Note that in the proof stated above, there is no incorrect statement.
How is this so?The evidence is that when four lines are drawn starting from a point and making two right angles, the two angles between those lines are equal.
The proof begins by stating that when you have a right angle, the two angles that add up to produce the correct angle are referred to as complementary angles.
The Congruent Complements Theorem is then used to demonstrate that the two angles in the centre are equal.
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PLEASE HELP !!! MAJOR GRADE!!!!
Column A
1. A set of two of more linear equations that contain 2 or more variables.
2. When there is no answer to a system of equations or inequalities.
3. There is only one value for the variable that makes the equation true.
4. Terms with the same variables raised to the same exponent.
5. Equation is solved for one variable and that solution is substituted into the second equation.
6. A value that makes the equation true.
7. Adding subtracting or multiplying a system of equations to help solve a system.
8. A linear equation in one variable has infinitely
many solutions.
9. A letter that represents one or more numbers.
10.This is the number in front of the variables in a term
Column B
a. Elimination
b. Substitution
c. Solution
d. Infinitely Many Solutions
e. No solutions
f. System of Equations
g. Variable
h. Like Terms
i. One solution
j. Coefficients
Answer:
1. f. System of Equations
2. e. No solutions
3. i. One solution
4. h. Like Terms
5. b. Substitution
6. c. Solution
7. a. Elimination
8. d. Infinitely Many Solutions
9. g. Variable
10. j. Coefficients
Step-by-step explanation:
Ur welcome :)
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 8.2 mg and a standard deviation of 1.45 mg. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 42 cigarettes with a mean nicotine amount of 7.73 mg.
Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 42 cigarettes with a mean of 7.73 mg or less.
P(M < 7.73 mg) = ???
The probability of randomly selecting 42 cigarettes with a mean of 7.73 mg or less is: 0.0179
How to find the p-value from z-score?The formula to find the z-score of the given normal distribution is:
z = (x' - μ)/(σ/√n)
where:
x' is sample mean
μ is population mean
σ is standard deviation
n is sample size
We are given:
x' = 7.73 mg
μ = 8.2 mg
σ = 1.45 mg
n = 42
Thus:
z = (7.73 - 8.2)/(1.45/√42))
z = -2.1
From online p-value from z-score calculator, we have:
p = 0.0179
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A researcher is analyzing bacteria on a door handle after cleaning it with antibacterial disinfectant. Initially there were 15 bacteria, but the researcher noticed that the number of bacteria quadruples every hour,t. Write a function B(t) to represent the number of bacteria t hours after the initial measurement. Write a exponential function
The exponential function representing the number of bacteria t hours after the initial measurement is B(t) = 15 (4[tex])^t[/tex].
The function B(t) can be represented by an exponential function of the form:
B(t) = a[tex]b^t[/tex]
where 'a' is the initial number of bacteria and 'b' is the growth factor or rate at which the number of bacteria quadruples.
Given that the initial number of bacteria is 15 and the number of bacteria quadruples every hour, we can express 'b' as:
b = 4¹ = 4
Substituting the values of 'a' and 'b' in the general form of exponential function, we get:
B(t) = 15 (4[tex])^t[/tex]
Therefore, the exponential function representing the number of bacteria t hours after the initial measurement is B(t) = 15 (4[tex])^t[/tex].
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A medical researcher claims that the proportion of people taking a certain medication that develop serious side effects is 12%. To test this claim, a random sample of 900 people taking the medication is taken and it is determined that 93 people have experienced serious side effects. The following is the setup for this hypothesis test: H0:p=0.12 Ha:p≠0.12 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places. The following table can be utilized which provides areas under the Standard Normal Curve:
The p-value from the hypothesis is 0.0583 which is not significant at p<0.05
What is the p-valueTo determine the p-value of the hypothesis, we need to use the formula;
z = (x - a) / √(a(1 - a)/n)
a = hypothesized proportionx = sample proportionn = sample sizex = 93 / 900 = 31/300 = 0.103
a = 12% = 12/100 = 0.12
n = 900
Substituting the values into the formula;
z = (0.103 - 0.12)/√(0.12(1 - 0.12)/900)
z = -0.017 / √0.0001173
z = -1.569
Using a standard normal distribution table;
p-value = 0.058324
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step-by-steps to Solve a system of linear equations using matrices.
