A candidate for one of Ohio's two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered voters in the northern half of the state is selected, of which 1062 support the candidate. Additionally, a random sample of 2000 registered voters in the southern half of the state is selected, of which 900 support the candidate. A 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is:
Answer:
The 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is (0.05, 0.112).
Step-by-step explanation:
Before building the confidence interval, the central limit theorem and subtraction of normal variables is explained.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Northern half:
1062 out of 2000, so:
[tex]p_N = \frac{1062}{2000} = 0.531[/tex]
[tex]s_N = \sqrt{\frac{0.531*0.469}{2000}} = 0.0112[/tex]
Southern half:
900 out of 2000, so:
[tex]p_S = \frac{900}{2000} = 0.45[/tex]
[tex]s_S = \sqrt{\frac{0.45*0.55}{2000}} = 0.0111[/tex]
Distribution of the difference:
[tex]p = p_N - p_S = 0.531 - 0.45 = 0.081[/tex]
[tex]s = \sqrt{s_N^2 + s_S^2} = \sqrt{0.0112^2 + 0.0111^2} = 0.0158[/tex]
Confidence interval:
The confidence interval is:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
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].
The lower bound of the interval is:
[tex]p - zs = 0.081 - 1.96*0.0158 = 0.05[/tex]
The upper bound of the interval is:
[tex]p + zs = 0.081 + 1.96*0.0158 = 0.112[/tex]
The 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is (0.05, 0.112).
You are driving 2760 miles across the country. During the first 3 days of your trip, you drive 1380 miles. If you continue to drive at the same rate each day, how many days will the entire trip take? Show your work and circle your answer.
The entire trip will take 6 days.
(Encircle this answer, as said on the directions)
Step-by-step explanation:
We know that the first three days of the trip, we traveled 1380 miles.
Find the UNIT RATE of MILES PER day:
1380/3 = 460
Unit rate = 460 miles per day
If we were to drive at this (460 mi per day) rate EACH day and the whole journey takes 2760 miles across the country.
FInd the NUMBER of DAYS of the ENTIRE TRIP:
2760/460 = 6
It will take us 6 days to drive to the destination.
Help pls ?? I really don’t know what to do
Answer:
The answer is "C" f(x)= x+ 4 and g(x)= x^3 - 1
Step-by-step explanation:
all you have to do is replace the x in "G" with the "F" function
F(x) = x+4 and G(x) = x^3-1
===========================================================
Explanation:
Let's try choice A to see if it works or not
G(x) = (x+4)^3
G( F(x) ) = ( F(x)+4 ) ^3 .... replace every x with F(x)
G( F(x) ) = ( x-1+4 ) ^3 .... plug in F(x) = x-1
G( F(x) ) = (x+3)^3
This isn't the same as (x+4)^3 - 1. You can confirm this with a graph or a table of values. We cross choice A off the list.
------------
Let's try choice B
G(x) = x+4
G( F(x) ) = F(x)+4
G( F(x) ) = x^3-1 + 4
G( F(x) ) = x^3 + 3
Similar to choice A, this isn't the same as (x+4)^3-1. We can cross this off the list as well.
--------------
Now choice C
G(x) = x^3 - 1
G( F(x) ) = ( F(x) )^3 - 1
G( F(x) ) = (x+4)^3 - 1
We found the final answer.
Plzzzz someone help. Will mark brainiest is correct!!!!
Photo attached
Answer:
Your last step ( step 5 ) :
[tex] {x}^{2} + \frac{b}{a} x + \frac{ {b}^{2} }{4 {a}^{2} } = - \frac{c}{a} + \frac{ {b}^{2} }{4 {a}^{2} } [/tex]
Step 6:
[tex]{ \boxed{x + ( \frac{b}{2a}) = ± \frac{ \sqrt{ {b}^{2} - 4ac } }{ \sqrt{4a^2} } }}[/tex]
Step-by-step explanation:
[tex] {x}^{2} + \frac{b}{a} x + \frac{ {b}^{2} }{4 {a}^{2} } = - \frac{4ac}{4 {a}^{2} } + \frac{ {b}^{2} }{4 {a}^{2} } \\ \\ {x}^{2} + \frac{b}{a} x = \frac{4ac}{4a {}^{2} } \\ \\ {x} = \sqrt{ \frac{ - 4ac + b {}^{2} }{4a {}^{2} } } [/tex]
.,............. ..... ..nnkkjk
Help! ASAP. The question is in the attachment below
Answer:
Step-by-step explanation:
The most obvious answer is the line y = 1.
