How many voters should be sampled for a 95% confidence interval? Round up to the nearest whole number.
Answers
Answer:
467 voters
Step-by-step explanation:
Given
See attachment for complete question
Required
Sample size at 95% confidence interval
From the attachment, we have:
[tex]p = 65\% = 0.65[/tex]
[tex]E = 4.33\% = 0.0433[/tex]
[tex]CL = 0.95[/tex]
[tex]\alpha = 0.05[/tex] i.e. 1 - CL
First, we calculate the critical level
At [tex]CL = 0.95[/tex] and [tex]\frac{\alpha}{2}[/tex]
[tex]z^* = 1.96[/tex] --- the critical level
So, we have:
[tex]n = p * (1 - p) * (\frac{z^*}{E})^2[/tex]
[tex]n = 0.65 * (1 - 0.65) * (\frac{1.96}{0.0433})^2[/tex]
[tex]n = 0.65 * (1 - 0.65) * (45.3)^2[/tex]
[tex]n = 0.65 * 0.35 * 2052.1[/tex]
[tex]n = 466.9[/tex]
[tex]n = 467[/tex] --- approximated
Related Questions
Factor out the greatest common factor.
Answers
Answer:
The answer to your question is given below.
Step-by-step explanation:
6x⁴ + 4x³ – 10x
The greatest common factor can be obtained as follow:
6x⁴ = 2 * 3 * x * x * x * x
4x³ = 2 * 2 * x * x * x
10x = 2 × 5 * x
Greatest common factor = 2 * x
= 2x
Thus, the expression 6x⁴ + 4x³ – 10x can be written as:
6x⁴ + 4x³ – 10x = 2x(3x³ + 2x² – 5)
You own a small storefront retail business and are interested in determining the average amount of money a typical customer spends per visit to your store. You take a random sample over the course of a month for 12 customers and find that the average dollar amount spent per transaction per customer is $116.194 with a standard deviation of $11.3781. Create a 90% confidence interval for the true average spent for all customers per transaction.1) ( 114.398 , 117.99 )2) ( 112.909 , 119.479 )3) ( -110.295 , 122.093 )4) ( 110.341 , 122.047 )5) ( 110.295 , 122.093 )
Answers
Answer:
(110.295, 122.093).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 12 - 1 = 11
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 11 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.7959
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.7959\frac{11.3781}{\sqrt{12}} = 5.899[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 116.194 - 5.899 = 110.295
The upper end of the interval is the sample mean added to M. So it is 116.194 + 5.899 = 122.093
So
(110.295, 122.093).
HELP ASAP I WILL GIVE BRAINLIST
Convert 7π OVER 4 radians to degrees. Which quadrant does this angle lie in?
What are the sine, cosine and tangent of the angle 7π over 4? Be sure to show and explain all work.
Answers
Answer:
7π/4 radians = 315°, Quadrant IV
sin(315°) = -√2/2
cos(315°) = √2/2
tan(315°) = -1
Step-by-step explanation:
simplify 2x²y²÷m³×m²÷2xy
Answers
Find the equation of the line passing through (3,5) with a slope of 1
WILL GIVE BRAINLIEST
Answers
Slope-intercept form:
y = x + 2
Point-slope form:
y − 5 = 1 ⋅ ( x − 3 )
I hope this is correct and helps!
If V= {i}, subset of V are?
Answers
Answer:
Defintion. A subset W of a vector space V is a subspace if
(1) W is non-empty
(2) For every v, ¯ w¯ ∈ W and a, b ∈ F, av¯ + bw¯ ∈ W.
Expressions like av¯ + bw¯, or more generally
X
k
i=1
aiv¯ + i
are called linear combinations. So a non-empty subset of V is a subspace if it is
closed under linear combinations. Much of today’s class will focus on properties of
subsets and subspaces detected by various conditions on linear combinations.
Theorem. If W is a subspace of V , then W is a vector space over F with operations
coming from those of V .
In particular, since all of those axioms are satisfied for V , then they are for W.
We only have to check closure!
Examples:
Defintion. Let F
n = {(a1, . . . , an)|ai ∈ F} with coordinate-wise addition and scalar
multiplication.
