Answer:
The standard error of the sample proportion is 0.0993.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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]
73% of voters support it.
This means that [tex]p = 0.73[/tex]
Sample of 20 voters
This means that [tex]n = 20[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.73[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.73*0.27}{20}} = 0.0993[/tex]
The standard error of the sample proportion is 0.0993.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is
12/20 = 0.6, so this is the p-value of Z when X = 0.6.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.6 - 0.73}{0.0993}[/tex]
[tex]Z = -1.31[/tex]
[tex]Z = -1.31[/tex] has a p-value of 0.0951.
So
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951.
The standard error of the sample proportion is 0.0098.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951
Given that,
Suppose that there is a school bond referendum in Greensboro, and 73% of voters support it.
You randomly ask 20 Greensboro voters whether they support the bond referendum.
We have to determine,
The standard error of the sample proportion is.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is .
According to the question,
There is a school bond referendum in Greensboro, and 73% of voters support it.
20 Greensboro voters whether they support the bond referendum.
To find standard deviation of sample proportion.
[tex]standard \ deviation = \sqrt{\dfrac{p(1-p)}{n}}[/tex]
Where, p = 73% = 0.73
And n = 20
Therefore,
[tex]Standard \ deviation = \sqrt{\dfrac{p(1-p)}{n}}\\\\ Standard \ deviation = \sqrt{\dfrac{0.73(1-0.73)}{20}}\\\\Standard \ deviation = \sqrt{\dfrac{0.73\times 0.27}{20}}\\\\Standard \ deviation = \sqrt{\dfrac{0.19}{20}}\\\\Standard \ deviation = 0.0098[/tex]
The standard error of the sample proportion is 0.0098.
The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is,[tex]\dfrac{12}{20 }= 0.6[/tex]
This is the p-value of Z when X = 0.6.
Therefore,
[tex]Z = \dfrac{X-\mu}{\sigma}\\\\Z = \dfrac{0.6-0.73}{0.993}\\\\Z = -1.31\\\\[/tex]
Z = -1.31 has a p-value of 0.0951.
Hence, The probability that 12 or fewer people (out of 20) in your sample support the bond referendum is 0.0951.
To know more about Probability click the link given below.
https://brainly.com/question/24248147
pythagorean theorem round to the nearest tenth !!
Answer:
8,06
Step-by-step explanation:
c = Va^2+b^2 = V4*4+7*7 = v65 = 8,06
Help !!!!!!!!!!!!!!!!!!!!!
Answer:
The first option being 12/25
Can somebody tell me exactly what to put in the answer please
Answer:
I am sorry I don't know it, but once I find out I will tell you
Step-by-step explanation:
Answer:
Cylinder has no sharp points but cone as sharp edge.
27leejaey avatar
I hope that helps :D
Step-by-step explanation:
Cylinder has no sharp points but cone as sharp edge.
27leejaey avatar
I hope that helps :D
HELPP ASAP DONT SEND A FILE PLS DESCRIBE THE TRANSFORMATION RULE FOR ROTATIONS !!! Only ANSWER IF YOU KNOW I NEED THE ANSWR FOR 1 and 3
Answer:
Step-by-step explanation:
I will not give the answer but the rules are:
90 Degree Rotation. When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). ...
180 Degree Rotation. When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). ...
270 Degree Rotation.
Hope at least that helps.
Write an addition equation or a subtraction equation (your choice!) to describe the diagram.
3/8 x 2 what would the answer be to this statement
Answer:
6/16
Step-by-step explanation:
Find the volume of this triangular prism.
25 cm
10 cm
10 cm
Answer:
volume of the triangular prism
[tex] (\frac{1}{2} \times 10 \times 10) \times 25 \\ 1250 {cm}^{3} [/tex]
Answer:
1250cm2Step-by-step explanation:
BY: [tex]ζBenjamin[/tex]
some body help meee!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
x=3
Step-by-step explanation:
This is a vertical line.