In order to properly solve a system of linear equations utilizing matrices, you must abide by the below instructions:
How to explain the equationFirst, create a matrix representation of the system of equations.
Second, generate an augmented matrix by merging the coefficient matrix together with the constant matrix.
Third, apply elementary row operations in order to transform the augmented matrix into either row echelon or reduced row echelon form.
Fourth, use back substitution to accurately determine the variable values.
Ultimately, enter this solution into the original equation in order to obtain the primary variable value.
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Solving linear equations using matrices involves steps ranging from creating an augmented matrix, performing row operations, back substitution, and then interpreting results
To solve a system of linear equations using matrices, follow these step-by-step instructions:
Step 1: Write the system of linear equations in matrix form.
Represent the coefficients of the variables as a matrix (called the coefficient matrix), and the constants on the right side of the equations as another matrix (called the constant matrix).
Step 2: Create the augmented matrix.
Combine the coefficient matrix and the constant matrix into a single matrix by appending the constant matrix as an additional column. This combined matrix is called the augmented matrix.
Step 3: Perform row operations to achieve row-echelon form.
Use row operations (swapping rows, multiplying a row by a constant, or adding/subtracting rows) to manipulate the augmented matrix into row-echelon form. Row-echelon form has zeroes below the diagonal and non-zero elements on the diagonal.
Step 4: Perform back-substitution.
Starting from the last row of the row-echelon form matrix, solve for the variables using back-substitution. Substitute the values of the variables you find into the previous rows to determine the remaining variable values.
Step 5: Interpret the results.
Once you have solved all the variables, you have found the solution to the system of linear equations. If there are infinitely many solutions or no solutions, this will be indicated by the row-echelon form.
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Madison tossed a paper cup and records wether it lands on its side. In 20 trails the cup lands on its side 19 times. In 90 trials the cup lands on its side 81 times
Answer:90% probability
Step-by-step explanation:
To calculate the experimental probability of the cup landing on its side, we can use the formula:
experimental probability = number of times the cup landed on its side / total number of trials
For the first set of trials, the experimental probability is:
experimental probability = 19/20 = 0.95
For the second set of trials, the experimental probability is:
experimental probability = 81/90 = 0.9
So the experimental probability of the cup landing on its side for the first set of trials is higher than for the second set of trials. However, since the number of trials is relatively small, it is possible that this difference is due to chance and does not reflect a real difference in the probability of the cup landing on its side. To determine this with more confidence, we would need to conduct more trials and perform statistical tests to determine whether the difference is statistically significant.
A car and a bus left Sunrise Village for Sunset Village of the same time, travelling along the
same route. After travelling for 4 h, the car reached Sunset Village, but the bus had only
completed 5/8 of the journey. The bus travelled at a speed which was 30 Km/h slower than the car
a) Find the distance between the two villages.
b) Find the average speed of the bus.
Answer:
a) 192Km
b) 50
Step-by-step explanation:
Solve for x.
A
Set up the proportion.
XI7
The solution for the variable x is x = 8.4
How to determine the solution for the variable xfrom the question, we have the following parameters that can be used in our computation:
The right triangle
Using the proportion of similar triagles, we have
x/7 = 10/x
This gives
x * x = 7 * 10
So, we have
x² = 70
Next, we have
x = √70
Evaluate
x = 8.4
Hence, the solution for the variable x is x = 8.4
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1. A sample of 250 high-school students in a city results in an average number of text messages sent per month of 172.6, with a margin of error of + 4.8. If there are 3000 high-school students in the city, what is the estimated number of text messages sent in a month? between______ and____text messages
Answer:
Step-by-step explanation:
1) Find the upper bound of the confidence interval:
Upper bound = sample mean + margin of error
= 172.6 + 4.8
= 177.4
2) Find the lower bound of the confidence interval:
Lower bound = sample mean - margin of error
= 172.6 - 4.8
= 167.8
3) Estimate the total number of text messages sent in a month:
Total number of text messages sent = (number of students in the population / number of students in the sample) x sample mean
= (3000 / 250) x 172.6
= 2071.2
Therefore, the estimated number of text messages sent in a month is 2071.2, with a 95% confidence interval between 167.8 and 177.4 text messages.
