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

Answers

Answer 1

(i) Large Table Required are 3 and Small Table required are 8

(ii) Price of Student Ticket is $5.5 and Adult Ticket is $7.5

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

(i)

Seats in Large Table = 12

Cost of Large Table = $50

Seats in Small Table = 8

Cost of Small Table = $25

Let, Number of Large Tables = x

Number of Small Tables = y

According to the Question:

12x + 8y = 100

50x + 25y = 350

x = 3, y = 8 (refer graph 1)

(ii)

Cost of Student Ticket = x

Cost of Adult Ticket  = y

According to the Question:

16x + 3y = 110.5

12x + 4y = 96

x = $5.5, y = $7.5 (refer graph 2)

To learn more about Linear Equation in Two Variables from the given link

https://brainly.com/question/24085666

#SPJ1

For Each Of The Following, Define Variables, Write A System, And Solve The Systemalgebraically:a) An
For Each Of The Following, Define Variables, Write A System, And Solve The Systemalgebraically:a) An

Related Questions

The mulraneys hired a contractor to build an addition to their home. The contractor proposed a rectangular room with a perimeter of 50 feet. The mulraneys asked the contractor to change the perimeter to 60 feet by increasing both he length and the width by the same distance. By how many feet did the mulranys ask the contractor to increase the length of the room?

Answers

Answer is 220 and what’s up

HELPPPP ME NOW PLS LLS

Answers

Answer:

Angle one is 107 degrees and angle 2 is 83 degrees

Step-by-step explanation:

40 points for this answer thank you

Answers

A = 6%
B = 36%
C = 16/25
D = 80%
M = 11/50
R = 45%
T = 14/25
X = 7/10


Those are all the answers that I got, I’m NOT saying all of them are correct! I hope this helps tho- :)

Find the area of the figure. Round your answer to the nearest tenth.

Answers

Answer:

18.0

Step-by-step explanation:

Please help me name the parts of the circle

Answers

Answer:

radius is gf diametor is ce chord is Ab and secant is ge tangent is dc

Probably shouldn’t click they link

True or false.

A counter-clockwise turn of 270° will land you at the same location as a 90° clockwise turn.

Answers

True. There is no difference between the two, they are the same thing and any time you will come up to the same place.

Figure AAA maps to figure BBB with a scale factor of 0.750.750, point, 75.

Answers

Answer:

7.5

Step-by-step explanation:

x=10*0.75 = 7.5

note that b is smaller than a

I don’t have any of the stuff pls help

Answers

Answer:

so 6/10 prefered ebooks pretty much and 1/10 didn't have a preference the other 3/10 liked traditional books you should be able to do the rest after that

A recent article in Business Week listed the "Best Small Companies." We are interested in the current results of the companies' sales and earnings. A random sample of 8 companies was selected and the sales and earnings, in millions of dollars, are reported below. Sales ($million) 89.2 18.6 18.2 71.7 58.6 46.8 17.5 11.9 Earnings ($million) 4.9 4.4 1.3 8 6.6 4.1 2.6 1.7 Let sales be the independent variable and earnings be the dependent variable. (i) Determine the estimated regression equation and comment on the coefficient of X. (ii) For a small company with $50.0 million in sales, estimate the earnings. (iii) Calculate the standard error of estimate and comment on it. (iv) Find the coefficient of determination and interpret the result.

Answers

Answer:

(i) The estimated regression equation is;

[tex]\hat y[/tex] ≈ 1.6896 + 0.0604·X

The coefficient of 'X' indicates that [tex]\hat y[/tex] increase by a multiple of 0.0604 for each million dollar increase in sales, X

(ii) The estimated earnings for the company is approximately $4.7096 million

(iii) The standard error of estimate is approximately 29.34

The high standard error of estimate indicates that individual mean do not accurately represent the population mean

(iv) The coefficient of determination is approximately 0.57925

The coefficient of determination indicates that the probability of the coordinate of a new point of data to be located on the line is 0.57925

Step-by-step explanation:

The given data is presented as follows;

[tex]\begin{array}{ccc}Sales \ (\$million)&&Earning \ (\$million) \\89.2&&4.9\\18.6&&4.4\\18.2&&1.3\\71.7&&8\\58.6&&6.6\\46.8&&4.1\\17.5&&2.6\\11.9&&1.7\end{array}[/tex]

(i) From the data, we have;

The regression equation can be presented as follows;

[tex]\hat y[/tex] = b₀ + b₁·x

Where;

b₁ = The slope given as follows;

[tex]b_1 = \dfrac{\Sigma(x_i - \overline x) \cdot (y_i - \overline y)}{\Sigma(x_i - \overline x)^2}[/tex]

b₀ = [tex]\overline y[/tex] - b₁·[tex]\overline x[/tex]

From the data, we have;

