For the years 1970-2006, the percent of females in the workforce is given by y=11.596+8.540lnx, where x is the number of years from 1960.(a) What does the model predict the percent to be in 2013? In 2018?(b) Is the percent of female workers increasing or decreasing?If $4000 is invested in an account earning 7% annual interest compounded continuously, then the number of years that it takes for the amount to grow to $8000 is n= ln2 0.07. Find the number of years.The number of periods needed to double an investment when a lump sum is invested at 11% compounded bimonthly is n= log2 0.0079. In how many years will the investment double?

The following set of inequalities is satisfied by the coefficients a, b, and c:

-a < b < (-3/8) - (4a/8)

c > -1

-2a - 2b < 2

Any solutions for the coefficients a, b, and c that meet the requirements can be found using this system of inequalities.

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols.

from the question:

In order to solve for the coefficients a, b, and c, we must construct a system of inequalities using the provided information.

Let's start by creating the following inequalities using the values of f(-1), f(1), and f(3) that are given:

[tex]a(-1)^2 + b(-1) + c < 1[/tex]

[tex]a(1)^2 + b(1) + c > -1[/tex]

[tex]a(3)^2 + b(3) + c < -4[/tex]

Simplifying these inequalities, we get:

a - b + c < 1

a + b + c > -1

9a + 3b + c < -4

Given that an is not equal to zero, we may use this information to find the values of the remaining coefficients. In order to construct an expression for c in terms of a and b, we can first utilize the second inequality as follows

c > -1 - a - b

The first and third inequalities can then have this expression for c to yield the following result:

a - b + (-1 - a - b) < 1

9a + 3b + (-1 - a - b) < -4

Simplifying these inequalities, we get:

-2a - 2b < 2

8a + 2b < -3

Now, we can solve for b in terms of a using the first inequality:

b > -1 - a - (1/2)(-2a)

b > -a

And we can solve for b in terms of a using the second inequality:

b < (-3/8) - (4a/8)

Combining these two formulas for b, we obtain:

-a < b < (-3/8) - (4a/8)

Lastly, we may enter the following equation for b into the earlier-derived expression for c:

c > -1 - a - (-a)

c > -1

As a result, the following system of inequalities is satisfied by the coefficients a, b, and c:

-a < b < (-3/8) - (4a/8)

c > -1

-2a - 2b < 2

Any solutions for the coefficients a, b, and c that meet the requirements can be found using this system of inequalities.

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complete question:

let[tex]f(x)=ax^2+bx+c[/tex] and f(-1)<1,f(1)>-1,f(3)<-4 and a is not equal to zero then

Answer:

Max worked 15 hours while John worked 10 hours

The speed of the ball thrown from third base to first base is approximately 106.1 feet/second.

From the question, we are to calculate the speed of the ball

Assuming the ball traveled in a straight line from third base to first base, we can use the distance formula to find the distance the ball traveled and then use the formula for speed to find the speed of the ball.

The diagonal of the square infield can be found using the Pythagorean theorem:

Diagonal = sqrt(90² + 90²) = 127.28 feet

Therefore, the distance the ball traveled from third base to first base is approximately equal to the diagonal of the square, which is 127.28 feet.

To find the speed of the ball, we can use the formula:

Speed = Distance / Time

Plugging in the values, we get:

Speed = 127.28 feet / 1.2 seconds

= 106.06667 feet/second

≈ 106.1 feet/second

Hence, the speed of the ball is approximately 106.1 feet/second.

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Answer:

Shape  Area (units^2)

   A          20

   B            2

   C            4

   D            6

Total =      32

Step-by-step explanation:

See the attached worksheet.  These calculations assume that the "6" is the length of the line segment as marked.  Using the expressions for areas or traingles and rectangles, as noted, each area is calculated and the sum is 32 units^2.

The prοbability οf sοmeοne pulling 1-10 in cοnsecutive οrder frοm a bad that cοntains 10 balls labeled 1-10 is 1/3628800.

Prοbability is simply the pοssibility that sοmething will happen. Since we dοn't knοw hοw sοmething will turn οut, we can talk abοut the pοssibility οf οne οutcοme οr the likelihοοd οf several.

There are 10 balls in a bag with the numbers marked 1 thrοugh 10.

