A circle x² + y² + 2x-2y-1=0 expressed in the following form (x-h)² + (y=k)² = r² where h, k are the coordinates of the centre and r the radius is given as:
The center and the radius is (h, k) = (-1, 1) and r = √3
Given is a circle equation x² + y² + 2x - 2y - 1 = 0, firstly we will change it in (x-h)² + (y-k)² = r² form and then find the center and the radius,
So,
x² + y² + 2x - 2y - 1 = 0
Add 2 to both side,
x² + y² + 2x - 2y - 1 +2 = 0 + 2
x² + y² + 2x - 2y + 1 + 1 = 2+1
(x+1)² + (y-1)² = 3
(x+1)² + (y-1)² = (√3)²..............(i)
In the standard form of equation of a circle (x-h)² + (y-k)² = r²,
(h, k) is the center and r is the radius,
So, comparing the equation (i) with the standard form of equation of a circle.
We get,
(h, k) = (-1, 1)
and r = √3
Hence the center and the radius is (h, k) = (-1, 1) and r = √3
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the conditions that the sum of forces and the sum of the torques both vanish:
Answer and Explanation: The conditions when the net force and the net torque are zero are called static equilibrium.
The spinner below is spun once. Find each probability as a percent rounded to the nearest whole number.
P(unshaded) = __%
P(even and less than 10) =__ %
The probabilities are given as follows:
P(unshaded) = 33%.P(even and less than 10) = 33%.How to calculate a probability?The parameters that are needed to calculate a probability are given as follows:
Number of desired outcomes in the context of a problem/experiment.Number of total outcomes in the context of a problem/experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
Out of the 12 regions, 4 are unshaded, hence the probability is given as follows:
P(unshaded) = 4/12 = 1/3 = 0.33 = 33%.
Out of the 12 regions, 4 are even and less than 10, hence the probability is given as follows:
P(even and less than 10) = 4/12 = 1/3 = 0.33 = 33%.
Missing InformationThe spinner is given by the image presented at the end of the answer.
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What is m/XWZ, in degrees?
V
Z
62.5⁰
AY
X
The value of angle XWZ is 117.5°
What is angle on a straight line?Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line.
The sum of angles on a straight line is 180°. This means that if there angles A, B, C lie on a straight line, therefore ;
A+B + C = 180°
angle XWY is 90° and angle VWZ Iis 62.5°
therefore to find angle XWZ
ZWY= 90- 62.5
= 27.5°
Therefore angle XWZ = 90+ 27.5°
= 117.5°
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A zorb is a large inflated ball within a ball. The formula for the radius r of a sphere with surface area A is given by r=\sqrt((A)/(4\pi )) . Calculate the radius of a zorb whose outside surface area is 49.29 sq m.
The radius of the zorb with an outside surface area of 49.29 sq m is approximately 1.98 meters.
We are given the surface area (A) of the zorb and asked to find its radius (r) using the formula r = √(A / 4π). Let's follow these steps to solve for the radius:
1. Write down the given information:
A (surface area) = 49.29 sq m
2. Write down the formula for the radius of a sphere:
r = (√A / 4π)
3. Plug in the given surface area (A) into the formula:
r = √(49.29 / 4π)
4. Calculate the value inside the square root:
49.29 / 4π ≈ 3.923
5. Take the square root of the calculated value:
r = √(3.923) ≈ 1.98
So, the radius of the zorb with an outside surface area of 49.29 sq m is approximately 1.98 meters.
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Which series of transformations correctly maps rectangle ABCD to rectangle LMNO?
O
Translate rectangle ABCD right 9 units, then dilate the result by a scale factor of centered at the
origin.
Reflect rectangle ABCD in the y-axis, then dilate the result by a scale factor of 3 centered at the
origin.
Rotate rectangle ABCD 90° clockwise about the origin, then dilate the result by a scale factor of
centered at the origin.
Dilate rectangle ABCD by a scale factor of 3 centered at the origin, then rotate the result 90°
clockwise about the origin.
