Answer:
The level of significance to be used is α = 0.0025
Step-by-step explanation:
Here, we are interested in calculating the the level of significance which at most must be used for each of the hypothesis test
We proceed as follows;
P(type 1 error) = α
From the question, n = number of hypotheses = 20
P( of one or more type one error) ≤ 0.05
1- P(no type one error) ≤ 0.05
Hence;
1- (1-α)^20 ≤ 0.05
(1-α)^20 ≥ 0.95
1- α ≥ 0.997438621223
α ≤ 0.00256
Thus α = 0.0025
The population of fruit flies in a laboratory grows geometrically and is checked everyday at noon. If the population began with 80 fruit flies and reached 125 in two days, what is the population after 4 days?
Answer:
[tex]\boxed{195}[/tex]
Step-by-step explanation:
The fruit flies grows geometrically.
[tex]125=80k^2[/tex]
Find the value of k.
[tex]\sqrt{\frac{125}{80} } =k[/tex]
[tex]1.25=k[/tex]
[tex]P=80(1.25)^t[/tex]
[tex]t[/tex] is number of days.
[tex]P=80(1.25)^4[/tex]
[tex]P=195[/tex]
In the following problem, the expression is the right side of the formula for cos (alpha - beta) with particular values for alpha and beta. cos (79 degree) cos (19 degree) + sin (79 degree) sin (19 degree)
Identify alpha and beta in each expression.
The value for alpha: degree
The value for beta: degree
Write the expression as the cosine of an angle. cos degree
Find the exact value of the expression. (Type an exact answer, using fraction, radicals and a rationalized denominator.)
Answer:
1. [tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex]
2. [tex]cos(60)[/tex]
3. [tex]cos(60) = \frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]cos(\alpha - \beta )[/tex]
[tex]cos(79)cos(19) + sin(79)sin(19)[/tex]
Solving for [tex]\alpha[/tex] and [tex]\beta[/tex]
In trigonometry;
[tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex]
Equate the above expression to [tex]cos(79)cos(19) + sin(79)sin(19)[/tex]
[tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex] and [tex]cos(\alpha - \beta ) = cos(79)cos(19) + sin(79)sin(19)[/tex]
By comparison
[tex]cos\alpha\ cos\beta + sin\alpha\ sin\beta = cos(79)cos(19) + sin(79)sin(19)[/tex]
Compare expression on the right hand side to the left hand side
[tex]cos\alpha\ cos\beta = cos(79)cos(19) \\\\ sin\alpha\ sin\beta = sin(79)sin(19)[/tex]
This implies that
[tex]cos\alpha\ = cos(79)\\cos\beta = cos(19) \\\\ and\\\\sin\alpha\ = sin(79)\\sin\beta = sin(19)[/tex]
By further comparison
[tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex]
Substitute [tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex] in [tex]cos(\alpha - \beta )[/tex]
[tex]cos(\alpha - \beta ) = cos(79 - 19)[/tex]
[tex]cos(\alpha - \beta ) = cos(60)[/tex]
Hence, the expression is [tex]cos(60)[/tex]
Solving for the exact values;
Express [tex]cos(60)[/tex] as a difference of angles
[tex]cos(60) = cos(90 - 30)[/tex]
Recall that [tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex]
So;
[tex]cos(90- 30 ) = cos(90) cos(30) + sin(90) sin(30)[/tex]
------------------------------------------------------------------------------------
In trigonometry;
[tex]cos(90) = 0[/tex]; [tex]cos(30) = \frac{\sqrt{3}}{{2}}[/tex]; [tex]sin(90) = 1[/tex]; [tex]sin(30) = \frac{1}{2}[/tex];
---------------------------------------------------------------------------
[tex]cos(90- 30 ) = cos(90) cos(30) + sin(90) sin(30)[/tex] becomes
[tex]cos(90- 30 ) = 0 * \frac{\sqrt{3}}{2} + 1 * \frac{1}{2}[/tex]
[tex]cos(90- 30 ) = 0 + \frac{1}{2}[/tex]
[tex]cos(90- 30 ) = \frac{1}{2}[/tex]
Hence;
[tex]cos(60) = \frac{1}{2}[/tex]
taking a test- Which expression represents the surface area of the cone? A cone with diameter 12 inches, height 8 inches, and slant height 10 inches. S A = pi r l + pi r squared (pi) (6) (10) + (pi) (6 squared) (pi) (8) (10) + (pi) (8 squared) (pi) (12) (10) + (pi) (12 squared) (pi) (10) (12) + (pi) (10 squared)
Answer:
[tex]SA = \pi (6) * 10+\pi ( 6)^2[/tex]
Step-by-step explanation:
The surface area of a cone is given by
[tex]SA = \pi rl +\pi r^2[/tex]
r is the radius and l is the slant height.