Answer:
Between 503400 and 532200 text messages----------------------------
Determine the average number of text messages sent per student within the margin of errorFind lower bound:
172.6 - 4.8 = 167.8 text messagesFind upper bound:
172.6 + 4.8 = 177.4 text messages Estimate the total number of text messages for all 3000 studentsLower bound:
167.8 text messages × 3000 students = 503400 text messagesUpper bound:
177.4 text messages × 3000 students = 532200 text messagesThe estimated number of text messages sent in a month for all 3000 high-school students in the city is:
Between 503400 and 532200 text messagesExpress each of the following as (i)Percentage (ii)Decimal :
a) 3¾ (b) 6½/50
find x
find x
find x
Can someone please help me with this
Answer:
cot(65 deg)
Step-by-step explanation:
cot(x) is the complimentary func. of tan(x) with the relation:
tan x = cot (90 - x) and
cot x = tan (90 - x)
<
1
0.964
8.92
-0.982 increasing decreasing strong
z, hours
y.gallons
Generate a linear regression equation and a correlation coefficient for these data.
1
9.2
2
The linear regression equation is y =
This means there is a ¦
8.4
The correlation coefficient is
O
The number of of gallons is
3
7.7
4
6.1
weak -1.17 10.69
O+O
5
4.5
correlation between the gallons and hours.
as the hours are increasing.
-0.82
Please help bro. Im struggling.
1. The linear regression equation is y = -1.17x+ 10.69
2. The correlation coefficient is -0.982.
3. This means there is a strong negative correlation between the gallons and hours.
4. The number of gallons is decreasing as the hours are increasing.
How do we calculate for the linear regression equation and correlation coefficient?Step 1: find slope.
Formula for slope m = (n × Σ(xy) - Σx × Σy) / (n × Σ(x²) - (Σx)²)
Σx = 1 + 2 + 3 + 4 + 5 = 15
Σy = 9.2 + 8.4 + 7.7 + 6.1 + 4.5 = 35.9
Σ(xy) = (1 × 9.2) + (2 × 8.4) + (3 × 7.7) + (4 × 6.1) + (5 × 4.5) = 96
Σ(x²) = 1 + 4 + 9 + 16 + 25 = 55
n = 5
Therefore ∴
m = (5 × 96 - 15 × 35.9) / (5 × 55 - 15²) = -1.17
y-intercept b = (Σy - m × Σx) / n
b = (35.9 - (-1.17) × 15) / 5 = (53.15) / 5 = 10.63
Therefore the linear regression equation is y = -1.17x + 10.63
correlation coefficient (r): (n × Σ(xy) - Σx × Σy) / sqrt((n × Σ(x²) - (Σx)²) × (n × Σ(y²) - (Σy)²))
r = (5 × 96 - 15 × 35.9) / sqrt((5 × 55 - 15²) × (5 × 271.95 - 35.9²)) = -0.982
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Can someone please answer these 2 questions asap and please show me the breakdown of it so I learn a better way of doing it.
Answer:
x = 5√2, x = 3√2
Step-by-step explanation:
Question 1:
Using the 30-60-90 triangle properties, YX = WX /√3.
YX = 5√3 /√3 = 5.
Using the 45-45-90 triangle properties, x = YX *√2.
x = 5 *√2 = 5√2.
Question 2:
Using the 45-45-90 triangle properties, BC = AB *√2.
