follows a binomial distribution  

i.e  

         [tex]X  \~ \ \ \  B(n , p)[/tex]

Generally the mean is mathematically represented as

       [tex]\mu = n * p[/tex]

=>    [tex]\mu = 808 * 0.52[/tex]

=>    [tex]\mu = 420.16[/tex]

Generally the standard deviation is mathematically represented as

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

=>      [tex]\sigma = \sqrt{808 * 0.52(1- 0.52 )}[/tex]    

=>      [tex]\sigma = 14.2[/tex]

Generally 54% of the population proportion is

         [tex]\^ p = 0.54 * 808[/tex]

=>     [tex]\^ p = 436.32[/tex]

Generally by normal approximation of the binomial distribution the probability that the proportion of persons with a college degree will be less than 54% is mathematically evaluated as

      [tex]P(p < \^ p ) = P(\frac{p - \mu }{\sigma } < \frac{\^ p - \mu }{\sigma } )[/tex]

[tex]\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )[/tex]

=>  [tex]P(p < 436.32 ) = P( Z < \frac{436.32 - 420.16 }{14.20 } )[/tex]

applying continuity correction

      [tex]P(p < (436.32-0.5) ) = P( Z < \frac{(436.32-0.5) - 420.16 }{14.20 } )[/tex]

=>  [tex]P(p < (435.82 ) = P( Z < \frac{435.82 - 420.16 }{14.20 } )[/tex]

=>  [tex]P(p < (435.82 ) = P( Z < 0.1028 )[/tex]

From the z table  the area under the normal curve to the left corresponding to 0.1028  is

   [tex]P( Z < 0.1028 ) = 0.54094[/tex]

=> [tex]P( p < 435.82 ) = 0.54094[/tex]

Answer:

It’s 40 I’m pretty sure because of the square. That’s how I was taught.

Answer:

A-9:1 is correct i can confirm since i took the test

Step-by-step explanation:

Answer:

The cost would be $0.10. You would figure this out because 10 cents is a 10th of a dollar

Step-by-step explanation:

Answer:

The probability that exactly 4 are in favor the new building project is 0.1672.

Step-by-step explanation:

Let X denote the number of people who are in favor of a new building project.

The proportion of people who are in favor of a new building project is, p = 0.60.

A random sample of n = 9 people are chosen.

Every person has independent opinion about the new building project.

Thus, the random variable X follows a binomial distribution with parameters n = 9 and p = 0.60.

Compute the probability that exactly 4 are in favor the new building project as follows:

[tex]P(X=4)={9\choose 4}(0.60)^{4}(1-0.60)^{9-4}\\\\=126\times 0.1296\times 0.01024\\\\=0.167215104\\\\\approx 0.1672[/tex]

Thus, the probability that exactly 4 are in favor the new building project is 0.1672.

Answer:

doesn't it give you the angles for each letter? If that is the case then it would be 33

Step-by-step explanation:

May I have brainliest please? :)

Answer:

RT

Step-by-step explanation:

RT

Since angle S is the smallest angle, the smallest side is opposite that.

Answer:

B

Step-by-step explanation:

======================================================

Explanation:

x and y are the two numbers

The product of those values is 1856, so xy = 1856

The sum is 90, so x+y = 90. Solve for y to get y = 90-x

Plug this into the first equation

xy = 1856

x(90-x) = 1856

90x-x^2 = 1856

0 = x^2-90x+1856

x^2-90x+1856 = 0

Now use the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-90)\pm\sqrt{(-90)^2-4(1)(1856)}}{2(1)}\\\\x = \frac{90\pm\sqrt{676}}{2}\\\\x = \frac{90\pm26}{2}\\\\x = \frac{90+26}{2} \ \text{ or } \ x = \frac{90-26}{2}\\\\x = \frac{116}{2} \ \text{ or } \ x = \frac{64}{2}\\\\x = 58 \ \text{ or } \ x = 32\\\\[/tex]

If x = 58, then,

y = 90-x

y = 90-58

y = 32

So one pair of values is (x,y) = (58,32)

We see that x*y = 58*32 = 1856

If x = 32, then,

y = 90-x

y = 90-32

y = 58

Showing (x,y) = (32,58) is the other solution. But this is just a mirror copy of the first solution. Effectively we're saying the same thing.

The two numbers 58 and 32 multiply to 1856, and they add to 90.

The difference in the two values is 58-32 = 26 which is the final answer.

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

In summary,

58*32 = 1856

58+32 = 90

58 - 32 = 26

Answer:26

Step-by-step explanation:

x+y=90

xy=1856

x*(90-x)=1856

-x^2 +90x -1856=0

or x^2 -90x +1856=0

Using quadratic equation

(x-58)*(x-32)=0

x=58, y=32

58-32=26

Answer:

60degree ...........

