The parent function f(x) = 1.5x is translated such that the function g(x) = 1.5x + 1 + 2 represents the new function. Which is the graph of g(x)? On a coordinate plane, an exponential function increases from quadrant 2 to quadrant 1. It crosses the y -axis at (0, 2.5). On a coordinate plane, an exponential function increases from quadrant 3, through quadrant 4, to quadrant 1. It crosses the y-axis at (0, negative 0.5). On a coordinate plane, an exponential function increases from quadrant 3, through quadrant 4, to quadrant 1. It crosses the y-axis at (0, negative 1.5). On a coordinate plane, an exponential function increases from quadrant 2 to quadrant 1. It crosses the y -axis at (0, 3.5).

Answer:

C. The divergence of F is StartFraction 1 Over StartAbsoluteValue Bold r EndAbsoluteValue squared EndFraction

∇•F = 1/|r|²

Step-by-step explanation:

The position vector r = (x, y, z)

r = xi+yj+zk

|r| = √x²+y²+z²

|r|² = x²+y²+z²

Given the radial field F = r/|r|²

Divergence of the radial field is expressed as:

∇•F = {δ/δx i+ δ/δy j + δ/δy k} • {(r/|r|²)

∇•F = {δ/δx i+ δ/δy j + δ/δy k} • {xi/|r|² + yj/|r|² + zk/|r|²}

∇•F = δ/δx(x/|r|²) + δ/δy(y/|r|²)+δ/δz(z/|r|²)

Check the attachment for the complete solution.

Answer:

20 meters square

Step-by-step explanation:

Surface Area of this square based pyramid =  A  = base area + 4* (face area)

A = (2 *2)  +  4* ( (1/2)*2 * 4) )

A = 4 + 4*(4)

A = 4 + 16 = 20

A = 20 square meters

Answer:

for AAS triangles or SSA

Step-by-step explanation:

Answer:

ny triangle whose two sides and 1 angle is known or 2 angles are known and 1 side is known

Step-by-step explanation:

Answer:

17 feet

Step-by-step explanation:

Length of the diagonal=50 feet

Let the shorter part of the sidewalk =x

Since the longer part of the sidewalk is twice the shorter length,

Length of the longer part of the sidewalk =2x

First, we determine the value of x.

Using Pythagoras Theorem and noting that the diagonal is the hypotenuse.

[tex]50^2=(2x)^2+x^2\\5x^2=2500\\$Divide both sides by 5\\x^2=500\\x=\sqrt{500}=10\sqrt{5} \:ft[/tex]

The length of the shorter side =[tex]10\sqrt{5} \:ft[/tex]

The length of the longer side =[tex]20\sqrt{5} \:ft[/tex]

Total Distance =[tex]10\sqrt{5}+ 20\sqrt{5}=67 \:feet[/tex]

Difference in Distance

67-50=17 feet

The children are saving 17 feet by cutting the lawn diagonally.

Answer:

Step-by-step explanation:

Answer: The answer is D 12 i am pretty sure.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:  117 centimeters

Step-by-step explanation:

Answer:

117 cm³

Step-by-step explanation:

To calculate the volume of a Rectangular Prism, we must use the formula:

l×w×h=V.

In this case, l= 13, w= 3, and h= 3.

When these values are substituted in, we get:

13×3×3= 117 cm³

Answer:

that answer is D

Step-by-step explanation:

I used pythagreum theurum a^2+b^2=c^2

then i divided square root 260 by 4 the largest perfect square factor which gives us 2 square root 65 because 4 is a perfect square that equal 2

Answer:

There is a 11/14 chance that the result is a multiple of 3 or a multiple of 2.

Step-by-step explanation:

Since the spinner is from 1 to 14, find all of the multiples of 3 and multiples of 2.

There are 4/14 multiples of 3 and 7/14 multiples of 2.

Add both of these numbers together 4/14 + 7/14 = 11/14

If this answer is correct, please make me Brainliest!

The probability of landing on a multiple of 2 or 3 when spinning a spinner numbered 1 through 14 is 4/7.

