For each of the following, define variables, write a system, and solve the system
algebraically:
a) An organization is holding a banquet in honor of its member of the year. Tables and
chairs must be rented in order to seat all the guests. A large table seats 12 and costs
$50. A small table seats 8 and costs $25. How many of each type of table must be
rented to seat 100 guests for $350?
b) The jazz band and choir are attending a concert. The jazz band bought 16 student tickets and 3
adult tickets for $110.50. The choir bought 12 student tickets and 4 adult tickets for $96. Find the
cost of each type of ticket

Answer:

\(x - 12 \\ coefficent = 1 \\ constant = - 12 \\ thnk \: you\)

Answer:

The unknown number is -2

Step-by-step explanation:

Let n represent the unknown number then...

12=14+n

Subtract 14 from both sides:

12-14=14-14+n

-2=n

n=-2

Step-by-step explanation:

please check the attached picture..and rotate it

Answer: C. 108 degree

Step-by-step explanation:

We know that the angle of GFH = angle of ABC

So the equation is

2x + 36 = 3x

Subtract 2x from both sides

36 = x

Then put 36 back in the equation (3x)

36 times 3 = 108 degree

Answer:

3.7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here, we want to graph the given equations

1. y = 2x - 3

The general form of the equation of a straight line is;

y = mx + b

m is the slope and b is the y-intercept

To plot the line, we need the x intercept and the y-intercept

At the x-intercept, the value of y is zero

at the y-intercept . the value of x is zero

From the equation, we have the y-intercept as -3

To get the x-intercept, set y = 0

0 = 2x - 3

2x = 3

x = 3/2

x = 1.5

so to graph the line, we have to join the points ;

(0,-3) and (1.5,0)

b) y = -3x + 2

The y-intercept is 2

To get the x intercept, set y = 0

0 = -3x + 2

3x = 2

x = 2/3

so, we have to join the points (2/3,0) and (0,2)

We have the lines plotted as an attachment

Step-by-step explanation:

ok multiply the denominator by the whole number to get 8 and add it to the numerator to get 11. the denominator stays the same so you get 11/4

A system having ΔG equal to zero means that the system is at equilibrium at standard conditions. This is option c. In a chemical reaction, ΔG represents the change in Gibbs free energy, which is a measure of the energy available to do work.

When ΔG is equal to zero, it indicates that the system is balanced, with the forward and reverse reactions occurring at the same rate. At equilibrium, the concentrations of reactants and products remain constant over time. For example, consider the reaction A ⇌ B. Initially, if we have more A than B, the forward reaction will be favored until equilibrium is reached. At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of A and B remain constant. In this case, ΔG is zero.

It is important to note that while a ΔG of zero indicates equilibrium, it does not provide information about whether the reaction is spontaneous or nonspontaneous. The spontaneity of a reaction is determined by the sign of ΔG. If ΔG is negative, the reaction is spontaneous, while a positive ΔG indicates a nonspontaneous reaction.

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Answer:

6

Step-by-step explanation:

\(\frac{3}{4}*\frac{8}{1} = \frac{24}{4} = \frac{6}{1} = 6\)

Answer:

6

Step-by-step explanation:

3/4x8/1 simply we can change 8/1 to just 8 because 1 goes into 8 8 times sowe can multiply 3/4 by 8 to get 24/4and 4 goes into 24 6 times so the answer is 6/1 or 6

The value of (3.9 × 10⁻³) + 0.0026 in scientific notation is 6.5 × 10⁻³.

Decimal numbers are numbers which has basically a whole number part and a fractional or decimal part after a point called decimal point.

Decimal number system describes the base 10 number system.

Given are numbers 3.9 × 10⁻³ and 0.0026 added together.

We have to do it in scientific notation.

0.0026 can be written as 2.6 × 10⁻³.

Adding these two numbers together, and taking the common term,

(3.9 × 10⁻³) + (2.6 × 10⁻³) = (10⁻³) (3.9 + 2.6)

                                        = (10⁻³) (6.5)

                                        = 6.5 × 10⁻³

Hence the answer of the sum of (3.9 × 10⁻³) + 0.0026 is 6.5 × 10⁻³ in scientific notation.

