Paul will select a random sample of students to create a 95 percent confidence interval to estimate the proportion of students at his college who have a tattoo. Of the following, which is the smallest sample size that will result in a margin of error of no more than 5 percentage points?

Answers

Answer 1

Answer:

385

Step-by-step explanation:

Given that:

Margin of Error (MOE) = 5% = 0.05

Zcritical, 95% = Z(1-α/2) = Z0.025 = 1.96

MOE = Zcritical * (√p(1-p))/n)

p is taken as 0.5 when not stated ;

5 = 1.96 * sqrt[(0.5 * 0.5) / n]

5 = 1.96 * sqrt(0.25/n)

Square both sides

(0.05/ 1.96)² = 0.25/n

0.0006507 = 0.25/n

0.0006507 * n = 0.25

n = 0.25 / 0.0006507

n = 384.20162

Sample size = 385


Related Questions

Plz guys I rlly need help

Answers

The answer should be c

The government of Japan between World War I and World War II can best
be described as *
democratic
communist
militaristic
Nazi

Answers

Answer:

I believe communist just because or there influences in world war I and world war II they were on the communist side and part of the USSR at the time

help me please :)




iiiiiiiiiiiiiiiiiiiiiiiiiiiiii

Answers

Answer:

[tex]x = \frac{5}{3}[/tex]

Step-by-step explanation:

The expression under the square root is [tex]\sqrt{4x^2 - 20x + 25}[/tex]

This is equivalent of [tex](2x-5)^2[/tex]

We can check this by using the formula
[tex](a+b)^2 = a^2 + 2ab + b^2[/tex]

where [tex]\\a = 2x so a^2 = (2x)^2 = 4x^2\\\\b = -5 so b^2 = (-5)^2 = 25\\\\2ab = (2)(2x)(-5) = -20x\\[/tex]

So

[tex]\sqrt{4x^2 - 20x + 25} = \sqrt{(2x-5)^2}[/tex] which is [tex](2x-5)[/tex]

(The square root of the square of an expression is the expression itself)

So that gives us

[tex]2x - 5 = 5-2x\\[/tex]

Collecting like terms on each side gives us

[tex]2x + 2x = 5 -(-5)\\\\4x = 10\\\\x = 10/4 = 5/3[/tex]

Given points A(2,1,3) and B(0,5,0), find a point C in the xy-plane that creates an isosceles right triangle such that:_______

a. AB and BC are the legs of the right triangle
b. AB is the hypotenuse of the right triangle (for part ii, just doing all the set-up work is sufficient; you do not need to solve and find the points)

Answers

Answer:

a.)Point C will be either (4.82, 7.41) or ( -4.82, 2.59)

b.) -x² + 2x + 6y - y² - 5= 0  , 8y - 4x = 11

Step-by-step explanation:

As given A(2,1,3) and B(0,5,0)

a.)

We have to find C  in the xy-plane

⇒ C is of the form (x, y, 0)    ( Because in xy plane , z coordinate is zero)

Now, given AB and BC are the legs of the right triangle .

AB = (0, 5, 0) - (2, 1, 3) = ( -2, 4, -3)

BC = (x, y, 0) - (0, 5, 0) = ( x, y-5, 0)

As AB and BC are legs of triangle

⇒AB is perpendicular to BC

⇒(AB).(BC) = 0

⇒( -2, 4, -3).( x, y-5, 0) = 0

⇒ -2x + 4(y-5) -0 = 0

⇒ -2x + 4y- 20 = 0

⇒ -x + 2y- 10 = 0

⇒ 2y = 10 + x

⇒ y = 5 + [tex]\frac{x}{2}[/tex]         ......(1)

As ABC is making an isosceles right triangle

It means two sides of the triangle are equal

Now,

|AB| = √(-2)² + (4)² + (-3)² = √4+16+9 = √29

|BC| = √(x)² + (y-5)² + 0² = √(x)² + (y-5)²

Now,

AS AB = BC

⇒|AB| = |BC|

⇒|AB|² = |BC|²

⇒29 = (x)² + (y-5)²

⇒29 = (x)² + (5 + [tex]\frac{x}{2}[/tex] -5)²

⇒29 = (x)² + ( [tex]\frac{x}{2}[/tex] )²

⇒29 = x²( 1 + [tex]\frac{1}{4}[/tex] ) = x²(  [tex]\frac{5}{4}[/tex] )