[tex]{\Sigma(x_i - \overline x) \cdot (y_i - \overline y)}[/tex] = 364.05

[tex]\Sigma(x_i - \overline x)^2}[/tex] = 6,027.259

[tex]\overline y[/tex] = 4.2

[tex]\overline x[/tex] = 41.5625

∴ b₁ = 364.05/6,027.259 ≈ 0.06040059005

b₀ = 4.2 - 0.06040059005 × 41.5625 ≈ 1.68960047605 ≈ 1.69

Therefore, we have the regression equation as follows;

[tex]\hat y[/tex] ≈ 1.6896 + 0.0604·X

The coefficient of 'X' indicates that the earnings increase by a multiple of 0.0604 for each million dollar increase in sales

(ii) For the small company, we have;

X = $50.0 million, therefore, we get;

[tex]\hat y[/tex] = 1.6896 + 0.0604 × 50 = 4.7096

The estimated earnings for the company, [tex]\hat y[/tex] = 4.7096 million

(iii) The standard error of estimate, σ, is given by the following formula;

[tex]\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu \right )^{2} }{n - 1}}[/tex]

Where;

n = The sample size

Therefore, we have;

[tex]\sigma =\sqrt{\dfrac{6,027.259 }{8 - 1}} \approx 29.34[/tex]

The standard error of estimate, σ ≈ 29.34

The high standard error of estimate indicates that it is very unlikely that a given mean value within the data is a representation of the true population mean

(iv) The coefficient of determination (R Square) is given as follows;

[tex]R^2 = \dfrac{SSR}{SST}[/tex]

Where;

SSR = The Sum of Squared Regression ≈ 21.9884

SST = The total variation in the sample ≈ 37.96

Therefore, R² ≈ 21.9884/37.96 ≈ 0.57925

The coefficient of determination, R² ≈ 0.57925.

Therefore, by the coefficient of determination, the likelihood of a new introduced data point to located on the line is 0.57925

This table shows how many male and female students attended two different

movies. What is the probability that a randomly chosen person from this
group is male?
Round your answer to two decimal places.
Action
Drama
Total
Male
105
124
229
Female
99
151
250
Total
204
275
479

Answers

Answer:

the correct answer is

229/479 = 0.48

The probability that a randomly chosen person from this group is male is 0.48.

What is the probability that a male is chosen?

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

The probability of choosing a male = number of males / total number of males and females

229/479 = 0.48

To learn more about frequency tables, please check: https://brainly.com/question/26577861

Please help NO LINKS
LINKS=REPORTED

Answers

Answer:

They didn't multiply the whole equation by 2 or -3 and only the first part

Answer:

when the first equation was multiplied by 2, the -22 did not get multiplied by 2

when the second equation was multiplied by -3, the -14 did not get multiplied by -3

the result is that x should be = 2

Step-by-step explanation:

Which statement is true about the equation (x – 4)(x + 2) = 16? O The equation x - 4 = 16 can be used to solve for a solution of the given equation. O The standard form of the equation is x2 - 2x - 8 = 0. O The factored form of the equation is (x + 4)(x - 6) = 0. O One solution of the equation is x = -6. vity​

Answers

Answer:

The factored form of the equation is (x + 4)(x - 6) = 0

Step-by-step explanation:

(x - 4)(x + 2) = 16

[tex]x^{2} -2x - 8 = 16[/tex]

[tex]x^{2} -2x - 24[/tex] = 0

(x - 6)(x + 4) = 0

x = 6  or x = -4

use distributive property to rewrite the expression 3x(x+4)​

Answers

Answer:

3x^2 + 12x

Step-by-step explanation:

3x(x +4)

3x^2 + 12x

- Multiply 3x * x = 3x^2

- Multiply 3x * 4 = 12x

Which Gives You 3x^2 + 12x  

When Bruce won a contest, he got a bronze medal with a radius
of 5 centimeters. What is the medal's diameter?

Answers

Answer:

10 centimeters

Step-by-step explanation:

diameter = 2r

r = radius

diameter = 2(5cm)

diameter = 10 cm

8 squared + B squared = 10 squared

Right triangle Pythagorean theorem

Answers

Answer:

6

Step-by-step explanation:

It's 6. The Pythagorean Theorem details how to find the length of a right triangle's hypotenuse.

The equation is a² + b² = c²

C is the length of the hypotenuse. The side lengths you have are a leg as 8 and hypotenuse as 10. By substituting these values into the equation, we get 8² + b² = 10²

Therefore, 64 + b² =100

So b² = 36

By square rooting both sides we finally reach the answer b=6.