The series of transformations that correctly maps rectangle ABCE to LMNO is: Translate rectangle ABCD right 9 units, then dilate the result by a scale factor of 3 centered at the origin.
How to explain the transformationBased on the diagram, translation is by adding 9 to the x-coordinates of all the points in the rectangle.
Also,the dilation us by multiplying the coordinates of all the points in the translated rectangle A'B'C'D' by a factor of 3.
Hence, the series of transformations that correctly maps rectangle ABCE to LMNO is to teanslate rectangle ABCD right 9 units, then dilate the result by a scale factor of 3 centered at the origin.
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Help me please need this done
Write an equation in slope-intercept form for the line where x is the number of hours the kayak is rented and y is the total cost of renting the kayak.
Slope is:
S=rise/run
S=Y/X
Fig. 15.20 shows a composite solid consisting of a cube of edge 28 cm and a square-based pyramid of height 16 cm. Calculate the volume of the solid.
The volume of the composite solid consisting of a cube and a square-based pyramid will be 26,099.2 cm³.
The volume of the cube is given by;
V_cube = s³ = 28³
V = 21,952 cm³.
The volume of the pyramid is given by V_pyramid = (1/3)Bh,
where; B = area of the base and h = height .
The base of the pyramid is a square with sides equal to the base of the cube therefore we have
B = s² = 28² = 784 cm².
Thus, V_pyramid = (1/3)(784)(16)
V = 4,147.2 cm³.
The total volume of the composite solid is the sum of the volumes of the cube and the pyramid then we get;
V_total = V_cube + V_pyramid = 21,952 + 4,147.2
V_total = 26,099.2 cm³.
Therefore, the volume of the solid is; 26,099.2 cm³.
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which equation represents a line with a slope of -5/11 and a y-intercept 3/11
Answer:
y=-5/11x+3/11 (B)
Step-by-step explanation:
m= -5/11
b=3/11
substitute: y=-5/11x+3/11
Find the sum of (x3 + 12x2 – 5x + 4) + (2x3 – 5x2 – 14).
Answer:
3x^3 + 7x^2 - 5x - 10
Step-by-step explanation:
In order to find the sum, we need to add all of the like terms together between the two polynomials.
[tex](x^3+12x^2-5x+4)+(2x^3-5x^2-14)[/tex]
Lets begin with x^3 terms. There is a 1 in front of the x, so 2 + 1 = 3
[tex]3x^3[/tex]
Now x^2 terms. 12 - 5 = 7
[tex]3x^3+7x^2[/tex]
We can keep x terms the same since there is no x terms in the second polynomial.
[tex]3x^3+7x^2-5x[/tex]
Finally integers. -14 + 4 = -10
[tex]3x^3+7x^2-5x-10[/tex]
Given Triangle ABC, whose vertices are A(-4,4) B(2,0) and C(-1,-4). Which ordered pair gives the coordinates of P, the point of concurrency, of the medians?
A P(-1,0)
B P(-2,1)
C P(0,-1)
D P(-2,-1)
The concurrency of the median of the triangle is P ( -1 , 0 )
Given data ,
Let the triangle be represented as ΔABC
Now , the coordinates of the triangle are A(-4,4) B(2,0) and C(-1,-4)
On simplifying , we get
Midpoint of AB:
x-coordinate: (x₁ + x₂) / 2 = (-4 + 2) / 2 = -1
y-coordinate: (y₁ + y₂) / 2 = (4 + 0) / 2 = 4/2 = 2
Midpoint of BC:
x-coordinate: (x₂ + x₃) / 2 = (2 + (-1)) / 2 = 1/2 = 0.5
y-coordinate: (y₂ + y₃) / 2 = (0 + (-4)) / 2 = -4/2 = -2
Midpoint of AC:
x-coordinate: (x₁ + x₃) / 2 = (-4 + (-1)) / 2 = -5/2 = -2.5
y-coordinate: (y₁ + y₃) / 2 = (4 + (-4)) / 2 = 0
Now, we have the midpoints of the sides of the triangle:
Midpoint of AB: (-1, 2)
Midpoint of BC: (0.5, -2)
Midpoint of AC: (-2.5, 0)
The point of concurrency of the medians is the centroid of the triangle, which can be found by taking the average of the midpoints.