The diameter is 12 inches, the radius is 12/2 = 6 inches.
The slant height is 10 inches.
[tex]SA = \pi (6) * 10+\pi ( 6)^2[/tex]
Answer:
SA of cone = [tex](\pi )(6)(8) + (\pi )(6)^2[/tex]
Step-by-step explanation:
Surface Area of cone = [tex]\pi rh+\pi r^2[/tex]
Where r = 6 inches (Diameter = 12 inches) , h = 8 inches (We'll not consider the slant height)
SA of cone = [tex](\pi )(6)(8) + (\pi )(6)^2[/tex]
WHY CAN'T ANYONE HELP ME? Twice last month, Judy Carter rented a car in Fresno, California, and traveled around the Southwest on business. The car rental agency rents its cars for a daily fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 440 miles, and the rental cost her $286. On her second business trip she drove 190 miles in 3 days, and paid $165.50 for the rental. Find the daily fee and the mileage charge.
Answer:
The daily rate is $33 and the per mile rate is $0.35
Step-by-step explanation:
4x + 440y = 286
3x + 190y = 165.5
We can solve this systems of equations by multiplying the second statement by [tex]-\frac{4}{3}[/tex] to try and eliminate the x variable.
4x + 440y = 286
-4x - [tex]\frac{760}{3}[/tex]y = -220[tex]\frac{2}{3}[/tex]
[tex]\frac{560}{3}[/tex] y= [tex]\frac{196}{3}[/tex]
560y = 196
y = 0.35
So, the rate per mile is 0.35. Now, with this info, let's find the daily rate by plugging it into the equation.
[tex]4x + 440\cdot0.35 = 286\\4x + 154 = 286\\4x = 132\\x = 33[/tex]
So, the daily rate is $33 and the mile rate is $0.35.
Hope this helped!
Answer:
the daily fee =33 dollars
and the mileage charge.=0.35
let d: be daily fee and m for mileage
cost of rental =(d*number of days)+ (m*number of mileage)
her first trip: 4d+440m=286
her second trip: 3d+190m=165.5
solve by addition and elimination
4d+440m=286 ⇒ multiply by 3 ⇒12d +1320m=(3)286
3d+190m=165.5⇒ multiply by 4⇒12d+190(4)m=4(165.5)
12d+1320m=858
12d+760m=662
subtract two equation to eliminate d
12d+1320m-12d-760m=858-662
560m=196
m=7/20=0.35 for on mileage
d: 4d+440m=286
4d=286-440(0.35)
d=(286-154)/4 33 dollars
Find y................
Answer:
[tex] y = 3 [/tex]
Step-by-step explanation:
Given the above right angled triangle, we would use a trigonometric ratio formula to find y.
Given angle = 30°
Hypotenuse = 6
Opposite side = y
Solve for y using the trigonometric ratio formula as follows:
[tex] sin(X) = \frac{opposite}{hypotenuse} [/tex]
[tex] sin(30) = \frac{y}{6} [/tex]
Multiply both sides by 6
[tex] sin(30)*6 = \frac{y}{6}*6 [/tex]
[tex] 0.5*6 = y [/tex]
[tex] 3 = y [/tex]
[tex] y = 3 [/tex]
Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.
