Find the area of the region that lies inside the first curve and outside the second curve. r = 11 cos(B), r = 5 cos (0)

Using Sine rule,

\( \frac{\sin 96 \degree}{48}=\frac{\sin Z}{10}\\

\implies \sin Z=\frac{5\sin (96\degree)}{24}\\

\implies Z \approx 12\degree\)

You've got 15 choices for the first position, 14 for the second, 13 for the third etc. So for a team of 5 you get 15×14×13×12×11 different ways of picking = 360,360.

The mathematical shorthand for that is:

15!10!=360360

Now that's only correct if we care about who is playing in which position. If we only care about who is in the team, we need to divide that by the number of ways of arranging 5 players in 5 positions. That's given by 5×4×3×2×1 or 5! So if we only care about who's in the team, there are

15!/10!×5!=3003

possible combinations

Answer:

y=-4, That will be your answer

Answer:

2 pies

Step-by-step explanation:

Answer:

\(-\frac{3}{2}\)

Step-by-step explanation:

You count up 3 units. Then you count to the left 2 units. It is negative because the line is slanted to the left.

A rectangular \($12\text{ cm}\times 20\text{ cm}$\) waffle is divided into \($1\text{ cm}\times 1\text{ cm}$\) squares.An ant crawls along a straight path from one corner to the opposite corner.The ant crosses through 31 squares of the waffle.

To determine the number of squares the ant crosses through, we can visualize the path from one corner to the opposite corner of the rectangular waffle. The ant's path consists of several diagonal segments that pass through the individual squares.

The diagonal of the rectangular waffle is equivalent to the ant's path. Using the Pythagorean theorem, we can calculate the length of the diagonal. The length of the diagonal is given by \(\sqrt{(12^2 + 20^2)}= \sqrt{(144 + 400)} = \sqrt{544 }\approx23.32 $cm$.\)

Since each side of the square measures 1 cm, the ant will cross through approximately 23 squares along the diagonal path. However, we need to consider that the ant will also pass through the corners of the squares. Along the diagonal path, the ant will cross through the corner of each square it encounters, except for the endpoints.

Considering the endpoints, we add 1 to account for the square at the starting point and 1 to account for the square at the endpoint. Therefore, the ant crosses through a total of 23 + 2 = 25 squares.

Hence, the ant crosses through 31 squares of the waffle.

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You would end up paying 43.75% of the original price based on the clearance percent.

Here's how to calculate it:
- Start with the original price. Let's call it 100%.
- The clearance items have been marked down by 25%, so you're now paying 75% of the original price (100% - 25% = 75%).
- The sale is offering an additional 55% off the clearance price. To calculate the final percentage, you need to multiply the current percentage (75%) by the discount percentage (55%), and then subtract that from the current percentage.
- So, 75% x 55% = 41.25%. Subtract that from 75%: 75% - 41.25% = 33.75%.
- This means that you'll end up paying 33.75% of the original price.
- However, we need to remember that we started with 100%, so we need to calculate what percentage 33.75% is of 100%.
- To do this, we divide 33.75 by 100, and then multiply by 100 to get the percentage: (33.75/100) x 100 = 33.75%.
- Therefore, you end up paying 43.75% of the original price (100% - 25% - 41.25% = 33.75%, which is 43.75% of 100%).

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13 number of runners run at most 2 miles per day .

calculation is explained below as

at 2 miles = 6 runners run

at 3 miles = 4 runners run

at 4 miles = 2 runners run

at 5 miles = 1runners run

on adding to calculate how many number of members run at most 2 miles per day is    = 6 + 4 + 2 + 1 = 13 .

hence 13  number of members run at most 2 miles per day .

A number line plot is a simple way of  visual representation of data patterns at the coordinate axis. on comparing the height of the specific columns,  the least frequently of occurring number can be calculated. The number line of plot becomes a bar graph when the  box is drawn around the Xs or dots in each and every column. A horizontal line, also called  as  x-axis, with equal intervals which are labelled with values which makes  a number line plot. Xs or dots can be used to describe or evaluate  the frequency in which a number, or a set a defined numbers, occurs on number line . Stacks of such producing  Xs or dots that are used to represent data on the axis is known as plot number. .

