bc = ad

solve for a

Answer:

To raise the maximum amount of money, 120 adults and 60 students should attend.

Step-by-step explanation:

Let x be the number of adults attending the program.

Let y be the number of students attending the program.

From the given constraints, we can form the following inequalities:

The theater can hold a maximum of 180 people.

For every two adults, there must be at least one student. So the number of students attending the event must be greater than or equal to half the number of adults attending the event.

The number of students and adults must be greater than or equal to zero.

Given the admission is $8.00 for adults and $4.00 for students, the expression for the total amount of money raised, z, is:

z = 8x + 4y

To maximize the value of z, first graph the inequalities and find the feasible region. (The feasible region is the region that is shaded by all of the inequalities).

The corner points of the feasible region are the points of intersection of the boundary lines.

The feasible region is bounded by the corner points:

Evaluate the objective function z = 8x + 4y at each of these corner points:

Point (0, 0):  z = 8(0) + 4(0) = 0

Point (0, 180):  z = 8(0) + 4(180) = 720

Point (120, 60):  z = 8(120) + 4(60) = 1200

Therefore, the maximum value of z is 1200, which occurs at the corner point (120, 60).

Therefore, the maximum amount of money that can be raised is $1,200.

To raise the maximum amount of money, 120 adults and 60 students should attend.

z+6>3 minus 6 from both sides

z>-3

2z<-12 divide both sides by 2

z<-6

Then substitute the z values into one inequality

-3<z<-6

This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

Ratio refers to the quantitative relationship between two or more quantities, expressing the proportion of one quantity to the other(s). It is typically expressed as a fraction, where the numerator represents one quantity, and the denominator represents the other quantity.

For example, the ratio of the number of boys to the number of girls in a class of 30 students might be expressed as 2:3, which means there are 20 girls and 10 boys in the class. Similarly, the ratio of the length to the width of a rectangle might be expressed as 4:3, indicating that the length is four times greater than the width.

The ratio of sheep to horses is 4:1, which means that for every 4 sheep on the farm, there is 1 horse. We can also say that the total ratio of sheep and horses on the farm is 4+1=5.

To express the relationship between the chickens and the sheep, we need to use the fact that there are 32 chickens and 12 sheep on the farm. We can write this as a ratio:

\(chickens : sheep = 32 : 12\)

We can simplify this ratio by dividing both sides by 4:

\(chickens: sheep = 8: 3\)

This means that for every 8 chickens on the farm, there are 3 sheep.

To determine the number of horses on the farm, we can use the fact that the total ratio of sheep and horses is 5. We know that the ratio of sheep to horses is 4:1, so we can write:

\(sheep : horses = 4 : 1\)

We can simplify this ratio by dividing both sides by 4:

\(sheep : horses = 1 : 0.25\)

This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

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On solving the provided question, we can say that Area of Rhombus is 24 cm²

A rhombus is an equal-sided quadrilateral in Euclidean plane geοmetry. The term "equilateral triangle" alsο refers to a quadrilateral whose sides are of the same length. A parallelοgram has a unique variation knοwn as a rhombus. In a rhombus, the οpposite sides and angles are parallel and equal.

A rhombus's diagοnal is split in half by a right angle, and each of its sides is the same length. Rhombic diamοnds and diamonds are other names for rhοmbuses. The length οf every side is the same. Diagοnals are equal in a rhοmbus. At a 90° angle, parallel lines split in half, 180 degrees is the sum of adjacent angles.

By distance formula

BD = \(\sqrt{(-2-4)^2 + (-1-5)^2}\)

BD = \(\sqrt{36 + 36}\)

BD = 6√2

similarly,

AC = 4√2

and, Area = 1/2 × (product of diagonals)

Area of Rhombus = 1/2 × 6√2 × 4√2 = 24 cm²

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nose si entendí bien el problema pero espero poder ayudar

Step-by-step explanation:

8 es igual a 100%, por lo que podemos guardarlo como 8 = 100% El valor que buscamos puede llamarse x Ahora sabemos que xes 72 del valor de salida, por lo que podemos escribirlo como x = 72. Así que tenemos dos ecuaciones simples: 1) 8=100% 2) = 72%Cuando comparamos estas dos ecuaciones, obtenemos: 8 / x = (100%) / (72%)Ahora solo tenemos que resolver la ecuación simple. Nosotros calculamos 72 por ciento de 8: 8 / x = 100/72(8 / x) * x = (100/72) * x8 = 1,3888888888889 * X8 / 1.3888888888889 = X5.76 = xx = 5,76

Answer:

Step-by-step explanation:

Hello, we want to prove that a proposition depending on n, that we can note P(n), is true for any n positive integer greater than 1. We need to follow several steps.