16 sin4x
16sin4x = _____
Answer:
[tex]6-8cos2x+2cos4x[/tex]
Step-by-step explanation:
We are given that
[tex]16sin^4 x[/tex]
We can write the given expression as
[tex]16(sin^2x \times sin^2 x)[/tex]
[tex]16(\frac{1-cos2x}{2})(\frac{1-cos2x}{2})[/tex]
By using the formula
[tex]sin^2\theta=\frac{1-cos2\theta}{2}[/tex]
[tex]4(1-cos2x)^2[/tex]
[tex]4(1-2cos2x+cos^2(2x)[/tex]
Using the identity
[tex](a-b)^2=a^2+b^2-2ab[/tex]
[tex]4(1-2cos2x+\frac{1+cos4x}{2})[/tex]
[tex]4-8cos2x+2+2cos4x[/tex]
[tex]6-8cos2x+2cos4x[/tex]
This is required expression.
PLEASE HELP ASAP!! Write a polynomial f(x) that satisfies the following conditions. Polynomial of lowest degree with zeros of -4 (multiplicity of 1), 2 (multiplicity of 3), and with f(0)=64
Answer:
See below.
Step-by-step explanation:
So, we have the zeros -4 with a multiplicity of 1, zeros 2 with a multiplicity of 3, and f(0)=64.
Recall that if something is a zero, then the equation must contain (x - n), where n is that something. In other words, for a polynomial with a zero of -4 with a multiplicity of 1, then (x+4)^1 must be a factor.
Therefore, (x-2)^3 (multiplicity of 3) must also be a factor.
Lastly, f(0)=64 tells that when x=0, f(x)=64. Don't simply add 64 (like what I did, horribly wrong). Instead, to keep the zeros constant, we need to multiply like this:
In other words, we will have:
[tex]f(x)=(x+4)(x-2)^3\cdot n[/tex], where n is some value.
Let's determine n first. We know that f(0)=64, thus:
[tex]f(0)=64=4(-2)^3\cdot n[/tex]
[tex]64=-32n, n=-2[/tex]
Now, let's expand:
Expand:
[tex]f(x)=(x+4)(x^2-4x+4)(x-2)(-2)[/tex]
[tex]f(x)=(x^2+2x-8)(x^2-4x+4)(-2)[/tex]
[tex]f(x)=(x^4-4x^3+4x^2+2x^3-8x^2+8x-8x^2+32x-32)(-2)[/tex]
[tex]f(x)=-2x^4+4x^3+24x^2-80x+64[/tex]
This is the simplest it can get.
You visit a farm and notice that white chickens lay white eggs and colored chickens lay colored eggs, so you decide that only white chickens lay white eggs. What type of reasoning is this?
Answer:
This is called an Inductive reasoning.
Step-by-step explanation:
It is a logical process in which a number of premises all believed true combine to come up with specific conclusions. This is a generalisation based on observations.
Hope it helps.
Three of the sides will require fencing and the fourth wall already exists. If the farmer has 116 feet of fencing, what are the dimensions of the region with the largest area
Answer:
29 ft x 58 ft
Step-by-step explanation:
Let x be the length of each side perpendicular to the wall, and y be the length of the side parallel to the wall.
The amount of wire available is:
[tex]116 = 2x+y\\y=116-2x[/tex]
The area of the region is:
[tex]A=xy=x(116-2x)\\A(x)=116x-2x^2[/tex]
The value of 'x' for which the derivate of the area function is zero will yield the maximum area:
[tex]A(x)=116x-2x^2\\A'(x) = 116-4x=0\\x=29\ ft[/tex]
The value of y is:
[tex]y=116-2*29\\y=58\ ft[/tex]
The dimensions of the region with the largest area are 29 ft x 58 ft.
Samantha has 5 granola bars. She wants to give 1/3 of a granola bar to each friend. Which expression can she use to find the number of friends to whom she can give granola bars?