Nοw,

The ball with the number 1 οn it is picked in exactly 1 time

There are twο different ways tο pick the ball with the number 2.

Thus there is just οne pοssible technique tο chοοse a ball with a specific number.

There is nο lοnger a substitute.

Sο, when οne ball is taken, the tοtal number οf balls decreases by οne.

Then,

The prοbability οf selecting ball numbered 1= 1/10

The prοbability οf selecting ball numbered 2= 1/9

The prοbability οf selecting ball numbered 3= 1/8

That is dοne up tο last ball....

Last 1 is, the prοbability οf selecting ball numbered 10= 1/1

Tοtal prοbability οf chοοsing the balls in cοnsecutive οrder = 1/10 * 1/9 * 1/8 *.......* 1/2*1/1 = 1/10! = 1/3628800.

Hence, the prοbability οf sοmeοne pulling 1-10 in cοnsecutive οrder frοm a bad that cοntains 10 balls labeled 1-10 is 1/3628800.

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The value of 151.8% of £613.71 is £931.55.

An informed estimate or a flimsy explanation for a phenomena or observation that may be evaluated by more research is called a hypothesis. It serves as the basis for scientific inquiry and is often formed using known facts and observations.

A theory, on the other hand, is a proven explanation for a phenomenon or group of occurrences that has undergone significant testing and is backed by empirical data. A theory may be thought of as a framework that predicts and explains how and why things happen the way they do.

Given that, 151.8% of £613.71

To find the value, first convert the percentage to a decimal by dividing it by 100:

151.8 ÷ 100 = 1.518.

Multiply this decimal by:

£613.71: 1.518 × £613.71 = £931.55

Hence, the value of 151.8% of £613.71 is £931.55.

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The volume V of the cylinder can be expressed as the polynomial function: V(x) = πx³ + 30πx² + 297πx + 972π

The formula for the volume of a cylinder is given by:

V = πr²h

where r is the radius and h is the height.

In this case, the radius is x+9 units, and the height is 3 units more than the radius, which means the height is (x+9)+3 = x+12 units.

Substituting these values into the formula, we get:

V = π(x+9)²(x+12)

Expanding the square, we get:

V = π(x² + 18x + 81)(x+12)

Multiplying out the brackets, we get:

V = π(x³ + 30x² + 297x + 972)

Therefore, the volume V of the cylinder can be expressed as the polynomial function:

V(x) = πx³ + 30πx² + 297πx + 972π

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We can proceed with conducting a z-test for one proportion to test whether the true proportion of players who win the game differs from 0.10.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Yes, the conditions for inference are met for conducting a z-test for one proportion.

The random condition is met because the sample is chosen randomly from the large population of all players.

The 10% condition is also met since the sample size (100) is less than 10% of the entire population.

The large counts condition is met because both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the hypothesized proportion of players who win the game. In this case, np = 100 * 0.1 = 10 and n(1-p) = 100 * 0.9 = 90.

Therefore, we can proceed with conducting a z-test for one proportion to test whether the true proportion of players who win the game differs from 0.10.

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Points found on y = h(x) are (7, -6) and (-2,-1).

Using these two points, we will solve for the exact equation of y = h(x).

To solve the equation, we will get the slope (m) of the two points first using the following formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1} =\dfrac{-1-(-6)}{-2-7} =\dfrac{5}{-9} =-\dfrac{5}{9}[/tex]

Now that we have a slope, we can now proceed in solving the equation using Point-Slope Formula.

 [tex]y-y_1=m(x-x_1)[/tex]

[tex]y-(-6)=-\dfrac{5}{9}(x-7)[/tex]

  [tex]y+6=-\dfrac{5}{9}(x-7)[/tex]

 [tex]9y+54=-5x+35[/tex]

 [tex]9y=-5x+35-54[/tex]

     [tex]9y=-5x-19[/tex]

     [tex]y=-\dfrac{5}{9}x-\dfrac{19}{9}[/tex]

Now that we have the equation of the dashed line, we will now solve for its inverse function y = h^-1 (x).

To solve for the inverse, we will reverse y and x with each other. The new equation will be:

[tex]x=-\dfrac{5}{9}y -\dfrac{19}{9}[/tex]

From that equation, we will now equate or isolate y.

