Using the z-distribution and the formula for the margin of error, it is found that:
a) A sample size of 54 is needed.
b) A sample size of 752 is needed.
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]\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]\frac{1+\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].
Item a:
The estimate is [tex]\pi = 0.213 - 0.195 = 0.018[/tex].
The sample size is n for which M = 0.03, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.018(0.982)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.018(0.982)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.018(0.982)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.018(0.982)}}{0.03}\right)^2[/tex]
[tex]n = 53.1[/tex]
Rounding up, a sample size of 54 is needed.
Item b:
No prior estimate, hence [tex]\pi = 0.05[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.5(0.5)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]
[tex]n = 751.7[/tex]
Rounding up, a sample of 752 should be taken.
A similar problem is given at https://brainly.com/question/25694087
what is the greatest number of obtuse angles that a right triangle can contain
Step-by-step explanation:
i think this is the answer
Answer:
ZeroStep-by-step explanation:
Obtuse angle is the angle greater than 90°.
A right triangle has one 90° and the sum of remaining angles is 90°.
It means a right triangle can't have an obtuse angle.
Write 5 • 5 • 5 • 5 • 5 • 5 • 5 using an exponent.
Answer:
5^6
Step-by-step explanation:
5 was multiplied repeatedly 6 times, so it's 5 to the power of 6
Answer:
5 to the power of 6 or 5^6
Step-by-step explanation:
this cubiod is made from 6 small cubes write how many small cubes there are in this cubiod
Pleas help
Answer:
16 I guess.
Step-by-step explanation:
lolololololol?
If a slingshot is used to shoot a marble straight up into the air from 2 meters above the
ground with an initial velocity of 30 meters per second, for what values of time t will the
marble be over 35 meters above the ground? (Refer to Exercise 25 in Section 2.3 for assistance
if needed.) Round your answers to two decimal places
Answer:
use this equation: GPE=mgh
Step-by-step explanation:
GPE = gravitational potential energy = J
m = mass = Kg
g = gravitational field = N/kg = world's gravitational field is 9.8N/kg
h = height = m
The graph of the linear function is shown on the coordinate grid. What is the equation of this line?
Study the visual fraction below.
Answer:
The answer would be D
Step-by-step explanation:
5 1/3 ÷ 2/3 = 8
16/3 ÷ 2/3 = 8
16 ÷2 = 8
-4/5 divided by 1/3
Please asap
the straight up answer is -12/5
Can someone help? anyone?
Answer:
The right answer is letter C.
Step-by-step explanation:
I hope it's help
have a nice day and night
Central/Inscribed angles w work pls i beg last one
=======================================================
Explanation:
Let point A be the center of the circle.
The inscribed angle CED doubles to the central angle CAD due to the inscribed angle theorem.
angle CAD = 2*(angle CED)
angle CAD = 2*(7x+6)
angle CAD = 14x+12
Angle CAD is the same as minor arc CD. These are two different ways to describe the same thing more or less. This is because the central angle subtends or cuts off the minor arc CD.
-----------
The three arc pieces CE, ED and CD all combine to form a 360 degree circle.
(arc CE) + (arc ED) + (arc CD) = 360
(18x+1) + (13x+1) + (14x+12) = 360
(18x+13x+14x) + (1+1+12) = 360
45x+14 = 360
45x = 360-14
45x = 346
x = 346/45
This approximates to roughly x = 7.6889, but I have a feeling your teacher will want the fraction form.
Xy3-9xyz2 is my math problem and I need help with the complete breakdown
(x • (y³)) - 32xyz²
Pull out like factors :
xy³ - 9xyz² = xy • (y² - 9z²)
Factoring: y² - 9z²
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A² - AB + BA - B² =
A² - AB + AB - B² =
A² - B²
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 9 is the square of 3
Check : y² is the square of y¹
Check : z² is the square of z¹
Factorization is : (y + 3z) • (y - 3z)
Final result :
xy • (y + 3z) • (y - 3z)
4. Simplify: -3(2x - 5)-2(4x+3)
A.14x-9
B.-2x+21
C.-14x+9
D.-14x+ 21
Can someone help me ?
