Answer:
x= 5,77 *∛ K₂ / ( K₁ + K₅ ) the side f the square bottom-top
h = 2,88/ [∛ K₂ / ( K₁ + K₅ ) ]² heigh of the box
Step-by-step explanation:
Data from problem statement only gives one relation between dimensions of the box, we need two, in order to express surface area as a function of just one variable. In such a case we must assume the box is of square bottom and top.
Then
Area of the bottom A(b) = x² ⇒ C(b) = K₁*x²
Area of the top A(t) = x² ⇒ C(t) = K₅*x²
Total lateral area ( 4 sides) A(l) = 4*x*h ⇒ C(l) = 4*K₂*x*h
V(bx) = 96 in³
V(bx) = x²*h = 96
h = 96/x²
Then total cost as a function of x
C(x) = K₁*x² + K₅*x² + 4*K₂*(96)/x
Taking derivatives on both sides of the equation
C´(x) = 2*K₁*x + 2*K₅*x - 384*K₂/x²
C´(x) = 0 ⇒ 2*K₁*x + 2*K₅*x - 384*K₂/x² = 0
2*K₁*x³ + 2*K₅*x³ = 384*K₂ or K₁*x³ + k₅*x³ = 192*K₂
x³ ( K₁ + K₅ ) = 192*K₂
x = ∛192*K₂ / ( K₁ + K₅ )
x= 5,77 *∛ K₂ / ( K₁ + K₅ )
If we obtain the second derivative
C´´(x) = 2*K₁ + 2*K₅ - (-2*x)*384*K₂/x⁴
C´´(x) = 2*K₁ + 2*K₅ + 768*K₂/x³
As x can not be negative the expression C´´ wil be C´´> 0
then we have a minimum for the function for x = 5,77 *∛ K₂ / ( K₁ + K₅ )
and h = 96 / [ 5,77 *∛ K₂ / ( K₁ + K₅ )]²
h = 2,88/ [∛ K₂ / ( K₁ + K₅ ) ]²
What are the zeros of the quadratic function f (x) = 2x^2 -10x-3?
Answer:
x=2.5+sqrt(300)/4, 2.5-sqrt(300)/4
Step-by-step explanation:
1. Need to factor or can use the quadratic formula
2x^2-10x-3=0
a=2, b=-10, c=-3
[-b+-sqrt(b^2-4*a*c)]/(2*a)
[10+-sqrt(100-4*(-200)]/4
[10+- sqrt(300)]/4
x=2.5+sqrt(300)/4, 2.5-sqrt(300)/4
Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answer:
15 pt
Step-by-step explanation:
Answer:
15 pintsStep-by-step explanation:
1 quarts = 2 pints
From the question we were given 7.5 quarts to to get the desired result multiply 7.5 by 2
Which is 7.5 × 2 = 15 pints
Hope this helps you
What rule (i.e. R1, R2, R3, R4, or R5) would you use for the hawk and for the grizzly bear? a. R2 and R5 b. R1 and R3 c. None of the above d. R1 and R4
Answer:
I NEED POINTS
Step-by-step explanation:
Sung Lee invests $10,000 at age 18. He hopes the investment will be worth $30,000 when he turns 25. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.
Answer:
r=17%
Step-by-step explanation:
P is the investment
A is the targeted amount
t= time (25-18=7 years)
A=P(1+r)^t
30000=10000(1+r)^7
(1+r)^7=30000/10000
r=\root(7)(3)-1
r=0.16993 ≅0.17= 17%
check: A=P(1+r)^t ⇒10000(1+0.17)^7=30012≅30000
URGENT It is given that a regular n-sided polygon has 5 sides more than a
regular m-sided polygon. If the sum of interior angles of the regular
n-sided polygon is twice that of the latter, find the values of m and n.
Answer:
m = 7; n = 12
Step-by-step explanation:
"a regular n-sided polygon has 5 sides more than a
regular m-sided polygon"
n = m + 5
The sum of the measures of the interior angles is
180(n - 2) for the n-sided polygon and
180(m 2) for the m-sided polygon.
"If the sum of interior angles of the regular
n-sided polygon is twice that of the latter"
180(n - 2) = 2(180)(m - 2)
We have a system of equations with 2 equations.
n = m + 5
180(n - 2) = 2(180)(m - 2)
Simplify the second equation:
n - 2 = 2m - 4
n + 2 = 2m
Substitute m + 5 for n.
m + 5 + 2 = 2m
7 = m
m = 7
n = m + 5 = 7 + 5 = 12
Answer: m = 7; n = 12
A first number plus twice a second number is 14. Twice the first number plus the second totals 10. Find the numbers.