This gives us a few examples. Let W ⊂ F
n be those points which are zero except
in the first coordinate:
W = {(a, 0, . . . , 0)} ⊂ F
n
.
Then W is a subspace, since
a · (α, 0, . . . , 0) + b · (β, 0, . . . , 0) = (aα + bβ, 0, . . . , 0) ∈ W.
If F = R, then W0 = {(a1, . . . , an)|ai ≥ 0} is not a subspace. It’s closed under
addition, but not scalar multiplication.
We have a number of ways to build new subspaces from old.
Proposition. If Wi for i ∈ I is a collection of subspaces of V , then
W =
\
i∈I
Wi = {w¯ ∈ V |w¯ ∈ Wi∀i ∈ I}
is a subspace.
Proof. Let ¯v, w¯ ∈ W. Then for all i ∈ I, ¯v, w¯ ∈ Wi
, by definition. Since each Wi
is
a subspace, we then learn that for all a, b ∈ F,
av¯ + bw¯ ∈ Wi
,
and hence av¯ + bw¯ ∈ W. ¤
Thought question: Why is this never empty?
The union is a little trickier.
Proposition. W1 ∪ W2 is a subspace iff W1 ⊂ W2 or W2 ⊂ W1.
i hope this helped have a nice day/night :)
Find the radius of a circle with a diameter whose endpoints are (-7,1) and (1,3).
Answers
Answer:
r = 4.1231055
Step-by-step explanation:
So to do this, you need to find the distance between the two points:
(-7,1) and (1,3).
To do this, the distance or diameter (d) is equal to:
d = sqrt ((x2-x1)^2 + (y2-y1)^2)
In this case:
d = sqrt( (1 - (-7))^2 + (3 - 1)^2 )
d = sqrt( 8^2 + 2^2)
d = sqrt( 64 + 4)
d = sqrt( 68 )
The radius is half of the diameter, so:
r = 1/2 * d
r = 1/2 * sqrt( 68 )
r~ 4.1231055
Decide which of the two given prices is the better deal and explain why.
You can buy shampoo in a 5-ounce bottle for 3,89$ or in a 14-ounce bottle for 11,99$.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.The -ounce bottle is the better deal because the cost per ounce is $
nothing per ounce while the -ounce bottle is $
nothing per ounce.
B.The -ounce bottle is the better deal because the cost per ounce is $
nothing per ounce while the -ounce bottle is $
nothing per ounce.
(Round to the nearest cent as needed.)
Answers
Answer:
The 14-ounce bottle is the better deal
Step-by-step explanation:
I know this beause inorder to figure out which one is better you have to make them the same price and then see which bottle has more ounces. So I made each price 1$ so there is 1.58-ounces per dollar in the 5-ounce bottle and 1.17 -ounces per dollar in the 14-ounce bottle.
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 100 mm
Answers
Answer:
The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.
Step-by-step explanation:
Volume of a sphere:
The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
How fast is the volume increasing:
To find this, we have to differentiate the variables of the problem, which are V and r, implicitly in function of time. So
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
The radius of a sphere is increasing at a rate of 2 mm/s.
This means that [tex]\frac{dr}{dt} = 2[/tex]
How fast is the volume increasing (in mm3/s) when the diameter is 100 mm?
Radius is half the diameter, so [tex]r = \frac{100}{2} = 50[/tex]
Then
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt} = 4\pi (50)^2(2) = 62832[/tex]
The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.
A wooden log 10 meters long is leaning against a vertical wall with its other end on the ground. The top end of the log is sliding down the wall. When the top end is 6 meters from the ground, it slides down at 2m/sec. How fast is the bottom moving away from the wall at this instant?
Answers
Answer:
Step-by-step explanation:
This is a related rates problem from calculus using implicit differentiation. The main equation is Pythagorean's Theorem. Basically, what we are looking for is [tex]\frac{dx}{dt}[/tex] when y = 6 and [tex]\frac{dy}{dt}=-2[/tex].
The equation for Pythagorean's Theorem is
[tex]x^2+y^2=c^2[/tex] where x and y are the legs and c is the hypotenuse. The length of the hypotenuse is 10, so when we find the derivative of this function with respect to time, and using implicit differentiation, we get:
[tex]2x\frac{dx}{dt}+2y\frac{dy}{dt}=0[/tex] and divide everything by 2 to simplify:
[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex]. Looking at that equation, it looks like we need a value for x, y, [tex]\frac{dx}{dt}[/tex] and [tex]\frac{dy}{dt}[/tex].
