37. Think About a Plan At a certain high school, 350 students are taking an algebra course. The ratio of boys to girls taking algebra is 33:37. How many more girls are taking algebra than boys? • How can you write a system of equations to model the situation? • Which equation will you solve for a variable in the first step of solving the system? Why? • How can you interpret the solution in the context of the problem?​

The optimal allocation is x = -1/2, y = 3/2, with a shadow price of 1.50.

To maximize profit, the firm needs to determine the optimal allocation of inputs x and y within the budget constraint of $100.

Let's assume the firm uses 'a' units of input x and 'b' units of input y. Since each unit of x costs $2 and each unit of y costs $3, the total cost constraint can be expressed as:

2a + 3b ≤ 100

To maximize profit, we need to differentiate the profit function P(x, y) with respect to both inputs and set the derivatives equal to zero:

∂P/∂x = 2y - 3 = 0 ---> y = 3/2

∂P/∂y = 2x + 1 = 0 ---> x = -1/2

However, x and y cannot have negative values, so these values are not feasible. To find the feasible values, we can substitute the values of x and y into the cost constraint:

2(-1/2) + 3(3/2) = 0 + 9/2 = 9/2 ≤ 100

This constraint is satisfied, so the feasible allocation is x = -1/2 and y = 3/2.

To find the shadow price, we need to determine the rate at which the maximum profit would change with respect to a one-unit increase in the budget constraint. We can do this by finding the derivative of the profit function with respect to the cost constraint:

∂P/∂(2a + 3b) = λ

Where λ represents the shadow price or the marginal value of an additional dollar in the budget. In this case, λ is the shadow price.

Taking the derivative of the profit function with respect to the cost constraint:

∂P/∂(2a + 3b) = ∂(2xy - 3x + y)/∂(2a + 3b) = 0

2y - 3 = 0 ---> y = 3/2

Thus, the shadow price (λ) is 3/2 or 1.50 when rounded to two decimal places.

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The range of the given graph is [5, ∞).

Range.

Range refers the set of possible output values, and if we have the graph, then the set of all possible y values on the graph is defined as the range.

Given,

Here we have the graph.

Through the given graph we have to find the range of the line.

As per the definition of range, we have identified that the range take the value of y axis.

While we lookin into the given graph, we have identified that the starting point of the line is

=> (0, 5)

In this point 0 refers the x coordinate and 5 refers the y coordinate. So, the starting range is 5.

And the end of the line is not pointed.

So, we can consider that this line goes infinitely.

So, the range of the graph is  [5, ∞).

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y varies directly as x means

\(y=kx\)

y varies inversely with z means

\(y=k\div z\)

therefore

\(y=(kx^2)\div z\)

k=constant of variation

\(6=(k9^2)\div 27\)

\(6=(k81)\div27\)

\(6=3k\)

divide both sides by 3

\(2=k\)

the constant of variation is 2

If the quantity y varies directly with the square of x and inversely with z, then we can write the following equation:

What is equation ?

A assertion that two mathematical expressions are equal is known as an equation. It typically consists of variables, constants, and mathematical operations, and it may also include functions, exponents, and other mathematical symbols. Equations are used to represent relationships between quantities in mathematics and to solve problems in various fields such as physics, engineering, and economics.

y = k * (x^2) / z

where k is the constant of variation.

We are given that when x is 9, z is 27, and y is 6. Substituting these values into the equation, we get:

6 = k * (9^2) / 27

Simplifying, we get:

6 = k * 3

k = 6 / 3

k = 2

Therefore, the constant of variation is 2.
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Answer: is 5/4

Step-by-step explanation:

Writing as a fraction of the expression 3/4+1/2 with the fraction calculator

To calculate the addition fraction, the fractions are reduced to a common denominator and then added numerators.

We obtain 3/4+1/2=3⋅2+44⋅2

The GCD of the fraction is equal to 2.

By dividing the numerator and denominator by the GCD, we obtain: 10/8=5/4

The result of the calculation is : 3/4+1/2=54

Possible calculations with the fraction: 5/4

Answer:

what could be written?

Answer:

The correct answer is 7¹⁰

Step-by-step explanation:

I think you wrote 1.7 because i wrote 1. 7¹⁰

but I meant that 1. as the first question i was answering, sorry if I wasn't clear

Answer:

❘-40 - 140❘

Step-by-step explanation:

Given that,

Franky’s SAT score was 140 points above the average score.

Francesca’s SAT score was 40 points below the average score.

We need to find the expression that represents the difference in their scores. It can be calculated as follows :

d = ❘-40 - 140❘

= -180

Hence, the correct option is (A) "❘-40 - 140❘".