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Answer:

x = 1 and y = 6

Step-by-step explanation:

Add these equations

-2x+y=4

2x+y=8

2y=12

    2

y = 6

Plug in 12 for y.

-2x+(6) = 4

     -6    -6

-2x = -2

     -2

x = 1

Answer:

21/4-3

Step-by-step explanation:

Hope this helps! :)

/= divided by.

Answer:

Step-by-step explanation:

There are two options as below.

1. JL/JK = 5 : 1

Find the coordinates of L:

The point is L(8, - 10)

2. JL/JK = 1 : 5

Find the coordinates of L:

The point is L(0, 6)

Answer:

9.4 x 11 = 103.4

15 + 7 = 22, 22 x 5 = 110, 110 divided by 2 = 55

55 x 2 (since there are two trapezoids) = 110

5 x 11 = 55

7 x 11 = 77

15 x 11 = 165

Now we add all the areas up:

103.4 + 110 + 55 + 77 + 165 = 510.4 square feet2 is your answer.

Answer:

x=-303

Step-by-step explanation:

Answer:

9x^2+24x+3x+8

9x^2+27x+8

Step-by-step explanation:

Answer:

9x^2 + 27x + 8

Step-by-step explanation:

well you have to break this down and simplify it so that'll give us

9x^2 + 24x + 3x + 8

9x^2 + 27x + 8

there's ur answer

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The required inequality is 4f<36 and at most 9 fishes can be bought.

An inequality is an inequation separated by <,>≥,≤. In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given here: The price of each fish is $4 and total budget is $36

Let ffishes can be brought then we have

4f<36

f<9

Hence, The required inequality is 4f<36 and at most 9 fishes can be bought.

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The expression is equivalent is 6x/4 + 24y/12

Algebraic expressions are described as expressions composed of variables, terms, factors, constants, and coefficients.

These expressions also consisting of mathematical operations, such as;

Given the expression;

1/4(3x+4y) + 3(1/4x+ 2/3y)

expand the bracket

3x/4 + 4y/4 + 3/4x + 3/3y

collect like terms

3x/4 + 3/4x + 4y/4 + 3/3y

add like terms

3x + 3x/4 +  12y + 12y /12

add the numerators

6x/4 + 24y/12

Hence, the expression is 6x/4 + 24y/12

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Answer:

its b

Step-by-step explanation:

its esay for even a non smart person to know not saying your one!! never mind.IT IS BBBBBBBB!!!!!!

The values of E(X) = 3.25 and Var(X) ≈ 2.238 for the number of spades in a hand of 13 cards chosen at random from a 52-card deck.

To find E(X) and Var(X) for the number of spades in a hand of 13 cards chosen at random from a 52-card deck, we will use the concepts of probability and statistics.

E(X), or the expected value, is the average number of spades you would expect to get in a hand of 13 cards. To find E(X), we can use the formula:

E(X) = (Number of spades in the deck / Total number of cards in the deck) * Number of cards drawn

E(X) = (13 spades / 52 cards) * 13 cards drawn
E(X) = (1/4) * 13
E(X) = 3.25

So, the expected number of spades in a 13-card hand is 3.25.

Next, let's find Var(X), or the variance, which is a measure of how much the number of spades can vary from the expected value. We can use the formula for variance of a hypergeometric distribution:

Var(X) = (Number of cards drawn * Number of spades * Number of non-spades) / ((Total number of cards in the deck)^2 * (Total number of cards in the deck - 1))

Var(X) = (13 cards drawn * 13 spades * 39 non-spades) / ((52 cards)^2 * (52 cards - 1))
Var(X) = (13 * 13 * 39) / (52 * 52 * 51)
Var(X) ≈ 2.238

So, the variance for the number of spades in a 13-card hand is approximately 2.238.

