Answer:
a) A sample of 385 must be taken.
b) The 95% confidence interval for the proportion of workers who have changed jobs within the past year is (0.1216, 0.2784).
c) A sample of 246 is needed.
Step-by-step explanation:
Question a:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Absence of preliminary data:
This means that we use [tex]\pi = 0.5[/tex], which is when the largest sample will be needed.
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
How large a sample must be taken to ensure that a 95% confidence interval will specify the proportion to within ±0.05?
A sample of n must be taken.
n is found when [tex]M = 0.05[/tex]. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96*0.5[/tex]
Dividing both sides by 0.05
[tex]\sqrt{n} = 1.96*10[/tex]
[tex](\sqrt{n})^2 = (19.6)^2[/tex]
[tex]n = 384.16[/tex]
Rounding up,
A sample of 385 must be taken.
Question b:
In a sample of 100 workers, 20 of them had changed jobs within the past year.
This means that [tex]n = 100, \pi = \frac{20}{100} = 0.2[/tex]
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 - 1.96\sqrt{\frac{0.2*0.8}{100}} = 0.1216[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 + 1.96\sqrt{\frac{0.2*0.8}{100}} = 0.2784[/tex]
The 95% confidence interval for the proportion of workers who have changed jobs within the past year is (0.1216, 0.2784).
Question c:
Same procedure as question a, just with [tex]\pi = 0.2[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.2*0.8}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96\sqrt{0.2*0.8}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.2*0.8}}{0.05}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.2*0.8}}{0.05})^2[/tex]
[tex]n = 245.8[/tex]
Rounding up
A sample of 246 is needed.
The length of a rectangle is 3 times the width. The area of this rectangle is 243 feet squared.
What are the dimensions?
Width =____feet (this is the short side)
Length=____feet (this is the long side that is 3 times the width)
Step-by-step explanation:
width = x
length= 3x
Area = length * width
243=3x * x
3÷243 =3x^2÷3
√81=√x^2
x=9
3x=3*9=27
Width=9
Length=27
Acellus
Find the measure of < 4.
44
158°
{
*4 = [?]
Fnter
<4=22°
Answer:
<4+158=180 co interior angle
<4=180-158=22°
Answer:
solution given:
<4+<158°=180°[co- interior angle]
<4=180°-<158°=22°
<4=22° is your answer
Three vans can carry
18 adults. How many
adults are in 7 vans?
Answer:
42
Step-by-step explanation:
18/3= 6
6x7= 42
Answer:
42 with u need me to explain just say it in the comments :) hope this help
Step-by-step explanation:
Corinna rowed 4/5 mile on a rowing machine in 1/6 hour. What is her rowing rate in miles per hour
Answer: 8.20 miles I believe
I would appreciate if someone could help me with this problem and answer it I will give you a brainlist :)
help, can you tell if im right?
Answer:
Yes, all of your answers are 100% correct
Step-by-step explanation:
You correctly set the values equal to the numerator or denominator (minutes = minutes) and any value will equal the same value.
what is 1000x45 how do i get the anwser
Answer:
45000
Step-by-step explanation:
put the equation like this
1000
x 45
And multiple form right to left or just take 45 and add 3 0's because anything multiplied by 1 is what number u multiplied it by
Answer:45000
Step-by-step explanation:
so you know that 10x45=450 just add 2 more zeros and thats ur answer may i be marked brainliest
which number multiplied by itself will give the output as 12345678987654321?
Answer:what we observe is that the square of the number follows a pattern: 2 1's gives 121. 3 1's gives 12321. so to get 12345678987654321 we need to get square of 9 1's(111,111,111).
Marcus is painting the outside of a shoe box for an art project. The box is 9 cm x 10 cm x 3 cm. How much paint does Marcus need?
Answer:
294 cm^2
Step-by-step explanation:
This question is asking for the surface area of all 6 sides of the Shoe box. Hence we will have to multiply all the dimensions with each other twice to get the surface area of all the sides.
9x10x2=180
9x3x2=54
10x3x2=60
Adding them together we get 294 cm^2.
What is the radius and diameter of the following circle?
16 cm
Answer:
radius is 16
diameter is 32
Step-by-step explanation:
Your radius is the line starting from the point in the middle to any part of the edge of the circle. A diameter is when there is a long straight line from both ends reaching the edges of the circle crossing the point.
A diameter is just the radius doubled but except it all has to be straight coming reaching both edges.
A radius is half of a diameter.
Answer:
radius = 16 cm
diameter = 32 cm
Step-by-step explanation:
radius = a straight line from the center of the circle to any point on the circle's circumference
We are given the radius (16 cm)
The diameter is equal to twice the length of the radius
So diameter = 16 * 2
16*2=32 so the length of the diameter is 32 cm
Write rational numbers between 0 and 1
-----------------------------------------------------------------------------------------
please also say how did you solve it
this question has 10 points
I will mark you as Brillant if you answer it
Step-by-step explanation:
0/1 , 1/1
Multiply there denominators with any number...
0/1×60=0/60
1/1××60=60/60
Now,
You have many choices...
1/60,10/60,30/60,2/60,5/60........so on....
Question 9 of 10
Thurston deposited $8400 into a savings account that earns 2.5% simple
interest each year calculated annually. What is the future value of Thurston's
account after 14 years?