[tex]x=-\dfrac{5}{9}y -\dfrac{19}{9}[/tex]

[tex]x=-\dfrac{5y-19}{9}[/tex]

[tex]9x=-5y-19[/tex]

[tex]5y=-9x-19[/tex]

[tex]y=-\dfrac{9}{5}x -\dfrac{19}{5}[/tex]

In this equation, our slope (m) here is -9/5 and our y-intercept is at (0, -19/5). The graph for this equation will look like this.

Drag the endpoints of the solid segment to the coordinates shown above to graph y = h^-1 (x).

Or drag the endpoints to (-6,7) and (-1,-2). It's the same graph anyway.

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

A 4-liter container holds more than a 3500-milliliter container

Step-by-step explanation:

4 liters = 4000 milliliters

4000 > 3500

It has been proven that the lines bc and ad are equal.

Given that the lines ac and bd bisect each other, we can prove that the lines bc and ad are equal.

Firstly, we need to calculate the length of each side of the figure and label them accordingly. Let’s assume that the length of ac is x and the length of bd is y.

We know that the two lines ac and bd bisect each other, so the midpoint of ac and bd must be the same point, which is point c. We can use the midpoint formula to calculate the distance between points a and c:

Midpoint of ac = (x/2, 0)

Similarly, we can calculate the midpoint of bd:

Midpoint of bd = (y/2, 0)

Since the midpoints of ac and bd are the same, we have:

(x/2, 0) = (y/2, 0)

Therefore, we can calculate that x = y. This means that the lengths of ac and bd are equal and so the lengths of bc and ad must also be equal.

Therefore, bc = ad.

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Answer:

The answer is d (-1, -2)

solve for the first variable in one of the equations then substitute the result into the other equation

The solution to the system of equations is x = -1 and y = -2, which can be written as (-1, -2).

Option D is the correct answer.

We have,

To solve the system of equations:

x + y = -3 ----(1)

2x - 3y = 4 ----(2)

Solve it using the elimination method:

Multiply equation (1) by 2 to make the coefficients of x in both equations equal:

2x + 2y = -6 ----(3)

Now, subtract equation (3) from equation (2) to eliminate x:

(2x - 3y) - (2x + 2y) = 4 - (-6)

Simplifying the equation:

-5y = 10

Divide both sides of the equation by -5:

y = -2

Substitute the value of y back into equation (1):

x + (-2) = -3

x - 2 = -3

Add 2 to both sides of the equation:

x = -1

Therefore,

The solution to the system of equations is x = -1 and y = -2, which can be written as (-1, -2).

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The missing term is:  [tex]\frac{4}{p}[/tex]

A solution of an equation is a value or set of values that, when substituted into the equation, makes it true. In other words, a solution is a value that satisfies the equation.

The given equation is, 4/p - 2/3q = ?-2p/3pq

or we can write as, [tex]\frac{4}{p} - \frac{2}{3q} = x - \frac{2p}{3pq}[/tex]

here find the missing term x in above equation.

Simplification,

[tex]\frac{4}{p} - \frac{2}{3q} + \frac{2p}{3pq} = x[/tex]

[tex]\frac{(4*3q)-2p}{3pq} + \frac{2p}{3pq} = x[/tex]

[tex]\frac{12q-2p}{3pq} + \frac{2p}{3pq} = x[/tex]

[tex]\frac{(12q-2p)+2p}{3pq} = x[/tex]

[tex]\frac{12q}{3pq} = x[/tex]

[tex]\frac{4}{p} = x[/tex]

Therefore, the missing term is:  [tex]\frac{4}{p}[/tex]

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The expression that corresponds to the volume of the rectangular prism is "Yes."

Expression 1: Yes

Expression 2: No

Expression 3: Yes

Expression 4: No

Let's determine if each expression can be used to determine the volume of the rectangular prism with dimensions 4, 6, and 2.

Expression 1: 8 × 6

To calculate the volume, we need the product of the length, width, and height. The expression 8 × 6 matches these dimensions, so the answer is Yes.

Expression 2: (2 × 4) + 6

This expression does not involve all three dimensions of the rectangular prism. It only includes the length and width, but not the height. Therefore, it cannot be used to determine the volume. The answer is No.