BC = 6 *√2 = 6√2.
Using the 30-60-90 triangle properties, x = BC / 2.
x = 6√2 / 2 = 3√2.
In a coordinate plane, what is the distance between the points (6,−10)
and (6,−7)
?
The distance between the points (6,−10) and (6,−7) is 3 units
What is the distance between the points (6,−10) and (6,−7)?From the question, we have the following parameters that can be used in our computation:
Points (6,−10) and (6,−7)
Because the points have the same x coordinate, the distance between the points (6,−10) and (6,−7) is the difference between the y coordinates
Using the above as a guide, we have the following:
Distance = -7 - -10
Evaluate
Distance = 3
Hence, the distance between the points (6,−10) and (6,−7) is 3 units
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Select the expression that is less than 10 2/3.
A. 10 2/3 x 9/10
B. 1 x 10 2/3
C. 10 2/3 x 2 1/3
D. 2 1/8 x 10 2/3
Answer:
A
Step-by-step explanation:
Factor out the Greatest Common Factor (GCF): 64d³ - 24d²
The factored form of 64d³ - 24d² is 8d²(8d³ - 3).
Define greatest common factorThe greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that divides evenly into two or more given numbers. For example, the GCF of 12 and 18 is 6, since 6 is the largest number that divides both 12 and 18 without leaving a remainder.
The greatest common factor (GCF) of the given terms is 8d². We can factor it out by dividing each term by 8d²:
64d³/8d² - 24d²/8d²
Simplifying the fractions:
8d³ - 3
Therefore, the factored form of 64d³ - 24d² is 8d²(8d³ - 3).
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A bank charges a monthly fee of 0.5% for a checking account. Lily’s account has $325 in it. Which function models the balance B of Lily’s account in dollars, as a function of time in months?
A. B(t) = 325(1 − 0.005)t
B. B(t) = 325(1 + 0.0005)t
C. B(t) = 0.05(1 − 3.25)t
D. B(t) = 325 + 12(1 + 0.0005)t
The correct function that models the balance B of Lily’s account as a function of time in months is option A, which is B(t) = 325(1 − 0.005)ᵗ.
To see why, we can start with the initial balance of $325 and note that each month, the bank charges a monthly fee of 0.5%, which is equivalent to a monthly interest rate of 0.005. This means that after one month, the balance will be reduced by 0.5% or 0.005 times the original balance, giving:
B(1) = 325 - 0.005(325)
Similarly, after two months, the balance will be reduced by another 0.5% of the new balance, giving:
B(2) = (325 - 0.005(325)) - 0.005(325 - 0.005(325))
We can simplify this expression by factoring out the common factor of 325(1 - 0.005) after each term, giving:
B(2) = 325(1 - 0.005)²
Generalizing this pattern, we can see that after t months, the balance will be:
B(t) = 325(1 - 0.005)ᵗ
Therefore, option A is the correct function that models the balance of Lily’s account.
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Please help !!!!!
!!!!!
Answer: 10w + 3 + 4.5w = 90
Step-by-step explanation:
a right angle is 90 degrees, so 10w + 3 and 4.5w have to add up to 90 degrees
50 Points! Multiple choice algebra question. Identify the type of regression that returns the equation y=3x^2. Photo attached. Thank you!
Answer:
C Exponential
Step-by-step explanation:
3x^2 -- its using an exponent
lmop are the angles LN is the diagonal the sides are missing
All four angles of the rhombus are 20, 160, 20, and 160 degrees.
What is meant by diagonal of an angle ?Diagonals are the parts of a shape, in geometry, a diagonal is a line that join two vertices of a polygon or a solid shape , whose vertices are not on the same edge. In general, a diagonal is called as a sloping line or the slant line, that connects to the vertices of a shape.
According to question a rhombus , all four sides are congruent and opposite angles are equal. Let's call the rhombus ABCD, where AB, BC, CD, and DA are the four sides, and AC and BD are the diagonals.