An

2 pie/3

Step-by-step explanation:

Answer:

802456

Step-by-step explanation:

Answer:

74° is the answer

In the triangle

112°+33°+a=180. (sum of angles of triangle)

a=180-145

a=35°

a+b+71°=180. (linear pair)

35°+b+71°=180

b=180-106

{b= 74°}

Answer:

4

Step-by-step explanation:

32+20=52

8+5=13

52/13=4

Answer:

400 total

Step-by-step explanation:

so 100 is 25% of 100% and 25%x4=100%

so do 100x4=400=100% of the middle schoolers

Answer:

[tex]0\leq d\leq 7[/tex]

Step-by-step explanation:

[tex]11.79=11(1.01^d)\\1.01^d=\frac{11.79}{11} \\1.01^d=1.0718\\ln(1.01^d)=ln(1.0718)\\d ln(1.01)=ln(1.0718)\\d=\frac{ln(1.0718)}{ln(1.01)} \\d=\frac{0.069}{0.0099} \\d=6.9696[/tex]

By rounding up.

d=7

Hence, the domain is

[tex]0\leq d\leq 7[/tex]

Answer:

0<x<d

its so easy if you need help

Answer:

The correct answer is that x = 0.

Answer:

x=0

Step-by-step explanation:

6+x=6

x=6-6

x=0

Answer:

Step-by-step explanation:

y = mx + b

[tex]m_{LN} = m_{NP }[/tex] = - [tex]\frac{10}{4}[/tex] = - [tex]\frac{5}{2}[/tex]

y-intercept is 1

y = - [tex]\frac{5}{2}[/tex] x + 1

Answer:

11 (positive)

Step-by-step explanation:

Answer:

e=11

Step-by-step explanation:

3(2e+5)+8(1-e)=1

6e+15+8-8e=1

-2e+23=1

-2e=-22

e=11

Answer:

its A dont know how to explain it but i did the math and yes it is (2,3,1)

Step-by-step explanation:

Answer:

the answer is d (3,2,1) according to the picture given

Step-by-step explanation:

the system you wrote is different from the picture

Answer:

Step-by-step explanation:

Given that:

The height of the dock (h) = 6

Let represent d to be the distance between the boat and the dock

Let the length of the rope between the boat and the drum be denoted by (l)

Then, the rate of change for the length of the rope be:

dl/dt = -5 ft/s

Using Pythagoras rule to determine the relationship between these values, we have:

[tex]l^2 = h^2 +d^2[/tex]

[tex]l^2 = 6^2 + d^2[/tex]

[tex]l^2 = 36 + d^2[/tex]

We relate to:  [tex]2l * \dfrac{dl}{dt} = 2d* \dfrac{dd}{dt}[/tex]

From the question;

l = 34,

So to find [tex]\dfrac{dd}{dt}[/tex], we get;

[tex]d = \sqrt{l^2 - 36}[/tex]

[tex]d = \sqrt{34^2 - 36}[/tex]

[tex]d = \sqrt{1156- 36}[/tex]

[tex]d = \sqrt{1120}[/tex]

d = 33.46

So, we have:

[tex]\dfrac{dd}{dt}= \dfrac{l}{d} \times \dfrac{dl}{dt}[/tex]

[tex]\dfrac{dd}{dt}= \dfrac{34}{33.46} \times - 5[/tex]

[tex]\dfrac{dd}{dt}= 1.016 \times - 5[/tex]

[tex]\dfrac{dd}{dt}=-5.08 \ ft/sec[/tex]

Answer:

(f o g)(x) = x + 5

General Formulas and Concepts:

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

f(x) = x + 2

g(x) = x + 3

(f o g)(x) = f(g(x))

Step 2: Find

Answer:

f(x+3)=x+5

Goodluck to you

Answer:$5804

Step-by-step explanation:

P=6200/e^(0.022)(3)

Answer:

5804 just trust me i got it right

Answer:

The volume that a 200 g gold sample would have is 10.36 mL.

Step-by-step explanation:

Density is defined as the property that matter, whether solid, liquid or gas, has to compress into a given space. In other words, density is a quantity that allows us to measure the amount of mass in a certain volume of a substance. Then, the expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:

[tex]density=\frac{mass}{volume}[/tex]

In this case it is known that the density of gold is 19.3 g / mL. This indicates that in 1 mL there are 19.3 g. Then the following rule of three can be applied: if 19.3 g is contained in 1 mL, how much volume is 200 g of gold?

[tex]volume=\frac{200 g*1mL}{19.3g}[/tex]

volume= 10.36 mL

The volume that a 200 g gold sample would have is 10.36 mL.

Answer:

b

Step-by-step explanation:

Each box represents 1/3. 5/3 of white is 2 boxes more so red needs 2 boxes more than white. 5 red and 3 white is the only one that follows the criteria.

Answer:

0, 5

Step-by-step explanation:

5 * 0 = 0

5 * 1 = 5

5 * 2 = 10

5 * 3 = 15

5 * 4 = 20

5 * 5 = 25

etc.

Answer: 0, 5