The cost of a pen is three times and Rs 4 more than the cost of a pencil. If three pencils and two pens cost Rs 71, find the cost of each item.
Answer:
1.
= Here,
cost of pen = 3+4 ( x ) = 7x
costs of two pen = 7x
cost of three pencils = 71 - 7x = 64x
cost of 1 pencil = 64/3
= 21.333334
c
13. A pair of shoes sell for $27 per pair. There is a sale tomorrow on shoes offering two pairs for $45.
How much will 3 pairs of shoes cost today?
Answer:
$72
Step-by-step explanation:
The sale offers 2 pair of shoes for $45, but the price is same for 1 pair of shoes.
The cost of 3 pair of shoes
= The sale price of 2 pair of shoes + Regular price of 1 pair of shoes
= $45 + $27
= $72
So, 3 pairs of shoes will cost $72 today.
Help pls will give brainliest
Answer:
195.06
Step-by-step explanation:
area of circle = πr^2 = π8^2 = 64π
area of triangle = 1/2 x 4 x 3 = 6
area of shape = 64π-6 = 195.061929 = 195.06
Write a slope-intercept equation for a line passing through the point (5,-5) that is parallel to the line x = -2. Then write a second equation for a line passing through the point (5,-5) that is perpendicular to the line x=-2.
Answer:
1. y=-2x+5
2. y=1/2x-7.5
Step-by-step explanation:
you plug in the cordinates for the y intercept and you already have the slope.
y=mx+b
m= slope which is -2
CAN SOMEBODY HELP ME PLS GIVE THE CORRECT ANSWER IM FAILING BUT ITs PYTHAGOREAN THEOREM
Answer:
c=65
Step-by-step explanation:
Answer:
c=65
Step-by-step explanation:
c=a2+b2=63
632+162=65
A student said that since -9 is less than 4, then |-9| is less than |4|. Is the student correct? Explain why or why not.
Answer:
No.
Step-by-step explanation:
They are not correct because the "| |" signs mean absolute value. What ever is inside the signs must be positive. So -9 becomes 9 and 9 is greater than 4. So, the student is not correct.
Determining the Domain and Range from a Graph
Determine the domain and range of the given function.
The domain is
ty
4
The range is
2
-4
-2
4
Into
Answer:
Domain is all real numbers, and range is all numbers greater than or equal to -2. If thee was anything you didn't understand let me know.
Step-by-step explanation:
The domain is what x values work, or it may be better to say the horizontal axis. is there any number you cannot use? if you cannot tell, this is a parabola, like x^2. Is there any number you cannot plug into x^2. The answer is no, the domain for all parabolic functions is all real numbers.
The range you really want to look at visually here. Range is y values you can get, or values on the vertical axis. I would also compare it to x^2 again. You should know you can make it as high as you want, here is the same. but at -2, there is no point below that. so the range is -2 and up
The other options are just specific numbers. you can disprove those by choosing a number not on their lists. For the domain literally any other number. For range any number not on the list greater than -2
Find the exact value of the indicated trigonometric function for the acute angle a:
Given: sin a=5/13, Find: cos a and tan a
Answer:
cos a = 12/13
tan a = 5/12
You use these properties to solve the question,
sin²a+cos²a=1
tana=sina/cosa
Solve the equation :
-3 • ( 2 - x ) + 4 = 2 • ( 1 - 2x) + 3
thanks :)
Isolate the variable by dividing each side by factors that don't contain the variable.
x = 1
-6+3x+4=2-4x+3
-8+7x+1=0
7x=7
x=1
Answer:
x=1
Step-by-step explanation:
SEE IMAGE for Solution
which of the following functions are an example of exponential decay???