⇒ x² = [tex]\frac{116}{5}[/tex] = 23.2

⇒ x = 4.82 , -4.82

⇒y = 7.41 , 2.59

so, Point C will be either (4.82, 7.41) or ( -4.82, 2.59)

b.)

As given AB is the hypotenuse of the right triangle

S, AC and CB will perpendicular to each other

Now,

AC = (x, y, 0) - ( 2, 1, 3) = ( x-2, y-1, -3)

CB = (0, 5, 0) - (x, y, 0) = (-x, 5-y, 0)

As, AC and CB is perpendicular

⇒(AC).(CB) = 0

⇒( x-2, y-1, -3).(-x, 5-y, 0) = 0

⇒(x-2)(-x) + (y-1)(5-y) - 0 = 0

⇒-x² + 2x + 5y - y² - 5 + y = 0

⇒-x² + 2x + 6y - y² - 5= 0    ..........(2)

As ABC is making an isosceles right triangle

It means two sides of the triangle are equal

Now,

|AC| = √(x-2)² + (y-1)² + (0-3)² = √(x-2)² + (y-1)² + 9

|BC| = √(x)² + (y-5)² + 0² = √(x)² + (y-5)²

Now,

AS AC = BC

⇒|AC| = |BC|

⇒|AC|² = |BC|²

⇒(x-2)² + (y-1)² + 9  = (x)² + (y-5)²

⇒x² + 4 - 4x + y² + 1 - 2y + 9 = x² + y² + 25 - 10y

⇒ 4 - 4x + 1 - 2y + 9 = 25 - 10y

⇒14 - 4x - 2y  = 25 - 10y

⇒10y - 2y - 4x = 25 - 14

⇒8y - 4x = 11            ........(3)

Now, we have 2 equations

-x² + 2x + 6y - y² - 5= 0  , 8y - 4x = 11

Solve these equations to find x, y

4. Use the table of values for a quadratic function to identify the following.
X
direction the graph opens:
-3
axis of symmetry:
vertex:
ON W
range:
y-intercept:
(as an ordered pair)
-3
-4
1
-3
x-intercepts:
(as ordered pairs)
2
3
4
interval of increase:
interval of decrease:

Answers

5 if you don’t know just go to khan academy they help you with every thin

(x2 - 3)(x2 + 12) = 0

Answers

Answer:

x=1.7320508075688772 or x=−1.7320508075688772

Step-by-step explanation:

(x2−3)(x2+12)=0

x4+9x2−36=0

(x2−3)(x2+12)=0

x2−3=0 or x2+12=0

x=1.7320508075688772 or x=−1.7320508075688772

Add, Subtract, or Multiply, as indicated.
(5x^2+3x-7)+(6x+7)

Answers

answer would be: 5x^2+9x

Solve the absolute
[x] - 7 =-3

Answers

x=4 because -7 would be +7 on both sides

Find the length of side x in simplest radical form with a rational denominator.

Answers

Answer:

[tex] x = 6\sqrt{2}[/tex]

Step-by-step explanation:

Reference angle = 45°

Adjacent side = 6

Hypotenuse = x

Applying trigonometric ratio, we have:

[tex] cos(45) = \frac{6}{x} [/tex]

Multiply both sides by x

[tex] x*cos(45) = 6 [/tex]

Divide both sides by cos(45)

[tex] x = \frac{6}{cos(45)} [/tex]

[tex] x = \frac{6}{\frac{\sqrt{2}}{2} [/tex] (cos 45 = √2/2)

[tex] x = \frac{6}*{\frac{2}{\sqrt{2}} [/tex]

[tex] x = \frac{12}{\sqrt{2}} [/tex]