Answer:
5/(1/3)
Step-by-step explanation:
She has 5 granola bars and gives 1/3 of one to each of her friends. To find how many friends she can give it to, divide 5 by 1/3. You would get a total of 15 friends that you can give granola bars to. The question is asking for an expression so the expression would be 5/(1/3) or 5*3
Answer:
1/3 x = 5
x=15
Step-by-step explanation:
You’re multiplying 1/3 times the number of friends (x), and then multiplying both sides by the reciprocal to solve for x
hhhelpp meeee!! I WILL GIVE BRAINLIEST
Answer:
We're solving for CD. If we look at ΔABD we notice that it's a 30-60-90 triangle which has a side length ratio of 1:√3:2 and in this case the 1 is 300 so side BD = 300√3. Similarly, ΔABC is also a 30-60-90 triangle but this time the √3 is 300 so side BC = 100√3. We know that CD = BD - BC using PWP so the answer is 300√3 - 100√3 = 200√3 = 346.4 feet.
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps
Answer:
123 domestic stamps
89 foreign stamps
Step-by-step explanation:
Answer:
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
Which equation represents the total number of stamps Malik collected?
✔ x + y = 212
Which equation represents the difference in the number of foreign and domestic stamps Malik collected?
✔ x – y = 34
Which system of linear equations represents the situation?
✔ x – y = 34 and x + y = 212
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
This system of equations models the given information for both stamp types.
x – y = 34
x + y = 212
Solve the system of equations.
How many foreign stamps does Malik have?
✔ 89 foreign stamps
How many domestic stamps does Malik have?
✔ 123 domestic stamps
Step-by-step explanation:
its right on 2021 edge! :) hope this helps
Exhibit 3-3Suppose annual salaries for sales associates from Hayley's Heirlooms have a bell-shaped distribution with a mean of $32,500 and a standard deviation of $2,500.The z-score for a sales associate from this store who earns $37,500 is ____
Answer:
The z-score for a sales associate from this store who earns $37,500 is 2
Step-by-step explanation:
From the given information:
mean [tex]\mu[/tex] = 32500
standard deviation = 2500
Sample mean X = 37500
From the given information;
The value for z can be computed as :
[tex]z= \dfrac{X- \mu}{\sigma}[/tex]
[tex]z= \dfrac{37500- 32500}{2500}[/tex]
[tex]z= \dfrac{5000}{2500}[/tex]
z = 2
The z-score for a sales associate from this store who earns $37,500 is 2
The chart below lists the original and sale prices of items at a clothing store.
Clothing Prices
Original price Sale price
$7.99
$5.59
$10.99
$7.69
$12.99
$9.09
$15.99
$11.19
$24.99
$17.49
$29.99
$20.99
Which statement best describes why the sale price is a function of the original price?
As the original price increases, the sale price also increases.
The sale price is always less than the original price.
For every original price, there is exactly one sale price.
The sales price is never less than zero.
Answer: C) For every original price, there is exactly one sale price.
For any function, we always have any input go to exactly one output. The original price is the input while the output is the sale price. If we had an original price of say $100, and two sale prices of $90 and $80, then the question would be "which is the true sale price?" and it would be ambiguous. This is one example of how useful it is to have one output for any input. The input in question must be in the domain.
As the table shows, we do not have any repeated original prices leading to different sale prices.
Answer:
C STAY SAFE!!!
Step-by-step explanation:
Ok we know this cant be A the reason is It says tha the original price is increasing so thats FALSE... its trying to trick you so no
The second choice says The sale price is always less than the original price. well take a look at the sale prices are they? Obiously not so False
Ok the third option For every original price, there is exactly one sale price. well this is true ask yourself each it helps.
Last option The sales price is never less than zero. erm FALSE OBIOUSLY THIS IS TRUE JUST NOT TRUE ITS WRONG
THE ANSER IS C
The parabola y= x2 - 4 opens:
O up
O down
O right
O left
Answer:
it opens up
goes up 4 but doesn't move left or right
think about whether the diagram represents a function.
Step-by-step explanation:
im sorry but i need more info or a picture or something to actually anwser the question...
An anchor lowered at a constant rate into the ocean takes 5 seconds to move -17.5 meters. What is the rate of the anchor in meters per second?
Answer:
-3.5 meters per second
Step-by-step explanation:
Take the distance and divide by the time
-17.5 meters/ 5 seconds
-3.5 meters per second
Answer:
-3.5 m/s
Step-by-step explanation:
Rate of the anchor = [tex]\frac{distance}{time}[/tex]
[tex]\frac{-17.5}{5}[/tex]
-3.5 meters per second.