The range is the set between all of the possible output values, which always shown on y-axis by identify any given domain and then finding the range of any functions is by taking graphs into consideration.

To discover the area and variety, we without a doubt remedy the equation y = f(x) to decide the values of the unbiased variable x and gain the area. To calculate the variety of the feature, we without a doubt explicit x as x=g(y) after which discover the area of g(y).

Because the area refers back to the set of viable enter values, the area of a graph includes all of the enter values proven at the x-axis. The simplest approach of locating the variety of a feature, say y = f(x), is to explicit x as g(y) and pick out the area set for g(y). This might be the variety for the given feature f(x).

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Answer:

$1417.50+$4500= 5917.50

Answer:

She wont think it is perfect

Step-by-step explanation:

The ratio of Ari's perfect ice cream is

333 caramel : 555 scoops

Freeze zone ratio is

666:888

Not proportional because you multiply 333 x 2 to get 666, but when you multiply 555 x 2 you wont get 888.

And tell her to cut down on the sugar.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

A

Step-by-step explanation:

Answer:

3X3/2 is greater

Step-by-step explanation:

Go left to right and solve the equations.

Equation 1: 3 multiplied by 3 is 9. 9 divided by 2 is 4.5

Equation 2: 3 multiplied by 2 is 6. 6 divided by 3 is 2

Equation 1 yields a greater value.

Answer:

The 3x3/2 is greater than 3x2/3

Step-by-step explanation:

Here is a simple tip when solving these questions:

Decimal form is always great to use because you get the answer instantly instead of finding a common denominator while involving fractions.

Let's solve 3x3/2.

First, do 3x3 which is 9.

Your problem should be 9/2

Now, you could do this as a mixed number but like I said there shall be more work so you should do 9/2 on a calculator or divide but involve decimal point if you have a remainder.

9 divided by 2 is 4.5

9/2 is 4.5 (Above is the interpretation in words)

Next, do 3x2/3

The same thing as last, do 3x2 first.

Your problem should be 6/3  

If we know our division facts then 6 divided by 3 is 2.

Lastly, compare our numbers.

The 3x3/2 is 4.5 and the 3x2/3 is 2
Line the numbers up:

4.5

2.0

The tens digit clearly shows that 4 is greater than 2.

Therefore,

The 3x3/2 is greater than 3x2/3

The length and the width include the following:

L = 21.5 km.

W = 7.5 km.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

Since the length is 1 km. less than 3 times the width, we have:

L = 3W - 1

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

62 = 2(3W - 1 + W)

62 = 2(4W - 1)

31 = 4W - 1

W = 30/4

W = 7.5 km.

For the length, we have:

L = 3(7.5) - 1

L = 21.5 km.

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The current, i, to the capacitor is given by i = -2e^(-2t)cos(t) Amps.

To find the current, we need to differentiate the charge function q with respect to time, t.

Given q = e^(2t)cos(t), we can use the product rule and chain rule to find the derivative.

Applying the product rule, we have:

dq/dt = d(e^(2t))/dt * cos(t) + e^(2t) * d(cos(t))/dt

Differentiating e^(2t) with respect to t gives:

d(e^(2t))/dt = 2e^(2t)

Differentiating cos(t) with respect to t gives:

d(cos(t))/dt = -sin(t)

Substituting these derivatives back into the equation, we have:

dq/dt = 2e^(2t) * cos(t) - e^(2t) * sin(t)

Simplifying further, we get:

dq/dt = -2e^(2t) * sin(t) + e^(2t) * cos(t)

Finally, rearranging the terms, we have:

i = -2e^(-2t) * sin(t) + e^(-2t) * cos(t)

Therefore, the current to the capacitor is given by i = -2e^(-2t) * sin(t) + e^(-2t) * cos(t) Amps.

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To rotate a point 180° clockwise about the origin, we essentially need to flip the point across the x-axis and then across the y-axis. So the x-coordinate of point A' is -3.

This means that the x-coordinate of the point will become its opposite (negation) and the y-coordinate of the point will also become its opposite.

So, in this problem, we have the point A with coordinates (3, 2). To rotate this point 180° clockwise about the origin, we will negate both the x and y coordinates of the point:

The negation of 3 is -3, so the new x-coordinate of the point will be -3.

The negation of 2 is -2, so the new y-coordinate of the point will be -2.

Putting these together, we get the new coordinate of the point A' as (-3, -2).

So the x-coordinate of point A' is -3.

