Answer:
a. The minimum sample size required is of 60,025.
b. The minimum sample size required is of 20,465.
c. The minimum sample size required is 9,589.
Step-by-step explanation:
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 z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Question a:
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
p and q unknown means that we use [tex]\pi = 0.5[/tex], which is when the largest sample size is needed.
Margin of error: 0.004
We have to find n for which M = 0.004. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.004 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.004\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.004}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.004})^2[/tex]
[tex]n = 60025[/tex]
The minimum sample size required is of 60,025.
b. Margin of error: 0.009, confidence level: 99%; p and q unknown
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
Margin of error: 0.009
We have to find n for which M = 0.009. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.009 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.009\sqrt{n} = 2.575*0.5[/tex]
[tex]\sqrt{n} = \frac{2.575*0.5}{0.009}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575*0.5}{0.009})^2[/tex]
[tex]n = 20464.9[/tex]
Rounding up:
The minimum sample size required is of 20,465.
c. Margin of error: 0.01; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 52%.
Here we have [tex]\pi = 0.52[/tex].
The minimum sample size is n for which M = 0.01. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.01 = 1.96\sqrt{\frac{0.52*0.48}{n}}[/tex]
[tex]0.01\sqrt{n} = 1.96\sqrt{0.52*0.48}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.52*0.48}}{0.01}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.52*0.48}}{0.01})^2[/tex]
[tex]n = 9588.6[/tex]
Rounding up:
The minimum sample size required is 9,589.
Draw and label the circle given by the equation (x - 5 + y + 10 = 6^2
Answer:
See attachment for circle
Step-by-step explanation:
Given
[tex](x -5)^2 + (y + 10)^2 = 6^2[/tex]
Required
Draw and label the circle
The equation of a circle is:
[tex](x -a)^2 + (y - b)^2 = r^2[/tex]
Where:
[tex]Center = (a,b)[/tex]
[tex]Radius = r[/tex]
So, we have:
[tex]Center = (5,-10)[/tex]
[tex]Radius = 6[/tex]
See attachment for circle
You have land that you would like to use to create two distinct fenced-in areas in the shape given below. You have 410 meters of fencing materials to use. What values of x and y would result in the maximum area that you can enclose
Answer:
[tex]x = \frac{205}{3}[/tex]
[tex]y =\frac{195}{4}[/tex]
Step-by-step explanation:
Given
[tex]p = 410[/tex] --- perimeter
See attachment for fence
Required
x and y
The perimeter of the fence is:
[tex]p = 2(x + y +5 + y) +x[/tex]
Open bracket
[tex]p = 2x + 2y +10 + 2y +x[/tex]
Collect like terms
[tex]p = 2x+x + 2y + 2y+10[/tex]
[tex]p = 3x + 4y+10[/tex]
Substitute: [tex]p = 410[/tex]
[tex]3x + 4y+10 =410[/tex]
Make 4y the subject
[tex]4y =410-10-3x[/tex]
[tex]4y =400-3x[/tex]
Make y the subject
[tex]y =\frac{400-3x}{4}[/tex]
The area (A) of the fence is:
[tex]A = (y + y + 5) * x[/tex]
[tex]A = (2y + 5) * x[/tex]
Substitute: [tex]y =\frac{400-3x}{4}[/tex]
[tex]A = (2*\frac{400-3x}{4} + 5) * x[/tex]
[tex]A = (\frac{400-3x}{2} + 5) * x[/tex]
Take LCM
[tex]A = (\frac{400-3x+10}{2}) * x[/tex]
Solve like terms
[tex]A = (\frac{410-3x}{2}) * x[/tex]
Open bracket
[tex]A = \frac{410x-3x^2}{2}[/tex]
Remove fraction
[tex]A = 205x-1.5x^2[/tex]
Differentiate both sides
[tex]A' = 205 - 3x[/tex]
To maximize; set [tex]A' =0[/tex]
[tex]205 - 3x =0[/tex]
Solve for 3x
[tex]3x = 205[/tex]
Solve for x
[tex]x = \frac{205}{3}[/tex]
Recall that: [tex]y =\frac{400-3x}{4}[/tex]
So, we have:
[tex]y =\frac{400-3*205/3}{4}[/tex]
[tex]y =\frac{400-205}{4}[/tex]
[tex]y =\frac{195}{4}[/tex]
j-27.5=3.9 solve for the variable
Answer:
31.4
Step-by-step explanation
I think
Use the order of operations to simplify the given expression. −2⋅[16÷(8−4)2]2
2. Identify the variables that are contained in the expression.
2m2 + 3mn + 4p
Answer:
m, n and p
Step-by-step explanation:
Given
[tex]2m^2 + 3mn + 4p[/tex]
Required
List out the variables
Literally, the variables are the alphabets in the expression
And they are:
m, n and p
please help me pleaseee!!