x-coordinate: (-1 + 0.5 - 2.5) / 3 = -3 / 3 = -1
y-coordinate: (2 - 2 - 0) / 3 = 0
Hence , the coordinates of point P, the point of concurrency of the medians, are P(-1, 0)
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Look at picture below
Answer:
we cannot solve this as there is no picture shown, try linking in the picture please
A drug company claims that its new painkiller has exactly 5 mg. of codeine. You test the claim at a significance level (alpha) of 0.05. You randomly sample 100 pills made by the company and find the sample mean to be 4.7 milligrams of codeine with a sample standard deviation of 0.75 grams.
(a) What are the null and alternate hypotheses?
(b) Draw the picture of the distribution of the test statistics (under H0). Include critical value(s) and region(s) of rejection.
(c) What is the calculated (computed) value of the test statistic?
(d) What is your conclusion?
This means that there is evidence to suggest that the mean amount of codeine in the painkiller is not exactly 5 mg.
(a) The null hypothesis is that the mean amount of codeine in the painkiller is exactly 5 mg. The alternate hypothesis is that the mean amount of codeine in the painkiller is not exactly 5 mg.
(b) The picture of the distribution of the test statistics (under H0) would be a normal distribution with a mean of 5 mg and a standard deviation of 0.75 mg/sqrt(100) = 0.075 mg. The critical values for a two-tailed test at a significance level of 0.05 are -1.96 and +1.96. The region(s) of rejection are the values outside of this range. This can be represented in a graph as shaded areas on both sides of the distribution curve.
(c) The calculated value of the test statistic is (4.7 - 5) / (0.75 / sqrt(100)) = -2.67.
(d) Since the calculated value of the test statistic (-2.67) falls within the region of rejection, we reject the null hypothesis. This means that there is evidence to suggest that the mean amount of codeine in the painkiller is not exactly 5 mg.
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the null hypothesis for the single factor anova states that all means are equal.
T/F
The null hypothesis for the single factor ANOVA states that all means are equally true.
The null hypothesis for a single-factor ANOVA (analysis of variance) states that all means are equal.
The alternative hypothesis, on the other hand, suggests that at least one of the means is different from the others.
The purpose of the ANOVA test is to determine whether there is sufficient evidence to reject the null hypothesis and conclude that there are significant differences between the means. A statistical formula used to compare variances across the means (or average) of different groups.
Hence, the statement is true .
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the price of a gallon of milk follows a normal distribution with a mean of $3.4 and a standard deviation of $0.2. find the price for which only 35% of milk vendors lower than?
Answer: $3.32
Step-by-step explanation:
-0.3853 = (x - 3.4) / 0.2
Solving for x, we get:
X = 3.32
Therefore, the price for which only 35% of milk vendors is lower than $3.32.
Casey buys a bracelet. she pays for the bracelet and pays $0.72 in sales tax. The sales tax is 6% what is the original price of the bracelet , before tax
The Original price of the bracelet, before tax, is $12.
Let's assume that the original price of the bracelet is x dollars.
The sales tax is 6%, which means that the tax paid is 6/100 * x = 0.06x dollars.
We know that Casey paid $0.72 in sales tax, so we can set up the equation:
0.06x = 0.72
Solving for x, we get:
x = 0.72/0.06
x = 12
Therefore, the original price of the bracelet, before tax, is $12.
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Somebody help asap please.