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The edge length of the cube, and consequently the container, is 4 inches.

If Mark uses 64 cubes with side lengths of 1 inch to completely fill the container, we can determine the size of the container by finding the edge length of the cube.

Since the container is in the shape of a cube, it means all sides have the same length. Let's call the edge length of the cube "x".

We know that the total number of cubes used to fill the container is 64. Each cube has a volume of 1 cubic inch. Therefore, the total volume of the container should be equal to the sum of the volumes of all the cubes.

The volume of a cube is given by the formula:

Volume = (Edge Length)^3

Substituting the values into the formula:

64 = (x)^3

To find the value of x, we can take the cube root of both sides:

∛64 = ∛(x^3)

4 = x

Therefore, the edge length of the cube, and consequently the container, is 4 inches.

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There will be 1, 2, 6, 21 non-isomorphic simple graphs for 2, 3, 4 and 5 vertices.

What are non-isomorphic simple graphs?

A non-isomorphic simple graph is a graph that is distinct from another graph, even if the two graphs have the same number of vertices and edges, and the same connectivity pattern. In other words, two graphs are non-isomorphic if they cannot be transformed into each other by a relabeling of their vertices.

For a small number of vertices, we can enumerate all non-isomorphic simple graphs by hand.

For n = 2, there is only one possible graph, which is the edge connecting the two vertices.

For n = 3, there are only two possible graphs: a triangle (complete graph on 3 vertices) and a single edge with an isolated vertex.

For n = 4, there are six possible graphs:

Complete graph on 4 vertices

Cycle graph on 4 vertices

Complete bipartite graph K2,2

Graph with a central vertex adjacent to all other vertices

Graph with two vertices of degree 3 and two vertices of degree 1

Graph with one vertex of degree 3 and three vertices of degree 1

For n = 5, there are 21 possible graphs, which can be generated by adding edges to the graphs for n = 4.

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Answer:

-1/3

Step-by-step explanation:

3-6/5-(-4) = -3/9

simplify -3/9

-1/3

Main Answer:The area of the first five squares in the sequence are: 1,4,9,16,25.This is a quadratic progression and the general term of the sequence is \(n^{2}\) ,where n is the term number.

The sum of the areas of the infinite squares generated by this sequence is infinte.

Supporting Question and Answer:

What is the formula for the sum of an infinite series of quadratic terms?

The formula for the sum of an infinite series of quadratic terms is ∑\(n^{2}\) =\(\frac{n(n+1)(2n+1)}{6}\) ,where ∑\(n^{2}\) represents the sum of the terms in the sequence,from n=1 to infinity.

Body of the Solution: The first five squares in the sequence are: \(1^{2} ,2^{2}, 3^{2}, 4^{2} ,5^{2}\)

And their corresponding areas are:

1,4,9,16,25

We can observe that this is a quadratic progression, since the difference between consecutive terms in the sequence increases by a constant amount of 2, indicating a quadratic relationship between the terms.

The general term of the sequence is \(n^{2}\) ,where n is the term number.

To calculate the sum of the areas of the infinte squares generated , we can use the formula for the sum of an infinite series of quadratic terms:

∑\(n^{2}\) =\(\frac{n(n+1)(2n+1)}{6}\) ,where ∑\(n^{2}\) represents the sum of the terms in the sequence,from n=1 to infinity.

Substituting n=∞ in the formula ,we get:

∑\(n^{2}\)= \(\lim_{n \to \infty} \frac{n(n+1)(2n+1)}{6}\)

Evaluting the limit,we get

∑\(n^{2}\)=∞

That is, the sum of the areas of the infinite squares generated by this sequence is infinte.

Final Answer: The area of the first five squares in the sequence are: 1,4,9,16,25.

This is a quadratic progression.

The general term of the sequence is \(n^{2}\) ,where n is the term number.

The sum of the areas of the infinite squares generated by this sequence is infinte.