Answer:
first number(x) = 2 second number(y)= 6
Step-by-step explanation:
This is an example of a simultaneous equation.
First write this word problem as equations, where x is the "first number" that you've mentioned and y is the "second number".
x + 2y = 14 (equation 1)
2x + y = 10 (equation 2)
This is solved using the elimination method.
We need to make one of the coefficients the same - in this case we can make y the same. In order to do this we need to multiply equation 2 by 2, so that y becomes 2y.
2x + y = 10 MULTIPLY BY 2
4x + 2y = 20 (this is now our new equation 2 with the same y coefficient)
Now subtract equation 1 from equation 2.
4x - x + 2y - 2y = 20 - 14 (2y cancels out here)
3x = 6
x = 2
Now we substitute our x value into equation 1 to find the value of y.
2 + 2y = 14
2y = 12
y = 6
Hope this has answered your question.
Answer:
6 and 2
Step-by-step explanation:
Let the first number =a
Let the second number =b
A first number plus twice a second number is 14.
a+2b=14Twice the first number plus the second totals 10.
2a+b=10We solve the two equations simultaneously
[tex]a+2b=14 \implies a=14-2b\\$Substitute into the second equation$\\2(14-2b)+b=10\\28-4b+b=10\\-3b=10-28\\-3b=-18\\b=6[/tex]
Recall:
a=14-2b
=14-2(6)
=14-12
a=2
The two numbers are 6 and 2.
3)
Rick says he has
two miles already.
Which form of the verb best completes the sentence?
A)
ran
B)
run
C)
running
D)
runs
Step-by-step explanation:
Because the sentence is speaking that he has done already so we will use the past verb ran
Rick says he has ran two miles already
Answer:
b. run
Step-by-step explanation:
Rick says he has run two miles already
It will be "ran" if the sentence had said, "Rick 'ran' two miles already."
BRAINLIST PLS!
A pretzel company calculated that there is a mean of 75.4 broken pretzels in each production run with a standard deviation of 5.2. If the distribution is approximately normal, find the probability that there will be fewer than 66 broken pretzels in a run.
Answer:
P [ Z < 66 ] = 35,15 %
Step-by-step explanation:
Normal Distribution
Population mean μ₀ = 75,4
Standard deviation σ = 5,2
Then:
P [ Z < 66 ] = ( 66 - 75,4 ) / 5,2
P [ Z < 66 ] = - 9,4 / 5,2
P [ Z < 66 ] = - 1,81
In z-table we look for the reciprocate area for that z score and find
P [ Z < 66 ] = 0,3515
P [ Z < 66 ] = 35,15 %
PLEASE HELP QUICK!!!! What is the solution to the equation Two-thirds x + 1 = one-sixth x minus 7? x = negative 16 x = negative 4 x = 4 x = 16
Answer:
-16
Step-by-step explanation:
I solved it out.
Answer:
its d 16
Step-by-step explanation:
i did the test
The area of each square below is 1 square unit. How can we calculate the area of the striped region? A: 7/5 x 1/2 B: 6/12 x 2/10 C: 7/5 x 2/10
Answer:
wrong thing
Step-by-step explanation:
13 arent shaded of the 20 units
7/20 are shaded, 7X1=7, 2X5=10
905,238 In a word form
Answer:
nine hundred five thousand two hundred thirty-eight
Use the formula m= v 2 -v 1 x 2 -x 1 to calculate the slope of the line The slope of the line is
Answer: I actually do not know but i know that the answer is A.
Step-by-step explanation:
I'm smart
Show all work! I don't understand this! Brainleist!
I attached a picture this time!
Answer:
2.94 seconds.
Step-by-step explanation:
The ball will hit the ground when the height of the ball is 0 meters.
The equation is...
h = 61 - 6t - 5t^2.
-5t^2 - 6t + 61 = 0
5t^2 + 6t - 61 = 0
We can use the quadratic formula to solve.
[please ignore the A-hat; that is a bug]
[tex]\frac{-b ± \sqrt{b^2 - 4ac} }{2a}[/tex], where a = 5, b = 6, and c = -61.