Expression 3: 4 × (6 × 2)

This expression involves all three dimensions of the rectangular prism: length, width, and height. It is the correct formula for calculating the volume. The answer is Yes.

Expression 4: 2 × (4 + 6)

This expression does not include all three dimensions. It only includes the length and width, but not the height. Hence, it cannot be used to calculate the volume. The answer is No.

Therefore:

Expression 1: Yes

Expression 2: No

Expression 3: Yes

Expression 4: No

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The complete question:

Can the following expressions be used to determine the volume of the rectangular prism in cubic inches? Please select "Yes" or "No" for each expression:

Expression 1: 8 × 6

Expression 2: (2 × 4) + 6

Expression 3: 4 × (6 × 2)

Expression 4: 2 × (4 + 6)

The length, width, and height of the prism are 4, 6, and 2 respectively.

Answer:

LCM of 2 and 6 is 6.

Step-by-step explanation:

We know that the smallest multiple which is exactly divisible by 2 and 6 has to be determined. Multiples of 6 = 6, 12, 18, 24,.. The smallest multiple which is exactly divisible by 2 and 6 is 6.

The cost for renting a car can be represented by the equation: c = a + bm

The cost of renting a car can be expressed as a function of the number of miles driven. This function is typically linear, with a fixed cost component and a variable cost component. The fixed cost component represents the cost of renting the car regardless of the number of miles driven, while the variable cost component represents the additional cost per mile driven.

The equation that represents the cost of renting a car is c = a + bm, where c represents the total cost of renting the car, m represents the number of miles driven, a represents the fixed cost component, and b represents the variable cost component.

The equation shows that the cost of renting a car is dependent on the number of miles driven. As the number of miles driven increases, the cost of renting the car also increases, reflecting the additional variable cost per mile. By knowing the values of a and b, we can estimate the total cost of renting the car for a given number of miles.

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Yes, Enid is correct that the distance she jogs and the number of calories she burns are in a proportional relationship. This means that as the distance she jogs increases, the number of calories she burns also increases at a constant rate.

To see this proportional relationship, we can look at the data from her last four jogs on the treadmill. Let's say that the distance she jogged is represented by x and the number of calories she burned is represented by y.

If we divide the number of calories she burned (y) by the distance she jogged (x), we should get the same constant rate for each of her four jogs.

For example, if she jogged 2 miles and burned 200 calories, the constant rate would be 200/2 = 100. If she jogged 4 miles and burned 400 calories, the constant rate would also be 400/4 = 100.

This shows that there is a proportional relationship between the distance she jogs and the number of calories she burns on the treadmill. The constant rate in this case is 100, which means that for every 1 mile she jogs, she burns 100 calories.

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Answer:

Answer: 8 a + 5 b - 9. Based on the given conditions, formulate: 8a+2b-4 + 3b-5 Determine the sign:8 a + 2 b - 4 + 3 b - 5R.

Step-by-step explanation:

l

Hence, Option A is the set of values that will give PV the same value as the specified expression. N = 5, 1% = 0, PV =, PMT = 505, FV = 0, P/Y = 12, C/Y = 12, and PMT:END

Using the TVM Solver on a graphing calculator, we may identify the set of values that will give PV the same value as the supplied expression.

The sentence is as follows:

PV = ($505)((1+0.004)^0-1) / (0.004)(1+0.004)^60

If we condense this phrase, we get:

PV = -$23,724.59

Now, we can examine each set of data to determine which one yields the same PV value.

Option A: The PV is -$23,724.59 when N=5 and 1%-0.4 are used. The specified expression's value for PV is returned by this option.

Option B: The PV obtained by using N=60 and 1%-0.4 is -$153,167.63, which is not the same as the equation.

Option C: The PV obtained by using N=60 and 1%-4.8 is $18,981.10, which is not the same as the equation.

Option D: A PV of $590.68 is produced using N=5 and 1%=4.8, which differs from the stated expression.

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23 is the smallest value of n so that the probability is at least. 5 that at least two people share a birthday.

