Find the linear trend forecast for period 8 given the following data:  Period            Sales 1                     19 2                     18 3                     15 4                     20 5                     18 6                     22  7                     20

Answer:

I am not entirely sure what you are asking, but I believe the answer is 4*2=8

Step-by-step explanation:

This is because:

8 increased by the product of a number and 4 is at most 20.

8      +                           p                               +    4    = 20

We are trying to find p.

8 +4= 12

20 - 12= 8

So I believe the answer is 8.

(If the answer is wrong, plz tell me in the comments)

Answer:

3

Step-by-step explanation:

eight increased by the product of a number and 4 is at most 20

these implies

8 + a x4 = 20

a is the number whose product with 4 is increased by eight to give at most 20

8 + a x4 = 20

8 + 4a = 20

subtract 8 from both sides

4a = 20 -8

4a= 12

divide both sides by 4

a = 12/4 = 3

the number is 3

Answer:

x+10

Step-by-step explanation:

An algebraic expression is an expression which consist of variables(whose values are not fixed like in the form of x,y,a,...), the constants and operators (like +,×,±,-,≤,≥,=,...).

Now for this question we have to give a an algebraic expression for 10 more than a number.

Let the number be x.

We have to show a relation of 10 more than the number. Thus are algebraic expression is of the form x+10.

Algebraic expression: x+10

where x is our variable

+ is our operator and

10 is a constant.

Answer:

Step-by-step explanation:

Given that there are 20 non ionized containers and 73 ionized containers

Two samples are drawn without replacement

a) the probability that the first one selected is not ionized=[tex]\frac{20}{93} =0.215[/tex]

b)  the probability that the second one selected is not ionized given that the first one was ionized

= When first one was ionized we got left over as 20 and 72

Hence = [tex]\frac{20}{92} =0.217[/tex]

c) If with replacement left over 20 and 73 and hence prob = 0.215 as in part a

d) the probability that both are ionized=[tex]\frac{73C2}{93C2} =0.614[/tex]

Answer:

The solution for this differential equation is [tex]y=\sqrt{-2cos(x)+6}[/tex]

Step-by-step explanation:

This differential equation [tex]\frac{dy}{dx}=\frac{sin(x)}{y}[/tex] is a separable First-Order ordinary differential equation.

We know this because a first-order differential equation is separable if and only if it can be written as

[tex]\frac{dy}{dx}=f(x)g(y)[/tex] where f and g are known functions.

And we have

[tex]\frac{dy}{dx}=\frac{sin(x)}{y}\\ \frac{dy}{dx}=sin(x)\frac{1}{y}[/tex]

To solve this differential equation we need to integrate both sides

[tex]y\cdot dy=sin(x)\cdot dx\\ \int\limits {y\cdot dy}= \int\limits {sin(x)\cdot dx}[/tex]

[tex]\int\limits {y\cdot dy}=\frac{y^{2} }{2} + C[/tex]

[tex]\int\limits {sin(x) \cdot dx}=-cos(x) + C[/tex]

[tex]\frac{y^{2} }{2} + C=-cos(x) + C[/tex]

We can make a new constant of integration [tex]C_{1}[/tex]

[tex]\frac{y^{2} }{2}=-cos(x) + C_{1}[/tex]

We need to isolate y

[tex]\frac{y^{2} }{2}=-cos(x) + C_{1}\\y^2=-2cos(x)+2*C_{1}\\\mathrm{For\:}y^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}y=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\y=\sqrt{-2cos(x)+c_{1} } \\y=-\sqrt{-2cos(x)+c_{1} }[/tex]

We have the initial conditions y(0)=2 so we can find the value of the constant of integration for [tex]y=\sqrt{-2cos(x)+c_{1} } [/tex]

[tex]2=\sqrt{-2\cos \left(0\right)+c_1}\\2= \sqrt{-2+c_1} \\c_1=6[/tex]

For [tex]y=-\sqrt{-2cos(x)+c_{1} } [/tex] there is not solution for [tex]c_{1}[/tex] in the domain of real numbers.