If one of the angles formed by diagonals and adjacent sides is 20 degrees, let's say that angle is ABD. We can draw a line from point A to point C, which will divide the rhombus into two congruent triangles, ABC and ACD.
Since triangle ABC is isosceles, with sides AB = BC, angles ABC and BCA are equal. Similarly, in triangle ACD, angles ACD and CDA are equal.
∴ angles ABD and CDA are adjacent angles formed by intersecting lines, they must add up to 180 degrees. Therefore, angle CDA is 160 degrees.
If triangles ABC and ACD are congruent, angle CAD is also 20 degrees.
Now we can use the fact that opposite angles in a rhombus are equal. Angles BCD and ABD are opposite angles, so angle BCD is also 20 degrees. Similarly, angles BAC and ADC are opposite angles, so angle BAC is also 160 degrees.
Therefore, all four angles of the rhombus are 20, 160, 20, and 160 degrees.
Complete question If one of the angles formed by diagonals and adjacent sides. of Is 20, all four angles of the a rhombus are.
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I have two similar triangles and can't find x. since I'm too lazy to download the app, the larger one has two sides of 6 and 12 and the smaller has two sides of x-3 and x+1. what is x??
Answer:
7
Step-by-step explanation:
We can use the fact that the corresponding sides of similar triangles are in proportion to each other.
Let's compare the corresponding sides of the two triangles:
Corresponding sides and ratio
larger triangle's side of length 6 larger triangle's side of length 12Ratio
smaller triangle's side of length x-3smaller triangle's side of length x+1Since the triangles are similar, we know that these ratios are equal. That is,
6 / (x-3) = 12 / (x+1)
We can simplify this equation by cross-multiplying:
6(x+1) = 12(x-3)
Expanding and simplifying:
6x + 6 = 12x - 36
42 = 6x
x = 7
Therefore, x has a value of 7.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
The result of the logarithm function is equal to 9. (Correct choice: D)
How to determine the missing component in a logarithm
The statement shows an incomplete logarithm, whose result must be found by understing relationships between trascendent functions. Logarithm functions and exponential functions are related in the following way:
aᵇ = n ↔ ㏒ₐ n = b
Where:
a - Baseb - Exponentn - ResultIf we know that (base) a = 3 and (exponent) b = 2, then the value of the result (n) is now defined:
n = 9
3² = 9
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Is the antiderivative of 20c to the 9th power dc equal to 20c to the 10th power over (divided by) 10?
In general, an antiderivative of a function f(x) is a function F(x) whose derivative is equal to f(x). The antiderivative of a polynomial function is obtained by adding one to the exponent of each term and dividing by the new exponent ⁵.
Another Statistics question pls help me
Answer:
55
Step-by-step explanation:
0* .4
28*.5
410*.1
According to the graph, what is the maximum number of passengers he can transport What is the maximum amount he can collect? Use the graph to determine the amount he charges a single passenger.
I can't see the chart...
A science class measured the mass of an amount of sand.about how many grains of sand are there in 7 grams of sand
Therefore , the solution of the given problem of expressions comes out to be there are roughly 7,000 grains of sand in 7 grammes of sand.
What exactly is an expression?Instead of using random estimates, it is preferable to use shifting numbers that may also prove increasing, reducing, variable or blocking. They could only help one another by trading tools, information, or solutions to issues. The justifications, components, or quantitative comments for tactics like further disagreement, production, and blending may be included in the assertion of truth equation.
Here,
A kilogramme (1000 grammes) of sand is thought to contain around 1 million grains of sand. This indicates that 1 gramme of sand contains roughly 1000 grains of sand.
Using this calculation, we can determine how many sand grains there are in 7 grammes roughly as follows:
=> Number of sand grains in 7 grammes = (# of sand grains in 1 gramme) x (7 grams)
=> 1000 x 7 = the number of sand grains in 7 grammes.
=> 7,000 sand grains are included in 7 grammes.
In accordance with this calculation, there are roughly 7,000 grains of sand in 7 grammes of sand.
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Solve the system of equations.
y=4x2+3x−5y=2x2+x+7
What is the sum of the y-coordinates of the solutions to the system?
Enter your answer in the box.
Answer:
37
Step-by-step explanation:
We are given the system of equations:
y = 4x^2 + 3x - 5
y = 2x^2 + x + 7
We can set the two equations equal to each other to get:
4x^2 + 3x - 5 = 2x^2 + x + 7
Simplifying, we get:
2x^2 + 2x - 12 = 0
Dividing both sides by 2, we get:
x^2 + x - 6 = 0
Factoring the left-hand side, we get:
(x + 3)(x - 2) = 0
Therefore, the solutions are x = -3 and x = 2.
To find the corresponding y-coordinates, we can plug these values of x into either of the original equations. Using the first equation, we get:
y = 4(-3)^2 + 3(-3) - 5 = 16
and
y = 4(2)^2 + 3(2) - 5 = 21
Therefore, the sum of the y-coordinates of the solutions is:
16 + 21 = 37
Answer: 37.
y = 25 - 2x need input x and output y 21 and 19
If we substitute x = 21 into the equation Y = 25 - 2x, we get:
Y = 25 - 2(21)
Y = 25 - 42
Y = -17
Therefore, if x = 21, then Y = -17.
If we substitute x = 19 into the equation Y = 25 - 2x, we get:
Y = 25 - 2(19)
Y = 25 - 38
Y = -13
Therefore, if x = 19, then Y = -13.
A recent study of high school students shows the percentage of females and males who took advanced math courses. A simple random sample of high school students was interviewed. The students were asked whether they had taken an advanced math course. Of the 150 females, 53 answered yes, as did 89 of the 275 males.
Part A: Construct and interpret a 98% confidence interval for the difference in population proportions of females and males who took advanced math courses. Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (8 points)
Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain. (2 points)
Construct and interpret a 98% confidence interval for the difference in population proportions of females and males who took advanced math courses.
The parameter of interest is the difference in population proportions of females and males who took advanced math courses. We can denote this parameter by p₁ - p₂, where p₁ is the population proportion of females who took advanced math courses, and p₂ is the population proportion of males who took advanced math courses.
To construct a confidence interval for the difference in population proportions, we need to check the following conditions,
The sample of high school students should be a simple random sample.
The sample of high school students should be independent of each other.
Both groups of females and males who took advanced math courses should have at least 10 successes and 10 failures.
The sample proportions of females and males who took advanced math courses can be calculated as follows,
p₁ = 53/150 = 0.353
p₂ = 89/275 = 0.324
The sample size of females and males can also be calculated as follows,
n₁ = 150
n₂ = 275
The standard error of the difference in sample proportions can be calculated as follows,
SE = √[(p₁(1 - p₁))/n₁ + (p₂(1 - p₂))/n₂]
= √[(0.353(1 - 0.353))/150 + (0.324(1 - 0.324))/275] ≈ 0.048
Using a t-distribution with (n₁ + n₂ - 2) degrees of freedom and a 98% confidence level, we can construct a confidence interval for the difference in population proportions as follows:
(p₁ - p₂) ± t*SE
where t is the t-score corresponding to a 98% confidence level and (n₁ + n₂ - 2) degrees of freedom. Using a t-table, we can find that t ≈ 2.33.
Substituting the values into the formula, we get,
(0.353 - 0.324) ± 2.33*0.048
0.029 ± 0.112
True difference in population proportions of females and males who took advanced math courses lies between 0.029 and 0.147.
Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain.
Yes, our interval from part A gives convincing evidence of a difference between the population proportions because it does not contain zero. The interval (0.029, 0.147) is entirely positive, which means that the proportion of females who took advanced math courses is higher than the proportion of males who took advanced math courses. Additionally, the interval does not contain the value of one, which means that the difference in population proportions is not due to chance. Therefore, we can conclude that there is a significant difference in the population proportions of females and males who took advanced math courses.
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