You want to put up a fence that encloses a triangular region with an area greater than or equal to 60 square feet.The possible values of c are described by the inequality -------
(The base of the triangle is 12 and the height is c)
After heating up in a teapot, a cup of hot water is poured at a temperature of 20 3 ∘ 203 ∘ F. The cup sits to cool in a room at a temperature of 6 9 ∘ 69 ∘ F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below: � = � � + ( � 0 − � � ) � − � � T=T a +(T 0 −T a )e −kt � � = T a = the temperature surrounding the object � 0 = T 0 = the initial temperature of the object � = t= the time in minutes � = T= the temperature of the object after � t minutes � = k= decay constant The cup of water reaches the temperature of 18 5 ∘ 185 ∘ F after 1.5 minutes. Using this information, find the value of � k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes. Enter only the final temperature into the input box.
The final temperature is 165 degree F.
Given that,
Ta = the temperature surrounding the object = 69ºF
T₀ = the initial temperature of the object = 203ºF
t = 1.5 min
T after 1.5 min = 185ºF
We know the temperature equation,
T = [tex]T_{\alpha}[/tex] + [tex](T_{0} - T_{\alpha })e^{-kt}[/tex]
Substitute the values,
185 = 69 + (203 - 69)[tex]e^{-1.5k}[/tex]
solving it we get
k = 0.077
To find the Fahrenheit temperature of the cup of water, to the nearest degree, after 4. minutes.
Substitute into the formula and compute:
T = 69 + (203 - 69)[tex]e^{-(0.75)(4.5)}[/tex]
Hence,
T = 165 degree F.
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Find an angle in each quadrant with a common reference angle with 53°, from 0°≤θ<360°
The angle of 53° is equals to,
53° in the first quadrant127° in the second quadrant 233° in the third quadrant307° in the fourth quadrant.The given angle = 53°
The given angle is present in the first quadrant only. To find the equivalent angle in the second quadrant, we have to subtract the given angle from 180°. So,the equivalent angle in the second quadrant = 180° - 53° = 127°.
To find the equivalent angle in the third quadrant, we have to add the given angle to 180°. So,equivalent angle in third quadrant = 180° + 53° = 233°.
To find the equivalent angle in the fourth quadrant, we have to subtract the given angle from 360°. So,equivalent angle in fouth quadrant = 360° - 53° = 307°.
From the above analysis, we have found the equivalent angles in all quadrants.
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In inferential statistics, the objective is to determine how probable it is that:
The alternative hypothesis is true.
The null hypothesis is true.
The alternative hypothesis is false.
The null hypothesis is false.
In inferential statistics, the objective is to determine the probability of the alternative hypothesis being true or the null hypothesis being true.
This involves using sample data to make inferences and draw conclusions about a larger population. By analyzing the data and performing statistical tests, we assess the likelihood of the alternative hypothesis or the null hypothesis being accurate.
The alternative hypothesis represents a claim or statement that contradicts the null hypothesis and suggests that there is a significant relationship or difference between variables. To determine its probability, statistical methods such as hypothesis testing and p-values are employed. These methods evaluate the strength of evidence against the null hypothesis and support the alternative hypothesis when the evidence is substantial.
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What is the sum of 4 and 5
Answer: 9
Step-by-step explanation: it just is
Answer:
9
Step-by-step explanation:
How do u not know what the sum of 4 and 5 is? I'm not trying to be mean I'm just wondering
Need help asap please
Answer:
21x^2 + 7x
Step-by-step explanation:
The formula for the area of a rectangle is L x W. The length in this case is 3x+1 and the width is x. Multiply those together and you get 3x^2 + x.
The formula for the area of a triangle is 1/2BH. When you plug in the numbers, the area of the triangle is 24x^2 + 6x.
Now, you want to subtract the area of the triangle from the area of the rectangle. When you do this, you get your answer: 21x^2 + 7x.
Find the radius of convergence, R, of the series (-1)nx" n-1 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) Need Help? RaItTalk to a Tutor Read It 5. + --2 points scalc8 11.8.007 MI Find the radius of convergence, R, of the series. xn+ 5 R= Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) Watch ItMaster It Talk to a Tutor Need Help? Read it Submit Answer Save ProgressPractice Another Version
The radius of convergence, R, of the series (-1)nx^n-1 can be found using the ratio test the interval of convergence is (-1, 1) in interval notation. .