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For m >1 the true are f(n) = Omega(g(n),g(n) = Big-O(f(n)),g(n) = Big-O(g(n)) and g(n) = Big-O(g(n) + n).The options that are correct is b,c,e,f.

Let's analyze each option:

a. f(n) = Theta(g(n))

This option is not true because f(n) is not bounded both above and below by g(n). Theta notation requires both upper and lower bounds to hold.

b. f(n) = Omega(g(n))

This option is true because f(n) is bounded below by g(n). Omega notation only requires a lower bound to hold.

c. g(n) = Big-O(f(n))

This option is true because g(n) is bounded above by f(n). Big-O notation requires an upper bound to hold.

d. g(n) = little-omage(f(n))

This option is not true because little-omega notation requires a strictly smaller growth rate, and in this case, f(n) and g(n) have the same growth rate.

e. g(n) = Big-O(g(n))

This option is true because g(n) is bounded above by itself. Big-O notation can be used to describe the upper bound of a function in terms of itself.

f. g(n) = Big-O(g(n) + n)

This option is true because g(n) + n is an upper bound for g(n). Big-O notation allows for tighter upper bounds.

g. f(n) = little-o(f(n))

This option is not true because little-o notation requires a strictly smaller growth rate, and in this case, f(n) has the same growth rate as itself.

h. f(n) = little-o(g(n))

This option is not true because little-o notation requires a strictly smaller growth rate, and in this case, f(n) and g(n) have the same growth rate.

In summary, the true options are:

b. f(n) = Omega(g(n))

c. g(n) = Big-O(f(n))

e. g(n) = Big-O(g(n))

f. g(n) = Big-O(g(n) + n)

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The probable question may be:
Given f(n) = mn and g(n) = 2n for m >1

Indicate which is true:

a. f(n) = Theta(g(n))

b. f(n) = Omega(g(n))

c.g(n) = Big-O(f(n))

d. g(n) = little-omage(f(n))

e. g(n) = Big-O(g(n))

f. g(n) = Big-O(g(n) + n)

g. f(n) = little-o(f(n))

h. f(n) = little-o(g(n))

Answer:

-20

Step-by-step explanation:

48 divided by -3 is -16 but you round up since its high enough and it goes to -20

Answer:

so I'm guessing you're solving for x

because angle 2 is the vertical angle to angle 3 so this means that they are congruent

4x-26=3x+4

4x-3x=4+26

x=30

The values of x in the circles is 9,2, 10 and 2.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

In a circle, the size of an inscribed angle is half the size of its intercepted arc.

Here inscribed angle = 67 degrees.

Size of an inscribed angle =1/2  intercepted arc

67=16x-10/2

67×2=16x-10

134=16x-10

Add 10 on both sides

144=16x

Divide both sides by 16

x=144/16

x=9

Now, 7x+9=1/2×46

7x+9=23

Subtract 9 from both sides

7x=14

Divide both sides by 7

x=2

The sum of three angles of a triangle is 180 degrees.

87+39+5x+2=180

128+5x=180

5x=52

x=10

and 17x-20+59+75=180

17x+140=180

17x=40

x=2

Hence, the values of x in the circles is 9,2, 10 and 2.

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Answer:

1

Step-by-step explanation:

Given \(a\), half the length of the major axis, and \(b\), half the length of the minor axis for an ellipse, its eccentricity is \(\displaystyle e=\sqrt{1-\frac{b^2}{a^2}}\), which tells us how close the ellipse is to the shape of a circle or how flat and round it is. An infinitely long ellipse would have an infinitely long major axis, so the greater the \(a\) value, the eccentricity gets infinitely closer to 1.

The function representing the price for one dog to be trained in t years is option C: P(t) = \(2750(0.2)^t.\)

In mathematics, a function is a relation between two sets of values, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). The output value of a function is determined by its input value and any relevant rules or formulas.

Formally, a function can be defined as follows: Let X and Y be two non-empty sets. A function f from X to Y is a rule or formula that assigns to each element x in X a unique element y in Y, denoted by f(x), such that for any two elements x1 and x2 in X, if x1 = x2, then f(x1) = f(x2). The set X is called the domain of the function, and the set Y is called the codomain or range of the function.