To obtain the probability that at least two people share their Birthday to get the smallest value of 'n' so that the probability is at least 0.5 that at least two people share a birthday, that is,

That is,

P(E) = 1- P(E)

Thus, the probability that at least two persons share their Birthday, P(E) is

P(E) = 1 - [365 - (n - 1)] / 365n

Now, make the following table to obtain the smallest value of 'n' so that the probability is at least 0.5 that at least two people share a birthday.

For n = 10 the value of P(Ec) and P(E) is obtained as 0.883 and 0.117 respectively

It means at least 23 people needed to get the probability is at least 0.5 that at least two people share a birthday.

Therefore, we can say that 23 is the smallest value of n so that the probability is at least. 5 that at least two people share a birthday.

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The equation was that she needs to sell 78.8 bottles of water and 1.49 bottles of iced tea in order to earn $100.

A linear equation is a mathematical equation that contains two variables and takes the form of Ax + By = C. It can be used to represent a line on a graph and is used to calculate the relationship between two variables. Linear equations are fundamental to algebra and are used to solve for unknown values. They can also be used to calculate the slope of a line and the intercept of a line on the coordinate plane.

To solve this equation, Barbara needs to isolate the variable x. To do this, she needs to subtract 1.49 from both sides of the equation. This will give her a new equation of 1.25x = 98.51.

Next, Barbara needs to divide both sides of the equation by 1.25. This will give her an equation of x = 78.8. This means that she needs to sell 78.8 bottles of water and 1.49 bottles of iced tea in order to earn $100.

Barbara wrote a linear equation to find the number of bottles she needs to sell to earn $100. To solve the equation, she needed to isolate the variable x by subtracting 1.49 from both sides of the equation, and then dividing both sides by 1.25. The solution to the equation was that she needs to sell 78.8 bottles of water and 1.49 bottles of iced tea in order to earn $100.

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The statements about the right - triangle that are true are:
AC > BC (Option B) ;and  AC < AB (Option D). This can be established using the open mouth theorem and the law of sines.

A right triangle is a type of triangle that has one angle measuring 90 degrees. The side opposite the right angle is the longest side and is called the hypotenuse.

The Open Mouth Theorem states that in any triangle, the side opposite the largest angle is the longest side. Therefore, in triangle ABC with angle measures of 90°, 60°, and 30°, the side opposite the 90° angle is the longest side.

Let the side opposite the 90° angle be labeled as c, the side opposite the 60° angle be labeled as b, and the side opposite the 30° angle be labeled as a. By the Open Mouth Theorem, we know that c is the longest side.

To show that b is longer than a, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all three sides. That is,

a/sin(30°) = b/sin(60°) = c/sin(90°)

Since sin(30°) = 1/2 and sin(60°) = √3/2, we can write:

a/(1/2) = b/(√3/2) = c/1

Simplifying, we get:

a = c/2 and b = c√3/2

Therefore, we can see that b is longer than a since b = c√3/2 > c/2 = a√3.

Thus, we have shown that the side provided by the ∠90° is greater than the side provided by the ∠60°, and the side provided by the ∠60° is greater than the side provided by the ∠30°, using the Open Mouth Theorem and the Law of Sines.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

On a piece of paper, use a protractor to construct △ABC with m∠A = 30° , m∠B = 60°, and m∠C = 90°.

Which statements about the triangle are true?

A. AC > AB

B. AC > BC

C. AC < BC

D. AC < AB

The probability that Brian does not win as required is; -2 / (n - 2).

As evident from the task content; the probability that Brian wins a raffle is given by the expression;

n / (n + 2)

Hence, it can be inferred from convention that the probability that Brian does not win is given by;

P (not win) = 1 - n / (n - 2)

Hence, when expressed as a single fraction; we have that;

P (not win) = (n - 2 - n) / (n - 2)

P (not win) = -2 / (n - 2)

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Using perimeter fοrmula , 521 ft tabe is used tο cοver baseball cοurt.

The whοle length οf a shape's bοundary is referred tο in geοmetry as the perimeter οf the shape. Adding the lengths οf all the sides and edges that surrοund a fοrm yields its perimeter. It is calculated using linear length units such centimetres, metres, inches, and feet.

Here the basketball cοurt is cοmbined with twο half circle , οne circle and οne rectangle.

In the rectangle , Length = 94ft and width = 44ft.

Perimeter οf rectange = 2(length+width) = 2(94+44) = 2*138 = 276 ft.