The student asked about the probability of getting a multiple of 3 or a multiple of 2 when spinning a spinner numbered 1 through 14. To determine this, we first list the multiples of 3 and 2 within the range of numbers on the spinner.

Multiples of 3: 3, 6, 9, 12
Multiples of 2: 2, 4, 6, 8, 10, 12, 14
Note that 6 and 12 are multiples of both 2 and 3, so we should not count them twice.

The total number of distinct multiples of 2 or 3 is 3 (multiples of 3) + 7 (multiples of 2) - 2 (common multiples) = 8 unique numbers. Since there are 14 possible outcomes on the spinner, the probability of landing on a multiple of 3 or 2 is 8 (favorable outcomes) divided by 14 (total possible outcomes).

The probability calculation is: 8/14, which simplifies to 4/7.

Answer:

b. 4:35 p.m

Step-by-step explanation:

Her speed in t minutes after 4:30 p.m. is modeled by the following equation:

[tex]v(t) = v(0) + at[/tex]

In which v(0) is her speed at 4:30 pm and a is the acceleration.

At 4:30 p.m. she looks down at her speedometer and notices that she is going 45 mph.

This means that [tex]v(0) = 45[/tex]

Ten minutes later she looks down at the speedometer again and notices that she is going 55 mph.

This means that [tex]v(10) = 55[/tex]

So

[tex]v(t) = v(0) + at[/tex]

[tex]55 = 45 + 10a[/tex]

[tex]10a = 10[/tex]

[tex]a = 1[/tex]

So

[tex]v(t) = 45 + t[/tex]

When was she moving exactly 50 mph?

This is t minutes after 4:30 p.m.

t is found when v(t) = 50. So

[tex]v(t) = 45 + t[/tex]

[tex]50 = 45 + t[/tex]

[tex]t = 5[/tex]

5 minutes after 4:30 p.m. is 4:35 p.m.

So the correct answer is:

b. 4:35 p.m

Answer:

79.85% probability that at least 5 of them use their smartphones in meetings or classes.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they use their smartphone during meetings or classes, or they do not. The probability of an adult using their smartphone in these situations are independent of other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Assume that when adults with smartphones are randomly​ selected, 58​% use them in meetings or classes.

This means that [tex]p = 0.58[/tex]

10 adults selected.

This means that [tex]n = 10[/tex]

Find the probability that at least 5 of them use their smartphones in meetings or classes.

[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{10,5}.(0.58)^{5}.(0.42)^{5} = 0.2162[/tex]

[tex]P(X = 6) = C_{10,6}.(0.58)^{6}.(0.42)^{4} = 0.2488[/tex]

[tex]P(X = 7) = C_{10,7}.(0.58)^{7}.(0.42)^{3} = 0.1963[/tex]

[tex]P(X = 8) = C_{10,8}.(0.58)^{8}.(0.42)^{2} = 0.1017[/tex]

[tex]P(X = 9) = C_{10,9}.(0.58)^{9}.(0.42)^{1} = 0.0312[/tex]

[tex]P(X = 10) = C_{10,10}.(0.58)^{10}.(0.42)^{0} = 0.0043[/tex]

[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.2162 + 0.2488 + 0.1963 + 0.1017 + 0.0312 + 0.0043 = 0.7985[/tex]

79.85% probability that at least 5 of them use their smartphones in meetings or classes.

The predicted percentage of games won for a team with these statistics is approximately 60.025%.

To address the given questions, we'll use the provided estimated regression equation:

[tex]\[ \hat{y} = 60.5 + 0.319x_1 - 0.241x_2 \][/tex]

where:

- [tex]\( \hat{y} \)[/tex] is the predicted percentage of games won,

- [tex]\( x_1 \)[/tex] is the average number of passing yards obtained per game on offense,

- [tex]\( x_2 \)[/tex] is the average number of yards given up per game on defense.

a. To predict the percentage of games won for a team that averages 225 passing yards per game on offense [tex](\( x_1 = 225 \))[/tex] and gives up an average of 300 yards per game on defense [tex](\( x_2 = 300 \))[/tex], we'll substitute these values into the regression equation:

[tex]\[ \hat{y} = 60.5 + 0.319(225) - 0.241(300) \][/tex]

[tex]\[ \hat{y} = 60.5 + 71.775 - 72.3 \][/tex]

[tex]\[ \hat{y} = 60.5 - 0.525 \][/tex]

[tex]\[ \hat{y} = 60.025 \][/tex]

Therefore, the predicted percentage of games won for a team with these statistics is approximately 60.025%.