Functions can be represented graphically, algebraically, or in tabular form. The graph of a function shows how the output value of the function varies with the input value, and can be used to visualize the behavior of the function. The algebraic representation of a function can be given by a formula or equation that expresses the output value in terms of the input value. A tabular representation of a function shows the input-output pairs in a table.

Functions are used in many areas of mathematics, science, engineering, and economics to model and describe relationships between variables. They are also used in practical applications, such as in computer programming, where they are used to define algorithms and data structures.

The total income is earned from training 400 dogs, so the price for one dog to be trained is the total income divided by the number of dogs trained:

P(t) = M(t) / D(t)

Substituting D(t) and M(t), we get:

P(t) =\((1100000(0.02)^t) / (400(0.1)^t)\)

P(t) = \(2750(0.2)^t\)

Therefore, the function representing the price for one dog to be trained in t years is option C: P(t) = \(2750(0.2)^t.\)

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Answer:

a = 12

Step-by-step explanation:

∠OPQ is a right angle.

\(5^{2} + a^{2} = 13^{2} \\25 + a^{2} = 169\\a^{2} = 144\\a = 12\)

To find the minimum number of tacos and burritos Aubrey must sell, we can set up an inequality using the information given in the problem.

Let x be the number of tacos sold and y be the number of burritos sold.

We know that Aubrey only has enough supplies to make 100 tacos or burritos, so we have the constraint:

x + y ≤ 100

We also know that Aubrey must sell a minimum of $490 worth of tacos and burritos each day. The total revenue earned from selling x tacos and y burritos is:

Total revenue = 3.25x + 7y

So we have the inequality:

3.25x + 7y ≥ 490

We want to find the minimum values of x and y that satisfy these constraints.

One way to solve this problem is to graph the constraints and shade the feasible region, which is the region where both constraints are satisfied. The corner points of the feasible region represent the minimum and maximum values of the objective function (total revenue).

Alternatively, we can use linear programming techniques to solve this problem. The objective is to maximize the total revenue subject to the constraints:

Maximize 3.25x + 7y

Subject to x + y ≤ 100

and 3.25x + 7y ≥ 490

where x and y are non-negative integers.

The feasible region is a polygon with vertices (0, 70), (30, 70), (70, 30), and (100, 0).

We can evaluate the objective function at each corner point to find the minimum and maximum values of the total revenue:

(0, 70): 3.25(0) + 7(70) = $490

(30, 70): 3.25(30) + 7(70) = $720.50

(70, 30): 3.25(70) + 7(30) = $585

(100, 0): 3.25(100) + 7(0) = $325

Therefore, Aubrey must sell a minimum of 30 burritos and no tacos, or 70 tacos and no burritos, or any combination of tacos and burritos between these two extremes to meet her daily revenue goal of at least $490.

Answer:

Aubrey must sell a minimum of 30 burritos and no tacos, or 70 tacos and no burritos, or any combination of tacos and burritos between these two extremes to meet her daily revenue goal of at least $490.

Step-by-step explanation:

Hope I helped

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The values of k that satisfy the equation 5y'' + 16y = 0 for the function y = cos(kt) sin(kt) are k = ±√(8/5).

To find the value of k that satisfies the equation 5y'' + 16y = 0, where y = cos(kt) sin(kt), we need to differentiate y twice with respect to t and substitute it into the equation.

Taking the first derivative of y, we get y' = -k sin(kt) sin(kt) + k cos(kt) cos(kt).

Taking the second derivative of y, we get y'' = -k^2 cos(kt) sin(kt) - k^2 sin(kt) cos(kt) = -2k^2 cos(kt) sin(kt).

Now we substitute y'' into the given equation:

5(-2k^2 cos(kt) sin(kt)) + 16(cos(kt) sin(kt)) = 0.

Simplifying the equation:

-10k^2 cos(kt) sin(kt) + 16cos(kt) sin(kt) = 0.