A. $2940
B. $19,740
C. $11,340
D. $8610
SUBMIT
Answer:$11,340
Step-by-step explanation:
If Thurston deposited $8400 into a savings account that earns 2.5% simple
interest each year calculated annually. What is the future value of Thurston's account after 14 years will be is C. $11,340
Using this formula
Future value=Principal+[(Principal ×Rate ×Time)÷100]
Where:
Principal=$8,400
Rate=2.5%
Time=14 years
Let plug in the formula
Future valve=$8,400+[($8,400×2.5%×14)÷100]
Future valve=$8,400+($294,000÷100)
Future valve=$8,400+$2,940
Future valve=$11,340
Inconclusion if Thurston deposited $8400 into a savings account that earns 2.5% simple interest each year calculated annually. What is the future value of Thurston's account after 14 years will be is C. $11,340
Learn more here:https://brainly.com/question/9716053
For an F distribution, find the following:
(a) f 0.25,825
(b) f 0.10,12,15
(c) f 0.01,12,6
Answer:
1.39 ; 2.02 ; 2.90
Step-by-step explanation:
From the F - distribution calculator
F0.25, 8, 2 ;
u = 8 ; v = 25 ; cumulative probability = 1 - 0.25 = 0.75
F value = 1.39
F0.10,12,15 :
u = 12 ; v = 15 ; cumulative probability = 1 - 0.10 = 0.90
F value = 2.02
F0.01,12,6
u = 12 ; v = 6 ; cumulative probability = 1 - 0.01 = 0.90
F value = 2.90
How many 3 digit numbers can be constructed from the digits 3 4 5 6 7
Answer:
60 numbers
Step-by-step explanation:
3 4 5 6 7
for everything starting with 3
345
346
347
354
356
357
364
365
367
376
375
374
we know the results will be the same
there was 12 numbers in that sequence
theres 4 other numbers it could start with
12 + (12x4) = 12x5
60
Find the 11th term in the following geometric sequence.
-5,-10,-20,-40
choose the equation that describes the relationship in the following table. please answer ASAP ty
Answer:
C) y = -5x + 32
Step-by-step explanation:
Only choice where the all the x values equal the y values
Complete the square to find
the vertex of this parabola.
x2 - 8x - y - 4 = 0
([?], [ ]
Answer:
-20
Step-by-step explanation:
Complete the square to find the vertex of this parablola x^2-8x-y-4=0 {the second one of -20; so 4,-20}
Step-by-step explanation:
The answer would be (4,-20)
Fill in 4 and -20
Diego needs rug with an area of 540sq feet what are all the ways to get 540 square feet
Answer:
260*2
540*1
180*3
135*4
108*5
Step-by-step explanation:
There are 63 students marching in a band, and they’re marching in 7 rows. How many students are in each row?
Solving two-step equations:
106 = 1 + 7n
Answer:
n = 15
Step-by-step explanation:
106 = 1 + 7n
1- 1-
-------------------
105 = 7n
÷7 ÷7
------------------
15 = n
your goal is to get the variable by itself
which of the following describes the data set? 6,7,11,14,20,30,35
Answer:
D
The numbers are already in order so you don't need to do anything
Answer:
its b for me but d for yall
Step-by-step explanation:
all you do is count up hope this helps can u mark me brainlest
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Answer:
Second one
Step-by-step explanation:
Answer:
C. A 90° clockwise rotation about the origin
Write the standard form of an equation with p=3sqrt2, theta=135.
a. x-y+sqrt2=0
b. x-y+6=0
c. x-y+3sqrt2=0
d. x+y+sqrt2=0
Its b In normal form of a straight line, the equation is given by where p is the perpendicular distance of the line from the origin and is the angle between the perpendicular line and the positive direction of the x-axis.
convert 320% to an equivalent decimal.
Answer:
Answer is 3.2
Step-by-step explanation: you can take any percent and divide it by 100. So in this example you would divide 320/100 and it will give you 3.2
PLEASE HELP!
Find the area and circumference of the following. Leave in terms of pi. * 2 poir
16
Area = 100pi and Circumference = 50 pi
Area = 256pi and Circumference = 32 pi
Area = 100 pi and Circumference = 55 pi
Answer:
B. Area = 256pi & Circumference = 32pi
Step-by-step explanation:
Area = pi r^2
A = pi (16)^2
A = 256pi
Circumference = 2pi r
C = 2(pi)(16)
C = 32pi
PLEASE HELP !!!! ILL GIVE BRAINLIEST !!!
Answer:
x=15
Angle (5x+6): 81
Angle (8x-39): 81
Step-by-step explanation:
5x+6=8x-39
add 39 to both sides
5x+45=8x
-5x on both sides
45=3x
divide both sides by 3
x=15
Which of the following is the equation of the circle shown below?
Answer:
Step-by-step explanation:
Center is 6, -2
Radius is 7
(x-6)^2 + (y + 4)^2 = 7^2
==============
Please give brainliest, I really want to rank up, thank you!
There are 45 students in a speech contest. Yesterday, 1/3 of them gave their speeches. Today, 2/5 of the remaining students gave their speeches. How many students still haven't given their speeches?
Complete the expression so that it forms a perfect square trinomial--don't forget the sign for an operation. Then write the expression for the perfect square binomial using ^ to make an exponent. x^2+5 perfect square binomial
The perfect square trinomial is x^2 + 45/4.
To complete the expression as a perfect square trinomial, we need to add a term to the given expression, x^2 + 5, in such a way that it becomes a perfect square.
A perfect square trinomial can be written in the form (a + b)^2, where a and b are real numbers.
In this case, we can observe that the coefficient of x^2 is already 1, so the value of a will be 1.
To find the value of b, we take half of the coefficient of x, which is (5/2), and square it: (5/2)^2 = 25/4.
Now, we can add this term to the given expression:
x^2 + 5 + 25/4
Combining the terms, we get:
x^2 + 25/4 + 20/4
Simplifying further:
x^2 + 45/4
For the perfect square binomial, we can write the expression using the exponent notation as follows:
(x + (sqrt(45/4)))^2
Note that sqrt denotes the square root.
For more questions on square trinomial
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Unit 10 circles homework 2 back side