Vertical lines are of the form x= since the x value does not change
x=3
3
Find the value of a
in the equation,(3+4√3)(2-a√3)=-18+2√3
Given:
The equation is:
[tex]\left(3+4\sqrt{3}\right)\left(2-a\sqrt{3}\right)=-18+2\sqrt{3}[/tex]
To find:
The value of a.
Solution:
We have,
[tex]\left(3+4\sqrt{3}\right)\left(2-a\sqrt{3}\right)=-18+2\sqrt{3}[/tex]
On simplification, we get
[tex](3)(2)+(4\sqrt{3})(2)+(3)(-a\sqrt{3})+(4\sqrt{3})(-a\sqrt{3})=-18+2\sqrt{3}[/tex]
[tex]6+8\sqrt{3}-3a\sqrt{3}-4a(3)=-18+2\sqrt{3}[/tex]
[tex]6+8\sqrt{3}-3a\sqrt{3}-12a=-18+2\sqrt{3}[/tex]
[tex](6-12a)+(8-3a)\sqrt{3}=-18+2\sqrt{3}[/tex]
On comparing both sides, we get
[tex]6-12a=-18[/tex]
[tex]-12a=-18-6[/tex]
[tex]a=\dfrac{-24}{-12}[/tex]
[tex]a=2[/tex]
And,
[tex]8-3a=2[/tex]
[tex]-3a=2-8[/tex]
[tex]a=\dfrac{-6}{-3}[/tex]
[tex]a=2[/tex]
Therefore, the value of a is 2.
{ 2 x [4 - (6 ÷ 2)]} x 3
Answer:
6x^2
Step-by-step explanation:
Answer:
6x²
Step-by-step explanation:
(2x(4 - (6 ÷ 2))) × 3x
(2x(4 - 3)) × 3x
2x(1) × 3x
2x × 3x
6x²
A study is done to find the 95% confidence interval for the difference in means between the ACT scores between two schools in a given city. One school had a random sample of 39 students had a sample mean of 25.90 with a sample standard deviation of 3.49. The second school had a random sample of 37 students had a sample mean 27.70 with a sample standard deviation of 2.47. What is the lower bound of the 95% confidence interval for the difference in means
Solution :
95% confidence interval for the difference between the means of ACT scores between two schools, is given by :
[tex]$[(\overline X_1 - \overline X_2)-ME, (\overline X_1 - \overline X_2)+ME]$[/tex]
[tex]$\overline X_1 = 25.90 , \ \ \ \overline X_2 = 27.70$[/tex]
[tex]$S_1=3.49, \ \ \ S_2 = 2.47$[/tex]
[tex]$n_1=39, \ \ n_2=37$[/tex]
M.E. , Margin of error,
[tex]$=t_{n_1+n_2-2,0.025} \times \left( s \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$[/tex]
[tex]$s^2 = \frac{(n_1-1)S_1^2+(n_2-1)S^2_2}{n_1+n_2-2}$[/tex]
[tex]$=\frac{38(3.49)^2+36(2.47)^2}{39+37-2}$[/tex]
= 9.222
s = 3.03
[tex]$t_{74,0.05} = 1.99$[/tex]
[tex]$M.E. = 1.99 \times 3.03 \times \sqrt{\frac{1}{39}+\frac{1}{37}}$[/tex]
= 1.4
Therefore, 95% CI = [(25.90-27.70) - 1.4 , (25.90-27.70) + 1.4]
= [-3.2, -0.4]
Therefore, the lower bound is -3.2
Anita opened a savings account and deposited $600.00 as principal. The account earns 6% interest, compounded continuously. What is the balance after 1 year?
Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years.
Round your answer to the nearest cent. ( help please)
Answer:
$637.10
Step-by-step explanation:
Given:
P = 600
r = 6% or 0.06
t = 1
Work:
[tex]A=Pe^{rt}\\\\A=600e^{0.06*1}\\\\A=600e^{0.06}\\\\A=637.10[/tex]
5. What is the value of 8 in the unit circle below?
30°
600
b.