= [tex]\frac{-6 ± \sqrt{6^2 - 4 * 5 * (-61)} }{2 * 5}[/tex]
= [tex]\frac{-6 ± \sqrt{36 - 20 * (-61)} }{10}[/tex]
= [tex]\frac{-6 ± \sqrt{36 + 1,220)} }{10}[/tex]
= [tex]\frac{-6 ± \sqrt{1,256} }{10}[/tex]
= [tex]\frac{-6 ± 35.44009029}{10}[/tex]
Since time cannot be negative, we will not minus the 35.44009029.
(-6 + 35.44009029) / 10 = 29.44009029 / 10 = 2.944009029
That is approximately 2.94 seconds.
Hope this helps!
Answer:
[tex]\boxed{t = 2.94 \ seconds}[/tex]
Step-by-step explanation:
When the ball hits the ground, h = 0
Putting this in the equation:
=> [tex]0 = 61-6t-5t^2[/tex]
=> [tex]61-6t-5t^2 = 0[/tex]
Taking -1 as common
=> [tex]-1(5t^2+6t-61) = 0[/tex]
Dividing both sides by -1
=> [tex]5t^2+6t-61 = 0[/tex]
Using Quadratic Equation:
=>t = [tex]\frac{-b+ / - \sqrt{b^2-4ac} }{2a}[/tex]
=> [tex]\frac{-6 +/- \sqrt{6^2-4(5)(-61)} }{2(5)}\\\frac{-6 +/- \sqrt{36+1220} }{10}[/tex]
=> t = [tex]\frac{-6 +/- 35.44}{10}[/tex]
Either:
t = [tex]\frac{-6+35.44}{10}[/tex] OR t = [tex]\frac{-6-35.44}{10}[/tex]
t = 29.44/10 OR t = -41.44/10
t = 2.94 OR t = -4.14
Time can never be negative so t = 2.94 secs
Find the slope of the line passing through the points (-4, 2) and (-6,5).
Answer:
-3/2
Step-by-step explanation:
Hey there!
Well to find the slope of a line with 2 points we use the following formula,
y2 - y1 / x2 - x1
5 - 2 = 3
-6 - -4 = -2
Slope = -3/2
Hope this helps :)
Answer:
[tex]Slope = -\frac{3}{2}[/tex]
Step-by-step explanation:
[tex](-4, 2) \:(-6,5).\\\\m =\frac{y_2-y_1}{x_2-x_1} \\\\x_1 = -4\\y_1 =2\\x_2 = -6\\y_2 =5\\\\m = \frac{5 -2}{-6-(-4)}\\ m = \frac{3}{-6+4}\\ m = \frac{3}{-2}\\ \\Slope = -\frac{3}{2}[/tex]
A building has eight levels above ground and one level below ground. The height of each level from floor to ceiling is feet. What is the net change in elevation going from the floor of the underground level to the ceiling of the fourth level above ground? Assume the floor at ground level is at an elevation of zero feet.
Answer:
72.5 feet
Step-by-step explanation:
The height of each level from floor to ceiling is 14 1/2 feet.
We want to find the net change in elevation going from the floor of the underground level to the ceiling of the 4th level above ground.
In other words, the change in elevation in going 5 floors up.
Each level has a height of 14 1/2 feet (29/2 feet).
Therefore, the height of the fourth level above ground from the underground level will be 5 times the height of one level:
h = 5 * 29/2 = 72.5 feet
The net change in elevation from the floor of the underground level to the 4th level above ground is:
ΔE = [tex]h_4 - h_0[/tex]
[tex]h_0 = 0 feet\\\\h_4 = 72.5 feet[/tex]
Therefore:
ΔE = 72.5 - 0 = 72.5 feet
Answer:
72.5
Step-by-step explanation:
Question 12 of 20 :
Select the best answer for the question.
12. If a number is divisible by both 2 and 3 then we can say the number is divisible by
O A.2.
OB.4.
O C.5.
OD.6.
Mark for review (Will be highlighted on the review page)
<< Previous Question
Next Question >>
Answer:
The number must be divisible by 6
Step-by-step explanation:
Being divisible by 2 means that 2 is a factor of the number. Same with being divisible by 3, so that means the number has 2 and 3 as factors, therefore, 6 is also a factor, and the number will be divisible by it.
butter and flour are mixed in the ratio 2:3. paul has 640 grams of butter and 880 grams of flour. how much more flour does he need? Can you explain again in a simpler format.