Answer:
AOB = 65
DOE = 35
AOC = 90
EOB = 115
DOB = 80
a line and a line segment are exactly the same. true or false
Answer:
false
Step-by-step explanation:
a line is infinite but a line segment has starting and end point. line segment is a small segment taken out from that infinite line
PLS HELP!! need the answer asap
Answer:
1.) 113 degrees and 2.) 67 degrees
Step-by-step explanation:
(x + 33) + (x - 13) = 180
Add like terms:
2x + 20 = 180
2x = 160
x = 80
x + 33 =
80 + 33 =
113 =
x - 13 =
80 - 13 =
67 =
If f(x)=1/x
and g(X) = x-2, which of the following is the graph of
(f•g)(x)?
Answer:
The correct answer would be A) on edge.
Step-by-step explanation:
Edge 2021.
Which expression is equivalent to 250 + 150 ?
Answer:
if 25c + 15d = 0, then d = -25/15c
Step-by-step explan
just yes, that
If 4 containers of yogurt cost $2.76, how many containers of yogurt can you purchase with $9.66?
14 containers
2.76 / 4 = 0.69
9.66/0.69= 14 containers
ayudaaaaa por favor
Answer:
La respuesta es treinta coma seis.
Espero que esto ayude.
PLEASE ANSWER ASAP!!! FULL ANSWERS ONLY!!!!!! WILL GIVE BRAINLIEST!!!!!!!!!
Two cyclists, 68 miles apart, start riding toward each other at the same time. One cycles 3 miles per hour faster than the other, and they meet after 4 hours of riding.
a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.
b. What are the speeds of the two cyclists? _______________
Answer:
4r + 4(r + 3) = 68
r = 7 miles per hour
r + 3 = 10 miles per hour
Step-by-step explanation:
distance = rate * time
a)
4r + 4(r + 3) = 68
Distribute
4r + 4r + 12 = 68
8r + 12 = 68
8r = 56
r = 7 miles per hour
r + 3 = 10 miles per hour
a) The given equation using the information as it is given above that can be solved to answer this problem is 4r + 4(r+3) = 68
b) The speed of both cyclists are 3mi/hr and 10mi/hr respectively
The formula for calculating the distance covered is expressed as:
Distance = speed * time
Let the speed covered by one cyclist be t
If one cycles 3 miles per hour faster than the other, the speed of the other will be t + 3
If both meet after 4 hours of riding, then their time will be 4 hours
Distance covered the first cyclist = 4r
Distance covered by the second = 4(r+3)
If the two cyclists are 68 miles apart, then:
4r + 4(r+3) = 68
a) The given equation using the information as it is given above that can be solved to answer this problem is 4r + 4(r+3) = 68
b) Expand the equation in a to get "r"
4r + 4r + 12 = 68
8r + 12 = 68
8r = 68 - 12
8r = 56
r = 56/8
r = 7miles per hour
Speed of the first cyclist = 7mi/hr
Speed of the second cyclist = 3 + 7mi/hr = 10mi/hr
Hence the speed of both cyclists are 3mi/hr and 10mi/hr respectively
Learn more here: https://brainly.com/question/19915685
The cost of renting a car is $55/wk plus $0.15/mi traveled during that week. An equation to represent the cost would be y = 55 + 0.15x, where x is the number of miles traveled. If your cost was $64.75, how many miles were you charged for traveling?
Answer:
65 miles
Step-by-step explanation:
y=55+0.15x
64.75=55+0.15x
9.75=0.15x
x=9.75/0.15
x=65 miles
Find the length x (plz help giving BRAINLY)
Answer:
x=3
Step-by-step explanation:
2 triangles are proportional so we have
4/6=x/4,5
--> x=(4.4,5)/6=3
You can also use sin cos but this way is faster
Let point C be the center of the circle below. What is the
approximate length of minor arc XZ? Answers are in inches.
NEED ANSWER ASAP please, check the picture
Answer:
8.58
Step-by-step explanation:
the length of minor arc XZ
= 82/360 × 2 × 3.14 × 6
= 8.58 in
You have $3.40 and would like to buy some coffee. If a pound costs $8, how many ounces can you buy?
Answer:
6.8 ounces
Step-by-step explanation:
1 lb = 16 oz
3.40/8 * 16 = 6.8
Which graph represents an exponential function?i
PLEASEEEE HELPPP IM BEING TIMEDDD WILL GIVE BRAINLIEST AND POINTS
Choose the polynomial written in standard form.
xy2 + 4x4y + 10x2
x4y2 + 4x3y + 10x
x4y2 + 4x3y5 + 10x2
x6y2 + 4x3y8 + 10x
Answer:
Can you please organize them so that the exponents are marked as x^2?
Step-by-step explanation:
To me, none of this is in standard form because the numbers are before the variables.
Using AJKL, what is the length of JK? Answers are in feet.
NEED HELP ASAP
Answer:
JK = 21 ft
Step-by-step explanation:
To find JK = x, apply Trigonometry function.