In the half circle , Diameter = 44 ft  then radius = 44/2 = 22ft

Perimeter οf circle = πr+d = 3.14*22+44 =113.08 ft

Nοe , In the circle , Diameter = 12ft ,then radius = 12/2=6 ft.

perimeter οf circle = πd = 3.14*6=18.84 ft

Then Tοtal perimeter = 276+113.08+113.08+18.84 = 521 ft.

Hence 521 ft tabe is used tο cοver baseball cοurt.

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The linear equation in the point slope form for the online hockey game tickets is: y = 32.5x + 11.95.

The slope of a line and any points it contains determine the point-slope form of the line.

When a point mostly on line as well as the slope are provided, the form's objective is to represent the equation of the complete line. For instance, in calculus, the line tangent to a variable at a specific x-value can be described using point-slope form.

Given data:

cost for 5 tickets =  $174.45 : (5, 174.45)

cost for 8 tickets =  $$271.95 : (8, 271.95)

Slope m = (271.95 - 174.45)/(8 - 5)

m = 32.5

Consider point (x1, y1) = (5, 174.45)

Standard equation of point slope:

y - y1 = m(x - x1)

y - 174.45 = 32.5(x - 5)

y = 32.5x -5*32.5 + 174.45

y = 32.5x + 11.95

Thus, linear equation in the point slope form for the online hockey game tickets is: y = 32.5x + 11.95.

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Answer:

182

Step-by-step explanation:

A= 1/2r^2Θ

= 1/2π *81*4π/3

=58π

=58*22/7

= 182

Answer: 169.65

Step-by-step explanation:

Area of circle = πr² =  81π

Acute angle of TVU = 360 - 240 = 120°

Area of sector TVU = [tex]\frac{120}{360} \pi \times 9^2[/tex] = 27π

Shaded area = 81π - 27π = 54π = 169.65

Factοring is the prοcess οf reversing the distributive prοperty sο that a pοlynοmial can be written as the prοduct οf simpler pοlynοmials is true.

Factοring is the prοcess οf finding the factοrs οf a pοlynοmial, that is, rewriting the pοlynοmial as the prοduct οf simpler pοlynοmials. The distributive prοperty is used in reverse during the factοring prοcess tο find the cοmmοn factοrs οf a pοlynοmial.

Fοr example, cοnsider the pοlynοmial expressiοn [tex]2x^2 + 6x[/tex]. We can factοr οut a cοmmοn factοr οf 2x tο get:

2x(x + 3)

This is the reverse οf the distributive prοperty, which is used tο expand expressiοns. In this case, we are taking the cοmmοn factοr 2x and distributing it tο each term οf the pοlynοmial tο write it as a prοduct οf simpler pοlynοmials.

Factοring is an impοrtant skill in algebra and calculus because it helps simplify expressiοns and sοlve equatiοns. It is alsο used in many οther areas οf mathematics and science, including number theοry, graph theοry, and physics.

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Answer:

  about $10

Step-by-step explanation:

You want the difference in interest earned after 5 years between an account earning 4.3% compounded quarterly and one earning 4% compounded continuously when the investment in each is $590.

The account balance when interest is compounded quarterly for t years is ...

  A = P(1 +r/4)^(4t) . . . . . P is the principal invested at annual rate r

The account balance with interest is compounded continuously for t years is ...

  A = Pe^(rt)

The attached calculator screen shows the account balances for an investment of $590 for 5 years in accounts earning 4.3% compounded quarterly and 4% compounded continuously.

Scarlett's account, compounded quarterly, earns about $10 more interest over 5 years than does Ajay's account compounded continuously.

Answer:13

Step-by-step explanation:

Let's represent the number of students as "S" and the number of rooms as "R".

From the problem, we can set up the following system of equations:

Equation 1: 3S + 20 = R

Equation 2: S + 2 = (1/3)R

We can solve for S and R by substituting Equation 1 into Equation 2:

S + 2 = (1/3)(3S + 20)

S + 2 = S + (20/3)

(2/3) = (20/3) - S

S = 18

Now we can substitute S = 18 into Equation 1 to solve for R:

3(18) + 20 = R

R = 74

Therefore, there are 18 students and 74 rooms in the boarding school.