Answer:
80 grams of butter
Step-by-step explanation:
640/2=329
3x320=960
960-880=80
Derek is building a deck. The sum of the interior angles is 10800 and each interior angle is 1350. How many sides does his deck have
sum of angles = 10800
measurement of a single angle= 1350
Therefore,
No. of sides = sum of angles / single angle
No of sides = 10800 / 1350
No of sides = 8
Answer:
8 sides.
Step-by-step explanation:
If the sum of the angles is 10,800 degrees, and each angle is 1,350 degrees, the deck will have the number of sides of the sum of the angle measurements divided by each angle's measurements.
10,800 / 1,350 = 1,080 / 135 = 8 sides.
Hope this helps!
Help which of the following sets of ordered pairs represent a function?
Answer:
B
Step-by-step explanation:
B is the only set of ordered pairs to represent a function because it is the only one that has no repeating x values while the others do.
5(x + 3) – 12 = 43 solve
Answer:
[tex]x=8[/tex]
Step-by-step explanation:
We can solve this equation by isolating the variable x.
First let’s apply the distributive property:
[tex]5(x+3)-12=43\\5\cdot x + 5\cdot3 - 12=43\\5x + 15 - 12 = 43[/tex]
Combine like terms:
[tex]5x + 3 = 43[/tex]
Now we can subtract 3 from both sides:
[tex]5x + 3 - 3 = 43-3\\5x = 40[/tex]
Divide both sides by 5:
[tex]5x\div5 = 40\div5\\x = 8[/tex]
So [tex]x=8[/tex].
Hope this helped!
Answer:
x = 8
Step-by-step explanation:
5(x + 3) – 12 = 43
Add 12 to each side
5(x + 3) – 12+12 = 43+12
5(x+3) =45
Divide each side by 5
5(x+3)/5 = 55/5
x+3 = 11
Subtract 3 from each side
x+3-3 = 11-3
x = 8
Which of the following best describes an unpredictable event?
Answer:
B. The weather on a particular day a year from now
Step-by-step explanation:
We can only predict the weather in the near future, not long term or all time. The rest of the answer choices are predictable. We will always know the age of a person 10 years from now, we can predict the rating of the movie if we preview and watch it, and if a student studies enough/not enough we can predict the type of grade they will get on a test.
I believe the answer is B since to find the age of a person ten years from now, just add their age by ten. You can predict the rating of an upcoming movie by watching the trailer and seeing if it is good or bad. You can predict the grade a student gets on a test if you know that person is smart or not. You can’t predict weather from a year in the future because anything could happen in a year. This is why I think the answer is B.
An account is opened with an initial deposit of $100 and earns 3.0% interest compounded monthly. What will the account be worth in 25 years? Round your answer to the nearest dollar.
Answer:
A = $211.50
A = P + I where
P (principal) = $100.00
I (interest) = $111.50
Step-by-step explanation:
$209.37 will the account be worth in 25 years.
What is compound interest?Compound Interest is defined as interest earn on interest.
[tex]A = P(1 + \frac{r}{100})^{t}[/tex]
P= $100
r = 3%
t=25 years
substitute the values in formula,
[tex]A = 100(1 + \frac{3}{100})^{25}[/tex]
[tex]A = 100(1 + 0.03)^{25}[/tex]
[tex]A = 100(1.03)^{25}[/tex]
[tex]A=100(2.0937)[/tex]
[tex]A=209.37[/tex]
Hence, $209.37 will the account be worth in 25 years.
Learn more about Compound Interest
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Which of these is the opposite reciprocal of 3/4
Answer: -4/3
Step-by-step explanation: To find the negative reciprocal of a fraction, all you have to do is flip the fraction and change the sign.
So the negative reciprocal of 3/4 is -4/3.
jogged the track 5/9 miles long and jogged around it 4 times
Answer:
The answer is 2 1/5 miles.
Step-by-step explanation:
You have to multiply 5/9 with 4 since you are going around 4 times. You could also use addition which is 5/9 + 5/9 + 5/9 + 5/9.
Answer:
Hey there!
The person jogged a total of 20/9 miles.
Hope this helps :)
The lengths, in order, of four consecutive sides of an equiangular hexagon are 1, 7, 2 and 4 units, respectively. What is the sum of the lengths of the two remaining sides?
Answer:
9
Step-by-step explanation:
Extend every other side of the hexagon so that a triangle is formed. Since the hexagon is equiangular, the overall triangle is an equilateral triangle, as well as the smaller triangles in the corners.
The length of the sides of the overall triangle is 7 + 2 + 4 = 13.