Complete question:

In exercise 24, an estimated regression equation was developed relating the percentage of games won by a team in the National Football League for the 2011 season (y) given the average number of passing yards obtained per game on offense (x1) and the average number of yards given up per game on defense (x2). The estimated regression equation was y = 60.5 + 0.319x1 - 0.241x2.

Predict the percentage of games won for a particular team that averages 225 passing yards per game on offense and gives up an average of 300 yards per game on defense.

Answer:

V≈14,137.17m³ or 4500π

Step-by-step explanation:

Formula: V=(1 /6)πd³

V=(1/6)π(30³)= 14137.16694115406957308189522475776297888726229718797619438.....

Answer:

14137.17 meters cubed

Step-by-step explanation:

volume = 14137.17 meters cubed

Answer:

The top question = 189.25 rounded = 189.3 sq in

explanation: area= radius square x pi so radious is 5..sq will 25 then 25xpi(3.14)=78.50 78.50/2= 39.25 + 150 (area of rect) =189.25 rounded to 189.3

for the bottom question = 488 square cm

Step-by-step explanation:

17x22= 374

22-10=12

12x19=228 / 2 = 114

114 + 374 = 488 sq cm

EndFraction

StartFraction 24 Over 121 EndFraction

StartFraction 6 Over 11 EndFraction

StartFraction 10 Over 11 EndFraction

Answer:

StartFraction 24 Over 121 EndFraction

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation can be rearranged to vertex form:

  x^2 -4x = -5 . . . . . . . . . subtract 4x

  x^2 -4x +4 = -5 +4 . . . . add 4

  (x -2)^2 = -1 . . . . . . . . . show the left side as a square

  x -2 = ±√-1 = ±i . . . . . . take the square root; the right side is imaginary

  x = 2 ± i . . . . . . . . . . . . . add 2. These are the complex solutions.

_____

Comment on the question

Every 2nd degree polynomial equation has two solutions. They may be real, complex, or (real and) identical. That is, there may be 0, 1, or 2 real solutions. This equation has 0 real solutions, because they are both complex.

Answer:

D. c+14≤24

Step-by-step explanation:

A. c+14<24 is c<10 (subtract 14)

B. c+18≥24 is c≥6 (subtract 18)

C. c+18>24 is c>6 (subtract 18)

D. c+14≤24 is c≤10 (subtract 14)

The set is {5, 6, 8, 9, 10}, so it should include each one of those numbers. C and A don't include 6 and 10 respectively, so they can't be the answer. B contains all numbers 6 and above, which doesn't include 5. The remaining letter is D, so that's the final answer.

Final answer:

With a p-value of 0.1071 exceeding the significance level of 0.05, we do not reject the null hypothesis and conclude there is insufficient evidence to support the union's claim about child-care benefits in manufacturing firms.

Explanation:

The reported p-value of 0.1071 is greater than the significance level alpha (0.05). Based on this result, the appropriate statistical decision would be to do not reject the null hypothesis.

Therefore, at the 5 percent significance level, there is insufficient evidence to support the claim made by the union that more than 85% of firms in the manufacturing sector do not offer child-care benefits to their workers.

The higher p-value suggests that the data collected from the random sample of 330 manufacturing firms does not provide strong enough evidence to refute the possibility that the percentage of firms not offering child-care benefits is at or below 85%.