Step 1 - prove P(1)

For n = 1, n(2n+1)=1*3 =3 so we have

3 = 3, which is obviously true.

First step done!

Step 2 - for \(k\geq 1\) we assume P(k) and we need to prove P(k+1)

We assume that 3+7+11+...+(4k-1)=k(2k+1)

so we can write that

3+7+11+...+(4k-1)+(4(k+1)-1)=k(2k+1)+(4k+4-1)=k(2k+1)+4k+3

\(=2k^2+k+4k+3\\\\=2k^2+5k+3\)

and

(k+1)(2(k+1)+1)=(k+1)(2k+3)

\(=k(2k+3)+2k+3\\\\=2k^2+3k+2k+3\\\\=2k^3+5k+3\)

These two expressions are the same so it means that P(k+1) is true, meaning that

3+7+11+...+(4k-1)+(4(k+1)-1)=(k+1)(2(k+1)+1)

Step 3 - The conclusion

Finally, we have just proved that

3+7+11+...+(4n-1)=n(2n+1) for any n positive integer > 0

Thank you

The given sum of arithmetic progression series 3+7+11+... (4n-1) = n(2n+1) is true.

The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).

The arithmetic progression has wider use in mathematics for example sum of natural numbers.

Natural number = 1,2,3,4,5,6,7,8...

Now it has the same difference between any two consecutive terms d =2-1 = 3-2.

The Sum of n terms of an AP is given by,

S= n/2[2a + (n-1)d ] where a is first term and d is common difference.

In our series 3+7+11+... (4n-1)

First term (a) = 3

Common difference (d) = 7 - 3 = 4

So the sum will be

S = n/2[2(3) + (n-1)4]

S = n[3 + 2(n - 1)]

S = n (2n + 1 ) = Right hand side.

Hence "The given sum of arithmetic progression series 3+7+11+... (4n-1) = n(2n+1) is true".

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the answer is d just did it

The domain of (boa)(x) is [1, ∞].

In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular equation or function is defined.

Based on the information provided above, we have the following functions:

a(x) = 3x+1

\(b(x) = \sqrt{x-4}\)

Therefore, the composite function (boa)(x) is given by;

\(b(x) = \sqrt{3x+1 -4}\\\\b(x) = \sqrt{3x-3}\)

By critically observing the graph shown in the image attached below, we can logically deduce the following domain:

Domain = [1, ∞] or {x|x ≥ 1}.

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Answer:

552

Step-by-step explanation:

23×4=92

3×2=6

6×92=552

IF I'M WRONG I'M SORRYYYY :V

Answer:

Step-by-step explanation:

The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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An expression for given sequence of operations is: j + 3^9

In this question, we need to write an expression for the sequence of operations described below.

raise 3 to the 9th power, then add the result to j

Consider the part of given statement,

raise 3 to the 9th power

We write this as: 3^9

then we add this result to j.

So, we get an expression: 3^9 + j

Therefore, an expression for given sequence of operations is: j + 3^9

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The number of centilitres which is equivalent to 0.00005 liters as required to be expressed in standard form is; 5 × 10-² cL.

Recall that; it follows from metric systems that;

100 centilitres = 1 litres.

On this note, it follows from proportion that the number of centilitres present in 0.00005 litres as required is;

= 0.00005 × 100 centilitres

= 0.005 centilitres.

Ultimately, when expressed in standard form, it follows that the number of centilitres in 0.00005 liters is; 5 × 10-² cL.

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According to the factor theorem, if "a" is any real integer and "f(x)" is a polynomial of degree n larger than or equal to 1, then (x - a) is a factor of f(x) if f(a) = 0. Finding the polynomials' n roots and factoring them are two of their principal applications.

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(a) To compute the experimental probability of rolling a 1 or 6 from Latoya's results, we need to determine the number of times a 1 or 6 was rolled and divide it by the total number of rolls Latoya made.

Let's assume that Latoya rolled the dice 100 times and obtained 20 1's and 10 6's. The total number of successful outcomes (rolling a 1 or 6) is 20 + 10 = 30.

Therefore, the experimental probability of rolling a 1 or 6 is 30/100 = 0.3 or 30%.