Since we are looking for [tex]\frac{dx}{dt}[/tex], that can be our only unknown and everything else has to have a value. So what do we know?
If we construct a right triangle with 10 as the hypotenuse and use 6 for y, we can solve for x (which is the only unknown we have, actually). Using Pythagorean's Theorem to solve for x:
[tex]x^2+6^2=10^2[/tex] and
[tex]x^2+36=100[/tex] and
[tex]x^2=64[/tex] so
x = 8.
NOW we can fill in the derivative and solve for [tex]\frac{dx}{dt}[/tex].
Remember the derivative is
[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex] so
[tex]8\frac{dx}{dt}+6(-2)=0[/tex] and
[tex]8\frac{dx}{dt}-12=0[/tex] and
[tex]8\frac{dx}{dt}=12[/tex] so
[tex]\frac{dx}{dt}=\frac{12}{8}=\frac{6}{4}=\frac{3}{2}=1.5 m/sec[/tex]
An environmentalist would like to estimate the true mean weight of all cars. To do so, she selects a random sample of
30 cars and determines that the 90% confidence interval for the true mean weight to be 2.8 to 3.4 tons. Which of the
following would increase the margin of error for this confidence interval?
O selecting another sample
O increasing the sample size
O increasing the confidence level
O decreasing the confidence level
Answers
If the confidence level will increase, the margin of error will also increases.
What is margin of error?The margin of error is defined a range of values below and above the sample statistic in a confidence interval.
What is confidence interval?The confidence interval is a way to show what is uncertainty is with a certain statistic.
According to the given question
Environmentalist estimating true mean weight or all cars.
For the true mean weights of 2.8 to 3.4 tons the confidence level is 90%.
Since, the confidence level increases, the critical value increases and hence the margin of error increases.
Therefore, if the confidence level will increase, the margin of error will also increases.
Find out more information about confidence interval and margin error here:
https://brainly.com/question/15079850
#SPJ2
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 95 miles per hour. The westbound train travels at 75 miles per hour. How long will it take for the two trains to be 238 miles apart? Do not do any rounding.
Answers
Answer:
They are going away from each other.
So add up their speed.
combined speed = x+x-16
=2x-16
Time = 2 hours
Distance = 400 miles
Distance = speed * time
(2x-16)* 2
4x-32=400
4x=400+32
4x=432
/12
x=108 mph west bound
east bound = 108 -16 = 92 mph
Identify the transformation that occurs to create the graph of m(x)
m(x)=f(5x)
Answers
Answer:
m(x) is a dilation of scale factor K = 1/5 of f(x).
Step-by-step explanation:
The transformation is a horizontal dilation
The general transformation is defined as:
For a given function f(x), a dilation of scale factor K is written as:
g(x) = f(x/K)
If K > 1, then we have a dilation (the graph contracts)
if 0 < K < 1, then we have a contraction (the graph stretches)
Here we have m(x) = f(5*x)
Then we have a scale factor:
K = 1/5
So this is a contraction.
Then the transformation is:
m(x) is a dilation of scale factor K = 1/5 of f(x).
Estimate the student's walking pace, in steps per minute, at 3:20 p.m. by averaging the slopes of two secant lines from part (a). (Round your answer to the nearest integer.)
Answers
This question is incomplete, the complete question is;
A student bought a smart-watch that tracks the number of steps she walks throughout the day. The table shows the number of steps recorded (t) minutes after 3:00 pm on the first day she wore the watch.
t (min) 0 10 20 30 40
Steps 3,288 4,659 5,522 6,686 7,128
a) Find the slopes of the secant lines corresponding to the given intervals of t.
1) [ 0, 40 ]
11) [ 10, 20 ]
111) [ 20, 30 ]
b) Estimate the student's walking pace, in steps per minute, at 3:20 pm by averaging the slopes of two secant lines from part (a). (Round your answer to the nearest integer.)