Reference angle = 65°
Opposite side = JK = x
Adjacent side = KL = 10 ft
Apply TOA:
Tan 65° = Opp/Adj
Tan 65° = x/10
Multiply both sides by 10
10*Tan 65° = x
21.4450692 = x
x = 21 ft (nearest feet)
If the code AXISEM represents the number 9.54207, what number is represented by the code XlS + SEX? a.AIM b.MIM c.MES d.SIX
Answer:
B. MIM
Step-by-step explanation:
A = 9
X = 5
I = 4
S = 2
E = 0
M = 7
XIS = 542, SEX = 205
542 + 205 = 747
747 = MIM
I am Looking For help with applications of inductive reasoning
1=1*1
1+9=2*5
1+9+17=3*9
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{1\times1=1}\\\\\bullet\large\textsf{This statement is TRUE because anything times (or multiplied)\ by 1}\\\large\textsf{is mostly likely 1}[/tex]
[tex]\mathsf{1+9=2\times5}\\\mathsf{1+9=\bf 10}\\\mathsf{2\times5}\\\mathsf{= 5+5}\\\mathsf{= 2 + 2 + 2 + 2 + 2}\\\mathsf{= \bf 10}\\\\\\\bullet\large\textsf{This statement is also TRUE because BOTH NUMBERS are EQUIVALENT}\\\large\textsf{to EACH OTHER}[/tex]
[tex]\mathsf{1 + 9 + 17 = 9\times3}\\\\\mathsf{1+9+17}\\\mathsf{1 + 9 = \bf 10}\\\mathsf{\bold{10}+ 17}\\\mathsf{= \bf 27}\\\\\\\\\\\mathsf{9\times3}\\\mathsf{= 9+9+9}\\\mathsf{3 +3 +3 +3+ 3 +3 + 3 + 3+ 3}\\\mathsf{= \bf 27}\\\\\\\\\\\bullet\large\textsf{This statement as well is TRUE because BOTH NUMBERS are}\\\large\textsf{equivalent to each other}[/tex]
[tex]\boxed{\boxed{\large\textsf{ANSWER: All statements to these equations are \bf \huge TRUE}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Does the point (3,25) lie on the line y = 6x + 7?
Answer
YesStep-by-step explanation:
Replace x and y
[tex](3 \: \: \: 25)[/tex]
[tex]y = 6x + 7 \\ 25 = 6 \times 3 + 7 \\ 25 = 18 + 7 \\ 25 = 25[/tex]
So, the point (3,25) lie on the line y=6x+7
hope this helps you.
Have a nice day!
pic is there answer 20 points
Answer:
(x+8)^2=0
Step-by-step explanation:
x^2+16x+64=0
8x8=64
8+8=16
Therefore, 8 fits
(x+8)^2=0
If this helps please mark as brainliest
Solve for 2. Round to the nearest tenth, if necessary,
С
2.5
41
Answer:
3.8
Step-by-step explanation:
We can use sohcahtoa to solve this. First, we know that this triangle is a right triangle, as well as one angle and the opposite side to that angle. We are trying to find the hypotenuse.
Therefore, as sin takes opposite and hypotenuse into account, we can use that to get that sin(41°) = 2.5/x . Multiply both sides by x and divide both sides by sin(41°) to get x = 2.5/sin(41°) =3.8
The tree nearest to the classroom is 30 feet tall.
In another 10 years it will grow 5 more feet.
If the variable h stands for the height of the tree 10 years
from now,
which of the following units could apply to that variable?
A. Feet
B. Trees
C. Pounds
D. Years
Answer: Feet
Step-by-step explanation:
In the graph above, which vertical line (v) and horizontal line (H) can be used to graph point C
Answer:
V: x= -3
H: y= -3
Step-by-step explanation:
1. In two similar triangles, find the ratio of:
b. the perimeter, if the areas are 50cm and 16cm.
Answer:
54cm and 36cm
Step-by-step explanation:
triangle a : triangle b
50cm² : 16cm²
25 : 8
thus,
area of triangle a :
2cm×25cm
=50cm²
area of triangle b :
2cm×16cm
=32cm²
then,
perimeter of triangle a:
2cm+2cm+25cm+25cm
=54cm
perimeter of triangle b:
2cm+2cm+16cm+16cm
=36cm
Get brainiest if right?
The sum of four consecutive numbers is two more than three
times the greatest of these numbers. Find the numbers.
Answer:
1, 2, 3, 4
Step-by-step explanation:
x+(x+1)+(X+2)+(X+3)+2 = 3(X+3)
4X+8=3x+9
x=1
Answer:
5,6,7,8
Step-by-step explanation:
5+6+7+8=26
8*3=24
26-24=2
Classify each triangle as right triangle or not right triangle
Answer:
Step-by-step explanation:
pythagoras theorem
a^2+b^2=c^2
21^2+20^2=29^2
441+400=841
841=841
since the sum of square of two smaller sides is equal to the square of longest side .The given triangle can form right angle.