The solution for this differential equation is [tex]y=\sqrt{-2cos(x)+6}[/tex]

Answer:

$1895.64

Step-by-step explanation:

Given:

Principle for the first year = $100

rate of interest = 6% compounded monthly

thus,

rate per month, r = \frac{\etxtup{6}}{\textup{12}}= 0.5% = 0.005

Total time = 10 year\

Now,

for the first year

number of months, n = 12

Amount at the end of first year = Principle × ( 1 + r )ⁿ

on substituting the values, we get

Amount at the end of first year = 100 × ( 1 + 0.005 )¹²

or

Amount at the end of first year = $106.17

Therefore,

The principle amount for the consecutive years will be

= $1000 + Amount at the end of first year

=  $1000 + $106.17 = $1106.17

Thus, for the rest 9 years

n = 9 × 12 = 108

Principle = $1106.17

Final amount after the end of 10th year = Principle × ( 1 + r )ⁿ

or

Final amount after the end of 10th year = $1106.17 × ( 1 + 0.005 )¹⁰⁸

or

Final amount after the end of 10th year = $1895.64

Answer:$624

Total sales: $52 x 48 = $2,496

Cost of ingredients:  

$2,496

4

= $624

Step-by-step explanation:

$624

Total sales: $52 x 48 = $2,496

Cost of ingredients:  

$2,496

4

= $624

Answer:

The ingredients will cost $624 for all of the birthday cakes.

Step-by-step explanation:

This week the bakery has orders for 48 birthday cakes. Each cake sells for $52.

1/4 of each cake's selling price is spent on ingredients.

This becomes [tex]\frac{1}{4}\times52= 13[/tex] dollars

Hence, the total cost of ingredients for 48 cakes will be "

[tex]13\times48=624[/tex] dollars

Therefore, the ingredients will cost $624 for all of the birthday cakes.

Answer:

[tex]x^3-x^2.[/tex]

Step-by-step explanation:

The word "difference" represents a subtraction. Then the algebraic expression will be of the form a-b.

Now, the difference is between the cube of a number and the square of the number, then let's call the number x. The square of the number is raise to two. Then the square of the number is [tex]x^2[/tex].

The cube of the number is raise to three. Then the cube of the number is [tex]x^3[/tex].

So, the difference between the cube of a number and the square of the number (we are talking about the same number in the square and the cube) is [tex]x^3-x^2[/tex].

Answer:

0.000973236=m

Step-by-step explanation:

Given the question as;

7:(411m) = 56 : 3.2

7/411m =56/3.2

7×3.2=56×411m

(7×32)/(560×411)=m

224/230160=m

0.000973236=m

checking the answer

7: (411 *0.000973236) = 56: 3.2

7: (0.4)= 56 : 3.2

7/0.4 =56/3.2

70/4=560/32

17.5 =17.5

Answer and Explanation:

Given : [tex]P(n): 1 + 2 + 2^2 + 2^3 + . . . + 2^n = 2^{n+1} - 1[/tex], n=0,1,2,..

To find : The values of following expression ?

Solution :

The function is [tex]P(n)=2^{n+1} - 1[/tex]

1) Value of P(0),

[tex]P(0)=2^{0+1} - 1[/tex]

[tex]P(0)=2^{1} - 1[/tex]

[tex]P(0)=2 - 1[/tex]

[tex]P(0)=1[/tex]

2) Value of P(1),

[tex]P(1)=2^{1+1} - 1[/tex]

[tex]P(1)=2^{2} - 1[/tex]

[tex]P(1)=4- 1[/tex]

[tex]P(1)=3[/tex]

3) Value of P(2),

[tex]P(2)=2^{2+1} - 1[/tex]

[tex]P(2)=2^{3} - 1[/tex]

[tex]P(2)=8- 1[/tex]

[tex]P(2)=7[/tex]

4) Value of P(n+1),

[tex]P(n+1)=2^{n+1+1} - 1[/tex]

[tex]P(n+1)=2^{n+2} - 1[/tex]

Answer and Explanation:

Given : Sides of right triangle 5,12 and 13.

To find : Show that the area of a right triangle of sides 5, 12 and 13 cannot be a square ?

Solution :

If 5,12 and 13 are sides of a right angle triangle then

13 is the hypotenuse as it is largest side.

then we take perpendicular as 12 and base as 5.

The area of the right angle triangle is

[tex]A=\frac{1}{2}\times b\times h[/tex]

Here, h=12 and b=5

[tex]A=\frac{1}{2}\times 5\times 12[/tex]

[tex]A=5\times 6[/tex]

[tex]A=30[/tex]

The area of the right angle triangle is 30 units.