Simplify.
5x+3(x+2)+3
A. 8x + 9
B. 5x + 8
C. 8x + 5
D. 6x + 8
Answer:
A- 8x+9
Step-by-step explanation:
------------------------------------------
5x + 3 (x + 2) + 3
5x + 3x + 6 + 3
8x + 6 + 3
8x + 9
<3
What is the value of v?
By isosceles triangle theorem,
Angle ZXY = Angle ZYX
The sum of the angles in a triangle is 180 degrees.
106 + 2 same angles (-106) = 180 (-106) (Subtract 106 by both sides)
2 same angles (/ 2) = 74 (/ 2) (Divide 2 by both sides)
V = 37
Answer:
The value of v is 37°.
Step-by-step explanation:
Given that △ XYZ is an isosceles triangle where both sides have the equal angles. The total angle of △ is 180°. Let ∠ZXY and ∠ZYX be the same angles:
Let ∠ZXY = v, ∠ZYX = v, ∠ XZY = 106°,
∠ZXY + ∠ZYX + ∠XZY = 180°
v + v + 106° = 180°
2v + 106° = 180°
2v = 180° - 106°
2v = 74°
v = 74 ÷ 2
v = 37°
Given the definitions of f(x) and g(x) below, find the value of g(f(-3)). f(x) = 5x + 11 g(x) = x2 + 4x – 11
Answer:
g(f(-3)) = -11
Step-by-step explanation:
First, we evaluate f(-3) and then plug that value into g(x) for x:
f(x) = 5x + 11
f(-3) = 5(-3) + 11 = -15 + 11 = -4
Therefore:
g(f(-3)) = (-4)^2 + 4(-4) - 11 = 16 - 16 - 11 = 0 - 11 = -11
Answer: -11
Step-by-step explanation:
Find the value of g(f(-3)) given the two equations:
f(x) = 5x + 11
g(x) = x² + 4x - 11
Plug -3 into equation f(x).
f(-3) = 5(-3) + 11
Solve for f(x).
-4 = f(-3)
Plug -4 into the equation of g(x).
g(-4) = (-4)² + 4(-4) - 11
Solve for g(x).
g(-4) = (16) + (-16) - 11
g(-4) = -11
The value of g(f(-3)) is -11.
PLS HELP ASAP
x^2 - 4x-1=0
Solve using formula
Answer:
Your answer would be x=2±√5
Step-by-step explanation:
Multiply.
3 1/2 times 2 2/3
Answer:
Step-by-step explanation:
What the answer is please
Answer:its the first one
Step-by-step explanation:
becuase it tells more explanation if you look at the answer or what im saying is problem to make it more simpler.
Find the derivative of the function y = ln(3t+4)
Answer:
3 / (3t+4) is the answer
Helpppppppppppppppppppppppp
[tex]xy =-21~~.....(i)\\\\x+ y=20~~....(ii)\\\\\text{From equation (i):}\\\\xy = -21 \implies y = -\dfrac{21}x~~.....(iii)\\\\\text{Substitute y in equation (ii):}\\\\x - \dfrac{21}x = 20\\\\\implies x^2 -20x -21= 0\\\\\implies x^2 - 21x + x-21=0\\\\\implies x(x-21) +(x-21) =0\\\\\implies (x+1)(x-21)=0\\\\\implies x = -1 ~~\text{or}~~ x =21\\\\\text{Substitute x in equation (iii):}\\\\y = 21 ~~ \text{or}~~ y = -1\\\\\text{Hence,}~ (x,y)=(21,-1) ~~ \text{or}~~ (x,y) = (-1,21)[/tex]
Jessica's dog weighs 117 pounds. Her dog weighs 3 times as much as Evan's dog weighs.
How much does Evan's dog weigh?
Answer:
the answer is expkained below
Answer:
Evans dog would weigh 39 pounds
Step-by-step explanation:
117= 3 × X
Take 117 and divide it by 3 and the answer we would get is 39
117 ÷ 3 = 39
To double check the answer we could multiply 39 by 3 to see if we 117.