Answer:
C. II only
Step-by-step explanation:
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please help me solve this exercise.!!
find the value of tanx if sinx+cosx=1/5 and 0<x<π.
=============================================================
Explanation:
Let's square both sides and do a bit of algebra to get the following.
[tex]\sin(x) + \cos(x) = 1/5\\\\\left(\sin(x) + \cos(x)\right)^2 = \left(1/5\right)^2\\\\\sin^2(x) + 2\sin(x)\cos(x) + \cos^2(x) = 1/25\\\\\sin^2(x) + \cos^2(x) + 2\sin(x)\cos(x) = 1/25\\\\1 + 2\sin(x)\cos(x) = 1/25\\\\\sin(2x) = 1/25 - 1\\\\\sin(2x) = 1/25 - 25/25\\\\\sin(2x) = -24/25\\\\[/tex]
Now apply the pythagorean trig identity to determine cos(2x) based on this. You should find that cos(2x) = -7/25
This then means tan(2x) = sin(2x)/cos(2x) = 24/7.
From here, you'll use this trig identity
[tex]\tan(2x) = \frac{2\tan(x)}{1-\tan^2(x)}\\\\[/tex]
which is the same as solving
[tex]\tan(2x) = \frac{2w}{1-w^2}\\\\[/tex]
where w = tan(x)
Plug in tan(2x) = 24/7 and solve for w to get w = -4/3 or w = 3/4
So either tan(x) = -4/3 or tan(x) = 3/4.
If we were to numerically solve the original equation for x, then we'd get roughly x = 2.21; then notice how tan(2.21) = -1.345 approximately when your calculator is in radian mode.
Since tan(x) < 0 in this case, we go for tan(x) = -4/3
A rental car company charges $29 per day to rent a car and $0.09 for every mile driven. Claire wants to rent a car, knowing that:
She plans to drive 400 miles.
She has at most $210 to spend.
Use the drop-down menu below to write an inequality representing dd, the total number of days Claire can rent the car while staying within her budget.
The required inequality that expresses the given condition is 36 + 29x ≤ 210.
Given that,
A rental car company charges $29 per day to rent a car and $0.09 for every mile driven. Claire wants to rent a car, knowing that she plans to drive 400 miles. she has at most $210 to spend.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the number of days be x,
Total cost to drive 400 miles = 400(0.09) = $36.
According to the question,
36 + 29x ≤ 210
Thus, the required inequality that expresses the given condition is 36 + 29x ≤ 210.
Learn more about inequality here:
brainly.com/question/14098842
#SPJ5
Simplify xy-5x+y^2xy−5x+y 2 if x = -3 and y = 5.
The simplification of the expression [tex]xy-5x+y^2xy-5x+y ^2[/tex] gives - 335.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
Given;
[tex]xy-5x+y^2xy-5x+y ^2[/tex]
Substitute x = -3 and y = 5.
[tex]-3\times 5-5\times -3+5^2\times -3\times 5-5\times -3+5 ^2[/tex]
= -15 + 15 - 375 + 15 + 25
= -335
Learn more about simplification;
https://brainly.com/question/17579585
#SPJ1
please help me is for my homework
Answer:
50%
Step-by-step explanation:
so 1 half is colored in so 1/2 is also 50%
Answer:
it's 50% because it's half the circle
[tex]\frac{\sqrt{x} +1}{x-\sqrt{x} +1}[/tex] Với x≥0. Tìm GTLN
Answer:
Step-by-step explanation:
[tex]\frac{\sqrt{x}+1 }{x-\sqrt{x}+1 }=\frac{\sqrt{x}+1}{(x+1)-\sqrt{x}}\\\\=\frac{(\sqrt{x}+1)([x+1]+\sqrt{x})}{([x+1]-\sqrt{x})+([x+1)+\sqrt{x}])}\\\\=\frac{\sqrt{x}*x+\sqrt{x}*1+\sqrt{x}*\sqrt{x}+1*x+1*1+1*\sqrt{x}}{(x+1)^{2}-(\sqrt{x})^{2}}\\\\\\=\frac{x\sqrt{x}+\sqrt{x}+x+1+x+\sqrt{x}}{x^{2}+2x+1-x}\\\\=\frac{x\sqrt{x}+2\sqrt{x}+2x+1}{x^{2}+x+1}\\\\[/tex]
Taehyung was sitting on the ground flying a kite. He had 22 feet of line let out to fly his kite, and the kite was 14 feet in front of him. How high was the kite?