In summary, E(X) = 3.25 and Var(X) ≈ 2.238 for the number of spades in a hand of 13 cards chosen at random from a 52-card deck.

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Answer:

$2.25

Step-by-step explanation:

>givens:

2 pretzels + 1 lemonade = $5.75

2 lemonades = 1 pretzel + $0.25

>find from the first equation how much is 1 lemonade

2 pretzels + 1 lemonade = $5.75, subtract 2 pretzels from both sides

1 lemonade = 5.75 -2 pretzels

>substitute in the second equation 2 lemonades with 2(5.75-2 pretzels)

2 lemonades = 1 pretzel + $0.25

2(5.75-2 pretzels) =  1 pretzel + $0.25, distribute 2 in parentheses

11.5 -4 pretzels = 1 pretzel +0.25, isolate like terms

11.5-0.25 = 1+4 pretzels, combine like terms

11.25 = 5 pretzels, divide both sides by 5

1 pretzel = $2.25

*you can use the letter "p" for pretzel and "l" for lemonade to make the equations more concise

Answer:

10 years

Step-by-step explanation:

We are told that One year after you buy a tree, it is 10 feet tall. Thus, it's initial height after 1 year is 10 ft.

Now we are told that each year after you buy the tree, it grows 2 feet. This means that it's height after you bought it was; f(0) = 10 - 2 = 8ft

Thus,

f(1) = 8 + 2 = 10

f(2) = 8 + 2 + 2 = 12

f(3) = 8 + 2 + 2 + 2 = 14

The pattern here is;

f(x) = 8 + 2x

Where x is number of years

Thus, for it to reach a maximum height of 28 ft;

28 = 8 + 2x

Subtract 8 from both sides to give;

28 - 8 = 2x

2x = 20

x = 20/2

x = 10 years

The probability is a very small value, and when expressed as a decimal rounded to the nearest millionth, it is approximately 0.000011

The probability that the four flavors chosen consist of each of their favorite flavors can be calculated by considering the total number of possible outcomes and the number of favorable outcomes.

First, let's determine the total number of possible outcomes. Since there are 40 flavors in total and they are randomly choosing four flavors, the total number of possible outcomes can be calculated using combinations. We can use the formula for combinations: nCr = n! / (r!(n-r)!), where n is the total number of flavors (40) and r is the number of flavors they are choosing (4).

nCr = 40! / (4!(40-4)!)

    = 40! / (4!36!)

    = (40 * 39 * 38 * 37) / (4 * 3 * 2 * 1)

    = 91390

Next, let's determine the number of favorable outcomes, which is the number of ways they can choose one flavor from each of their favorites. Since each person has a different favorite flavor, the number of favorable outcomes is simply 1 for each person.

Therefore, the probability of choosing four flavors consisting of each of their favorite flavors is:

Probability = Number of favorable outcomes / Total number of possible outcomes

           = (1 * 1 * 1 * 1) / 91390

           = 1 / 91390

The probability is a very small value, and when expressed as a decimal rounded to the nearest millionth, it is approximately 0.000011.

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Answer:

She can read 24 pages in one hour.

Step-by-step explanation:

\(\frac{1}{5}*2\) = \(\frac{2}{5}*60pages = 24pages\)

hope this helps, good luck :)

Step-by-step explanation:

1/5 * 60 = 12 pages read in 1/2 hour

there are 2 half hours in an hour

so

12*2 = 24 pages in one hour.

sin I=opposite/hypothesis

sin I=√57/10

sin I=0.754983

=0.75

The main goal of data democratization is to make data accessible to all users. Option (a) is correct.

Given the primary goal of data democratization.

Data democratization is the ability to make information in a digital format accessible to the average end user. The goal of data democratization is to allow non-professionals to collect and analyze data without the need for outside help. This requires us to support access with an easy way for people to understand data, so they can use it to accelerate decision-making and uncover opportunities for a business. The goal is for everyone to be able to use the data at any time to make decisions without barriers of access or understanding.

Therefore, the main goal of data democratization is to make data accessible to all users.

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