Answer:

a = 65.37

b = 46.11

B = 35.2

Step-by-step explanation:

sin 54.8 = a / 80

a = 80 sin 54.8 = 65.3715 = 65.4

[tex]b^{2} = c^{2} - a^{2}[/tex]

b=[tex]\sqrt{80^2 - 65.3715^2}[/tex]

b=46.1147 = 46.11

B = 180 - 90 - 54.8 = 35.2

The sides and the angles as follows:

Therefore,

∠A = 54.8°

∠B = 35.2°

∠C = 90°

a ≈ 65.37

b ≈ 46.64

c = 80

The triangle is a right angle triangle. Using trigonometric ratios, let's find a.

sin 54.8 = opposite / hypotenuse

sin 54.8 = a / 80

a = 80 sin 54.8

a = 65.3715918668

a ≈ 65.37

let's use Pythagoras theorem to find b.

c² = a² + b²

b² = c² - a²

b² =  80² - 65²

b² = 6400 - 4225

b² = 2175

b = √2175

b = 46.6368952654

b ≈ 46.64

let's find ∠B

∠A +  ∠B +  ∠C = 180°

∠B = 180 - 54.8 - 90

∠B = 35.2°

Therefore,

∠A = 54.8°

∠B = 35.2°

∠C = 90°

The sides are as follows:

a ≈ 65.37

b ≈ 46.64

c = 80

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Answer:

See Explanation

Step-by-step explanation:

To determine the number of prime cards needed to build a composite number, we simply express the number as a product of its prime factors.

These are:

4=2X2

6=2X3

8=2X2X2

9=3X3

10=2X5

12=2X2X3

14=2X7

15=3X5

16=2X2X2X2

18=2X3X3

20=2X2X5

21=3X7

22=2X11

24=2X2X2X3

26=2X13

27=3X3X3

28=2X2X7

30=2X3X5

32=2X2X2X2X2

33=3X11

34=2X17

35=5X7

36=2X2X3X3

38=2X19

39=3X13

40=2X2X2X5

42=2X3X7

44=2X2X11

45=3X3X5

46=2X2X13

48=2X2X2X2X3

49=7X7

50=2X5X5

Therefore for each of the numbers, those are the prime number cards to be used.

Answer:

no

Step-by-step explanation:

The formula is (4*pi/3)*r^3, so 256*pi/3 cubic units = 268.08  cubic units. {whatever units r is in}

Answer:

(256/3)pi

Step-by-step explanation:

(4/3)(pi)(r^3) =

(4/3)(pi)(4^3) =

(4/3)(pi)(64) =

(256/3)pi

Answer:

[tex]z=\frac{0.565 -0.58}{\sqrt{\frac{0.58(1-0.58)}{600}}}=-0.744[/tex]  

Since is a bilateral test the p value would be given by:  

[tex]p_v =2*P(z<-0.744)=0.4569[/tex]  

And since the p value is higher than the significance level we have enough evidence to conclude that the true proportion is not significantly different from 0.58

Step-by-step explanation:

Information given

n=600 represent the random sample selcted

X=339 represent the number of females aged 15 and older that living alone

[tex]\hat p=\frac{339}{600}=0.565[/tex] estimated proportion of females aged 15 and older that living alone

[tex]p_o=0.58[/tex] is the value that we want to check

[tex]\alpha=0.01[/tex] represent the significance level

z would represent the statistic

[tex]p_[/tex] represent the p value

Sytem of hypothesis

We want to check if the true proportion females aged 15 and older that living alone is significantly different from 0.58.:  

Null hypothesis:[tex]p=0.58[/tex]  

Alternative hypothesis:[tex]p \neq 0.58[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.565 -0.58}{\sqrt{\frac{0.58(1-0.58)}{600}}}=-0.744[/tex]  

Since is a bilateral test the p value would be given by:  

[tex]p_v =2*P(z<-0.744)=0.4569[/tex]  

And since the p value is higher than the significance level we have enough evidence to conclude that the true proportion is not significantly different from 0.58

Answer:

  1353 ft

Step-by-step explanation:

The cliff height and the distance from its base to the boat form the legs of a right triangle. The cliff height is the leg opposite the elevation angle, and the distance to the boat is the leg adjacent. Given these two legs of the triangle, the tangent relation seems useful:

  Tan = Opposite/Adjacent

We want to find the cliff height (opposite), so we can multiply this equation by Adjacent:

  Opposite = Adjacent×Tan

  cliff height = (2994 ft)(tan(24°19')) ≈ 1353 ft

The cliff is about 1353 feet high.