30^∘ Another boy is standing on the roof of a 10 second string be x mIn Δ ABC sin 30^∘ = AC/AB 1/2 = AC/100 AC =
Answer: hope this helps ♡
The kite was 16.9 feet high.
Step-by-step explanation:
Pythagorean theorem
b = [tex]\sqrt{c^{2} - a^{2} }[/tex]
b = [tex]\sqrt{22^{2} - 14^{2} }[/tex]
b = [tex]\sqrt{484 - 196}[/tex]
b = [tex]\sqrt{288}[/tex]
b = 16.9
Write the ratio as a fraction in simplest form with whole numbers in the numerator and denominator
Answer:
3:8
Step-by-step explanation:
1.2 to 3.2 is 12:32 or 3:8
Answer:
3/8
Step-by-step explanation:
1.20/3.20
= 12/32
= 3/8 (divide top and bottom by 4)
I hope this helped! :D
pls helppppppp it’s due in 20 minutes
Answer:
hope this helps you
havea great dayy
Answer:
39
Step-by-step explanation:
3(6m-17)
3(30-17)
3(13)
39
I need help please Brainly fam
Answer:
The third one
Step-by-step explanation:
Just took the quiz
Which Venn Diagram is NOT correct?
2. Mr. McGrath is ordering pizza for the girls soccer team. A large cheese pizza costs $10, plus 80¢ for each
additional topping (including extra cheese!).
Complete the table below.
Answer:
i think iys 6 lol
Step-by-step explanation:
its wright
help please, i'll give brainliest
not sure how to solve
1. Paulina wants to find the width, AB, of a river. She walks along the edge of the river 200 ft and marks point C. Then she walks 60 ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location, as shown. (a) Can Paulina conclude that ΔABC and ΔEDC are similar? Why or why not? (b) Suppose DE = 40 ft. Calculate the width of the river, AB. Show all your work and round answer to the nearest tenth. Answer
Answer:
Step-by-step explanation:
a). In ΔABC and ΔEDC,
Since, AB and DE are parallel and AE is a transversal,
Therefore, ∠CAB ≅ ∠CED [Alternate interior angles]
m∠D = m∠B = 90°
ΔABC ~ ΔEDC [By AA property of similarity of two triangles]
b). Therefore, by the property of similar triangles,
"Corresponding sides of two similar triangles are proportional"
[tex]\frac{DC}{BC}= \frac{DE}{AB}[/tex]
[tex]\frac{60}{200}=\frac{40}{AB}[/tex]
AB = [tex]\frac{40\times 200}{60}[/tex]
= 133.33
≈ 133.3 ft
Please help me solve this fast!
Answer:
base = 18.89
legs = 16.89
Step-by-step explanation:
x + x + 68 = 180
2x + 68 = 180
2x = 112
x = 56
The altitude = 14
Tan(56) = opposite / adjacent
adjacent = base
opposite = altitude
Tan(56) = opposite / base Multiply both sides by the base
base * Tan(56) = opposite Divide by Tan(56)
base = opposite / Tan(56)
base = 14/tan(56)
base = 9.443
The base is actually twice this length because the altitude lands on the midpoint of the opposite side and is perpendicular to the third side (base).
base = 18.886
Legs are the hypotenuse formed by 1/2 the base and the attitude.
Sin(56) = opposite / hypotenuse
Sin(56) = altitude / hypotenuse
hypotenuse = altitude / Sin(56)
hypotenuse = 14 / sin(56)
hypotenuse = 16.887
Rounded
base = 18.89
legs = 16.89