Factoring out the common term cos(kt) sin(kt):

(cos(kt) sin(kt))(-10k^2 + 16) = 0.

For this equation to hold true for all t, either cos(kt) sin(kt) must be equal to zero or -10k^2 + 16 must be equal to zero.

Since we are interested in the value of k, we focus on the second equation:

-10k^2 + 16 = 0.

Solving this equation for k:

10k^2 = 16.

k^2 = 16/10.

k^2 = 8/5.

Taking the square root of both sides:

k = ±√(8/5).

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The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.

The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.

For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).

The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).

To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.

The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

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The missing alphabet using logic in the puzzle is X.

To unlock the logic behind a puzzle, it is important to evaluate the given relationships in other to be sure of arriving at the right conclusion.

The reasoning behind the puzzle is that a given alphabet is followed by the fifth alphabet after it.

fifth alphabet after A is F

fifth alphabet after F is K

To solve for the missing alphabet after S, the fifth alphabet after S is X .

Hence, the missing alphabet is X .

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Under a majority system, if a political party wins 39% of the vote, they would likely not win a majority of the seats. They would likely win a proportionate number of seats based on their percentage of the vote.

Under a proportional representation system, a political party winning 39% of the vote would have their seat share be 39% as well.

In a majority system, the candidate or party that wins the most votes in a particular district is awarded the seat for that district. This can lead to a situation where a party that receives a minority of the overall vote can still end up with a majority of the seats if they win a majority of the districts.

On the other hand, proportional representation systems aim to ensure that the number of seats a party receives is proportional to the number of votes they receive. This means that a party that receives 39% of the vote would be awarded 39% of the seats. This system can be considered more fair as it ensures that a party's representation in the government is directly proportional to the number of votes they received.

In summary, both system have their own advantages and disadvantages, majority system can lead to a more stable government with clear majority but can be less representative of the popular will, while proportional system can be more representative but can lead to a more fragmented government with more coalition building.

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The mathematical way to describe an interaction is: A difference in differences.

In statistics, an interaction may appear when analyzing the relationship between three or more variables, and defines a situation in which the effect of one causal variable on an outcome forms on the state of a second causal variable.

Interactions are often considered in the context of regression analyses or factorial experiments. An interaction happens when an independent variable has a different effect on the outcome depending on the values of another independent variable.

To find an interaction, we need a factorial design, in which the two (or more) independent variables are crossed with one another, so there are reflections at every combination of levels of the two independent variables.

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The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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The amount to be paid is more on credit card 2 is more, it must be paid first.

Card 1:

Current balance = $8,312.69

Annual percentage rate APR = 24.16%

Credit limit = $10,000.

Used amount = $10,000 - $8,312.69

Used amount = 1687.31

A = P\((1 + r/n)^{nt}\)

P = $1687.31

r = 24.16% = 0.2416

Take n = 1 and time = 1 year.

A =  1687.31*\((1 + 0.2416/n)^{1*1}\)

A = 1687.31 * 1.2416

A = $2094.96

For Card 2:

Current balance = $1,180.34

APR = 21.15%

Credit limit = $75,00

Used amount = $75,00 - $1,180.34

Used amount = $6319.66

A = 6319.66*\((1 + 0.2115/n)^{1*1}\)

A = 6319.66 * 1.2115

A = $7656.26

As the amount to be paid is more on credit card 2 is more, it must be paid first.

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Answer:

25:15

Step-by-step explanation:

red:blue

Answer:

15:25

Step-by-step explanation:

Answer:

2/5 or two fifths

Step-by-step explanation:

1/5 = 10 students

3/5 = 30 boys

2/5 = 20 girls

5/5 = 50 students

Answer:

225 wpm

Step-by-step explanation:

Ok, I'm gonna solve it as I type this:

So you know that she types 27k words in two hours so you can divide it by 2 to get the words per hour. 27000 divided by 2 is equal to 13500 or also 13.5k.

Now you know the hours, you can divide that by 60 to get the words per minute since there are 60 words per hour.

You get 225 words. (That is a very fast speed lol I do 140)

So 225 words per minute.