Answer:

Step-by-step explanation:

The nth term of a geometric sequence is expressed as Tn = [tex]ar^{n-1}[/tex] where;

a is the first term

r is the common ratio

n is the number of terms

Since we are to insert three geometric means between 2 and 81/8, the total number of terms in the sequence will be 5 terms as shown;

2, a, b, c, 81/8

a, b, and c are the 3 geometric mean to be inserted

T1 = [tex]ar^{1-1}[/tex] = 2

T1 = a = 2....(1)

T5= [tex]ar^{5-1}[/tex]

T5 = [tex]ar^{4}[/tex] = 81/8... (2)

Dividing equation 1 by 2 we have;

[tex]\frac{ar^{4} }{a}= \frac{\frac{81}{8} }{2}[/tex]

[tex]r^{4} = \frac{81}{16}\\\\r = \sqrt[4]{\frac{81}{16} } \\r = 3/2[/tex]

Given a =2 and r = 3/2;

[tex]T2=ar\\T2 = 2*3/2\\T2 = 3\\\\T3 = ar^{2} \\T3 = 2*\frac{3}{2} ^{2} \\T3 = 2*9/4\\T3 = 9/2\\\\T4 = ar^{3}\\T4 = 2*\frac{3}{2} ^{3} \\T4 = 2*27/8\\T4 = 27/4\\[/tex]

Therefore the three geometric means are 3, 9/2 and 27/4

In a geometric sequence where three terms lie between 2 and 81/8, the three geometric terms are:

[tex]\mathbf{T_2 =3 }[/tex]

[tex]\mathbf{T_3 =\frac{9}{2} }[/tex]

[tex]\mathbf{T_4 =\frac{27}{4} }[/tex]

Recall:

Given a geometric sequence, 2 . . . 81/8, with three other terms in the middle, first, find the value of r.

Thus:

First Term:

Fifth Term:

[tex]T_5 = ar^{n - 1}[/tex]

a = 2

n = 5

r = ?

T5 = 81/8

[tex]\frac{81}{8} = 2r^{5 - 1}\\\\\frac{81}{8} = 2r^4\\\\[/tex]

[tex]\frac{81}{8} \times 8 = 2r^4 \times 8\\\\81 = 16r^4\\\\[/tex]

[tex]\frac{81}{16} = \frac{16r^4}{16} \\\\\frac{81}{16} = r^4\\\\[/tex]

[tex]\sqrt[4]{\frac{81}{16}} = r\\\\\frac{3}{2} = r\\\\\mathbf{r = \frac{3}{2}}[/tex]

Find the three geometric means [tex]T_2, T_3, $ and $ T_4[/tex] between 2 and 81/8.

[tex]\mathbf{T_n = ar^{n - 1}}[/tex]

a = 2

r = 3/2

[tex]T_2 = 2 \times (\frac{3}{2}) ^{2 - 1}\\\\T_2 = 2 \times (\frac{3}{2}) ^{1}\\\\\mathbf{T_2 = 3}[/tex]

[tex]T_3 = 2 \times \frac{3}{2} ^{3 - 1}\\\\T_3 = 2 \times (\frac{3}{2}) ^{2}\\\\T_3 = 2 \times \frac{9}{4}\\\\\mathbf{T_3 =\frac{9}{2} }[/tex]

[tex]T_4 = 2 \times \frac{3}{2} ^{4 - 1}\\\\T_4 = 2 \times (\frac{3}{2}) ^{3}\\\\T_4 = 2 \times \frac{27}{8}\\\\\mathbf{T_4 =\frac{27}{4} }[/tex]

Therefore, in a geometric sequence where three terms lie between 2 and 81/8, the three geometric terms are:

[tex]\mathbf{T_2 =3 }[/tex]

[tex]\mathbf{T_3 =\frac{9}{2} }[/tex]

[tex]\mathbf{T_4 =\frac{27}{4} }[/tex]

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Answer:

  [tex]\sqrt[n]{x^m}=x^{\frac{m}{n}}[/tex]

Step-by-step explanation:

A radical represents a fractional power. For example, ...