Rationalize

[tex] x = \frac{12*\sqrt{2}}{\sqrt{2}*\sqrt{2} [/tex]

[tex] x = \frac{12*\sqrt{2}}{2} [/tex]

[tex] x = \frac{6*\sqrt{2}}{1} [/tex]

[tex] x = 6\sqrt{2}[/tex]

HELP PLZZZ EASY AREA MATH

Answers

Answer:

4,400

Step-by-step explanation:

The Humphrey family is traveling 1,325 miles for their family vacation. Last year, they traveled 724 miles. They drove 420 miles earlier in the week and have driven 130 miles so far today. How many miles do they have left to travel?

Answers

Answer: They have 775 miles left to be traveled

Step-by-step explanation:

Miles required to travel for vacation = 1,325 miles

Miles already traveled = Miles driven this week + miles driven today

= 420 miles + 130 miles

-=550 miles

Miles remaining to be covered =Miles required to travel for vacation --- Miles already traveled

= 1,325 miles - 550 miles

= 775 miles

Answer:

1762 is the answer

Step-by-step explanation:

A scuba diver dives 10 meters below the surface of the ocean, and then dives down another 8 meters. How many meters down does the diver dive? Show an absolute value equation that can be used to find your answer.

Answers

10 + 8 = 18
In feet: 59.0551

The Hollywood cats are a group of cats that have settled in along the Hollywood Beach in Florida. A group of volunteers feed them and care for them while trying to humanely reduce their numbers (as they are considered a nuisance). If there were 100 cats in the year 2012 and the rate of population change is given

Answers

Complete Question

The Hollywood cats are a group of cats that have settled in along the Hollywood Beach in Florida. A group of volunteers feed them and care for them while trying to humanely reduce their numbers (as they are considered a nuisance). If there were 100 cats in the year 2012 and the rate of population change is given

by     [tex]-\frac{1}{4} t-2[/tex]

where t is measured in years, how many cats are projected to be in the group in 2020.

Answer:

The number of total cats left after 8 years T

[tex]T=76[/tex]

Step-by-step explanation:

From the question we are told that

Number of cats 2012 n=100

Number of years t=2012-2020=>8 years

Generally the equation of change in population is mathematically Given as

   [tex]\frac{dp}{dt}= -\frac{1}{4} t-2[/tex]

  [tex]\int dp=\int_0^8 (-\frac{1}{4} t-2)[/tex]

  [tex]p=\frac{-64}{8} -16[/tex]

   [tex]p=-24cats[/tex]

Therefore the number of total cats left after 8 years T is given as

[tex]T=100-24[/tex]

[tex]T=76[/tex]

true false or not enough information??

Answers

Answer:

True.

Step-by-step explanation:

The range of the 10  values is 10 - 3 = 7  so that is true.

The median will be the mean of the 2 middle values so that is possible also. The distribution could be, for example:

3 3 3 4 4 4 7 8 8 10  when the median = (4 + 4) / 2 = 4.

Answer:

True.

Step-by-step explanation:

the range of 10 values is 10-3 = 7 so that is true

Yousef saves $25 each month for a year. One year is 12 months. How much money does he save in one year?

Answers

Answer:

300

Step-by-step explanation:

25 x 12

Answer:300

Step-by-step explanation: its just 25 x 12

2865 students participated in a competitive exam. There were 60 rooms in the
university. Equal number of students were placed in each room. How many students
were not seated in any one of the rooms?

Answers

47 students per room, 45 weren’t in a room

4x² when x = 5/6 and 1/2​

Answers

x = -6 I think!!! Good luck;)

Guided Practice
1. A manufacturer gets a shipment of 600 batteries of which 50 are
defective. The quality control manager tests a random sample of
30 batteries in each shipment. Simulate the test by generating random
numbers between 1 and 600. How well does your sample represent the
shipment? Explain. (Explore Activities 1 and 2)

Answers

Answer:

18.33

Step-by-step explanation:

