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:

18.0

Step-by-step explanation:

/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

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

Answer:

7.5

Step-by-step explanation:

x=10*0.75 = 7.5

note that b is smaller than a

Answer:

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

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  

Answer:

r=1

Step-by-step explanation:

-4(7r+7)

-28r-28

r=1

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!!!

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

Answer:

Hmmm

Step-by-step explanation:

Answer:

Angle one is 107 degrees and angle 2 is 83 degrees

Step-by-step explanation:

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%

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:

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)

Answer:

the correct answer is

229/479 = 0.48

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

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

Answer:

10 centimeters

Step-by-step explanation:

diameter = 2r

r = radius

diameter = 2(5cm)

diameter = 10 cm

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

Answer:

B, C, and D

Step-by-step explanation:

They are both true the ones I said.

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

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

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°

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: