A student was trying to write an exponential function to represent a fish population in a local stream decreasing at a rate of​ 3% per year. The original population was​ 48,000. The student made an error when writing their exponential function. Find and explain the error in the​ student’s work below.
y=48,000(1.03)^x

Answer:

it's answer is 10/-15.........

After two years, the account will have $121.00.

To find the amount in the account after two years, we need to use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount in the account, P is the principal (starting amount), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

In this case, P = $100, r = 0.10 (10% expressed as a decimal), n = 12 (monthly compounding), and t = 2. Plugging these values into the formula, we get:

A = $100(1 + 0.10/12)^(12*2) = $121.00

This means that after two years, the account will have grown to $121.00. This is because the interest earned each month is added to the account balance, and then the next month's interest is calculated based on the new balance (including the previous month's interest). Over time, this compounding effect leads to a larger overall return on the initial investment.
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Answer:

Less than a right angle.

Step-by-step explanation:

If you really think about it, a right angle is 90 degrees, and from the looks of it, that angle shown is an acute angle. Acute angles are always smaller than a right angle, so your answer is less than a right angle. :)

The IQR is the best measure of variability, and it equals 4.

Option C is the correct answer.

What is the interquartile range (IQR) supposed to mean?

The range provides us with a gauge of how dispersed our entire data collection is. The interquartile range, which reveals the distance between the first and third quartiles, depicts the dispersion of the middle 50% of our collection of data.

We have,

The appropriate measure of variability for the data is the interquartile range (IQR), which is the range of the middle 50% of the data.

In other words, it is the difference between the third quartile (Q3) and the first quartile (Q1).

From the box plot, we can see that the box extends from 17 to 21 on the number line, with a line at 19 inside the box.

This means that Q1 is 17 and Q3 is 21.

The IQR is:

IQR = Q3 - Q1 = 21 - 17 = 4

Thus,

The IQR is the best measure of variability, and it equals 4.

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Answer:

Domain: {x|-4<=x<=4}

Step-by-step explanation:

Domain refers to the set of the 1st elements, so the x values. In the image we see the ellipse go through both x and y axis but since the question is asking for domain and NOT range (range meaning y values) we can conclude that we need the x values, those being -4 and 4.

I took the review and got it right

On Edge 2020 it's answer C

Domain: {x|-4<=x<=4}

The domain of the relation graphed below will be Domain: \(( x|-4 \leq x\leq 4)\).

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

Domain refers to the set of the First elements, so the x values.

On a coordinate plane, an ellipse intercepts the x-axis at (-4, 0) and (4, 0) and intercepts the y-axis at (0, 1) and (0, -1).

Hence, Domain: \(( x|-4 \leq x\leq 4)\)

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The problem with Rodell's method for collecting data is that it may result in a biased sample.

Rodell is only polling the students on his football and basketball teams, which means the sample he collects is not representative of the entire student population at his school.

The favorite gaming app among the students on his teams may not be the same as the favorite gaming app among the broader student population.

To obtain a more accurate representation of the students' preferences, Rodell should aim for a random sample that includes students from various groups within the school, such as different grade levels or extracurricular activities.

This would help to minimize bias and ensure that the results reflect the overall preferences of the student body.

By solely relying on the football and basketball teams, Rodell's method limits the diversity of the sample, potentially leading to skewed results and an inaccurate conclusion about the favorite gaming app among all students at the school.

Therefore, Rodell's data collection method is flawed because it could lead to a biased sample, as it only includes students from his football and basketball teams.

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The respective probabilities are given as a) 0.4404, b) 0.8962, c) 0.0885.

a) The stochastic variable X is the proportion of correct answers on the math test for a random engineering student, which is normally distributed with expectation value µ = 57.9% and standard deviation σ = 14.0%. We have to find the probability that a randomly selected student has over 60% correct on the math test, i.e., P(X > 60).

x = 60.z = (x - µ) / σz = (60 - 57.9) / 14z = 0.15

Using a standard normal distribution table, we can find that the area under the curve to the right of z = 0.15 is 0.5596.Therefore, P(X > 60) = 1 - P(X ≤ 60) = 1 - 0.5596 = 0.4404.

b) We are considering 81 students from the same cohort. The probability that any one student has over 60% correct on the math test is P(X > 60) = 0.4404 (from part a). We need to find the probability that at least 30 students get over 60% correct on the math test. Since the students' results are independent, we can use the binomial distribution to calculate this probability.

Let X be the number of students who get over 60% correct on the math test out of 81 students. We want to find P(X ≥ 30).Using the binomial distribution formula:

P(X = k) = nCk * pk * (1 - p)n-k where n = 81, p = 0.4404P(X ≥ 30) = P(X = 30) + P(X = 31) + ... + P(X = 81)

This probability is difficult to calculate by hand, but we can use a normal approximation to the binomial distribution. Since n = 81 is large and np = 35.64 and n(1 - p) = 45.36 are both greater than 10, we can approximate the binomial distribution with a normal distribution with mean µ = np = 35.64 and standard deviation σ = sqrt(np(1-p)) = 4.47. The probability that at least 30 students get over 60% correct on the math test is:

P(X ≥ 30) = P(Z ≥ (30 - µ) / σ) = P(Z ≥ (30 - 35.64) / 4.47) = P(Z ≥ -1.26) = 0.8962. Therefore, the probability that at least 30 of the 81 students get over 60% correct on the math test is 0.8962.

c) We have to find the probability that X¯ is above 60%. X¯ is the sample mean of the proportion of correct answers on the math test for 81 students.Let X1, X2, ..., X, 81 be the proportion of correct answers on the math test for each of the 81 students. Then X¯ = (X1 + X2 + ... + X81) / 81.Using the central limit theorem, we can approximate X¯ with a normal distribution with mean µ = 57.9% and standard deviation σ/√n = 14.0% / √81 = 1.55%.

We have to find P(X¯ > 60). Using the z-score formula, we can find the standard score for x = 60.z = (x - µ) / (σ/√n)z = (60 - 57.9) / 1.55z = 1.35Using a standard normal distribution table, we can find that the area under the curve to the right of z = 1.35 is 0.0885. Therefore, the probability that X¯ is above 60% is 0.0885.

Therefore, the respective probabilities are given as a) 0.4404, b) 0.8962, c) 0.0885.

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Answer:

Proof is given below.

Step-by-step explanation:

Given 2 × 2 matrix:

\(\textbf{M}=\left(\begin{array}{cc}2&-2\\1&0\end{array}\right)\)

An identity matrix is a square matrix in which the elements on the leading diagonal (starting top left) are all 1 and the remaining elements are zero.

Therefore, the 2 × 2 identity matrix is:

\(\textbf{I}=\left(\begin{array}{cc}1&0\\0&1\end{array}\right)\)

To show that  \(\textbf{M}^2=2\textbf{M}-2\textbf{I}\) :

\(\begin{aligned}\textbf{M}^2&=\textbf{M} \cdot \textbf{M}\\\\&=\left(\begin{array}{cc}2&-2\\1&0\end{array}\right)\left(\begin{array}{cc}2&-2\\1&0\end{array}\right)\\\\&=\left(\begin{array}{cc}2\cdot2+(-2)\cdot1&2\cdot(-2)+(-2)\cdot0\\1\cdot2+0\cdot1&1\cdot(-2)+0\cdot0\end{array}\right)\\\\&=\left(\begin{array}{cc}2&-4\\2&-2\end{array}\right)\\\\&=2\left(\begin{array}{cc}1&-2\\1&-1\end{array}\right)\end{aligned}\)

      \(\begin{aligned} \\\\&=2\left[\left(\begin{array}{cc}2&-2\\1&0\end{array}\right)-\left(\begin{array}{cc}1&0\\0&1\end{array}\right)\right]\\\\&=2[\textbf{M}-\textbf{I}]\\\\&=2\textbf{M}-2\textbf{I}\end{aligned}\)

Therefore:

\(\begin{aligned}\textbf{M}^4 & =(\textbf{M}^2)^2\\\\&=(2\textbf{M}-2\textbf{I})^2\\\\&=4(\textbf{M}-\textbf{I})^2\\\\&=4\left[\left(\begin{array}{cc}2&-2\\1&0\end{array}\right)-\left(\begin{array}{cc}1&0\\0&1\end{array}\right)\right]^2\\\\&=4\left[\left(\begin{array}{cc}1&-2\\1&-1\end{array}\right)\right]^2\\\\&=4\left(\begin{array}{cc}1&-2\\1&-1\end{array}\right)\left(\begin{array}{cc}1&-2\\1&-1\end{array}\right)\end{aligned}\)

      \(\begin{aligned}&=4\left(\begin{array}{cc}1\cdot1+(-2)\cdot1&1\cdot(-2)+(-2)(-1)\\1\cdot1+(-1)\cdot1&1\cdot(-2)+(-1)(-1)\end{array}\right)\\\\&=4\left(\begin{array}{cc}-1&0\\0&-1\end{array}\right)\\\\&=-4\left(\begin{array}{cc}1&0\\0&1\end{array}\right)\\\\&=-4\textbf{I}\end{aligned}\)

Step-by-step explanation:

The proportion of similar triangles are

\( \frac{3}{4} = \frac{9}{r} \)

Solving for r

\( \frac{4}{3} = \frac{r}{9} \)

\( \frac{9 \times 4}{3} = r\)

\(12 = r\)

Answer:

\( \boxed{x = \frac{p + q {r}^{2} }{a - b {r}^{2} } } \)

Step-by-step explanation:

\(Solve \: for \: x: \\ = > r = \sqrt{ \frac{ax - p}{q + bx} } \\ \\

r = \sqrt{ \frac{ax - p}{q + bx} } \: is \: equivalent \: to \: \sqrt{ \frac{ax - p}{q + bx} } = r :\\ = > \sqrt{ \frac{ax - p}{q + bx} } = r \\ \\ Raise \: both \: sides \: to \: the \: power \: of \: two: \\ = > \frac{ax - p}{q + bx} = {r}^{2} \\ \\ Multiply \: both \: sides \: by \: (q + b x): \\ = > ax - p = {r}^{2} (q + bx) \\ \\ Expand \: out \: terms \: of \: the \: right \: hand \: side: \\ = > ax - p = q {r}^{2} + b {r}^{2}x \\ \\ Subtract \: b {r}^{2}x - p \: from \: both \: sides: \\ = > x(a - b {r}^{2} ) = p + q {r}^{2} \\ \\ Divide \: both \: sides \: by \: a - b {r}^{2} : \\ = > x = \frac{p + q {r}^{2} }{a - b {r}^{2} } \)

Answer:

41

Step-by-step explanation:

20+3(3y-4x)

plug in the given x and y values:

20+3(3*5-4*2)

-->20+3(15-8)

-->20+3*7

-->20+21=41

Answer:

10

Step-by-step explanation:

Because the triangles are similar, we can say:

\(\frac{35}{14} = \frac{40}{16}=\frac{25}{x}\) ⇒ \(x= \frac{16*25}{40}\) ⇒ \(x = 10\)

The probability of success is a measure of the likelihood that a specific event or outcome will occur successfully, typically expressed as a value between 0 and 1.

In a clinical trial with two treatment groups, group A and group B, the probability of success in group A is 0.5, while the probability of success in group B is 0.6. Each group consists of five patients.

To calculate the probability of a specific outcome, such as all patients in group A being successful, we can use the binomial distribution formula.

The binomial distribution formula is:
\(P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}\)

Where:
- P(X=k) represents the probability of getting exactly k successes
- nCk represents the number of ways to choose k successes from n trials
- p represents the probability of success in a single trial
- n represents the total number of trials

In this case, we want to find the probability of all five patients in group A being successful. Therefore, we need to calculate P(X=5) for group A.

Using the binomial distribution formula, we can calculate this as follows:
\($P(X&=5) \\\\&= \binom{5}{5} (0.5^5) (1-0.5)^{5-5} \\\\&= \boxed{\dfrac{1}{32}}\)

Simplifying the equation, we get:
\($P(X&=5) \\&= 1 (0.5^5) (1-0.5)^0 \\&= \boxed{\dfrac{1}{32}}\)

Simplifying further, we have:
\($P(X&=5) \\&= (0.5^5) (1) \\&= \boxed{\dfrac{1}{32}}\)

Calculating this, we get:
P(X=5) = 0.03125

Therefore, the probability of all five patients in group A being successful is 0.03125, or 3.125%.

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Usin a trigonometric relation we can see that the measure of the hypotenuse is 27.22 units.

Here we have a right triangle, and we want to get the value of x, the hypotenuse of that triangle.

We know an angle and the adjacent cathetus of that angle, then we can use a trigonometric relation:

cos(a) = adjacent cathetus/hypotenuse.

Replacing the values that we know we will get:

cos(54°) = 16/x

x = 16/cos(54°)

x = 27.22

The hypotenuse measures 27.22 units.

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The factored form of the polynomial function with zeros of -4, -3, 2, and 1 is:

(x+4)(x+3)(x-2)(x-1)

What is Polynomial function?

A polynomial function is a type of mathematical function that consists of a sum of terms, where each term is the product of a constant coefficient and one or more variables raised to non-negative integer exponents.

If the zeros of a polynomial function are -4, -3, 2, and 1, then its factors are (x+4), (x+3), (x-2), and (x-1), respectively. To find the factored form of the polynomial function, we can simply multiply these factors together, as follows:

(x+4)(x+3)(x-2)(x-1)

We can also expand this expression to get the polynomial in standard form, as follows:

(x+4)(x+3)(x-2)(x-1) = (x² + 7x + 12)(x²  - 3x + 2)

Multiplying this out gives:

\(x^{4} + 4x^3 -7x^2 - 28x + 24\)

Therefore, the factored form of the polynomial function with zeros of -4, -3, 2, and 1 is:

(x+4)(x+3)(x-2)(x-1)

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The factorization of x²-x will be x(x - 1 ).

Factorization or factoring in mathematics is the process of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

Given that the quadratic expression is  x² - x.

To factorize x² - x, we can first factor out the common factor of x:

x² - x = x(x - 1)

So the fully factorized form of x² - x is:

x(x - 1)

Therefore, the factorized form of the expression x²-x is, x(x - 1).

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Answer:

if it is a rectangular prism then it is a rectangle.

Step-by-step explanation:

Answer:

Rectangle

Step-by-step explanation:

The magnitude of the electric field at the point y = 2.0 m on the y-axis is 22.5 N/C.

The question asks for the magnitude of the electric field at a point on the y-axis, given a uniformly distributed charge along the x-axis. Each 20 cm length of the x-axis carries 2.0 nC of charge.

To find the electric field at a point, we can use the formula:

E = k * (Q / r^2)

Where E is the electric field, k is the electrostatic constant (9 * 10^9 N m^2 / C^2), Q is the charge, and r is the distance from the charge.

In this case, the charge is uniformly distributed along the x-axis, so we can consider each 20 cm length as a point charge. The charge of each 20 cm length is 2.0 nC.

Let's calculate the electric field at the point y = 2.0 m on the y-axis.

First, we need to find the distance (r) from each 20 cm length of charge to the point (0, 2.0 m) on the y-axis. Since the x-axis and y-axis are perpendicular, the distance is simply the y-coordinate, which is 2.0 m.

Now, let's calculate the electric field due to each 20 cm length of charge:

E1 = k * (Q / r^2)
  = (9 * 10^9 N m^2 / C^2) * (2.0 nC / (2.0 m)^2)
  = (9 * 10^9 N m^2 / C^2) * (2.0 * 10^-9 C / 4.0 m^2)
  = 4.5 N/C

Since the charges are uniformly distributed, we can assume that each 20 cm length of charge contributes the same electric field.

Next, let's calculate the total electric field at the point (0, 2.0 m) due to all the 20 cm lengths of charge. Since the charges are distributed along the entire x-axis, we can consider all the 20 cm lengths of charge together.

Since the charges are uniformly distributed, the total electric field is simply the sum of the electric fields due to each 20 cm length of charge.

Number of 20 cm lengths = (length of x-axis) / (length of each 20 cm length)
                         = (1 m) / (0.2 m)
                         = 5

Total electric field = (number of 20 cm lengths) * (electric field due to each 20 cm length)
                   = 5 * 4.5 N/C
                   = 22.5 N/C

Therefore, the magnitude of the electric field at the point y = 2.0 m on the y-axis is 22.5 N/C.

So, the correct answer is not listed in the options provided.

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Answer:

3+4+5+11= 56

Step-by-step explanation:

x = 147 / 0.5446 ≈ 270.2 ft

To find the length of the guy wire for a radio transmission tower, trigonometry concepts are applied. Given a tower height of 160 feet, with the wire attached 13 feet from the top and making an angle of 29° with the ground, we can solve for the length of the guy wire, represented by x.

Using the Pythagorean theorem and considering the right triangle formed by the tower height, the wire attachment point, and the ground, we can set up the equation:

x = √((160 - 13)² + x²)

Next, we apply the tangent function to the given angle:

tan(29°) = (160 - 13) / x

Simplifying, we have:

0.5446 = 147 / x

To solve for x, we rearrange the equation:

x = 147 / 0.5446 ≈ 270.2 ft

Rounding to the nearest tenth of a foot, the length of the guy wire required is approximately 270.2 feet. This wire is attached 13 feet from the top of the tower and makes a 29° angle with the ground.

Trigonometry plays a crucial role in solving real-world problems involving angles and distances. It provides a mathematical framework for calculating unknown values based on known information, enabling accurate measurements and constructions.

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Answer:

6

Step-by-step explanation:

Because 6 is 6 times as 1, 12 is 6 times as 2, 18 is 6 times as 3 and so on.

Answer:

M+N is defined

All others not defined

Step-by-step explanation:

Two matrices can be added or subtracted if and only if they have the same dimensions i.e. they must have the exact same number of rows and number of columns

Only M and N with dimensions (4 x 2) each can be added or subtracted.

(4 x 2 ) means 4 rows and 2 columns

So the only defined operation is
M + N

All the others are not defined

Answer:

\(\textsf{De\:\!fined}: \quad \boxed{M + N}\)

\(\textsf{Not\:de\:\!fined}: \quad \boxed{N - Q} \quad \boxed{Q + L} \quad \boxed{M - P}\)

Step-by-step explanation:

Generally, a matrix is referred to as \(n\times m\) where n is the number of rows and m is the number of columns.

Therefore:

Matrices can be added or subtracted only when they are the same size.

\(\boxed{N - Q}\)

Matrices N and Q are different sizes. Therefore, the operation is not defined.

\(\boxed{M + N}\)

Matrices M and N are the same size. Therefore, the operation is defined.

\(\boxed{Q + L}\)

Matrices Q and L are different sizes. Therefore, the operation is not defined.

\(\boxed{M - P}\)

Matrices M and P are different sizes. Therefore, the operation is not defined.

Answer:

okay

i am not sure the answer but hi i am ok

The requried simplified value of x in the given expression is given as x = 128/27.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
x ÷ 2/3= 7 1/9

Simplifying the above expression,
x = (7×9 +1 / 9) × 2/3
x = 64/9 × 2/3
x = 128/27

Thus, the requried simplified value of x in the given expression is given as x = 128/27.

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The approximate length of the midsegment parallel to xy is 6.63

The midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle and has the same length as each of the two sides.

To find the midpoint of a line segment, we average the x-coordinates and the y-coordinates of its endpoints.

Since the question stated that the midsegment is parallel to xy, we need to find midpoint of xw and yw.

First, let's find the midpoint of side xw:

Midpoint of xw : ((-14+10)/2, (20+4)/2) = (-2, 12)

Midpoint of yw : ((-14-2)/2, (20-4)/2) = (-8, 8 )

The length of a line segment between two points (x1, y1) and (x2, y2) in a two-dimensional coordinate system can be calculated using the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Length line of midpoint xw and midpoint yw :

√((-2-(-8))^2 + (12-(8))^2) = √(6^2 + 4^2) = √(36 + 8) = √44

So, the length of the midsegment is parallel to XY, which is approximately equal to √44 = 6.63

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The volume V of a cube is given by

where L is the lenght of one side. Hence, the side L measures

In the first case, the dog kennel has 27 ft^3 of volume, hence

that is, L is 3 feets of lenght.

In the same way, for the second case we have that,

that is, in the second case, L is 4 feet of lenght. This means that, 1 foot was added to each edge of the dog kennel.

Answer:

problem 1. 53/20 problem 2. 24/27. Problem 3. 22/48

Step-by-step explanation:

to solve the first two, the process is similar. For the first one, they can be simplifed back into fraction form and not mixed form, so 1 2/5 can be simplified by multiplying 5 by one then adding it to 2, which gives you 7/5, and the same process for 2 1/2, multiply 2 by two, get 4 add it to one to get 5/2. Now we have 7/5 + 5/2, when we have fractions that we need to add or subtract, but down have the same bottom number, the easiest way to get a answer is to multiply both bottom numbers together then multiply the top number by the opposite bottom number, so 5x4 = 20, 4x7=28, 5x5=25, and we get 28/20 + 25/20 = 53/20. The process for problem two is the same, but just with subtraction and different numbers.

for problem three, the process is almost the same, but the steps differ. The bag is made up of R G and P counters, 3/8 of them are red, 1/6 are green, and the rest are purple because nothing else is in the bag. So another way of saying this is 3/8 + 1/6 + purple = Full Amount in bag. But now we need purple, so we know 1/2 one half and so does 2/4, and since we have fractions we can find the amount in the bag by adding them, 3/8 + 1/6 = 26/48, and we know the full bag is 1/1 or 48/48, and fhe only one left is purple, so to get purple, we subtract 48/48 from 26/48 and get 22/48 which is the amount of purple.

The probability that a randomly chosen Latin student is a sophomore is 6/19, so the m + n is 25.

New schools have 40% freshmen with all freshmen taking Latin, 30% are sophomores with 80% sophomores taking Latin, 20% are juniors with 50% juniors taking Latin, and 10% are seniors with 20% seniors taking Latin.

So, the total students taking Latin is,

= 40%*100% + 30%*80% + 20%*50% + 10%*20%

= 76% of all students.

Then, the students that taking Latin is sophomore,

= 30% * 80%

= 24%

So the probability of a randomly chosen Latin student is a sophomore is,

m/n = chance event occurs / total event

= 24% / 76%

= 6 / 19

Since m is 6 and n is 19, so m + n is 6 + 19 or equal to 25.

Your question is incomplete, but most probably your full question was

(image attached)

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The value of m + n, where m and n are relatively prime positive integers, is 25.

We know that the percentage of students learning Latin are:

(40% * 100%) + (30% * 80%) + (20% * 50%) + (10% * 20%) = 76%

And the percentage of sophomore students learning Latin are:

30% * 80% = 24%

So, the desired probability is:

24 / 76 = 6 / 19

which means 6 is m and 19 is n.

Thus, m + n = 6 + 19 = 25.

Hence, the value of m + n, where m and n are relatively prime positive integers, is 25.

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Although part of your question is missing, you might be referring to this full question: In a new school 40 percent of the students are freshmen, 30 percent are sophomores, 20 percent are juniors, and 10 percent are seniors. All freshmen are required to take Latin, and 80 percent of the sophomores, 50 percent of the juniors, and 20 percent of the seniors elect to take Latin. The probability that a randomly chosen Latin student is a sophomore is m/n, where m and n are relatively prime positive integers. Find m+n.