(b) Assuming the cube is fair, the theoretical probability of rolling a 1 or 6 can be determined by considering the favorable outcomes (rolling a 1 or 6) divided by the total possible outcomes (rolling any number from 1 to 6).

Since there are two favorable outcomes (1 and 6) out of six possible outcomes (1, 2, 3, 4, 5, 6), the theoretical probability is 2/6 = 1/3 or approximately 0.3333.

(c) The correct statement is B. As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. This is due to the law of large numbers, which states that as more trials are conducted, the experimental probability tends to converge towards the theoretical probability. However, it is not necessary for them to be exactly equal. Random variations can cause some discrepancy, but with a larger number of rolls, the experimental probability should approach the theoretical probability more closely.

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Answer:

c) 118°

Step-by-step explanation:

PN is the diameter of the given circle.

\( \purple {\bold {\therefore m(\widehat{PMN}) = 180°}}.... (1)\\\)

Now, by inscribed angle theorem:

\( m\widehat {MN} = 2\times m\angle MPN\\

\therefore m\widehat {MN} = 2\times 31°\\

\red{\bold {\therefore m(\widehat {MN}) = 62°}}....(2) \\\\\)

Now,

\( \because m(\widehat{MP}) + m(\widehat{MN}) =m(\widehat{PMN})\\

\therefore m(\widehat{MP}) + 62° =180°\\

\therefore m(\widehat{MP}) =180°-62°\\

\huge \orange {\boxed {\therefore m(\widehat{MP}) =118°}} \\\)

Answer: Scalene means "a triangle that has three unequal sides"

therefore it is D

The solution to the equation is \(324=4(3)^2^x\)x = 2.

Given exponential equation

\(324=4(3)^2^x\\\)

\(4(3)^2^x=324\)

\(3^2^x=\frac{324}{4}\)

\(3^2^x=81\)

\(3^2^x=3^4\)

When bases are equal, power should be equal.

2x = 4

x = 2

Hence, the solution to the equation is x = 2.

An equation is a mathematical statement that asserts the equality of two expressions, usually separated by an equal sign (=). It typically involves one or more variables, which are unknowns to be determined or solved for. Equations can be algebraic or numerical, and they are often used in mathematics, science, engineering, and many other fields to model real-world situations, make predictions and solve problems. Solving an equation involves finding the values of the variables that satisfy the equation, and this can be done using various techniques such as substitution, elimination, graphing, or numerical methods.

We can simplify the left side of the equation using the exponent rule that states: \((a^n)^m = a^(n*m).\) Therefore, we have:

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The solution to the equation \($\mathrm{324 = 4 ( 3 )^{ 2x}}$\)  is x = 2. Thus, option C is correct.

An equation is a mathematical statement that asserts the equality of two expressions, usually separated by an equal sign (=). It typically involves one or more variables, which are unknowns to be determined or solved for.

Equations can be algebraic or numerical, and they are often used in mathematics, science, engineering, and many other fields to model real-world situations, make predictions and solve problems. Solving an equation involves finding the values of the variables that satisfy the equation, and this can be done using various techniques such as substitution, elimination, graphing, or numerical methods.

Given exponential equation:

\(324 = 4 ( 3 )^{ 2x}\)

\(4 ( 3 )^{ 2x} =324\)

\(( 3 )^{ 2x} = \dfrac{324}{4}\)

\(( 3 )^{ 2x} = 81\)

\(3 ^{ 2x} = 3^4\)

When bases are equal, power should be equal:

2x = 4

x = 2

Hence, the solution to the equation is x = 2.

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Complete question:

Select the correct answer.

What is the solution to this equation?

\(\mathrm{324 = 4 ( 3 )^{ 2x}}\)

A. x = 8

B. x = 1

C. x = 2

D. x = 4

Answer:

top box is 18, third on the bottom is 10 and fourth on the bottom is 12

Step-by-step explanation:

For two onions, add 9 tomatoes. If you have two onions, you have 9 tomatoes. This could be looked at as multiplying the amount of tomatoes by the (onions/2).

Answer: 264.0625

Step-by-step explanation:

let me know if im wrong

Answer:

C

Step-by-step explanation:

Let the first term be a and the common ratio be r.