39 × 3 = 117
X= 39 pounds, so Evans dog is 39 pounds
Melanie read 52 pages in 1 hours. If she continues reading at the same rate, how
many pages will she read in an hour?
If she read 52 pages in one hour, then she'll continue at a rate of 52 pages per hour.
Answer:
52 pages
Step-by-step explanation:
Since she reads 52 pages in 1 hour we multiply 52 by the amount of hours she reads.
52 pages times 1 hour equals 52 pages.
52 x 1 = 52
solve pls brainliest
Answer:
40
Step-by-step explanation:
Help help math please help help help help
Answer:
Answered is x= 55x
Step-by-step explanation:
13x+10 * 12x+20
soln:
or, 13x+12x+10+20
or, 25x+30
:., therefore, x=55x
How to determine the domain and range of a continuous graph
Answer:
Step-by-step explanation:
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
Solve ^3/x^2-8=2 pls help
Answer:
its the first one
Step-by-step explanation:
What is the answer to
2 3/8 - 1 5/8 =
Answer:
6/8
Step-by-step explanation:
you have to convert each fraction into an improper. because the denominators are already the same, you dont have to worry. once you have it as an impropper, you can now subtract it. 19/8 - 13/8 = 6/8
reduce if you can
Solve for z.
57 = –10z +7
Answer:
z = -5
Step-by-step explanation:
Hi there!
We are given the equation 57 = -10z + 7, and we want to solve for z
In order to solve an equation for a variable, we want to isolate that variable on one side; in other words, we want just z on one side of the equation.
So that means that we'll need to get rid of everything else that's also on the right side. That starts with subtracting 7 from both sides:
57 = -10z + 7
-7 -7
_____________
50 = -10z
Now on the right side, there aren't any other extra terms, but remember: we want just z (also written as 1z, with the coefficient of 1), not z written with a coefficient of -10
If you divide a number by itself, the result is 1. For example. [tex]\frac{3}{3}[/tex]= 1. So in order to get a coefficient of 1, let's divide both sides by -10
[tex]\frac{50}{-10} = \frac{-10z}{-10}[/tex]
Divide, and cancel:
The zeros cancel out, leaving the equation as:
[tex]\frac{5}{-1} = \frac{-1z}{-1}[/tex]
Dividing a number by -1 is pretty much the same as multiplying a number by -1; it simply changes the sign of the number
So 5/-1 will become -5, while -1z/-1 will become 1z, or z
Hence:
-5 = z, or written the other way: z = -5
We found z.
Hope this helps!
This circle is centered at the point (3,2) and the length of its radius is 5 what is the equation of the circle
Answer:(x-3)² + (y-2)² = 25
Step-by-step explanation:
A circle's equation is (x-h)² + (y-k)² = r². When centered at the origin, h and k equal 0. If you shift the circle, say, one unit up, then k equals 1, and the equation is x² + (y-1)² = r².
So for your circle, the equation would be (x-3)² + (y-2)² = 5² or (x-3)² + (y-2)² = 25.
Answer:
(x - 3)² + (y - 2)² = 25
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
Here (h, k ) = (3, 2 ) and r = 5 , then
(x - 3)² + (y - 2)² = 5² , that is
(x - 3)² + (y - 2)² = 25 ← equation of circle
please answer fully ?/'//////////////////////
Answer:
17.5
Step-by-step explanation:
i solved it and got that answer. hope this helps =)
A new cell phone costs $108.99 in the store. What would your total cost be if the sales tax is 4.5%? Round your answer to the nearest cent, if necessary.
Answer: $113.89
Step-by-step explanation:
108.99 * 0.045
= 4.90455
108.99 + 4.90455
= 113.89455
$113.89
Answer:
Total Cost = $113.89
Step-by-step explanation:
Total Cost = Cell phone cost + sale Tax % ( cell phone cost)
Total Cost = $108. 99 + .045 × $108.99
Total Cost = $108.99 + $4.90455
Total Cost = $108.99 + $4.90
Total Cost = $113.89