Therefore, the other two sides of the hexagon are 5 and 4.
The sum is 5 + 4 = 9.
12+[(15-5)]+(9-3)] what is the answer
Answer:
28
Step-by-step explanation:
12+[(15-5)]+(9-3)]
PEMDAS
Parentheses first
12+[(10)]+(6)]
Then add
12+10+6
Answer: 28
Step-by-step explanation:
select the decimal that is equivalent to the fraction 57 over 100
Answer:
0.57.
Step-by-step explanation:
57 / 100
We divide 57 by 100:
= 0.57
1. The following are the number of hours that 10 police officers have spent being trained in how to handle encounters with people who are mentally ill:
4 17 12 9 6 10 1 5 9 3
Calculate the (a) range, (b) inter-quartile range, (c) variance, and (d) standard deviation.
(Use N)
Answer:
[tex]Range = 16[/tex]
[tex]Inter\ Quartile\ Range = 6.75[/tex]
[tex]Variance = 20.44[/tex]
[tex]Standard\ Deviation = 4.52[/tex]
Step-by-step explanation:
Given
4, 17, 12, 9, 6, 10, 1, 5, 9, 3
Calculating the range;
[tex]Range = Highest - Lowest[/tex]
From the given data;
Highest = 17 and Lowest = 1
Hence;
[tex]Range = 17 - 1[/tex]
[tex]Range = 16[/tex]
Calculating the Inter-quartile Range
Inter quartile range (IQR) is calculates as thus
[tex]IQR = Q_3 - Q_1[/tex]
Where
Q3 = Upper Quartile and Q1 = Lower Quartile
Start by arranging the data in ascending order
1, 3, 4, 5, 6, 9, 9, 10, 12, 17
N = Number of data; N = 10
---------------------------------------------------------------------------------
Calculating Q3
[tex]Q_3 = \frac{3}{4}(N+1) th\ item[/tex]
Substitute 10 for N
[tex]Q_3 = \frac{3}{4}(10+1) th\ item[/tex]
[tex]Q_3 = \frac{3}{4}(11) th\ item[/tex]
[tex]Q_3 = \frac{33}{4} th\ item[/tex]
[tex]Q_3 = 8.25 th\ item[/tex]
Express 8.25 as 8 + 0.25
[tex]Q_3 = (8 + 0.25) th\ item[/tex]
[tex]Q_3 = 8th\ item + 0.25 th\ item[/tex]
Express 0.25 as fraction
[tex]Q_3 = 8th\ item +\frac{1}{4} th\ item[/tex]
[tex]Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)[/tex]
From the arranged data;
[tex]8th\ item = 10[/tex] and [tex]9th\ item = 12[/tex]
[tex]Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)[/tex]
[tex]Q_3 = 10 +\frac{1}{4} (12 - 10)[/tex]
[tex]Q_3 = 10 +\frac{1}{4} (2)[/tex]
[tex]Q_3 = 10 +0.5[/tex]
[tex]Q_3 = 10.5[/tex]
Calculating Q1
[tex]Q_1 = \frac{1}{4}(N+1) th\ item[/tex]
Substitute 10 for N
[tex]Q_1 = \frac{1}{4}(10+1) th\ item[/tex]
[tex]Q_1 = \frac{1}{4}(11) th\ item[/tex]
[tex]Q_1 = \frac{11}{4} th\ item[/tex]
[tex]Q_1 = 2.75 th\ item[/tex]
Express 2.75 as 2 + 0.75
[tex]Q_1 = (2 + 0.75) th\ item[/tex]
[tex]Q_1 = 2nd\ item + 0.75 th\ item[/tex]
Express 0.75 as fraction
[tex]Q_1 = 2nd\ item +\frac{3}{4} th\ item[/tex]
[tex]Q_1 = 2nd\ item +\frac{3}{4} (3rd\ item - 2nd\ item)[/tex]
From the arranged data;
[tex]2nd\ item = 3[/tex] and [tex]3rd\ item = 4[/tex]
[tex]Q_1 = 3 +\frac{3}{4} (4 - 3)[/tex]
[tex]Q_1 = 3 +\frac{3}{4} (1)[/tex]
[tex]Q_1 = 3 +0.75[/tex]
[tex]Q_1 = 3 .75[/tex]
---------------------------------------------------------------------------------
Recall that
[tex]IQR = Q_3 - Q_1[/tex]
[tex]IQR = 10.5 - 3.75[/tex]
[tex]IQR = 6.75[/tex]
Calculating Variance
Start by calculating the mean
[tex]Mean = \frac{1+3+4+5+6+9+9+10+12+17}{10}[/tex]
[tex]Mean = \frac{76}{10}[/tex]
[tex]Mean = 7.6[/tex]
Subtract the mean from each data, then square the result
[tex](1 - 7.6)^2 = (-6.6)^2 = 43.56[/tex]
[tex](3 - 7.6)^2 = (-4.6)^2 = 21.16[/tex]
[tex](4 - 7.6)^2 = (-3.6)^2 = 12.96[/tex]
[tex](5 - 7.6)^2 = (-2.6)^2 = 6.76[/tex]
[tex](6 - 7.6)^2 = (-1.6)^2 = 2.56[/tex]
[tex](9 - 7.6)^2 = (1.4)^2 = 1.96[/tex]
[tex](9 - 7.6)^2 = (1.4)^2 = 1.96[/tex]