30 is not a perfect square as [tex]30=2\times 3\times 5[/tex]

There is no square pair formed.

Answer:

The amount in the account at the end of 8 years is about $8070.71.

Step-by-step explanation:

Given information:

Principal = $5000

Interest rate = 6% = 0.06 compounded monthly

Time = 8 years

The formula for amount after compound interest is

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where,

P is principal.

r is rate of interest.

n is number of times interest compounded in a year.

t is time in years.

Substitute P=5000, r=0.06, n=12 and t=8 in the above formula.

[tex]A=5000(1+\frac{0.06}{12})^{(12)(8)}[/tex]

[tex]A=5000(1.005)^{96}[/tex]

[tex]A=5000(1.61414270846)[/tex]

[tex]A=8070.7135423[/tex]

[tex]A\approx 8070.71[/tex]

Therefore the amount in the account at the end of 8 years is about $8070.71.

Final answer:

To find the equation of a line that passes through a given point and has a given x-intercept, we can use the point-slope form of a line.

Explanation:

To find the equation of a line that passes through the point (-8, 4) and has an x-intercept of -10, we can use the slope-intercept form of a line, which is y = mx + b.

First, let's find the slope of the line using the given information. The x-intercept represents the point where the line crosses the x-axis, so if the x-intercept is -10, we know that the point (-10, 0) is on the line.

Using the formula for slope, which is m = (y2 - y1) / (x2 - x1), we can calculate the slope of the line as (0 - 4) / (-10 - (-8)) = -4 / -2 = 2.

Now, we can use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Substituting the values (-8, 4) and m = 2 into the equation, we have y - 4 = 2(x - (-8)).

Simplifying the equation, we get y - 4 = 2x + 16.

Finally, isolating y, we arrive at the equation of the line: y = 2x + 20.

Answer:

The amount of nuclear fuel required is 1.24 kg.

Step-by-step explanation:

From the principle of mass energy equivalence we know that energy generated by mass 'm' in an nuclear plant is

[tex]E=m\cdot c^2[/tex]

where

'c' is the speed of light in free space

Since the power plant operates at 1200 MW thus the total energy produced in 1 year equals

[tex]E=1200\times 10^6\times 3600\times 24\times 365=3.8\times 10^{16}Joules[/tex]

Thus using the energy produced in the energy equivalence we get

[tex]3.8\times 10^{16}=mass\times (3\times 10^{8})^2\\\\\therefore mass=\frac{3.8\times 10^{16}}{9\times 10^{16}}=0.422kg[/tex]

Now since the efficiency of conversion is 34% thus the fuel required equals

[tex]mass_{required}=\frac{0.422}{0.34}=1.24kg[/tex]

Answer: A. 10% of the time, the population parameter will lie outside of the interval.

Step-by-step explanation:

If we have [tex]b\%[/tex] confidence interval is that we are [tex]b\%[/tex] certain that it contains the true population parameter in it.

Similarly , if  we have a 90% confidence interval for a population parameter, then we are 90% certain that it contains the true population parameter in it.

i.e. 10% not certain that it contains the true population parameter in it.

i.e. 10% of the time, the population parameter will lie outside of the interval.

Answer:  Amount after 5 years become $5937.60.

Step-by-step explanation:

Since we have given that

Principal amount = $5000

Time period = 5 years

Rate of interest for 3 years = 6%

Rate of interest for 2 years = 8%

so, Amount becomes

[tex]Amount=5000(1+\dfrac{6}{1000})^3(1+\dfrac{8}{100})^2\\\\Amount=5000(1+0.006)^3(1+0.08)^2\\\\Amount=5000(1.006)^3(1.08)^2\\\\Amount=\$5937.60[/tex]

Hence, Amount after 5 years become $5937.60.

Answer: P=8

Step-by-step explanation:

3p-5=19

U turn -5 to +5

Then u add 5 to both sides, -5 and 19

3p-5=19

+5=+5

-5 and +5 cancel each other out so know it’s

3p=24

Because 19 plus 5 is 24

Now u have to get the variable by itself by dividing 3 on both sides of the equal sign 3p and 24

3 and 3 cancel each other out so now you only have p=24 but then 24 divided 3 is 8

A population is the entire group of interest in a researcher's study, while a sample is a subset of this group from which data is collected. The aim is for the sample to be representative of the population to accurately draw generalizations. Effective sampling strategies and recruitment are vital for this representation.