Answer:
a)
1) for [ 0, 40 ], slope is 96
11) for [ 10, 20 ], slope is 86.3
111) for [ 20, 30 ], slope is 116.4
b) the student's walking pace is 101 per min
Step-by-step explanation:
Given the data in the question;
t (min) 0 10 20 30 40
Steps 3,288 4,659 5,522 6,686 7,128
SLOPE OF SECANT LINES
1) [ 0, 40 ]
slope = ( 7,128 - 3,288 ) / ( 40 - 0
= 3840 / 40 = 96
Hence slope is 96
11) [ 10, 20 ]
slope = ( 5,522 - 4,659 ) / ( 20 - 10 )
= 863 / 10 = 86.3
Hence slope is 86.3
111) [ 20, 30 ]
slope = ( 6,686 - 5,522 ) / ( 30 - 20 )
= 1164 / 10 = 116.4
Hence slope is 116.4
b)
Estimate the student's walking pace, in steps per minute, at 3:20 pm by averaging the slopes of two secant lines from part .
Since this is recorded after 3:00 pm
{ 3:20 - 3:00 = 20 }
so t = 20 min
so by average;
we have ( [ 10, 20 ] + [ 20, 30 ] ) /2
⇒ ( 86.3 + 116.4 ) / 2
= 202.7 /2
= 101.35 ≈ 101
Therefore, the student's walking pace is 101 per minutes
PLEASE HELP WILL MARK BRAINLIST AND GIVE 20 POINTS
Answers
Answer:
The first one
Step-by-step explanation:
You just need to find the slope in the average of all the dots.
Answer:
the first option, y=3/7x-3
Step-by-step explanation:
the scatterplot begins around y=-3, so therefore the y-intercept is -3. The slope is obviously not higher than 1, so it is y=3/7x-3.
Find in the triangle. Round to the nearest degree.
Answers
Answer:
D. 34
Step-by-step explanation:
Because this is a right triangle we can use sin, cos, tan.
Use cosine because the values of the adjacent side and hypotenuse are already given.
cos(θ) = 72/87
Because we are solving for the angle measure (and not the measure of the side) we need to use inverse cos.
cos⁻¹ = 72/87
put into a calculator and answer is approximatelyn34 degrees.
according to byu idaho enrollment statisct there are 1200 femaile studnet here on campus during any given semester of those 3500 have serced a msion what is the probability that a radnoly selcted femal studne ton cmapus wil have served a mission g
Answers
Answer:
0.2917 = 29.17% probability that a randomly selected female student on campus will have served a mission.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
1200 female students, out of them, 350 have served a mission. So
[tex]p = \frac{350}{1200} = 0.2917[/tex]
0.2917 = 29.17% probability that a randomly selected female student on campus will have served a mission.
Which line is parallel to the line that passes through the points (1,7) and (-3, 4)? A. y=--x-5 B. y=+*+1 y=-x-8 O c. D. 11 v==x+3 4
Answers
Answer:
B
Step-by-step explanation:
because
Find the union {6, 11, 15} U Ø
Answers
Explanation:
The Ø means "empty set". It's the set with nothing inside it, not even 0.
We can write Ø as { } which is a pair of curly braces with nothing between them.
The rule is that if we union any set A with Ø, then we'll get set A
A U Ø = A
Ø U A = A
In a sense, it's analogous to adding 0. So it's like saying A+0 = A and 0+A = A.
So that's why {6, 11, 15} U Ø = {6, 11, 15}
There's nothing to add onto the set {6, 11, 15}, so we just get the same thing back again.
Find m < A
Round to the nearest degree.
CA = 6
CB = 13
AB = 10
Answers
CA=6 is 6.0
CB= 13 is 13.0
AB= 10 is 10.0
Look at the numbers in the bon
5
9
-11
6
-21
9
-6
-10
20
1
Find four numbers whose sum is 5
Answers
I need help answering this question.
Answers
Answer:
6x
Step-by-step explanation:
If x is the length of one side, and each side is the same length, you will multiply it by 6 times (there are 6 sides in a hexagon).
So, you will add it up 6 times, but you can say 6x for short.
Can someone pls help asap i will give Brainliest
Answers
Answer:
24/145
Step-by-step explanation:
Trigonometric identities are equalities involving trigonometric functions and remains true for entire values of the variables involved in the equation.