  [tex]\sqrt{x}=x^{\frac{1}{2}}[/tex]

This makes sense in view of the rules of exponents for multiplication.

  [tex]a^ba^c=a^{b+c}\\\\a^{\frac{1}{2}}a^{\frac{1}{2}}=a^{\frac{1}{2}+\frac{1}{2}}=a\\\\(\sqrt{a})(\sqrt{a})=a[/tex]

So, a root other than a square root can be similarly represented by a fractional exponent.

____

The power of a radical and the radical of a power are the same thing. That is, it doesn't matter whether the power is outside or inside the radical.

  [tex]\sqrt[n]{x^m}=x^{\frac{m}{n}}=(\sqrt[n]{x})^m[/tex]

Answer:

a) 1/3

Step-by-step explanation:

a) Probability of drawing a king of any suit

Number of kings = 4

P(king) = 4/52

= 1/13

b) Probability of drawing a face card that is also a spade

Number of face =3

P(king) = 3/ 52

Answer:

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 1,100 square feet

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 1,100 square feet

Step-by-step explanation:

We are given that the mean area of several thousand apartments in a new development is advertised to be 1,100 square feet.

A consumer advocate has received numerous complaints that the apartments are smaller than advertised.

Let [tex]\mu[/tex] = mean area of several apartments.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 1,100 square feet

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 1,100 square feet

Here, null hypothesis states that the mean area of apartments are same as advertised.

On the other hand, alternate hypothesis states that the mean area of apartments are smaller than advertised.

So, this would be the appropriate null and the alternative hypothesis to test this claim.

Answer:

The correct answer to the following question will be "0.0367".

Step-by-step explanation:

The given values are:

[tex]p1=p2=0.06[/tex]

[tex]q1=q2=1-p1=0.94[/tex]

[tex]n1=n2=400[/tex]

As we know,

[tex]E(p1-p2)=p1-p2=0\\[/tex]

[tex]SE(p1-p2)=\sqrt{\frac{p1q1}{n1}+\frac{p2q2}{n2}}[/tex]

On putting the given values in the above expression, we get

                   [tex]= \sqrt{p1q1(\frac{1}{400}+\frac{1}{400})}[/tex]

                   [tex]=0.0168[/tex]

Now, consider

[tex]P(p1-p2>0.03)=P[\frac{(p1-p2)-E(p1-p2)}{SE(p1-p2)}>\frac{0.03-0}{0.0168}][/tex]

                            [tex]=P(Z>1.7857)[/tex]

                            [tex]=P(Z>1-79)[/tex]

                            [tex]=0.036727[/tex]

Therefore, "0.0367" is the right answer.

Calculating the probability of the difference between two sample proportions being more than 0.03 involves executing a hypothesis test via a z-test due to our large sample size. We formulate and employ a formula to get the z-score and then determine the associated p-value using a statistical tool.

This question falls within the area of statistics, particularly dealing with hypothesis testing and comparison of two independent population proportions. Given that 0.06 of each population possess a certain characteristic and samples of size 400 are drawn from each, we are required to calculate the probability that the difference between the sample proportions exceeds 0.03.

First, we establish the null hypothesis (H0) and alternative hypothesis (Ha) for the test. H0: P1 = P2 and Ha: P1 ≠ P2. Here, P1 and P2 represent the populations respectively. Given a sufficiently large sample size (n > 30), we use a z-test for comparing the proportions.

In computing the z-score, we use the following formula: z = (P1 - P2) / √ ((P*(1 - P*) / n1) + (P*(1 - P*) / n2)). Here, P* = (x1 + x2) / (n1 + n2), where x is the number of successes in each sample (0.06*400 = 24 per population logistically).

The p-value associated with the calculated z-score, which represents the probability that the difference between the first sample proportion and the second sample proportion being more than 0.03, can be found using a statistical calculator or statistical software. The precise numerical value for p will depend on the computed z-score.

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