600 -50 ÷ 30

550 ÷30 = 18.333


Leena lives 1 4/7 miles from school. She walks the first 6/7 mile by herself. Then she
walks the rest of the way with her friend. How far did Leena walk with her friend? Plz help

Answers

Answer:

Leena walked 5/7 miles with her friend

Step-by-step explanation:

7/7 = 1

7 +4 =11

Answer:

5/7

Step-by-step explanation:

Please help and explain

True or False: The magnitude of a resultant vector will always be larger than individual vectors that are both in the first quadrant

Answers

Answer:true

Step-by-step explanation:

the correct answer is true.

which of these numbers has exactly two factors, 7,8,9,10​

Answers

Answer:

It's 7

Step-by-step explanation:

Find the value of m.

Answers

Answer:

Step-by-step explanation:

x=2

a=1.25

m=3.75

tell me if u need any steps

Drag Each expression to show whether it is equivalent to 6.7-(-2.5), 6.7+(-2.5), or neither.

Answers

Answer:

Step-by-step explanation:

6.7 – (-2.5)

2.5+6.7

6.7 + (-2.5)

-2.5+6.7

6.7-2.5

neither

-2.5-6.7

2.5-6.7

-6.7+2.5

hat is the product of 4.01 × 10-5 and 2.56 ×108?

Answers

Answer:

35.1 and 276.48

Step-by-step explanation:

Answer:

The correct answer is: 1.0266 ×104

Step-by-step explanation:

What is the geometric sequence formula for 1/5, 1/25, 1/125, 1/625, ...

Answers

The answer is 1/3125

HELP QUICK ILL GIVE TOU BRAINLIEST
find the surface area...

Answers

Answer: 483.09 in^2
Explanation: 12, 11, 10, 12

Can somebody please help me with this math problem please brainliest if your correct thanks picture is attached !!

Answers

Answer:

x = (3, 4)

(I'm assuming the missing sign in the picture is a negative (-))

Answer:

x={3, 4}

Step-by-step explanation:

that may answer po

A dish washer manufacturer introduced a new type of dish washer and conducted a survey on the new product. The survey showed 40% of the consumers had seen an advertisement for the new product, 20% had tried the new product, and 15% had both seen an advertisement and tried the new product. Let event A denote that the consumers had seen an ad for the new product, and event B denote that the consumers had tried the new product. What is the probability a randomly selected consumer had either seen an advertisement or tried the new product

Answers

Answer:

[tex]P(A \cup B) =0.45[/tex]

Step-by-step explanation:

From the question we are told that

Consumers seen the soap [tex]P_A=40\% =0.40[/tex]

Consumers used the soap [tex]P_B=20\% =0.2[/tex]

Consumers seen/tried the soap [tex]P_x=15\% =0.15[/tex]

Generally the probability that consumers have seen and tried the soap is

[tex]P(A \cup B=P(A)+P(B)-P(A \cap B[/tex]

[tex]P(A \cup B=0.4+0.2-0.15[/tex]

[tex]P(A \cup B) =0.45[/tex]

Solve.



log6x+log6(x−1)=1



Enter your answer in the box.

x = ?

Answers

Answer:

7

Step-by-step explanation:

hhfndbdbdbueheheheheheheh

Working together, it takes two computers 12 minutes to send out a company's email. If it takes the slower computer 30 minutes to do the job on its own, how
long will it take the faster computer to do the job on its own?
Do not do any rounding?

Answers

Answer:

The faster computer will complete the job in 20 minutes alone.

Step-by-step explanation:

Given that:

Time taken by both computers = 12 minutes

Time taken by slower computer = 30 minutes

Let,

x be the time taken by faster computer.

[tex]\frac{1}{x}+\frac{1}{30} = \frac{1}{12}[/tex]

[tex]\frac{1}{x} = \frac{1}{12}-\frac{1}{30}\\\\\frac{1}{x} = \frac{5-2}{60}\\\\\frac{1}{x} = \frac{3}{60}\\\\\frac{1}{x} = \frac{1}{20}\\\\x= 20[/tex]

Hence,

The faster computer will complete the job in 20 minutes alone.

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