45°
d.
90°
9514 1404 393
Answer:
θ = 60°
Step-by-step explanation:
The angle is more than 45° and less than 90°. The only viable choice is ...
θ = 60°
__
We can only read the x-coordinate of the point on the terminal ray. It is 1/2, which is the cosine of 60°. The angle must be 60°.
determine a if x-2 is a factor of f(x)=x^4-3x^3+ax^2-16x+20
Answer:
x-2 is factor so 2 is zero of f(x) =x^4-3x^3+ax^2-16x+20
Step-by-step explanation:
2^4-3×2^3+a×2^2-16×2+20
solve this Answer is come.THANK YOU.
If (x - 2) is a factor of the polynomial f(x) = x⁴ -3x³ + ax² -16x + 20.
Then the value of a is -17.
What is a polynomial?An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
A polynomial,
x⁴ -3x³ + ax² -16x + 20.
If x - 2 is a factor the x = 2 is the zeros of the polynomial.
When x = 2,
then,
x⁴ -3x³ + ax² -16x + 20 = 0
2⁴ -3(2)³ + a(2)² -16(2) + 20 =0
48 + 20 + 4a = 0
4a = -68
a = -17
Therefore, the value of a is -17.
To learn more about the Polynomials;
brainly.com/question/11536910
#SPJ2
Help I’ll give extra points
Plz help me well mark brainliest if you are correct!!....plzz
Answer: 11.
Step-by-step explanation: Simplify the 7 and 4 to positive numbers since your asking for the value of expression. Add 7 + 4 together and get 11.
Hey does anyone please can help me with this
Answer:
Step-by-step explanation:
Need help solving this problem.
-30x+147=-171-24x
Answer:
-30x+147= -171-24x
+24x +24x
-6x+147= -171
-147 -147
-6x= -318
x=53
Hope this helps!
PLEASE HELP! WILL AWARD BRAINLIEST TO THE FIRST CORRECT ANSWER!
If a/b=6, b/x=36, and a=36, what is the value of 1/x?
A) 1/2
B) 2
C) 3/2
D) 4
E) 6
Answer:
E) 6
Step-by-step explanation:
a/b = 6
36/b = 6
6b = 36
b = 36/6 = 6
b/x = 36
6/x = 36
36x = 6
x = 6/36 = 1/6
hence 1/x = 6
Answer:
E) 6
Step-by-step explanation:
a/b=6, b/x=36, and a=36
=>a = 6b
36 = 6b => b =6
b/x = 36 => x = b/36 = 6/36
so, 1/x = 36/6 = 6
Alicia, Carlos, Henry, and Zoe each completed a hike. The table shows their distances and times. Match each hiker to their unit rate.
3.20 mph
3.57mph
2.77 mph
3.08 mph
Answer:
3.57 mph I think it's 3.57 but if it's not I'm sorry
write the product in standard form (2x + 5) ^2
Answer:
4x^2+20x+25
Step-by-step explanation:
(2x+5)^2 = (2x+5) (2x+5)
Using the foil method : 2x(2x) = 4x^2
(2x) (5) = 10x
(2x) (5) = 10x
5 (5) = 25
Combine like terms
According to the graph, the __________________ is 57-43.
Answer:
Range
Step-by-step explanation:
The range is the max value minus the min value
Please Round 1.54 thank you
Answer:
okay so it would be 2 or 1.5 i dont know if you want it whole number but i will explain
if the number is 5 or more like 5.1 or even 5 you round up
if the number is under 5 like 4,3,2,1 your round down
Step-by-step explanation:
Answer:
To The Nearest Tenth : 1.5
To The Nearest Whole Number : 2
Tip:
If the number is 4 or below like 1.42 it would be rounded to 1.4
If the number if 5 or above like 2.58 it would be rounded to 2.6 or 3
I didnt know which one you wanted so I put both
A triangle has vertices (0, 2), (3, 1), and (6.2). What is the approximate perimeter of the triangle? Round your answer to the nearest hundredth.