To understand the concepts of population and sample in the context of statistics, we can differentiate between the two. Population refers to the entire group that is the focus of a researcher's study, which can be a broad group, like all adults over the age of 18 in the United States, or more specific, such as 'mid-season maturity corn plants on irrigated farms near Grand Island, Nebraska.'

A sample, on the other hand, is a subset of the population from which researchers actually collect data. It represents a smaller group selected to draw conclusions about the population. The validity of these conclusions often depends on how well the sample represents the population, aiming for the sample characteristics to match those of the population. For instance, if surveying the relative proportion of cars to trucks driving down a street, a sample observed during an uncharacteristic time of day may not provide a representative view of the overall traffic pattern.

In research, sampling strategies and recruitment techniques are important to ensure that the sample accurately reflects the population. For example, choosing individuals to participate in a study so that each has a known chance of being included makes for a better representation of the population. Researchers then analyze the sample data and attempt to generalize their findings to the entire population.

I assume the first equation is supposed to be

[tex]5x-3y+2z=13[/tex]

and not

[tex]5x-3x+2x=4x=13[/tex]

As an augmented matrix, this system is given by

[tex]\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\4&-2&4&12\end{array}\right][/tex]

Multiply through row 3 by 1/2:

[tex]\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\2&-1&2&6\end{array}\right][/tex]

Add -1(row 2) to row 3:

[tex]\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\0&0&5&5\end{array}\right][/tex]

Multiply through row 3 by 1/5:

[tex]\left[\begin{array}{ccc|c}5&-3&2&13\\2&-1&-3&1\\0&0&1&1\end{array}\right][/tex]

Add -2(row 3) to row 1, and add 3(row 3) to row 2:

[tex]\left[\begin{array}{ccc|c}5&-3&0&11\\2&-1&0&4\\0&0&1&1\end{array}\right][/tex]

Add -3(row 2) to row 1:

[tex]\left[\begin{array}{ccc|c}-1&0&0&-1\\2&-1&0&4\\0&0&1&1\end{array}\right][/tex]

Multiply through row 1 by -1:

[tex]\left[\begin{array}{ccc|c}1&0&0&1\\2&-1&0&4\\0&0&1&1\end{array}\right][/tex]

Add -2(row 1) to row 2:

[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&-1&0&2\\0&0&1&1\end{array}\right][/tex]

Multipy through row 2 by -1:

[tex]\left[\begin{array}{ccc|c}1&0&0&1\\0&1&0&-2\\0&0&1&1\end{array}\right][/tex]

The solution to the system is then

[tex]\boxed{x=1,y=-2,z=1}[/tex]

Answer:

2000ml = 2L of this IV fluid should be infused.

Step-by-step explanation:

This problem can be solved by a simple rule of three, in which the relationship between the measures is direct, which means that there is a cross multiplication.

The problem states that each 75 mg of the medication contains 500 ml of IV fluid. How many ml of IV fluid are there in 300 mg of the medication?

So

75mg - 500ml

300 mg - x ml

[tex]75x = 300*500[/tex]

[tex]x = \frac{300*500}{75}[/tex]

[tex]x = 4*500[/tex]

[tex]x = 2000[/tex]ml

2000ml = 2L of this IV fluid should be infused.

To administer 300 mg of Drug B, given that 75 mg is in 500 ml of IV fluid, you need infuse 2000 ml of the IV fluid. This was calculated using proportional relationships based on the concentration of the drug in the fluid.

To determine how much IV fluid should be infused to provide the patient with 300 mg of Drug B, we can use a simple proportion based on the concentration of the drug in the IV fluid.

0.15 mg/ml = 300 mg / X ml

Solving for X, we get:

X = 300 mg / 0.15 mg/ml

X = 2000 ml

Thus, 2000 ml of the IV fluid should be infused to provide the patient with 300 mg of Drug B.

The actual movement of the boat is calculated by adding the vectors representing the velocity of the boat and the water current. The net vector shows both the speed and direction of the actual movement.

The actual movement of the boat is determined by adding vectorially, the velocity of the boat and the velocity of the current. This is because we need to consider both the speed and direction of the boat (traveling due east) and the current (flowing southwest).

Let's assume East as +i direction, and North as +j direction. So, the velocity of the boat is 22i km/hr and the velocity of the current is -10i/√2 -10j/√2 km/hr (as it is moving southwest).