[tex](10 - 7.6)^2 = (2.4)^2 = 5.76[/tex]
[tex](12 - 7.6)^2 = (4.4)^2 = 19.36[/tex]
[tex](17 - 7.6)^2 = (9.4)^2 = 88.36[/tex]
Sum the result
[tex]43.56 + 21.16 + 12.96 + 6.76 + 2.56 + 1.96 + 1.96 + 5.76 + 19.36 + 88.36 = 204.4[/tex]
Divide by number of observation;
[tex]Variance = \frac{204.4}{10}[/tex]
[tex]Variance = 20.44[/tex]
Calculating Standard Deviation (SD)
[tex]SD = \sqrt{Variance}[/tex]
[tex]SD = \sqrt{20.44}[/tex]
[tex]SD = 4.52[/tex] (Approximated)
A weatherman stated that the average temperature during July in Chattanooga is 80 degrees or less. A sample of 32 Julys is taken. The correct set of hypotheses is:________. a. H0: μ ≠ 80 Ha: μ = 80b. H0: μ 80 Ha: μ > 80c. H0: μ < 80 Ha: μ > 80d. H0: μ 80 Ha: μ < 80
Answer:
u <= 80
u > 80
Step-by-step explanation:
The happiest would be
Null hypothesis: u <= 80
Alternative hypothesis: u > 80
The correct set of hypotheses for the sample in July is H0: μ ≠ 80 Ha: μ = 80.
What is the null and alternative hypothesis?The null hypothesis H0 which is also known as the default hypothesis states that there is no relationship between the population parameters. The alternative hypothesis (H1 ) states that there is a relationship between the population parameters.
To learn more about the null hypothesis, please check: brainly.com/question/4454077
In January 2011, The Marist Poll published a report stating that 66% of adults nationally think licensed drivers should be required to retake their road test once they reach 65 years of age It was also reported that interviews were conducted on 1, 018 American adults, and that the margin of error was 3% using a 95% confidence level.
a. Verify the margin of error reported by The Marist Poll.
b. Based on a 95% confidence interval, docs the poll provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65?
Answer:
a
The Margin of error is correct
b
No the polls does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65.
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 66[/tex]% = 0.66
The sample size is n = 1018
The margin of error is MOE = 3 % = 0.03
The confidence level is C = 95%
Given that the confidence level is 95% , then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5[/tex]%
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the standardized normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The reason we are obtaining critical values for [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because [tex]\alpha[/tex] represents the area under the normal curve where the confidence level ([tex]1-\alpha[/tex]) did not cover which include both the left and right tail while [tex]\frac{\alpha }{2}[/tex] is just considering the area of one tail which what we required to calculate the margin of error
Generally the margin of error is mathematically represented as
[tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{\frac{p (1-p )}{n} }[/tex]
substituting values
[tex]MOE = 1.96 * \sqrt{\frac{0.66 (1-66 )}{1018} }[/tex]
[tex]MOE = 0.03[/tex]
[tex]MOE = 3[/tex]%
The 95% is mathematically represented as
[tex]p - MOE < p < p +MOE[/tex]
substituting values
[tex]0.66 -0.03 < p < 0.66 +0.03[/tex]
[tex]0.63 < p < 0.69[/tex]
Looking at the confidence level interval we see that the population proportion is between
63% and 69%
shown that the population proportion is less than 70%
Which means that the polls does not provide convincing evidence that more than 70% of the population think that licensed drivers should be required to retake their road test once they turn 65.