Hope I helped!! (p.s. maybe brainliest)

help me find the perimeter please:)

Answers

Answer:

79.2 cm

Step-by-step explanation:

Add up all the lengths of all of the sides of the figure:

16.2 + 7.5 + 7.5 + 18 + 18 + 12  =  79.2

Answer:

79.2 m

Step-by-step explanation:

Well since all the units are the same and you have already labeled the missing/ congruent sides. Just add up all the sides and you’d end up with 79.2

HELPPPPP PLSSSSSSSSSS PLSSSSSSSS DRFTGYHUYGTFRDCGV PLSSSSSSSSSSSSSSSSSSSSSSSSSSSS PLSSSSSSSSSSSSSSSSSSSSSS FRTGYHUJTRCVBJHGB ASAPP PLSSSSSSSSS NNOWWW FGHUJIKHTFVBNGB.

Answers

Answer:

B, C, and D

Step-by-step explanation:

They are both true the ones I said.

B c d are the right ones

Can someone help asap

Answers

D is the answer because angle N would be 62 degrees if they were congruent

helppppppppppppppppppppp plzzzzzzzzzzz answer

Answers

Answer:

Maria randomly selects a number from the list of numbers below.

56, 90, 88, 76, 12

What is the probability that she selects an even number?

Step-by-step explanation:

so fd jwshydd +3 b4--

Answer:

3/2

Step-by-step explanation:

4x+17=23

-17 on both sides

4x=6

divided by 4

x=3/2

Jacob sells homemade skateboard decks for a profit of $27 per deck. He is considering switching to a new type of material that will increase his profit, as expressed by the function y = 32x, where x is the number sold and y is the amount of profit.

How many more dollars will Jacob earn on each skateboard deck if he switches to the new material? Explain how you found your answer. (5 points)

Answers

They had 30 I know this because I did 37 times 32x divided my y plus 15

Hmmmmmskksksksksksjsjsjdj

Answers

Answer:

Hmmm

Step-by-step explanation:

HELP I WILL GIVE BRIANLY
If 1/3 of my money is 80, what is 25% of my money?​

Answers

Answer:

60 = 25% of ur money

Step-by-step explanation:

80×3=100%of ur money (240)

to get 25% we need to divide 240 by 4 bcs 4= 25%

Please help me to do this question with steps

Answers

Answer:

x = 71°

Step-by-step explanation:

Segments of tangents from the same external point are congruent, that is

AT = BT

Then Δ ABT is isosceles with base angles congruent , so

x = [tex]\frac{180-38}{2}[/tex] = [tex]\frac{142}{2}[/tex] = 71°

HI can you guys please help with these

Answers

AnswerЯ могу помочь вам, но я не знаю, как мне так жаль, но вы можете найти ответ, если вы умны и в каком вы классе буквально вы, люди, такие тупыеЯ могу помочь вам, но я не знаю, как мне так жаль, но вы можете найти ответ, если вы умны и в каком вы классе буквально вы, люди, такие тупыеЯ могу помочь вам, но я не знаю, как мне так жаль, но вы можете найти ответ, если вы умны и в каком вы классе буквально вы, люди, такие тупые

Step-by-step explanation:

I NEED HELP RN PLSSS!!! (check whole picture) i’ll give brainiest if u don’t give a link just pls help immediately!!!)

Answers

Answer:

So I would say your answer is..............A

Step-by-step explanation:

For most places, global warming will result in more frequent hot days and fewer cool days, with the greatest warming occurring over land. Longer, more intense heat waves will become more common. Storms, floods, and droughts will generally be more severe as precipitation patterns change

Also, A is correct because lets say you put an ice cube in the sun...okay well if it keeps getting hotter and hotter multiply ice cubes into ice caps. Well same thing will happen. It will melt causeing water from the ice caps. Which will result into more water. Which will cause water to go above sea level!

Hope this helps!!!

Distribute and combine like terms: −4(7r + 7)

Answers

Answer:

r=1

Step-by-step explanation:

-4(7r+7)

-28r-28

r=1

The cost of boring a tube well 600 meter deep is as follows 25 paisa for the first metre and an additional 4paisa for every subsequent meter find the cost of boring a 500th meter long

Answers

The answer is 2021 paisa for the 500 metre long tube well

HELP!!! Use the properties of exponents to simplify the expression:

Answers

There you go the answer key


HELP FOR 7 AND 8 Pleaseeeee

Answers

I believe the answer to 7 would be;
B. 64 cm

This is was a guess. My reasoning is 8(6) =48 and 8(10)=80, so the number in between would be 64.

Another train of thought was the number in the middle of 6 and 10 is 8 and 8(8) = 64
6, 7, 8, 9, 10
X, X, • , X, X

I believe the answer to 8 would be;
C. 82.5 in

Following the equation, you would multiply 15 and 11 the divide the product by two

15(11)=165
165/2=82.5

Please correct me if I am wrong and have a good day!

Write an equation of the line that passes through the given points.
(-2,8) and (1, -1)

Answers

/Answer:

Short Answer Type:

P1 - (-2,8)

P2 - (1,1)

Slope: (1 - 8) / (1 + 2)

=> -7/3

Therefore: 1 = -7/3 + c

=> 10/3 = c

Therefore equation: y = -7x/3 + 10/3
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