Answer:
6 + 2√10 units.
Step-by-step explanation:
We can use the distance formula to find the distance between the points. The points are ,
(0,2)(3,1)(6,2)Distance 1 :-
=> D₁ = √{ (x₁ - x₂ )² + ( y₁ - y₂ )² }
=> D₁ = √{ (0-3)² + (2-1)² }
=> D₁ = √{ 3² + 1² }
=> D₁ = √{ 9+1}
=> D₁ = √10
Distance 2:-
=> D₂ = √{ (x₁ - x₂ )² + ( y₁ - y₂ )² }
=> D₂ = √{ (6-3)² + (2-1)² }
=> D₂ = √{ 3² + 1² }
=> D₂ = √{ 9 + 1}
=> D₂ = √10
Distance 3 :-
=> D₃ = √{ (x₁ - x₂ )² + ( y₁ - y₂ )² }
=> D₃ = √{ (6-0)²+(2-2)²
=> D₃ = √6²
=> D₃ = 6
→ Perimeter = D₁ +D₂ + D₃
→ Perimeter = √10 + √10 + 6
→ Perimeter = 6 + 2√10 units
Hence the perimeter is 6+2√10 units.What is the volume of this?
Answer:
1,832.4
Step-by-step explanation:
To find the base you multiply the radius by itself to pi. Then you multiply that by the height. The next step would be to divide that by 3.
Can someone help please with unit 12 homework 7??
Answer:
See answers below
Step-by-step explanation:
Using the sin rule
a/sinA = b/sinB = c/sinC
a) x/sin110 = 16/sin27
xsin27 = 16sin110
xsin27 = 15.035
x = 15.035/sin27
x = 33.1
2) Using the cosine rule;
x² = 30²+14²-2(30)(14)cos125
x² = 900 + 169 - 840cos125
x² = 1069 - 840(-0.5735)
x² = 1069 +481.80
x² = 1,550.80
x =39.4
3) 28² = 18²+12²-2(18)(12)cosx
784 = 324 + 144- 432cosx
784 - 468 = - 432cosx
316 = - 432cosx
Cos x = -316/432
x = - 42.99
x = 180 - 42.99
x = 137.0 degrees
4) Using the sine rule
20/sinx = 33/sin91
33sinx = 20sin91
sinx = 20sin91/33
sinx = 19.997/33
sinx = 0.6059
x = arcsin(0.6059)
x = 37.3degrees
20 POINTS PLEASE ANSWER THIS ASAP!!!!!
How many six-character code words can be formed if the first two characters are letters and the others are letters and/or digits? Repetition of numbers and letters is allowed.
a) 6,760,000
b) 723,465,600
c) 1,135,420,416
d) 918,918,000
2.Answer question # 1 if Repetition is NOT allowed.
a) 918,918,000
b)723,465,600
c)1,135,420,416
d)720
Answer:
A ; 3276000 (second answer)
Step-by-step explanation:
think of it like this:
L L # # # # ( six symbols, L for letters, # for numbers)
26 X 26 X 10 X 10 X 10 X10 = 6760000
If we take away repetition then the equation would look like this:
L L # # # # ( 26 then 25 due to the loss of a letter due to no )
26 X 25 X 10 X 9 X 8 X 7 ( Repetition. Same with 10,9,8,7 )
Therefore the answer to the second question isn't even up there which is 3276000.
Hope this helps...
Then find the values of x and y?
Answer:
x=76
Step-by-step explanation:
y+8=3y
-2y=-8
y=4
104*2=208
360-208=152
152/2=76
x=76
Find the area of the image below
Answer:
The answer is 65 square units
Helpp plzz will mark brainleast
Answer:
a d e
Step-by-step explanation:
hope this helps mark me brainleast :)