We have
lim |(-1)^(n+1)x^(n) / (-1)^nx^(n-1)| as n approaches infinity
= lim |x|
Since the limit exists only when |x| < 1, the radius of convergence is R = 1.
To find the interval of convergence, we need to check the endpoints x = -1 and x = 1.
When x = -1, the series becomes (-1)^n(-1)^n-1 = (-1)^2n-1 which diverges.
When x = 1, the series becomes (-1)^n1^n-1 = (-1)^(n-1) which also diverges.
Therefore, the interval of convergence is (-1, 1) in interval notation.
Note that the endpoints are not included in the interval of convergence because the series diverges at those points.
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The radius of convergence is R = 1 and the interval of convergence is (-1, 1).
To find the radius of convergence, we can use the ratio test:
lim┬(n→∞)|(-1)^(n+1)x^n|/|(-1)^(n)x^(n-1)| = lim┬(n→∞)|x|/1 = |x|
The series converges if |x| < 1 and diverges if |x| > 1. So the radius of convergence is R = 1.
To find the interval of convergence, we need to test the endpoints x = -1 and x = 1. When x = -1, the series becomes (-1)^n(-1)^n = 1, which is a divergent series. When x = 1, the series becomes (-1)^n, which is an oscillating series that does not converge.
Therefore, the interval of convergence is (-1, 1), where -1 is excluded and 1 is included, since the series converges for -1 < x < 1 and diverges for x ≤ -1 and x ≥ 1.
In summary, the radius of convergence is R = 1 and the interval of convergence is (-1, 1).
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When Maria took her dog to the vet, she was told that a healthy weight for her breed of dog would be approximately
16 pounds plus or minus
3 pounds. Write an absolute value inequality representing the unhealthy weights for her dog’s breed
Any weight between 13 and 19 pounds, however, would be considered healthy.
The absolute value inequality can be explained as follows: the absolute value of the difference between the weight of the dog and the healthy weight of 16 pounds represents the distance between the dog's weight and the healthy weight. The inequality states that this distance should be greater than 3 pounds, which means that any weight that is more than 3 pounds away from the healthy weight of 16 pounds is considered unhealthy.
For example, if the dog weighs 12 pounds, then the absolute value of the difference between the weight and the healthy weight is 4 pounds, which is greater than 3 pounds. Therefore, 12 pounds is an unhealthy weight for the breed. Similarly, if the dog weighs 20 pounds, then the absolute value of the difference between the weight and the healthy weight is 4 pounds, which is also greater than 3 pounds. Therefore, 20 pounds is also an unhealthy weight for the breed. Any weight between 13 and 19 pounds, however, would be considered healthy.
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The owner of a store buys a wooden branch for two dollars is Shemar up the place by 75% at the end of the season she sells the meaning branches for 30% off how much profit does the owner make on each branch at the end of the season
Let's calculate the profit made by the owner on each branch at the end of the season. The owner buys a wooden branch for $2. After marking up the price by 75%, the selling price becomes:
$2 + ($2 * 0.75) = $2 + $1.50 = $3.50
However, at the end of the season, the owner sells the branches for 30% off. So the selling price after the discount is:
$3.50 - ($3.50 * 0.30) = $3.50 - $1.05 = $2.45
To calculate the profit made on each branch, we subtract the original cost from the selling price:
$2.45 - $2 = $0.45
Therefore, the owner makes a profit of $0.45 on each branch at the end of the season.
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Find the product using the Distributive Property. (2x+3)(x−4)
Answer:
2x² - 5x - 12------------------
Distributive Property is:
(a + b)(c + d) = ac + ad + bc + bdUse same rule to find the product:
(2x + 3)(x − 4) = 2x(x) - 2x(4) + 3x - 4(3) = 2x² - 8x + 3x - 12 = 2x² - 5x - 12An closed box with a square base is to have a volume of 7500 cm3. What should the dimensions of the box be if the amount of material used is to be minimum? (Use decimal notation. Give your answers to three decimal places. ) Recall: The surface area of a rectangular box is: =2⋅⋅+2⋅⋅ℎ+2⋅⋅ℎ , where = length, = width, and ℎ= height. Hint: Draw a sketch of the box and note that the base of the box is a square
To minimize the amount of material used for the box, we want to minimize its surface area. Since the base of the box is a square, let's denote its side length as s. Then, the height of the box can be expressed as 7500/s^2, using the given volume.