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Ria and Sharan drank drank equal amount of milk

Given data

Ria drinks x number of glasses of milk, each containing y mL each day

Sharan drinks 2x number of glasses of milk, each containing -y/2)} mL each day

Ria

x glass contains y ml. hence Ria took xy ml of milk each day

Sharan

2x glass contains y/2 ml. hence Sharan took xy ml of milk each day

comparing both shows that they both contains xy ml of milk each day. Therefore Ria and Sharan took equal amount of milk each day

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Answer:

(m+n)(x+y)

Step-by-step explanation:

First, factor out the x from the first two terms and factor out the y from the last two terms:

x(m+n)+y(m+n)

Now, factorize (m+n) out from both numbers:

(m+n)(x+y)

Answer:

Division :)

Hope this helps!

Answer:

1024 pi

Step-by-step explanation:

r = 32 units.

Area = pi * r^2

Area = 3.14 * 32^2

Area = 1024 * pi

Tt = pi??

Answer:

The equation will be "\(y=-2.8 x+75\)".

Step-by-step explanation:

The given values are:

Started with,

= 75 gallons

After 15 hrs,

Tank has,

= 33 gallons

Now,

The slope will be:

=  \(\frac{33-75}{15}\)

=  \(\frac{-42}{15}\)

=  \(-2.8\)

Thus,

The equation is "\(y=-2.5x+75\)".

That year FTE was 26.

According to statement

Labor hours worked that year = 55,267

Total number of hours paid that year = 59,995

The total number of hours during the year

8 hours × 5 days × 52 weeks = 2080 hours

Now we find the FTE per year

So, FTE/YEAR = Labour works on that year / total number of hours in year

Substitute the values in it then

FTE/YEAR = 55267/2080

FTE/YEAR = 26

So, That year FTE was 26.

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The sample variance and standard deviation of the data sample, follow these steps:

1. Calculate the mean (average) of the data set.
2. Subtract the mean from each data point and square the result.
3. Add up the squared differences.
4. Divide the sum by the total number of data points minus 1 (n-1) for sample variance.
5. Take the square root of the variance to find the standard deviation.

Given data set: -6, 7, 7, 7, 15

1. Mean:\( (-6 + 7 + 7 + 7 + 15) / 5 = 30 / 5 = 6\)
2. Squared differences: \([(-6 - 6)^2, (7 - 6)^2, (7 - 6)^2, (7 - 6)^2, (15 - 6)^2] = [144, 1, 1, 1, 81]\)
3. Sum of squared differences:\( 144 + 1 + 1 + 1 + 81 = 228\)
4. Sample variance: \(228 / (5 - 1) = 228 / 4 = 57\)
5. Standard deviation: \(√57 ≈ 7.55\)

Therefore, the sample variance is 57, and the standard deviation is approximately 7.55, rounded to two decimal places.

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Answer:

0.04

is what the answer should be

Step-by-step explanation:

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 8000\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 8000\left(1+\frac{0.028}{1}\right)^{1\cdot 4}\implies A=8000(1.028)^4 \implies A \approx 8934.34\)

Answer:

5/100×$1500= 75 dollar

as it is annual income we can solve the answer relative to year and considering it as 1 so the interest would be 75 annually

For the given Z-transform X(z) = 2 + 3z^(-1) + 4z^(-2), the initial value and final value of the corresponding sequence x(n) can be determined. The initial value of x(n) is 2, and the final value of x(n) is 0.

To find the initial value of the sequence x(n), we need to calculate the coefficient of z^0 in the Z-transform X(z). In this case, the coefficient of z^0 is 2, so the initial value of x(n) is 2. To determine the final value of the sequence x(n), we need to evaluate the limit as z approaches infinity. Since the Z-transform X(z) is a rational function, the final value of x(n) can be found by evaluating the limit of the numerator divided by the limit of the denominator as z approaches infinity. In this case, as z approaches infinity, the terms 3z^(-1) and 4z^(-2) become negligible compared to the constant term 2. Therefore, the final value of x(n) is 0. In summary, the initial value of x(n) is 2, indicating the value of the sequence at n = 0, and the final value of x(n) is 0, indicating the value of the sequence as n approaches infinity.

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Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Answer:

Step-by-step explanation:

complex numbers , real numbers , rational numbers , natural numbers , whole numbers

Answer:

Any value you choose for x will make the equation a TRUE statement. This type of equation is called an identity, and the solution set is all real numbers.

An identity is an equation that, regardless of the values used, is always true.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

An identity is an equation that, regardless of the values used, is always true.

For the linear equation y = mx + c, all the values of the variable x are real numbers because the quadratic function is defined.

For the quadratic equation y = (x - h)² + k, all the values of the variable x are real numbers because the quadratic function is defined.

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