There are 6 brooms and 4 mops in a janitor's closet. What is the fraction of the number of brooms to the number of mops?
Answer:
6/4
Step-by-step explanation:
Answer:
6/4
Step-by-step explanation:
There are 6 brooms to 4 mops.
So you would write it that way as a fraction, but you could also write it like 6:4 or 6 to 4.
what is the value of this expression when a = 2 and b = -3 ? a^3 - b^3 / 5
Answer:
13 2/5
Step-by-step explanation:
a = 2 and b = -3
so the question asks whats.... a^3 - b^3/5
First we plug in the values of a and b
(2)^3 - (-3)^3 /5
Now we solve the ones in paranthesis first
(2)^3 = 8 because 2×2×2 and
-(-3)^3 forget about the - outside the parenthesis so
(-3)^3 = (-27) because (-3)×(-3)×(-3)
now we put it back together
8 -(-27)/5
the two minus become plus so
8 + 27/5
Now we solve it like fractions
8 and 27/5
simplify
13 and 2/5
Hope that helps!
plzzzz solve the second one
Answer:
x=10/3
Step-by-step explanation:
isolate the variable
Answer:
1. x = 4
2. x = 10/3
Step-by-step explanation:
1. 3x - 5 = 3 + x
3x - x = 3 + 5
2x = 8
x = 4
2. x/2 + 5/9 = 2x/3
(x/2 + 5/9) * 18 = (2x/3) * 18
9x + 10 = 12x
10 = 12x - 9x
10 = 3x
x = 10/3
A fisherman uses a spring scale to weigh a tilapia fish. He records the fish weight as a kilograms and notices that the spring stretches b centimeters. Which expression represents the spring constant (1 =9.8 )? A). 980ab B). 9.8ab C). 9.8ab D). 980ab
Answer:
k = [tex]\frac{980a}{b}[/tex]
Step-by-step explanation:
Fisherman noticed a stretch in the spring = 'b' centimetres
Weight of the fish = a kilograms
If force applied on a spring scale makes a stretch in the spring then Hook's law for the force applied is,
F = kΔx
Where k = spring constant
Δx = stretch in the spring
F = weight applied
F = mg
Here 'm' = mass of the fish
g = gravitational constant
F = a(9.8)
= 9.8a
Δx = b centimetres = 0.01b meters
Therefore, 9.8a = k(0.01b)
k = [tex]\frac{9.8a}{0.01b}[/tex]
k = [tex]\frac{980a}{b}[/tex]
Therefore, spring constant of the spring will be determined by the expression, k = [tex]\frac{980a}{b}[/tex]
HELP PLEASEEE!!!!!!!!!!
Answer:
100
Step-by-step explanation:
height = constant/ width
Taking the point (5,20)
where 5 is the width and 20 is the height
20 = constant/ 5
Multiply each side by 5
5*20 = constant
100 = constant
Suppose a car depreciates linearly the second you drive it off the lot. If you purchased the car for $31,500 and after 5 years the car is worth $20,500, find the slope of the depreciation line.
Answer: m = - 2200
Step-by-step explanation: Slope of a line is a number which describes the steepness and direction of a linear graph. It is represented by the letter m.
The year a car is bought and its price means:
f(0) = 31,500
Five years later, the price is $20,500, i.e.:
f(5) = 20,500
With these two pairs of value, slope is calculated as:
[tex]m = \frac{y-y_{0}}{x-x_{0}}[/tex]
[tex]m = \frac{20500-31500}{5-0}[/tex]
[tex]m = \frac{- 1100}{5}[/tex]
m = - 2200
The slope of the depreciation line is m = -2200 and it is negative because the line decreases along time.
solve for x in the diagram below
Answer:
45
Step-by-step explanation:
Both angles (2x+45) and x together form a straight angle which measures 180 degrees.
Together should make you think of adding the angle measurements.
So we have that (2x+45)+x should be 180 degrees.