Using this information, we can express the surface area of the box as a function of s: A(s) = 2s^2 + 4sh, where h is the height of the box. Substituting 7500/s^2 for h, we get A(s) = 2s^2 + 4(7500/s^2)s.
To find the minimum amount of material used, we need to find the value of s that minimizes A(s). We can do this by finding the critical points of A(s) and then using the second derivative test to determine if they correspond to a minimum. Taking the derivative of A(s) and setting it equal to zero, we get:
A'(s) = 4s - 30000/s^3 = 0
Solving for s, we get s = 15∛125 ≈ 12.247.
To confirm that this value corresponds to a minimum, we take the second derivative of A(s) and evaluate it at s = 12.247:
A''(s) = 4 + 90000/s^4
A''(12.247) ≈ 0.143
Since A''(12.247) is positive, we can conclude that s = 12.247 corresponds to a minimum of A(s). Therefore, the of the box should be approximately 12.247 cm by 12.247 cm by 41.666 cm to minimize the amount of material used.
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please help!!
A=100e 0.041/12t (it was a little blurred out in the question)
The account balances for the first 6 months are approximately $100.34, $100.68, $101.02, $101.36, $101.71, and $102.06, respectively.
The monthly balance of the account is given by [tex]A =e^{0.041t/12}[/tex] where t is measured in months.
To find the account balances for the first 6 months, we can simply plug in the values of t = 1, 2, 3, 4, 5, and 6 into the formula:
When t = 1,
[tex]A = e^{(0.041/12)}[/tex]
A ≈ $100.34
When t = 2,
[tex]A = e^{(0.041/6)}[/tex]
A ≈ $100.68
When t = 3,
[tex]A = e^{(0.041/4)}[/tex]
A ≈ $101.02
When t = 4,
[tex]A = e^{(0.041/3)}[/tex]
A ≈ $101.36
When t = 5,
[tex]A = e^{(0.041/2.4)}[/tex]
A ≈ $101.71
When t = 6,
[tex]A = e^{(0.041/2)}[/tex]
A ≈ $102.06
Therefore, the account balances for the first 6 months are approximately $100.34, $100.68, $101.02, $101.36, $101.71, and $102.06, respectively.
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many elementary school students in a school district currently have ear infections. a random sample of children in two different schools found that 11 of 40 at one school and 12 of 30 at the other have ear infections. at the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools?
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools.
To determine if there is sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools, we can use a two-sample z-test for the difference in proportions.
The null hypothesis is that there is no difference between the proportions of students with ear infections at the two schools, while the alternative hypothesis is that there is a difference.
Let p1 be the proportion of students with ear infections at the first school and p2 be the proportion at the second school. The test statistic is given by:
z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))
where p_hat is the pooled proportion, n1 and n2 are the sample sizes from the first and second schools, respectively.
The pooled proportion is given by:
p_hat = (x1 + x2) / (n1 + n2)
where x1 and x2 are the number of students with ear infections in each school.
Using the given data, we have:
n1 = 40, n2 = 30
x1 = 11, x2 = 12
p1 = x1/n1 = 11/40 = 0.275
p2 = x2/n2 = 12/30 = 0.4
p_hat = (x1 + x2) / (n1 + n2) = (11 + 12) / (40 + 30) = 0.355
The test statistic is:
z = (0.275 - 0.4) / sqrt(0.355 * 0.645 * (1/40 + 1/30)) = -1.197
Using a standard normal table or calculator, the p-value for a two-tailed test with a test statistic of -1.197 is approximately 0.231.
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