ATQ, ar^4=24 and ar^6=144, r=sqrt(6) and a=24/(sqrt(6))^2=24/36=2/3

Answer:

See explanation below

Step-by-step explanation:

Recall the identity for the cosine of an addition of angles:

\(cos(\theta+\gamma)= cos(\theta)*cos(\gamma)- sin(\theta)*sin(\gamma)\)

and that for a subtraction of angles:

\(cos(\theta-\gamma)= cos(\theta)*cos(\gamma)+sin(\theta)*sin(\gamma)\)

Now, use the property of addition of angles above to write :

\(cos(\frac{A+B}{2} +\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\)

but since :  \(\frac{A+B}{2} +\frac{A-B}{2}= A\)

Then the cosine of addition of angles above can be written as:

\(cos(\frac{A+B}{2} +\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\cos(A)=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\)

We do something similar now with the cosine of the subtraction of angles:

\(cos(\frac{A+B}{2} -\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\)

and we notice that: \(\frac{A+B}{2} -\frac{A-B}{2}= B\)

Then the cosine of subtraction of angles above can be written as:

\(cos(\frac{A+B}{2} -\frac{A-B}{2} )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\cos(B )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\)

and finally, we add term by term the expressions we got for cos (A) and for cos(B) and notice that the terms that contain the sine functions cancel each other because they have opposite signs, while the terms in cosine add up to double themselves:

\(cos(A )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )+sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\+\\cos(B )=cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )-sin(\frac{A+B}{2} )*sin(\frac{A-B}{2} )\\=\\cos(A) +cos(B)=2\,cos(\frac{A+B}{2} )*cos(\frac{A-B}{2} )\)

which is what we wanted to prove.

The way to convert counts into relative frequencies in a Two Way Relative Frequency Table is to divide the count by the total number of items

This refers to the depiction of the number of times in which an event occurs in the form of a table.

Hence, when a two-way frequency table is used, it shows the visual representation of the possible relationship between different sets of data.

Please note that your question is incomplete as you did not provide the frequency table needed and also the trends and generalizations to find, so a general overview was given.

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Answer:

The relative frequency table shows a trend that a majority of people prefer coffee over tea: the ratio in the total row for coffee is 0.65 and just 0.35 for tea. Similarly, more people are night owls than early birds: the total column for night owl is 0.6, but the early bird column is only 0.4.

FIFO - March cost of goods sold = $13,050. March 31 inventory = $7,350. LIFO - March cost of goods sold = $14,600. March 31 inventory = $5,800.

To calculate March cost of goods sold we need to add the given data for FIFO =

March cost of goods sold

= (2,800 + 3,700 + 6,550)

= 13,050

To calculate March cost of goods sold we need to add the given data for LIFO =

March cost of goods sold

= (3,400 + 4,400 + 6,800)

= 5,800

Sales data refers to the information collected and recorded about the transactions that occur when a business sells products or services to customers. This data typically includes details such as the date and time of the sale, the products or services sold, the quantity sold, the price paid, and the customer's information. Sales data is crucial for businesses as it helps them understand their sales performance, identify trends and patterns and make informed decisions about their pricing, marketing and inventory management strategies.

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Answer:

the mean weight is 22 tonnes

Step-by-step explanation:

mean=total sum/number of numbers you added

in this case the question already gave you the total so just divide right away

mean weight= 330/15 = 22 tonnes

Answer: WHAT ARE THESE IMAO

Step-by-step explanation:

Answer:

Step-by-step explanation:

Lol

An ordered array is an arrangement of numbers in a specific order, usually in increasing or decreasing order. 43, 73, 107, 158, 226, 305, 312

To rewrite the numbers in an ordered array: you need to arrange the numbers in either ascending or descending order. For example, the ordered array of the numbers in ascending order: 43 73 107 158 226 305 312

Note that it's important to read the instruction carefully when you have to order the numbers without using the factorial key on your calculator.

The factorial key on a calculator is typically represented by the symbol "!", and it is used to calculate the factorial of a number. The factorial of a number is the product of all the positive integers less than or equal to that number.

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Answer:

Therefore, in a scenario where mass is decreased, an increase in kinetic energy is possible if velocity increases. In the case of a decrease in mass and velocity, kinetic energy must decrease because both of the determining factors decreased.

Step-by-step explanation:

Step-by-step explanation:

Decreases in mass cause decreases in kinetic energy due to the aforementioned positive relationship between the two. ... In the case of a decrease in mass and velocity, kinetic energy must decrease because both of the determining factors decreased.

Answer:

B. ¼.

Step-by-step explanation:

Equation that represents a proportional relationship usually takes the form, y = kx. Where, k is the constant of proportionality.

Therefore, if we are given an equation that represents a proportional relationship, to be y = ¼x, the constant of proportionality is ¼.

Answer:

1/4

Step-by-step explanation:

Did the question Red Riot out