To find the net velocity or actual movement, we add these two vectors.

Resultant velocity = 22i -10i/√2 -10j/√2 // Adding the i-components and the j-components

 = (22 -10/√2)i -10/√2 j km/hr

Therefore, the actual movement of the boat is (22 -10/√2)i -10/√2 j km/hr.

https://brainly.com/question/31940047

Answer:

[tex]1.167 km[/tex]

Step-by-step explanation:

We are given with-

Height of airplane from water [tex]a[/tex] = [tex]425 m[/tex]

Angle of depression (∅)= 20°

Now,

[tex]tan(20) = \frac{b}{a}[/tex]

[tex]a = \frac{b}{tan(20)} \\a = \frac{425}{tan(20} \\a = 1167.677 m[/tex]

[tex]a = 1.167 km[/tex]

Answer:

  5/2

Step-by-step explanation:

You want to find x when f(x) = 4

  4 = 2x -1

  5 = 2x . . . . . add 1

  5/2 = x . . . . . divide by 2

The input corresponding to an output of 4 is 5/2.

Answer:

The correct option is B) The study is an observational study because the survey subjects were not given any treatment.

Step-by-step explanation:

Consider the provided information.

In a study sponsored by a​ company, 12,543 people were asked what contributes most to their happiness, and 87% of the respondents said that it was their job.

Observational study is the study in which observer only observe the subjects, and measure variables of interest without allocating treatments to subjects.

Experiment study is the study in which the researchers are applying treatments to experimental units in the research, then the effect of the treatments on the experimental units is observed.

Now consider the provided statement.

The research is based on information that nobody manipulates any experimental variables.

Hence, the study is an observational study where no treatment is given.

Thus, the correct option is B) The study is an observational study because the survey subjects were not given any treatment.

Answer:

They collected $12.73 in all.

Step-by-step explanation:

This problem can be solved by a simple system of equations.

I am going to say that x is the quantity that Travis collects, y the quantity that Jessica collects and z the quantity that Robin collects.

The problems asks how much money did they collect in all?

So [tex]T = x + y + z[/tex]

Solution

The problem states that Travis wants to collect 20% more than Jessica, so:

[tex]100%x = (100%+ 20%)y[/tex]

[tex]100%x = 120%y[/tex]

[tex]x = 1.2y[/tex]

Robin wants to collect 35% more than Travis, so:

[tex]100%z = (100%+35%)x[/tex]

[tex]100%z = 135%x[/tex]

[tex]z = 1.35x[/tex]

Travis collects $4, so [tex]x = 4[/tex]. So:

[tex]x = 1.2y[/tex]

[tex]1.2y = 4[/tex]

[tex]y = \frac{4}{1.2}[/tex]

[tex]y = 3.33[/tex]

------------

[tex]z = 1.35x = 1.35(4) = 5.40[/tex]

The total is:

[tex]T = x + y + z = 4 + 3.33 + 5.40 = $12.73[/tex]

They collected $12.73 in all.

Answer:

[tex]\lim_{x\rightarrow \infty}C=C[/tex]

Step-by-step explanation:

We are given that f(x)=c=Constant for all x in R

We have to find that why  f(x) not equal to zero when x approaches to zero.

[tex]\lim_{x\rightarrow \infty}f(x)[/tex]

[tex]\lim_{x\rightarrow \infty}C=C[/tex] not equal to zero

We are given that function which is constant for all x in R.

When x approaches then the value of function does not change. it remain same for all x in R because function is constant.

Hence, when x tends to infinity then f(x) is not equal to zero.

Answer:

The average rate of change of the population on the intervals [ 5 , 10 ] , [ 5 , 9 ] , [ 5 , 8 ] , [ 5 , 7 ] , and [ 5 , 6 ]  are 734.504, 733.06, 731.62, 730.185 and 728.75 respectively.

Step-by-step explanation:

The given function is

[tex]P(t)=181843(1.04)^{(\frac{t}{10})}[/tex]

where, P(t) is population after t years.