The equation we want to solve is:
(2x+45)+x=180
2x+45+x=180
(2x+x)+45=180
3x+45=180
3x=180-45
3x=135
x=135/3
x=45
Let's confirm that x is 45.
(2x+45) with x=45:
(2*45+45)
(3*45)
135
So (2x+45)+x at x=45 gives us:
135+45
180
Answer has been confirmed.
Answer:
[tex]\boxed{x = 45}[/tex]
Step-by-step explanation:
=> [tex]x+2x+45 = 180[/tex] (Angles on a straight line add up to 180 degrees)
=> [tex]3x+45 = 180[/tex]
Subtracting 45 to both sides
=> 3x = 180-45
=> 3x = 135
Dividing both sides by 3
=> x = 45
what is that is the derivative of
x^2-x+3 at the point
x=5
What value of x where
x²-x+3
a minimum?
Answer:
see explanation
Step-by-step explanation:
differentiate using the power rule.
[tex]\frac{d}{dx}[/tex]( a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] , thus
[tex]\frac{d}{dx}[/tex](x² - x + 3 ) = 2x - 1
x = 5 → 2(5) - 1 = 10 - 1 = 9
To find the value of x for minimum , equate [tex]\frac{d}{dx}[/tex] to zero
2x - 1 = 0 , then
2x = 1 and
x = [tex]\frac{1}{2}[/tex]
how many solutions if both slopes are the same but the y-intercepts are different
Answer:
No solutions.
Step-by-step explanation:
You will only have solutions when the two lines meet. But since the slopes are the same, the two lines are parallel. Since the y-intercepts are different, that means that the two slopes will never intersect, which means that there are no solutions.
Hope this helps!
Answer: no solution
Step-by-step explanation: When lines have the same slope, the graphs of the two lines are parallel which means they never intersect.
Let's look at an example.
Below, you will see two equations.
Both of the lines have a slope of 1.
So, they must be parallel which means they don't cross.
So there is no solution.
I _____ some stuff A)'ve done B)'s do C)'s doing D)'s did E) 've
Answer:
A and E
Step-by-step explanation:
If the answer was A, it would translate to:
I have done some stuff.
If the answer was D, it would translate to:
I have some stuff.
Both of the sentences are grammatically correct, so A and E are the answers.
Incorrect:
B. - I's do some stuff - doesn't make sense
C. - I's doing some stuff - doesn't make sense
D. - I's did some stuff - doesn't make sense
Determine the amount of paint required to cover a wall that is 11feet high and 15feet wide, if the wall has two rectangular windows (which are not to be painted), each measuring 3feet by 7feet.
Answer:
123 Square Feet. Of Paint. Probably gonna take a little more than a sample-size quart, let me know how it turns out.
Step-by-step explanation:
You would need 11*15=165 square feet of paint. BUT
You need 42 less square feet, because there are 2, 7*3=21 square-foot windows.
165-42
If the payment is not made on the credit card by the end of the grace period,
which of the following will occur?
Answer: C. Interest will be charged
Step-by-step explanation:
Answer:
Step-by-step explanation:
Interest will be charged is your answer!
A random sample of 144 observations produced a sample proportion of 0.4. An approximate 90% confidence interval for the population proportion p is between:_______
a) 0.320 and 0.480
b) 0.333 and 0.480
c) 0.333 and 0.467
d) 0.359 and 0.441
e) 0.313 and 0.487
Answer:
CI =(0.333, 0.480)
Step-by-step explanation:
The formula for calculating the confidence interval is expressed as shown;
CI = p±Z * √p(1-p)/n±0.5/n
Z is the z-score at 90% confidence
p is the sample proportion
n is the sample size
Given n = 144, p = 0.4 and z-score at 90% CI = 1.645 (from z table)
Substituting this values;
CI = p ± 1.645*√0.4(1-0.4)/144 ±0.5/n
CI = 0.4 ± 1.645*√0.4(0.6)/144 ± 0.5/144
CI = 0.4 ±1.645 * √0.24/144 ± 0.00347
CI = 0.4 ±1.645 * 0.04087± 0.00347
CI = 0.4±0.06723±0.00347
CI =(0.333, 0.480)