Some trigonometric identities are:
sin(a + b) = sinacosb + cosasinb; sin(a - b) = sinacosb - cosasinb
cos(a + b) = cosacosb - sinasinb; cos(a - b) = cosacosb + sinasinb
Given that sin a = 3/5. sin a = opposite/hypotenuse.
Hence opposite = 3, hypotenuse = 5. using Pythagoras:
hypotenuse² = opposite² + adjacent²
5² = 3² + adjacent²
adjacent² = 16
adjacent = 4
Given that sin a = 3/5. a = sin⁻¹(3/5) = 36.86
cos a = cos 36.86 = 4/5
cos b = -20/29; b = cos⁻¹(-20/29) = 133.6
sinb = sin(133.6) = 21/29
sin(a + b) = sinacosb + cosasinb = (3/5 * -20/29) + (4/5 * 21/29) = -12/29 + 84/145
sin(a + b) = 24/145
Young invested GH150,000 and 2.5% per annum simple interest. how long will it take this amount to. yield an interest of GH11,250,00
Answers
Answer: 3 years
Step-by-step explanation:
Interest is calculated as:
= (P × R × T) / 100
where
P = principal = 150,000
R = rate = 2.5%.
I = interest = 11250
T = time = unknown.
I = (P × R × T) / 100
11250 = (150000 × 2.5 × T)/100
Cross multiply
1125000 = 375000T
T = 1125000/375000
T = 3
The time taken will be 3 years
HELP HELP HELPPPP
ILL GIVE BRAINLIEST HELPPPPPPPPP
100 POINTSSS
Answers
Answer:
C. 0.48
Step-by-step explanation:
Probability = number of required outcome
_______________________
number of possible outcome
= total volleyball game events
_______________________
total sophomore + junior
= 66/137
= 0.48
Answer: D) 0.31
Step-by-step explanation:
Let A denote the event that a person is a sophomore.
Let B denote the event that a person has attended volleyball game.
A∩B denote the event that a person is a sophomore and attend volleyball game.
Let P denote the probability of an event.
We are asked to find:
P(A∩B)
From the table provided to us we see that:
A∩B=42
Hence,
P(A∩B)=42/137=0.3065 which is approximately equal to 0.31. Therefore ur answer will be 0.31.
please help with this quadratic equations
Answers
Answer:
I don't understand the question
1) 3(x+12)
2) 4x(x+14)
3) x^2-14x-40
4) (x-2)(x-12)
5) (x^2+4) (x+2) (x-2)
6) (9x+7) (9x-7)
7) 2(5x+6) (5x-6)
8) 2(x+1) (x-9)
9) (4x-3) (x+5)
10) 7x(5-2x)
11) (x-3) (x^2+5)
12) (s+5) (5r-3)
13) (5x-6x)
14) (5x-4) (25^2+20x+16)
15) 2(x+4y) (x^2-4xy+16y^2
:3
Which expression is equivalent to -9x-1y-9/-15x5y-3?
Answers
Answer: -9x-1y-9/
Step-by-step explanation:
Answer: b
Step-by-step explanation:
I really dont like edge
6(5x/3 -4/3 - 2)= 6 (3 - 6x/6 +4/6)
Answers
Answer:
21/8x
Step-by-step explanation:
10x -20 = -6x+22
+6x-20 = 22
16x-20 = 22
16x +20= +20
16x/16x = 42/16x
x = 21/8x
question:
A sequence is defined by the recursive function f(n + 1) = –10f(n).
If f(1) = 1, what is f(3)?
3
–30
100
–1,000
the answer is 100
Answers
Answer:
100
Step-by-step explanation:
f(1) = 1
f(2) = -10×f(1) = -10 × 1 = -10
f(3) = -10×f(2) = -10 × -10 × f(1) = -10 × -10 × 1 = 100
f(n) = -10 to the power of n-1
Answer:
c - 100
Step-by-step explanation:
I need help answering this question.
Answers
Answer:
hello dude
x - 9 = - 12
x = 9 -12
x = -3
HAVE A NİCE NİGHT
Step-by-step explanation:
Greetings from Turkey
We have to,
find the required value of x.
Let's start,
→ x - 9 = -12
→ x = -12 + 9
→ x = -3
Thus, -3 is the value of x.