At t=5,

[tex]P(5)=181843(1.04)^{(\frac{5}{10})}=185444.20[/tex]

At t=6,

[tex]P(6)=181843(1.04)^{(\frac{6}{10})}=186172.95[/tex]

At t=7,

[tex]P(7)=181843(1.04)^{(\frac{7}{10})}=186904.57[/tex]

At t=8,

[tex]P(8)=181843(1.04)^{(\frac{8}{10})}=187639.06[/tex]

At t=9,

[tex]P(9)=181843(1.04)^{(\frac{9}{10})}=188376.44[/tex]

At t=10,

[tex]P(10)=181843(1.04)^{(\frac{10}{10})}=189116.72[/tex]

The rate of change of P(t) on the interval [tex][x_1,x_2][/tex] is

[tex]m=\frac{P(x_2)-P(x_1)}{x_2-x_1}[/tex]

Using the above formula, the average rate of change of the population on the intervals [ 5 , 10 ] is

[tex]m=\frac{P(10)-P(5)}{10-5}=\frac{189116.72-185444.20}{5}=734.504[/tex]

The average rate of change of the population on the intervals [ 5 , 9 ] is

[tex]m=\frac{P(9)-P(5)}{9-5}=\frac{188376.44-185444.20}{4}=733.06[/tex]

The average rate of change of the population on the intervals [ 5 , 8 ] is

[tex]m=\frac{P(8)-P(5)}{8-5}=\frac{187639.06-185444.20}{3}=731.62[/tex]

The average rate of change of the population on the intervals [ 5 , 7 ] is

[tex]m=\frac{P(7)-P(5)}{7-5}=\frac{186904.57-185444.20}{2}=730.185[/tex]

The average rate of change of the population on the intervals [ 5 , 6 ] is

[tex]m=\frac{P(6)-P(5)}{6-5}=\frac{186172.95-185444.20}{1}=728.75[/tex]

Therefore the average rate of change of the population on the intervals [ 5 , 10 ] , [ 5 , 9 ] , [ 5 , 8 ] , [ 5 , 7 ] , and [ 5 , 6 ]  are 734.504, 733.06, 731.62, 730.185 and 728.75 respectively.

Answer:

$2,850,000

Step-by-step explanation:

Data provided in the question:

Investment amount asked for by the company = $950,000

Exchange of equity = 25%

Now,

Equity exchanged = [tex]\frac{\textup{Amount invested}}{\textup{Post money evaluation}}\times100[/tex]

or

Post money evaluation = [tex]\frac{\textup{950,000}}{\textup{25}}\times100[/tex]

or

Post money evaluation = $3,800,000

Therefore,

Implied valuation = Post money evaluation - Amount invested

or

Implied valuation = $3,800,000 - $950,000 = $2,850,000

Answer:

Step-by-step explanation:

Given that an experimenter is studying the effects of temperture, pressure, and type of catalyst on yield from a certain chemical reaction. Three different temperatures, four different pressures, and five different catalysts are under consideration.

a) Experimental runs possible if use of single temperature, pressure and catalyst is there = no of temperatures x no of pressures x no of catalysts

= [tex]3*4*5 = 60[/tex]

b) Here pressure and temperature have no choice as lowest is selected.

no of methods = no of catalysts x 1 x1

= 5

Answer: The ratio of boys to girls would be 3 : 5 .

Step-by-step explanation:

Since we have given that

Number of boys and girls = 32

Fraction of boys are going on a field trip = [tex]\dfrac{2}{3}[/tex]

Fraction of girls are going on a field trip = [tex]\dfrac{3}{4}[/tex]

Number of children left = 9

Let the number of boys be 'b'.

Let the number of girls be 'g'.

According to question, it becomes ,

[tex]b+g=32------------(1)\\\\32-9=\dfrac{2}{3}b+\dfrac{3}{4}g\\\\23=\dfrac{2b}{3}+\dfrac{3g}{4}-------------(2)[/tex]

From eq(1), we get that g = 32-b

So, it becomes,

[tex]\dfrac{2}{3}b+\dfrac{3}{4}(32-b)=23\\\\\dfrac{2}{3}b+24-\dfrac{3}{4}b=23\\\\\dfrac{2}{3}b-\dfrac{3}{4}b=23-24=-1\\\\\dfrac{8b-9b}{12}=-1\\\\\dfrac{-b}{12}=-1\\\\b=-1\times -12\\\\b=12[/tex]

so, number of girls would be 32 - b = 32 - 12 = 20

So, Ratio of boys to girls in class would be 12 : 20 = 3 : 5.

Therefore, the ratio of boys to girls would be 3 : 5 .